Rheological Properties of Fibrin Clots

Transcription

1 Rheological Properties of Fibrin Clots A THESIS SUBMITTED TO THE UNIVERSITY OF MANCHESTER FOR THE DEGREE OF MASTER OF PHILOSOPHY IN THE FACULTY OF ENGINEERING AND PHYSICAL SCIENCES Year of submission 2012 YUNCHU CHEN School of Physics and Astronomy

2 Declaration This Master Thesis is the result of my own work. The parts of it that are influenced by the ideas and the contributing work of other people are clearly indicated. I further declare that no portion of the work referred to in the dissertation has been submitted in support of an application for another degree or qualification of this or any other university or other institute of learning. 2

3 Copyright Statement i. The author of this thesis (including any appendices and/or schedules to this thesis) owns certain copyright or related rights in it (the Copyright ) and s/he has given The University of Manchester certain rights to use such Copyright, including for administrative purposes. ii. Copies of this thesis, either in full or in extracts and whether in hard or electronic copy, may be made only in accordance with the Copyright, Designs and Patents Act 1988 (as amended) and regulations issued under it or, where appropriate, in accordance with licensing agreements which the University has from time to time. This page must form part of any such copies made. iii. The ownership of certain Copyright, patents, designs, trademarks and other intellectual property (the Intellectual Property ) and any reproductions of copyright works in the thesis, for example graphs and tables ( Reproductions ), which may be described in this thesis, may not be owned by the author and may be owned by third parties. Such Intellectual Property and Reproductions cannot and must not be made available for use without the prior written permission of the owner(s) of the relevant Intellectual Property and/or Reproductions. iv. Further information on the conditions under which disclosure, publication and commercialisation of this thesis, the Copyright and any Intellectual Property and/or Reproductions described in it may take place is available in the University IP Policy (see in any relevant Thesis restriction declarations deposited in the University Library, The University Library s regulations (see and in The University s policy on presentation of Theses. 3

4 Contents List of Figures 6 List of Tables..8 Abstract..9 Acknowledgements..10 Preface..11 Introduction.12 1 Overview of Haemostasis Vascular constriction and the formation of the platelet plug Mechanism of blood coagulation Procoagulant activation a coagulation cascade Conversion of prothrombin to thrombin Thrombin generation on fibrin formation A cell-based model Fibrinolysis Clotting disorders Haemophilia Thrombotic disorders 28 2 Fibrinogen and fibrin clot structures Fibrinogen Conversion of fibrinogen to fibrin Covalent cross-linking fibrin network Physical and mechanical properties of clots Semi-flexible polymers and rheology.45 4

5 3.1 Semi-flexible polymers Statics and dynamics of single filaments Networks of semi-flexible polymers Rheology Linear viscoelasticity Cone-and-plate rheometer Materials and Methods Sample preparation Rheometer Microscopy Results and Data Analysis Gel point Rheological behaviours and clotting times Fibrin structures, rigidities and concentrations Discussion and Conclusion Sources of errors Discussion Conclusion Outlook Negative normal stress Viscosity and shear rate Refinement of experimental technique References Final word count (including footnotes and endnotes): 26,220 5

6 List of Figures 1-1 Schematic of coagulation cascade Transmission electron micrographs of fibrin structures X-ray crystallographic structure of fibrinogen Schematics of fibrinogen molecule, fibrin monomer and fibrin protofibril Diagram of complementary physical interactions in fibrin polymerization Scanning electron micrograph of twisted fibrin fibres Schematics of cross-linking fibrin network Transmission electron micrograph of human fibrin clot End-to-end distribution function of a semi-flexible polymer Models of Hookean spring and Newtonian dashpot Maxwell and Kelvin-Voigt models Frequency response of a Maxwell model Sketches of cone-and-plate rheometer and its shear flow geometry Instrument configuration of a Bohlin Gemini HR Nano Rheometer Correct loading instruction and oscillation geometry of rheometer Screenshots of fibrin gelation at 0.1 and 0.5 Hz from rheometer Time-dependent phase angle of fibrin clot at various frequencies Time-dependent storage and loss moduli of fibrin clot at various frequencies Screenshot of a 16 hr time-dependent data measurement from rheometer Full time developed viscoelastic data of a fibrin sample

7 5-6 Time dependent rigidities of the fibrin clots in Tris-EDTA buffer Time dependent rigidities of fibrin clots in Tris-EDTA plus NaCl buffer Concentration dependent clotting times of fibrin clots Zoomed-in results of time dependent rigidities in Tris-EDTA buffer Zoomed-in results of time dependent rigidities in Tris-EDTA plus NaCl buffer Concentration dependent rigidities of fibrin clots in Tris-EDTA buffer Concentration dependent rigidities of fibrin clots in Tris-EDTA plus NaCl buffer Optical microscopy images of clots at various thrombin concentrations Optical microscopy images of clots at various fibrinogen concentrations Optical microscopy images of clots at various thrombin concentrations with salt

8 List of tables 4-1 Expected errors from work with a cone-and-plate geometry The concentration compositions of the clots 77 8

9 Abstract University of Manchester Yunchu Chen Master of Philosophy Rheological Properties of Fibrin Clots 18/06/2012 A study of the rheological properties of fibrin, an important coagulant in human haemostasis, is presented in this MPhil thesis. Fibrin monomers are activated at the site of an injury to a blood vessel through the thrombin-induced cleavage of fibrinogen, a protein which circulates in the blood. These monomers self-assemble into networks by branching out and connecting with each other. This is the process which gives rise to a blood clot. There are a variety of factors which have an influence on the structure of the fibrin network, which in turn have an influence on the physical properties of the clot. The influence of two of these factors, fibrinogen concentration and thrombin concentration, is investigated in this paper. The motivation for this work is the need to determine what makes a perfect blood clot, and to find out if increasing the concentration of fibrinogen or thrombin increases the long-term stability of clots. Previous research has highlighted some of the remarkable rheological properties of this material, namely by frequency-dependent experiments. In this work frequencyindependent measurements of the time evolution of fibrin clot rigidity, and how this is related to the concentration of thrombin and fibrinogen, are presented. Measurements were taken using a Bohlin Gemini HR Nano Rheometer over a period of 16 hours. Samples were prepared with Tris-EDTA buffer, both with the addition of salt and without, either with a fixed concentration of thrombin and varying fibrinogen, or with a fixed concentration of fibrinogen and varying thrombin. It was found that the time evolution of the rigidity exhibited three separate phases, characterised by a steady increase in rigidity, followed by a sharp increase, and ending with a plateau, during which rigidity ceased to increase. Samples prepared with a higher concentration of thrombin or fibrinogen exhibited an increase in rigidity in the first phase, but this behaviour is not observed after the first phase. Consistent with previous research, it was determined that the clotting time of fibrin decreases with increasing concentration of thrombin or fibrinogen. This effect is also observed when salt is added to the Tris-EDTA buffer. The addition of salt was also found to have an effect on the long-term stability of clots, as the rigidity of samples prepared with salt experienced a sharp decline in the third phase. This can be related to the structure of fibrin, and the findings in this work can be used to help increase our understanding of how to make a perfect clot. 9

10 Acknowledgements First of all, thanks to my supervisor Dr. Thomas A. Waigh for the opportunity to explore my research in biophysics. I would like to thank Prof. Jian Lu for his cheerful smile. To study MPhil degree abroad as a mother made me realise how far I can extend my ability. During the study, I went through mental illness, pregnancy and was blessed with a little boy. These experiences make studying biological issues in physics a lot more significant to me. Without my parents and my husband s support and love, I would not able to finish this thesis. Besides academia, the biggest thing I have learned is no achievement could be done alone. Thanks to Dr. Mohammad for sharing his professional experiences in chemistry. Thanks to Alex, Faheem, Pantelis and Dr. Matthew Harvey for their help and friendship. Thanks to Dr. Shaden Jaradat for his advice. Thanks to Amy, Lisa and Lili for always being my company. Thanks to my lovely son, Leo, for being my inspiration. In memory of my dog Toutou ( ) and cat LULU ( ). 10

11 Preface Physics is the general analysis of nature. Physicists have been involved in finding the rules governing the world for decades, but dedicated enquiry into living matter only began in ernest during the second half of the 20 th century. Physics aims to answer comprehensive questions such as What is life?. The research in this area is called biophysics, and the people involved in this research call themselves biophysicists. Biophysics is an interdisciplinary area of physical sciences in the 21 st century which falls outside the conventional boundaries of the well-established scientific disciplines of chemistry, physics, biology, and medicine. A challenge remains to transfer some of the concepts developed in physics to living objects from the molecular scale to that of entire organisms. It requires collaborative and multidisciplinary approaches from physics, as well as mathematics and statistics, to apply the models and experiments to highly complex systems, for instance, tissues and organs. The ultimate goal of the research is to transfer the findings to medical applications to improve the diagnosis of diseases and clinical treatments. The body of a human being is extremely complex and sophisticated. Due to a lack of understanding, many patients still suffer from the symptoms of unknown diseases and are subject to painful unpleasant surgical procedures. The principle and spirit of science is to understand the phenomena involved to help improve the quality of people's life. This is my motivation for the following research. Biophysics and its related fields cover a massive range of topics. My research explores the mechanisms of haemostasis and fibrin network formation through a number of experimental methods although principally a rheometer is used. 11

12 Introduction Human beings have evolved a complex haemostatic clot system that is designed to seal injured vessels, stop bleeding and form the framework for healing wounds, but also to maintain the blood in a fluid state under physiological conditions. It is a wonder that haemostasis ever occurs properly due to the complex nature of the processes involved. The entire haemostatic process which serves to promote the perfect balance and location of haemostasis and recovery, involves platelets, clotting factors, and endothelium, as well as inhibitory mechanisms of platelet aggregation, clotting, and fibrinolysis. Thrombosis, however, is a pathological process, which may occur if the haemostatic stimulus is unregulated. Disturbance of any component of this complex process can produce an imbalance with a consequent haemorrhagic or thrombotic clinical disorder that may result in death. A central question for the understanding of haemostasis and thrombosis is What does it take to make the perfect clot? And, with the intention to develop remedy agents for the treatment of bleeding and thrombosis, the following question is How do we make a bad clot good? Generation of a haemostatic clot requires thrombin-mediated conversion of fibrinogen to fibrin. In the sealing process, the action of fibrinogen is an essential part of a finely tuned restrictive system that responds to maintain blood circulation. Fibrinogen circulates in the blood in an inert form that can be readily activated at the site of an injury. It is the action of the enzyme thrombin over cell surfaces, triggered by vessel injuries, that cleaves two 12

13 fibrinopeptides on the central domain of fibrinogen and thus transforms it into its active form which is called fibrin. The requirement to efficiently resist the blood outflow under heterogeneous conditions places extraordinary mechanical demands on the performance of fibrin clots. The determination of the origins of this biological process requires the investigation of the physical properties of fibrin on different length scales, from the overall network response (with respect to external forces) to the elastic behaviour of individual fibres. These important clot characteristics show such a great diversity, depending on the conditions of fibrin gel formation, that only a thorough knowledge of the interactions of fibres at levels of increasing complexity may finally lead to clinically relevant predictions of clot behaviour in vitro and in vivo. Moreover, recent studies suggest that patterns of abnormal thrombin generation produce clots with altered fibrin structure and that these changes are associated with an increased risk of bleeding or thrombosis, while most studies of clot formation have been performed by adding a fixed amount of refined thrombin to fibrinogen. These findings suggest that studies expressly evaluating fibrin formation during in vitro thrombin generation will help to explain the mechanisms of normal and abnormal fibrin clot formation in vivo. In common with many other biological materials of current interest (actin, DNA, microtubules, collagens etc.), fibrin may be physically viewed as a semi-flexible polymer. There is a large volume of theoretical and experimental research in soft condensed matter physics which aims to describe single filaments of these materials, especially on the ubiquitous model system F-actin. In addition, results derived for networks of cross-linked biopolymers may also be applicable in the case of fibrin. With the help of this background, the following study will compare the predictions of semi-flexible theory with the measured data. 13

14 Chapter 1 Overview of Haemostasis Haemostasis is a normal physiological process to prevent blood loss from a damaged vessel, whatever the injury, that provides an efficient seal to maintain the blood circulation volume until the vessel is restored. Haemostasis is achieved by several mechanisms: (1) vascular constriction, (2) platelet plug formation, (3) coagulation, and (4) fibrinolysis. These four mechanisms are closely linked one with another to build a highly efficient system. 1.1 Vascular constriction and formation of the platelet plug The trauma to the vessels itself causes a vasoconstrictive reaction directly after a blood vessel has been cut or ruptured, and the response reduces the flow of blood from the vessel rupture instantaneously. The constriction results from nervous reflexes, local myogenic spasm and local humoral factors from the traumatized tissues and blood plates. The local vascular spasm 14

15 during the process of platelet plugging and blood coagulation can last many minutes or even hours. Circulating platelets produce clumps or aggregate when subjected to a wide variety of stimuli. If the rent in the blood vessel is small, the platelet plug by itself can stop blood loss, but if there is a large wound, a blood clot in addition to the platelet plug is needed to stop the bleeding. It is important to discuss the nature of platelets themselves first. Platelets are minute round or oval discs, 1 to 4 micrometers in diameter. They are formed in the bone marrow from megakaryocytes which are extremely large cells of the hematopoietic series in the bone marrow. The normal concentration of platelets in the blood is between 150,000 and 300,000 per ml. Platelets do not have nuclei and cannot reproduce, although they have many functional characteristics of whole cells. The active factors in their cytoplasm include actin and myosin molecules, residuals of both the endoplasmic reticulum and the Golgi apparatus, mitochondria and enzyme systems that are capable of forming ATP and ADP, enzyme systems that synthesize prostaglandins, fibrin-stabilizing factors and a growth factor that produces vascular endothelial cells, vascular smooth muscle cells and fibroblasts. The cell membrane of the platelets is also important. On its surface is a coat of glycoproteins that opposes adhesion to the normal endothelium. Additionally, the platelet membrane contains large amounts of phospholipids. It has a half-life in the blood of 8 to 12 days and it is eliminated from the circulation mainly by the tissue macrophage system. Otherwise, physical factors such as blood-flow velocity, and blood viscosity critically influenced by the haematocrit and the consequent shear force at the blood-tissue interface, all influence platelet adhesion. Platelet repair of vascular openings is based on several important functions of the platelet 15

16 itself. The consequence of the sequential processes of adhesion and aggregation to stop bleeding is the mechanism of platelet plug formation. As platelets come in contact with a damaged vascular surface, the platelets themselves begin to swell; they take over irregular forms with numerous irradiating pseudopods protruding from their surfaces; their contractile proteins constrict forcefully and cause the release of granules that contain multiple active factors; they become sticky so that they adhere to collagen in the tissues and to a protein called von Willebrand factor that spreads throughout the plasma; they release large quantities of ADP; and their enzymes form thromboxane. The ADP and thromboxane successively act on nearby platelets to activate them as well, and the viscosity of these additional platelets makes them adopt the originally activated platelets. Consequently, at the site of any rent in a blood vessel wall, the damaged vascular wall elicits activation of increasing numbers of platelets that in turn attract more and more additional platelets thus forming a platelet plug. The platelet plug mechanism is sufficient to close the minute ruptures to small blood vessels, but not enough to secure permanent sealing of these or larger wounds, thus blood coagulation in addition to the platelet plug is required to construct an unyielding plug. 1.2 Mechanism of blood coagulation Blood coagulation is the important step in haemostasis which causes the traumatized vessel to stop bleeding. A clot should seal the ruptured vessel efficiently at the site of a wound without occluding it. The continuity of the blood flow should be maintained under all circumstances. 16

17 Normally, the anticoagulants predominate in the blood stream so the blood does not coagulate while it is circulating in the blood vessels. However, procoagulants when activated can override anticoagulants in the area of damaged tissue when an injury happens. More than 50 substances which are anticoagulants or procoagulants have been found in the blood or in tissue. 1 In response to the damage of the vessel or of the blood itself, plasma zymogens of serine protease transform into active enzymes and these enzymes act to convert procofactors into active cofactors which assemble the protease on the cell surface. The general mechanism of blood coagulation has three essential steps. Firstly, a complex cascade of chemical reactions in the blood results in a complex of activated substances called a prothrombin activator involving more than a dozen blood coagulation factors. Secondly, the prothrombin activator converts prothrombin into thrombin. Finally, the thrombin acts as an enzyme to transform soluble fibrinogen into unsoluble fibrin fibres that form the clot. It is a recurrent theme in blood coagulation to assemble cofactor, enzyme and substrate on a phospholipid-containing surface like a cell membrane, resulting in maximal efficiency and velocity of the molecular reaction. 1,2 The mechanisms of haemostasis have evolved to generate thrombin and hence localise the site of injury, preventing its action throughout the circulation. To initiate the clotting in the first place are the more complex mechanisms which form prothrombin activator, and these are produced as a result of trauma to the vascular wall, trauma to adjacent tissues, trauma to the blood, endothelium damage or biochemical alteration. A modification of the coagulation cascade was defined in 1960s. In the modern versions of the coagulation cascade, the interaction of the proteins are outlined in a Y-shaped scheme with distinct extrinsic and 17

18 intrinsic pathways initiated by factor XII and TF (tissue factor), thereafter converging onto a common pathway at the FXa/FVa complex Procoagulant activation - A coagulation cascade The major concept of blood coagulation is a cascade of steps in which plasma zymogens of proteases are transformed into active enzymes. The coagulation cascade proposed in the idea includes a series of proteolytic reactions that could act as a biological amplifier and this is a well-recognized paradigm to underlie many physiological processes. Classically, the coagulation system is divided into extrinsic and intrinsic pathways which converge on the common pathway to produce thrombin. A schematic of this process is displayed in figure 1-1. The extrinsic pathway is initiated for the formation of a prothrombin activator by exposure of the blood to components which are not present physiologically in the bloodstream, but revealed as a result of a mechanical injury, endothelium damage, denudation or biochemical alteration. Each of these events instigate the coagulation process through exposing blood to a single critical component, the tissue factor (TF), which is constitutively on most cells that do not normally contact the blood. TF is a single-chain membrane receptor for the major plasma component of the extrinsic pathway, factor VII. Only the TF-VIIa complexes are enzymatically active, although exposure of TF to plasma results in binding of both factor VII and factor VIIa. Then factor VII bound to TF is activated by TF-VIIa, termed auto-activation. Trace levels of active factor VII (factor VIIa), which is present in normal people's circulation is approximately 1% of the total factor VII concentration. 2 18

19 Figure 1-1: Schematic of the coagulation cascade which leads to the formation of thrombin, which paves the way for the formation of fibrin networks upon the interaction of thrombin with fibrinogen. Image adapted from King 3 The TF-VIIa enzyme complex which assembles on the fibroblast, activated monocyte, or perturbed endothelial cell, has two principal substrates, factor IX and factor X. Cleavage of either protein results in an active serine protease, factor IXa or Xa, which facilitates further reactions if appropriate cofactors are present. For example, factor VIII is required for factor IXa to catalyze the conversion of factor X to factor Xa, and factor V is required for Xa conversion of prothrombin to thrombin. 2 19

20 The intrinsic pathway which is parallel with the extrinsic pathway is initiated quickly in the vascular system by factors such as trauma to the blood itself or exposure of the blood to collagen from a traumatized blood vessel wall. A group of proteins, factor XII, HMWK (high-molecular-weight kininogen), and prekallikrein, labelled the contact system, mediates the activation of the intrinsic system through binding to negatively charged surfaces like kaolin, dextran sulphate and sulphatides. The action of the contact system results in the activation of factor XI, and then factor XIa activates K-dependent zymogen, factor IX. Consequently, factor IXa and its cofactor, factor VIII, assemble on a phospholipid-containing surface and form the tenase complex together which activates factor X. Factor IX provides a pathway that is independent of factor VII for blood coagulation. Nonetheless the activation of factor IX by VIIIa requires both calcium and the protein cofactor which is imbedded in the lipid bilayer of a cell membrane. The activation of factor IX by XIa requires only ionized calcium. The common pathway, conversion of prothrombin to thrombin, happens once factor Xa is formed from both the extrinsic and intrinsic pathways. To act efficiently prothrombin needs four components, factor Xa, factor Va, phospholipid, and calcium, generally called prothrombinase complex. Factor V is probably supplied by either fusion of plasma-derived factor V with the platelet membrane or via secretion from platelet α-granules, and is activated to factor Va by either factor Xa or thrombin. Factor Va then provides a receptor for factor Xa on the activated platelet surface as a cofactor in the prothrombinase complex. Once assembled, the prothrombinase complex increases the rate of prothrombin activation to more than 30,000 times faster than that with factor Xa and prothrombin alone. 2 It is clear that clotting occurs from both extrinsic and intrinsic pathways simultaneously after 20

21 blood vessels rupture. An important difference between the extrinsic and intrinsic pathways is that the extrinsic pathway can be detonative. Once the extrinsic pathway is initiated, its speed of occurrence is limited by the amount of tissue factor released from traumatized tissues and by the quantities of factors X, VII and V in the blood. The processing time of extrinsic pathway can be as little as 15 seconds while the intrinsic pathway usually requires 1 to 6 minutes to cause clotting slower than the extrinsic pathway Conversion of prothrombin to thrombin The conversion of prothrombin to thrombin which is generated by a prothrombinase complex, composed of factors Va, Xa, Ca 2+ and phospholipids, in turn, leads to the conversion of fibrinogen into fibrin fibers as a procoagulant factor that grounds platelets to the site of trauma and initiates processes of wound repair. The molecular weight of prothrombin is 68,700 and the molecular weight of thrombin is 33,700 which is less than half that of prothrombin. 1 Prothrombin is an unstable protein that can easily be split into smaller compounds such as thrombin. Prothrombin is expressed continually in the liver and is modified in a vitamin K-dependent reaction that converts ten glutamic acids on prothrombin to Gla (gamma-carboxyglutamic acid). In the presence of calcium, the Gla residues promote the binding of prothrombin to phospholipid bilayers. The enzymatic cleavage of two sites on prothrombin produces thrombin by factor Xa, which is enhanced by binding to factor Va. Thrombin is a Na + -activated allosteric serine protease of the chymotrypsin family which includes enzymes involved in digestion and degradative processes, blood coagulation, cellmediated immunity and cell death, complement, fibrinolysis, fertilization and embryonic development. Once generated in the blood from prothrombin, thrombin plays two diametric 21

22 and crucial functions. It transforms fibrinogen into insoluble fibrin that grounds platelets to the site of trauma and starts the process of wound repair as a procoagulant factor. Its other function is to act as an anticoagulant towards binding to thrombomodulin, which suppresses the ability of thrombin to cleave fibrinogen and PAR1 through the zymogen protein C. 4 Factors VII in the extrinsic pathway, IX in the intrinsic pathway and X in the common pathway, prothrombin and protein C are all K-dependent proteins which synthesize as zymogens and activate serine proteases by a limited number of proteolytic cleavages. These proteins are unique γ-glutamyl carboxyl acid (Gla) residues at the N-terminal end of the molecule that require vitamin K for proper synthesis by hepatocytes. This postribosomal modification of the protein is required for calcium binding, thus one calcium binds the two calcium groups of a Gla residue serving as a bridge for protein binding to the phospholipid surface Thrombin generation on fibrin formation Fibrinogen is formed in the liver and circulates at high concentrations of mg/ml in blood plasma with a molecular weight of The conversion of fibrinogen to fibrin is catalysed by thrombin through various steps. Thrombin acts on fibrinogen to remove fibrinopeptides A and B from the central domain of fibrinogen molecules by the serine protease forming a molecule of fibrin monomer. The fibrin monomer has the capability to polymerize with other fibrin monomer molecules, therefore forming fibrin. Through a process of spontaneous association, fibrin molecules polymerize into double-standed protofibrils with weak noncovalent hydrogen bonding. These newly formed fibres are not 22

23 cross-linked. Subsequence another process happens in a few minutes to the covalent bonds between fibrin monomer molecules with fibrin-stabilizing factor (factor XIII) which is normally present in small amounts in the plasma globulins, and is also released by platelet in the clot activated by thrombin. Furthermore, multiple cross-linkages between adjacent fibrin fibres add tremendous strength to the structure and form a stable three-dimensional meshwork. 5,6,7 Structures of fibrinogen, fibrin and its network are discussed in the following chapter. 1.3 A cell-based model Recently, a new model named the 'cell-based model of haemostasis' emerged as the limitations of the coagulation cascade were highlighted by certain clinical observations. For example, patients deficient in factor XII, high-molecular weight kininogen, or prekallikrein which are the initial components of the intrinsic pathway have an elongated activated partial thromboplastin time but no bleeding tendency. However, patients deficient in factor VIII or IX have a serious bleeding tendency even when the extrinsic pathway is complete. In addition to this, a serious bleeding tendency is observed in patients deficient in factor VII though the intrinsic pathway is uninjured. The cell-based model of haemostasis is thus very important to improve our understanding of clot performance in vivo. The basis of the cell-based model of haemostasis was determined with the knowledge of coagulation reactions happening on certain cell surface in vivo rather than on phospholipid vesicles. Haemostasis requires formation of an impermeable platelet and fibrin plug at the site of injury and the activation of clotting factors, and is accomplished by localizing clotting 23

24 factors on specific cell surfaces. This model proposes that haemostasis occurs in sequential phases: initiation, amplification and propagation, and requires two cell types: TFbearing cells and platelets. 8 The initiation phase happens on TF-bearing cell surfaces to produce small amounts of thrombin, normally outside the vasculature. The FVIIa/TF complex activates small amounts of factors IX and X. Factor Xa then associates with factor Va to form prothrombinase complexes on the TF-bearing cells. Zymogen factor Va for prothrombinase can be activated by platelet α granules through the processes of adhesion to the site of injury, factor Xa or noncogulation proteases. Any factor Xa localized to the cell surface is comparatively protected from inactivation by plasma protease inhibitors, but that which is dissociated from the cell is rapidly inhibited in the fluid phase by TF pathway inhibitor or antithrombin. However, factor IXa is not inhibited by TF pathway inhibitors and is inhibited much more slowly than factor Xa, so factor IXa can move from TF-bearing cell through the fluid phase to a nearby platelet or another cell surface. There is probably a constant low level of activity of the TF pathway in the extravascular space, but coagulation only proceeds at the site of the injury because the large components of the coagulation process such as platelets and factor VIII are completed with von Willebrand Factor and kept in the vascular space. In the amplification phase, there are several functions of the small amount of thrombin which is generated on TF-bearing cells during the initiation phase. The addition of thrombin can induce a higher level of procoagulant activity than adhesive interaction alone, while platelets have already adhered at the site of injury and become partially activated. Thrombin also activates factor XI on the platelet surface. On the other hand, the cofactors V and VIII have been activated on the platelet as another function of thrombin during the initiation 24

25 phase. In the end, the stage is set for large-scale thrombin generation in the propagation phase. It is thought that the propagation phase can only happen effectively on the platelet cell surface as the platelet surface is specialized to coordinate tense (factor IXa/VIIIa) and prothrombinase (factor Xa/Va) complexes. The key features of the propagation phase follow with factor IXa which binds to factor VIIIa on the platelet surface which is activated during the initiation phase. Factor VIIIa is supplied by platelet-bound factor XIa, and factor Xa which associates with platelet surface factor Va and generates a sufficient amount of thrombin to clot fibrinogen provided it is found on the platelet surface Fibrinolysis After the blood clot has formed around an injury, and sufficient time has passed for the wound to heal, the clot is dissolved and resorbed by a process called fibrinolysis, which acts through the plasmin enzyme. Plasmin is activated by plasminogen, a proenzyme, by one of two plasminogen activators (PAs), either tissue-type PA, or t-pa (found in tissue) or urokinase-type PA, or u-pa (found in urine). The process of fibrinolysis is highly dependent on molecular interactions between PA, plasminogen, fibrin, plasmin and α 2 -antiplasmin (which is responsible for the inhibition of fibrinolysis). 9 A range of thrombolytic agents are known which are responsible for the activation of plasminogen, including streptokinase (SK), two-chain u-pa (tcu-pa), anisoylated plasminogen streptokinase activator complex (APSAC), recombinant t-pa (rt-pa), and recombinant single-chain u-pa (rscu-pa), among others. The action of any number or combination of these agents results in the activation of 25

26 plasminogen, causing activation of the fibrinolytic system. This system induces the breakdown of several clotting factors which are responsible for the initial formation of fibrin which leads to a blood clot, including factors V and VIII, in addition to fibrinogen. Human plasminogen is a single-chain glycoprotein with a molecular weight of 92,000, and is found in plasma at a concentration of µmol/l. Initially, plasminogen has NH 2 - terminal glutamic acid (known as Glu-plasminogen), but it can be modified by the action of NH 2 -terminal lysine, valine or methionine via hydrolysis of the Arg-Met, Lys-Lys or Lys-Val peptide bonds to a form known as Lys-plasminogen. The subsequent cleavage of the Arg-Val peptide bond is the process by which Lys-plasminogen is converted to plasmin. Alternatively, the Arg-Val bond in Glu-plasminogen can also be cleaved to produce plasmin. The resulting plasmin molecule is a two-chain trypsin-like serine proteinase, with an active site composed of the His, Asp, and Ser amino acids. The ability of this molecule to interact with amino acids through so-called lysine binding sites means that plasmin is able to mediate the binding of plasminogen to fibrin, and the interaction of plasmin itself with α 2 -antiplasmin, thus plasmin is able to regulate the process of fibrinolysis. The presence of fibrin has an effect on the activation of plasminogen by t-pa, increasing its affinity for the enzyme. This means that the fibrinolytic process occurs when a clot is present, but plasminogen is not activated in the absence of a clot. 10 This is due to the slow inactivation of plasmin by α 2 -antiplasmin when it is bound to fibrin (half-life of seconds), while free plasmin is quickly inhibited when no fibrin is present (half-life of around 0.1 seconds). When fibrin is formed around an injury, a small amount of plasminogen is bound to it 26

27 through its lysine-binding sites. The release of t-pa into the blood is a slow process, and it is released by plasmin. 1.5 Clotting disorders Haemophilia Haemophilia is a hereditary disorder that slows the blood clotting process. There are two types of haemophilia (A and B), both of which are X-linked recessive disorders. Both forms of haemophilia are X-linked recessive disorders; the former is caused by a deficiency of factor VIII, while the latter is a result of a deficiency of factor IX. Clinically, haemophilia A is indistinguishable from haemophilia B; the condition must be diagnosed by specific factor assay. As it is a X-linked disorder, haemophilia is more likely to occur in males than in females. Mutations in the genes responsible for the formation of factors VIII and IX, genes F8 and F9, are observed in patients with haemophilia A and B, respectively. These mutations can either lead to the production of an abnormal version of factor VIII or factor IX, or they can cause an insufficient amount of these proteins to be formed. This results in faults in the blood clotting process, leading to excessive bleeding that can be difficult to stem. Since factors VIII and IX were cloned in and , respectively, significant advances have been made in the molecular characterisation of the defects which cause haemophilia. The excessive bleeding which occurs in haemophiliacs occurs due to the inadequate amount of factors VIII and IX, resulting in the failure of secondary haemostasis. This means that the platelet plug which is formed cannot be stabilised, as an insufficient 27

28 amount of thrombin is generated and the coagulation cascade cannot occur to produce fibrin. The measured concentration of the factor which is lacking is related to the bleeding tendency Thrombotic disorders A delicate balance exists in most people between the procoagulant (clotting) forces and the anticoagulant (fibrinolytic) forces, meaning that blood clots are formed, and are subsequently dissolved, when an injury occurs. There are, however, a variety of genetic and environmental factors which can shift this balance, increasing the rate of coagulation which occurs in veins, arteries or cardiac chambers, leading to the pathologic formation of thrombi even in the absence of an injury. This is undesirable, as these unwanted blood clots can block the flow of blood, leading to a pulmonary embolism or an embolic stroke, both of which are potentially life-threatening. There are wide variety of factors which can give rise to the formation of blood clots in the absence of injury, thus there exist a range of conditions related to this, some of which are potentially lethal. These conditions, labelled thrombotic disorders, include: atrial fibrillation, myocardial infraction (or heart attack), unstable angina, deep vein thrombosis, pulmonary embolism and embolic stroke. Due to the serious nature of these conditions, a better understanding of the causes of thrombotic disorders is necessary in order to learn how to combat them. Clotting is normally regulated by several antithrombotic mechanisms that slow down or halt the coagulation cascade. Antithrombin inhibits thrombin and Factors Xa and IXa, all of which are significant in the clotting process. Protein Z helps resist the formation of factor Xa via protein Z-dependent protease inhibitor (ZPI). Factors Va and VIIIa are inactivated by 28

29 activated protein C (APC) and its cofactor, protein S. Tissue factor pathway inhibitor (TFPI) downregulates the factor VIIa complex. It is clear that the combined action of all of these mechanisms give rise to a balance between clotting and fibrinolysis, and abnormalities in one or more of these mechanisms can lead to the development of one of the thrombotic disorders mentioned above. These abnormalities can be due either to a defect or deficiency in an antithrombotic protein (antithrombin, proteins C and S), or an increased level of a prothrombic clotting factor (factors VII, XI, IX, VIII, von Willebrand factor, prothrombin gene mutation G20210A, factor V Lieden). 13 Many people have a genetic predisposition to some of the thrombotic disorders mentioned above. The testing for these predisposing congenital factors involves testing for specific gene defects, and the measurement of the quantities of natural anticoagulant molecules in plasma. Several mutations of factor V can occur (of which factor V Lieden is the most common) which make it resistant to degradation by APC, giving rise to spontaneous venous thrombosis in many patients. 14 Another factor which can induce this condition, along with a venous thromboembolism, is a lack of APC or protein S, which can occur in patients with a deficiency of vitamin K. 15 Protein Z is another vitamin K-dependent protein, and while the exact pathophysiology of a deficiency of this protein or ZPI is, at the moment, unresolved, it is known that if a patient with a congenital coagulation abnormality (such as factor V Lieden) is also lacking protein Z or ZPI, the risk of thrombosis is increased, and the deficiency of ZPI causes a more significant risk than the deficiency of protein Z. 16 Finally, a lack of antithrombin can be an acquired deficiency in patients with liver disease, nephrotic syndrome or disseminated intravascular coagulation (DIC) 17, and can be potentially lethal to the foetus in utero. 29

30 Chapter 2 Fibrinogen and Fibrin Fibrin serves as the basic structural building blocks of a blood clot that mediate its formation, influence its structure and control its dissolution. Fibrin also plays a role as a scaffold that promotes cell growth and movement in wound healing due to trauma or other insults to normal tissue. Fibrin shows at least four structural levels in the blood coagulation process: fibrinogen molecule, fibrin monomer, fibrin fibre and fibrin network (figure 2-1). Fibrinogen is essential for haemostasis, wound healing, inflammation, angiogenesis and other biological functions, which is normally presented in human blood plasma at a concentration of about 2.5 g/l. The fibrinopeptides are cleaved by thrombin at the centre of fibrinogen to convert soluble fibrinogen molecules to insoluble fibrin monomers and gives the clot its shape. Fibrin monomers, therefore, polymerize via specific and tightly controlled binding interactions to make fibrin protofibrils. Fibrin fibres, from the lateral aggregation of protofibrils, support clotting structures as scaffolds and give the structures strength and flexibility. Finally, factor XIIIa covalently binds fibrin fibres to stabilize the clot against mechanical, chemical and proteolytic insults. 30

31 Figure 2-1: Transmission electron micrographs of (a) fibrinogen molecules, (b) protofibrils and (c) fibrin fibres (d) clot network. Fibrinogen molecules extend for nm, with two nodules at each end connected by a thin rod. In (b) the half-staggering property of protofibrils can be observed, and they also show signs of twisting. The fibrin fibres in (c) show a trimolecular branch point. The fibres appear to have a band pattern due to varying protein density across the fibres. The network in (d) is formed by branching of fibres with three-dimensional junctions. Images are from Weisel et al., ; Medved et al., 1990; 19 Weisel, 2004; 20 and Janmey et al., ) 31

32 2.1 Fibrinogen The mechanism of blood coagulation has been described briefly in the former chapter and this chapter will discuss properties and structures of fibrin at each stage of blood clotting. Fibrinogen is a soluble macromolecule, but forms a clot or insoluble gel on conversion to fibrin by the action of thrombin to prevent blood loss and promote wound healing. Besides, this is also necessary for the aggregation of blood platelets, which is an initial step in haemostasis. Fibrinogen is a globular and fibrous glycoprotein produced within liver cells at a rate of g/day. 7 A fibrinogen molecule is about 45 nm in length and 6.5 nm in thickness, which is made up of two sets of three polypeptide chains named Aα, Bβ and γ partially from fibrous districts of α-helical coiled-coils, while the globular parts contains two outer D regions and a central E region. The Aα-chain consists of 610, the Bβ-chain consists of 461 and the γ-chain consists of 411 residues. 7 Addition of asparagine-linked carbohydrates to the Bβ and γ chains, the three pairs of polypeptide chains with respectively molecular masses of 66,500, 52,000 and 46,500 Da, brings the total fibrinogen molecular weight to 340,000 Da. The N-terminal of Aα and Bβ chains of six polymers including fibrinopeptides A and B (FPA and FPB) are bonded through 29 disulfide bridges in the central E-region. The distal nodules of D regions contain separately folded C-terminal Bβ-chains and C-terminal γ-chains, called βc and γc. The C-terminal Aα-chains, called αc, fold back to comprise a short distance as the fourth chain of α-helical coiled coil, and then extend along the surface of the protein towards the central region. The αc domains are globular and sited close to the E region where they interact intra-molecularly. 5,21 The crystal forms of fibrinogen are unusual in that they are made up of end-to-end bonded molecules that form flexible filaments. The atomic resolution structure of fibrinogen in figure 2-2 has been built up from X-ray crystallographic studies of human γc module and fragment D, bovine fragment E, modified bovine fibrinogen, and 32

33 chicken fibrinogen. Three fragments were identified in the structure, containing a central region and two outer regions at each end connected by rods. Both the αc domains and the N- terminal of Aα and Bβ chains, including FPA and FPB, were not visible, likely because they 22,23 are flexible and/or disordered. The X-ray crystallographic structures of the entire fibrinogen molecule showed that there is a fourth strand for part of the coiled coil, formed from the Aα chain, which is folded back after the distal disulfide ring. Moreover, it appears that all of fibrinogen s carbohydrate chains are of biantennary structure, which has striking consequences for fibrin polymerization and clot structure. Figure 2-2: X-ray crystallographic structure of fibrinogen. The central domain is connected to the end domains through α-helical coiled-coil rodlike regions so that all three chains yield two D fragments and one E fragment. The areas of fragments D and E are indicated, while CH2O signifies the carbohydrate attachment sites. Most of Cα-chains are missing. The Aα chains are blue, as the Bβ chains are green, and the γ chains are red Conversion of fibrinogen to fibrin Fibrin polymerization is initiated by thrombin-catalyzed cleavage of the fibrinopeptides at particular Arg-Gly bonds owing to hydrophobic and structure-dependent interactions between the fibrinopeptides and thrombin s catalytic location, as well as noncatalytic binding of 33

34 enzyme to substrate. Besides binding at the catalytic site, thrombin also binds to the central region of fibrinogen through ionic interactions with positively charged residues on the thrombin B chain which is termed the anion-binding exosite I. 24 Thrombin binds strongly to fibrin in the clot or thrombus, thus thrombin is less likely to be inactivated or prolong clotting. The conversion of fibrinogen to fibrin monomer, which is shown in figure 2-3, happens after removal by thrombin of two pairs of fibrinopeptides, termed FPA and FPB, respectively from the N-terminus of Aα-chains and Bβ-chains. Thrombin is a trypsin-like enzyme with a very high specificity toward fibrinogen. The crystal structure of a complex shows how these two molecules, thrombin and fibrinogen, interacts with each other. The complex involves two thrombin molecules with reverence symmetrically bound to the three-stranded coiled coils on the opposite sides of the fibrinogen s central E fragment and makes an X-shaped structure. Each thrombin molecule is bound to the outer wall of the funnel-shaped E-region. As expected, the binding happens through thrombin s anion-binding exosite I in such a way that the active sites of both thrombin molecules are facing in the same direction, so that both pairs of fibrinogen s fibrinopeptides are well positioned for thrombin cleavage. 25 Replacement of particular amino acids in the fibrinopeptides and at thrombin s cleavage sites in recombinant fibrinogen has been used to understand thrombin specificity, such as the relative rates of fibrinopeptide cleavage and effects on polymerization. Cleavage of FPA from the central domain exposes the N-terminal sequence Gly-Pro-Arg- Pro-amide, an analog of A knobs, which consent to noncovalent E-region interaction with the corresponding complement a holes in the C-terminal γ chain of the D-region from another fibrinogen molecule. The knob-hole interactions (see figure 2-3) between the A:a 34

35 complementary binding sites produce aggregates in which the fibrin monomers are halfstaggered, since the central domain of one molecule binds to the end of the adjacent molecule. There are also B knobs, corresponding to the N-terminal sequence Gly-His-Arg-Pro-amide, consequently exposed in the central E-region on cleavage of FPB after polymerization begins, which reside in the b holes on the C-terminal Bβ chain of the D-region from another fibrinogen molecule with a structural orientation similar to the A:a interaction. Initially, a dimer is formed and then additional molecules are added to give a structure; the E:D interactions yield the self-generated formation of half-staggered, double-stranded protofibrils. 26,27,28,29 Figure 2-3: Schematics of (a) fibrinogen molecule, (b) fibrin monomer and its assembly into (c) fibrin protofibrils. Thrombin removes the fibrinopeptides (FpA and FpB) which cover knobs A and B which are in the centre of the fibrinogen molecule, allowing these knobs to interact with the corresponding a and b holes in other molecules. These A:a and B:b interactions, repeated many times, lead to the formation of fibrin protofibrils

36 Figure 2-4: Schematic diagram of complementary physical interactions in fibrin polymerization. FPA is cleaved by thrombin via ionic interactions to form desa monomers while FPB is cleaved primarily from polymeric structures. Fibrin monomers aggregate through knob-hole interactions to produce oligomers, which lengthen via protein-protein interactions to yield protofibrils. Fibrin protofibrils aggregate laterally to make fibres by intermolecular interactions with the Αc domains, and fibrin fibres finally form a complex fibrin network cross-linked by factor XIII through covalent bonds. Adapted from Weisel. 30 Removal of FpB happens due to fibrin oligomers and promotes the lateral aggregation of existing fibrin protofibrils, so that clots made up with thicker fibrin fibres are produced with 36

37 the release of both fibrinopeptides rather than from the release of FpA only. However, since the effects of FpB removal are not well understood, FpB release in normal fibrin formation is highly debatable. Alternatively, the release of FAP is crucial for normal protofibril formation, because delayed FPA release conducts to markedly delayed fibrin polymerization. 31 A schematic diagram of how the action of thrombin on fibrinogen gives rise to the formation of fibrin monomers, which in turn form fibrin protofibrils, is displayed in figure 2-4. Initially, a dimer is formed and then additional molecules are added to give a two-stranded protofibril by highly specific protein-protein interactions. From X-ray crystallography, the a and b binding holes are known to be always exposed, allowing even fibrinogen-fibrin interactions. While the a holes bind synthetic Gly-Pro-Arg- Pro peptides, the b holes preferentially bind Gly-His-Arg-Pro peptides. The interactions of Gly-Pro-Arg-Pro with residues in the a pocket define minimum features of the binding, however, the interaction site may be more extensive. Gly-Pro-Arg-Pro is held in the hole mainly by electrostatic interactions with residues including Gln329, Asp330, His340, and Asp The αc domains are important for the mechanical properties and stability of clots. The αc domains detach from the central region and are available for intermolecular interactions, because of a large-scale constructed change on the cleavage of the B fibrinopeptides. 33 Intermolecular interactions between αc domains are important for the enhancement of lateral aggregation during fibrin polymerization. 32,33,34 Figure 2-4 indicates corresponding physical forces that involve fibrin polymerization. When the fibrinpeptides are removed by thrombin due to ionic interactions, knob-hole interactions occur to form oligomers, then protein-protein interactions give rise to two-stranded protofibrils from halfstaggered molecules. The intermolecular interactions between αc domains enhance the twostranded protofibrils, which aggregate into fibres with a repeat of 22.5 nm. 37

38 Figure 2-5: Scanning electron micrograph of fibrin fibres shows that they are twisted structures. The band pattern with a repeat of 22.5 nm is characteristic of fibrin. Magnification bar = 1 μm. 20 Once protofibrils reach a sufficient length (usually about nm), they accumulate laterally to form fibres. Figure 2-5 shows that the protofibrils twist during aggregation and become entangled with one another, limiting the lateral growth of these fibres. Because the periodicity of 22.5 nm of fibrin is maintained, as new protofibrils are added to the fibre, those near to the surface of the fibre must stretch relative to those near the centre as the path length increases with fibre diameter. The twisting which occurs during aggregation is due to the intrinsic twisted nature of the fibrinogen molecule. The resulting fibre thus consists of an entangled network of taut protofibrils, which have been observed using scanning electron microscopy and confocal microscopy experiments. 35 Lateral aggregation ceases when the energy necessary to stretch an additional protofibril is equal to its bonding energy. 36 There appears to be no defined diameter which is preferred during the formation of a fibrin fibre, but measurements have shown that the diameter of a fibre can vary from 20 to over 450 nm. 36,37 This large variation in observed fibre diameters may be influenced by the type of buffer solution used. 38

39 2.3 Covalent cross-linking fibrin network Once the two-stranded protofibrils have aggregated into fibres of fibrin, complex threedimensional networks of fibrin are formed through lateral association and outward branching of the fibres. The branching of fibrin fibres is essential for the formation of a blood clot as it allows a space-filling gel to form. This gel can be produced with very low fibrinogen concentrations (<0.01 mg/ml protein). 28 There are two types of branches which fibrin fibres can form to create a network. The first type, described above, is known as a tetromolecular or bilateral branch point, and is formed when the double-stranded protofibrils converge side-to-side. Multiple bilateral branches with a greater strength and rigidity are produced when these protofibrils aggregate and form dense bundles of fibres. The second type of branching is known as trimolecular or equilateral branching, so called because it is formed by three fibrin molecules conjoining with three two-stranded protofibrils of equal width. Factors such as low ionic bond strength, increased concentrations of CaCl 2 and slow polymerisation of fibrin favour this second type of branching. The clot is stabilized by the formation of covalent bonds introduced by factor XIII which is important to make the fibrin a rigid, elastic structure resistant to proteolytic, chemical and mechanical disruption to thwart bleeding. Zymogen FXIII is a transglutaminase with a heterodemic structure which consists of two A- and two B-subunits. About half of the total factor XIII in human blood arises from platelets, which contain dimers consisting of only two A-chains. 38 It is inactive while circulating in the blood, mainly bound to fibrinogen, and it is converted to the activated enzyme factor XIIIa during the cleaving of fibrinogen and the subsequent release of fibrinopeptides. This activation process occurs when thrombin cleaves 39

40 a 37-amino-acid activation peptide from the N-terminal of the A-subunit. Following this dissociation (see figure 2-6), the factor XIIIa cross-links the α- and γ-chains of fibrin, but not the β-chains. Factor XIIIa produces strong bonds to fibrinogen via its β-chain, so that nearly all circulating zymogen is bound. The activation of factor XIIIa is dependent on the correct alignment of the fibrin D-E-D regions, as it occurs during protofibril formation. Factor XIIIa forms an isopeptide bond between γlys406 on one chain, and γglu398 and/or γglu399 on the other, forming structures that are generally dimeric. These γ-chain residues are located near the C-terminal end of the γ-chain. 39 The nature of the orientation of these bonds has long been debated; the factor XIIIa could be forming cross-linked γ-chains transversely between strands, 40 causing the bond to stretch between protofibrils, or it could be creating cross-links in a longitudinal fashion which act as a junction between two adjacent D-domains. 41 Figure 2-6: (a) Activated factor XIIIa introduces isopeptide bonds between the C-terminal γ- chain cross-linking sites in the protofibrils to form γ-dimers rapidly. (b) Cross-linking of the α- chain to other α-chains occurs more slowly and stabilises the three-dimensional fibre network. 42 In addition to the cross-linking of γ-chains, there are a large number of available glutamine residues which serve as cross-linking sites for α-chains. 43 This variety of cross-linking sites 40

41 may have an influence on the polymerisation process. The concentration of factor XIII has a significant influence on the rate and extent of cross-linking of α-chains. As the αc domains associate even in the absence of cross-linking, these interactions may promote the formation of isopeptide bonds by bringing the donor and acceptor sites into close proximity. These isopeptide bonds create a network of αc domains, connected by covalent bonds, although little is known of their structure. The degradation of a clot by fibrinolysis is dependent on this cross-linking, as the α-chains resist the digestion of the fibrin clot by plasmin in the coiled region between the D- and E-regions. 2.4 Physical and mechanical properties of clots The formation of fibrin networks is significant for the formation of blood clots, and a variety of parameters influence the stability of the clot. Fibrin gel is formed because of the nonlinear condensation polymerisation of fibrinogen. Thus, the gel point, which occurs at a defined stage during this polymerisation, the length of the polymers and the nonlinear interactions between them determine the final structure of the gel. The structure of fibrin fibres are also affected by the fibre thickness, the number of branch points, the porosity of the fibre, and its permeability. It is important to understand the internal structure of the clot and which factors influence it. In contrast to theoretical predictions, which assume that fibre diameter is uniform in a fibrin network; turbidity and permeability measurements, in addition to evidence from electron microscopy (as in Figure 2-7), have shown that the fibre diameter can vary considerably in such a network. The distribution of fibre diameters appears to bimodal, resulting in a fibrin 41

42 network consisting of thin and thick fibres, although there is a wide variation in diameter within each mode of the distribution. 44 The turbidity of the clot is determined by the networks of thicker fibres, while the permeability of the clot is dependent on the networks of thinner fibres. It has been observed that the mass-length ratio, µ, of a fibre decreases with increasing ph, and for a given value of ph, the presence of cations results in an increase in µ. The presence of calcium is necessary for the crosslinking of fibres; Factor XIII is activated only in clots formed when calcium is present. Calcium increases the affinity of Gly-His-Arg-Pro for fibrinogen, which allows the protofibril to increase in length and diameter. This results in the thinner network of fibres gaining additional strength, and contributing to the clot s resistance to flow. This, in turn, lowers the permeability of the clot, and the mass-length ratio of the fibres. Figure 2-7: Transmission electron micrograph of a clot made with purified human fibrinogen. Two distinct networks consisting of thin (labelled A) and thick (labelled B) strands of fibrin are identified. The diameter of thicker fibres can be up to 10 times larger than the thinner fibres. Adapted from Shah et al. 44 Nonetheless, the diameter of a fibrin fibre, and thus the overall structural properties of the clot, is influenced by the concentration of thrombin and that of fibrinogen. The diameter of 42

43 the fibre decreases with increasing thrombin or fibrinogen, with little effect on the length of the fibre. A lower concentration of thrombin (around U/ml) results in a lower rate of fibrinopeptide cleavage, meaning that the fibrin monomers are produced more slowly. This allows the protofibrils to grow longer and undergo more lateral aggregation, allowing the formation of thicker fibres. A higher concentration of thrombin (up to 1 U/ml) allows faster cleavage of fibrinopeptides, meaning that the protofibrils have less time to aggregate and thinner fibres are formed. 45 The observed decrease in fibre diameter with increasing fibrinogen concentration is attributed to higher rates of monomer formation due to higher substrate concentrations. It is also believed that salt concentration has a profound effect on the aggregation of protofibrils which leads to the formation of fibres, because high concentrations of salt inhibit this aggregation, forming a web of protofibrils. 46 Besides the concentration of thrombin and salt content, which determines the clotting rate, the concentration and activation rate of factor XIII influences the polymerisation rate, 47 chloride ions modulate fibre size and inhibit the formation of thicker, straighter fibres, 48,49 and the ph of the fibrin matrix can cause the growth of tubular structures. 50 Many factors that influence the clot structure have a great impact on fibrin s mechanical properties. The mechanical properties of the fibrin are essential for their function in haemostasis while the formed clot must be sufficiently stiff that it can stem the flow of blood through a wound, but it must also be digestible by lytic enzymes to prevent the formation of a thrombus, which can lead to heart attacks or strokes. Fibrin is a viscoelastic polymer, where stiffness or storage modulus characterizes the fibrin s elastic properties and creep compliance or loss modulus represents its viscous properties. The viscoelastic parameters determine how the clot responds to the applied forces in flowing blood, which have been measured under various conditions and methods. 43

44 Both elastic and viscous properties are very sensitive to small changes that affect polymerization and clot structure. For small strains or deformations, stress is directly proportional to strain, while at large strains, the stiffness of the clot increases by up to a factor of Strain hardening may be important biologically because it allows fibrin clots to be compliant at low strains and then become stiffer at higher strains that could otherwise threaten clot integrity. Measurements taken with laser tweezers have shown that fibrin fibres are much stiffer for stretching than for flexion. 52 For a homogeneous, isotropic and linearly elastic circular cylindrical rod of length L and diameter d, the ratio of displacement due to flexion to that from stretching is. For L/d = 30, a typical value for fibrin fibres, the flexural displacement is 300 times the stretching displacement. Thus, it is believed that the flexibility of a clot arises due to the ability of the individual fibres to bend. The rigidity of the clot is dependent on the thickness of the fibres, and the number of branching points between them. However, large fibre diameter and length is generally associated with minimal branching, so maximal rigidity of a clot is achieved when there is a balance between large fibres and extensive branching. However, these consequences of the listed factors for the clot structures and mechanical properties are still largely unknown. 44

45 Chapter 3 Semi-flexible Polymers and Rheology 3.1 Semi-flexible polymers Long threadlike molecules are formed from a very large number of identical units (monomers), producing so-called macromolecules (polymers), such as proteins and nucleic acids etc. A great deal of research is focused on the mechanical response of biological tissues and gels, which are composed of macromolecules, as this response is significant for many biological functions, for example cell motility. Many network-like biological tissues respond to deformation with an increase in stiffness which has been revealed through rheological experiments on fibrin, as well as on gels of cytoskeleton filaments in vitro, and by micropipette and microtwisting experiments on individual cells. Fibrin and these biological materials fall within the class of semi-flexible polymers. The key to understanding the dynamics of a stiff polymer in various situations is the relaxation of its tension after pulling at one side. It is now understood that the relaxation dynamics of a stiff polymer are quite different to that of a flexible polymer. 45

46 3.1.1 Statics and dynamics of single filaments Stiffening of semi-flexible polymers can be a result of the response of the polymeric filaments between cross-links, alterations in the network structure or both of these factors, due to interlinked structure of filaments. The model usually inferred for a theoretical description of semi-flexible chains is the wormlike chain model 53,54 (WLC). The statistical properties of the wormlike chain are modelled by a free energy function H which measures the total elastic energy of a particular conformation where is the tangent vector. The filament is described as a smooth inextensible line r(s) of length L parameterized in terms of the arc length s here. The total energy function H is integrated over the squared local curvature by using the bending modulus κ as a weight: 55 (3-1) The bending modulus is a property of the material which can be expressed in terms of Young s modulus of elasticity, E, and the second moment of inertia, I, (or the flexural rigidity), which depends on the geometry of the material. In the case of a slender rod with a circular cross-section of radius a, the bending modulus is given by 56 (3-2) The persistence length is another important concept related to the finite bending rigidity in d-dimensional space. This can be expressed analytically as the exponential decay of the tangent-tangent correlation function 57. (3-3) 46

47 The persistence length of a polymer is usually used to measure a polymer s flexibility. There are three standard classifications for the isolated chains which are the flexible chain for, the semi-flexible chain for and the rigid chain for. 58 Each polymer of a different class needs a different theoretical model to develop an understanding of their viscoelastic properties. It is possible to calculate the mean-square end-to-end distance within the WLC model as a measure of the average spatial dimensions of semi-flexible polymers. Correspondingly, the mean-square end-to-end distance reduces to the appropriate limits of a rigid rod, and a random coil when : 59. (3-4) A central quantity for characterizing the conformation of polymers is the radial distribution function of the end-to-end vector r, which gives the probability density of finding both ends of a polymer with length L separated by. As for any model with short-ranged interactions it converges quickly to a Gaussian distribution for an increasing number of segments. The distribution function of polymers which have a length comparable to their persistence length shows very different behaviour to those which are shorter than their persistence length, while flexible polymers can be described by corrections to Gaussian behaviour. A good approximate function is given by:, (3-5) where for, and for (fig 3-1)

48 Figure 3-1 Shows the end-to-end distribution function of a semi-flexible polymer (for various ratios L/lᴘ), calculated by numerical simulation. With weight of the distribution shifting towards full stretching, converges from a Gaussian to a completely non-gaussian form by increasing the stiffness of the polymer. 59 Due to the massive quantity of theoretical work describing the single chain behaviours over many years, fibrin fibres are well described as bundles of semi-flexible polymers. Within a network, the motion of a small segment of unit length of a fibrin fibre is described by the equation of motion: =, (3-6) Where m is the segmental mass per unit length, ζ is the friction or drag coefficient, int is the internal force and f ext is the contribution from an external force. If the motion of the polymer chain is sufficiently slower than that of the solvent molecules and only takes the inextensibility condition into account (assuming only small deviation s from a straight conformation), it is sufficient to consider only the local transverse deflection. 48

49 Describing the dynamics of semi-flexible polymers in solution is complicated because of two essential factors, the chain s local inextensibility and hydrodynamic interactions interceded by the solvent. However, considering only experimental situations where the forces acting on filaments are small and the chains are relatively stiff, semi-flexible polymers are restricted to weakly curved conformations and all nonlinear effects can be neglected. The dynamics of a semi-flexible polymer chain in solution is ordinarily dominated by the following Langevin equation ζ, (3-7) where is the transverse friction coefficient and may be either an external force or a random thermal force that satisfies and. Assuming, equation 3-6 with fluctuation wavelength Ɩ, the typical decay time of a thermally induced fluctuation can be obtained. Therefore, the time dependence of the meansquare displacement is found to be. (3-8) Networks of semi-flexible polymers In order to understand the physical behaviour of individual filaments, a good understanding of the viscoelastic response on the molecular level for networks of semi-flexible polymers is needed. This understanding is based on ideas like entanglements, the tube model and reptation theory. 61,62 In order to describe the material properties of fibrin fibres, the way in 49

50 which semi-flexible polymers are built up into statistical networks, and how stresses and strains are transmitted through these networks must be understood. The viscoelastic response is entropic in origin over a wide range of frequencies in standard polymer systems made up of long flexible chain molecules. 63 A comprehensive understanding of the viscoelastic response of semi-flexible polymers is complicated by numerous factors. Firstly, there are several ways by which forces in a network can be transmitted, either by solvent-mediated interactions or through viscous coupling between the filaments. Secondly, single filaments are anisotropic elastic elements which show very different responses for forces at different angles to its mean contour. Abundant issues have been raised about what kind of deformation perturbs the networks and whether the macroscopically affine deformation of the network stays affine locally. One of the issues is that solutions of semi-flexible polymers, will exhibit a rubber plateau when solutions are adequately thick and examined on suitably short time scales ( Hz) 57, caused by time scale separation between the internal dynamics and the centre of mass motions. Then an outwardly compulsory shear stress will be transmitted to the distinct threads and its response will establish the magnitude of the modulus. The phantom model is implemented to semi-flexible polymer systems in order to solve this many-chain problem that the path of a semi-flexible polymer between two entanglement points is supposed to be straightened or abridged in an affine way with the sample upon deformation macroscopically. Thus, the macroscopic modulus can be calculated from the free energy cost linked with the change in end-to-end distance. The modulus predicted in the affine model should scale as, leading to absolute values of the order of 10 Pa, which are surprisingly high values compared to the low values observed in the experiments of F-actin solutions, thus it was determined that such a model is a better description of cross-linked networks

51 Theoretical and experimental predictions suggest that the free energy cost of the concealed transverse fluctuations of polymers come about from an affine deformation of the tube diameter leading to the following form of free energy and hence the plateau modulus 64. (3-9) Recent experiments seem to prefer this idea that the plateau modulus rises with free energy cost, coupled with deformed tubes caused from macroscopic stresses. This issue was related and examined in this study which will be discussed in the final chapter by comparison with the existent results of the fibrin clot. There are two interesting phenomena involved in semi-flexible polymer network responses to an external force. The strain hardening phenomena of semi-flexible polymers provides a clear biological advantage, since it allows biomaterials to be easily stretched and sheared at small strains. Significantly, this behaviour also can be found in fibrin; the clots oppose deformation with an increasing resistance. This does not only help to prevent the blood streaming out of major vessels with raising deformations, but also helps the clot to follow a regular, small amplitude vascular extension-contraction cycle when the heart pumps blood in the circulation. The cause of this marvellous mechanical behaviour can be explained as the anisotropic elastic response of individual filaments when exposed to an external force. Geometrically, the network response of increasing strain might be due to reorientations in the network architecture during a bending-to-stretching transition with distinct non-affine characteristics. On the other hand, soft viscoelastic materials usually demonstrate a positive deformation orthogonal to the direction of the applied shear force, but fibrin tends to pull the plate together when sheared between the two parallel plates of rheometer. The negative normal 51

52 stress depends on the applied strain amplitude, but not its direction. This phenomenon leads to an astonishing consequence: that blood clots contract when sheared within the vessel. 65 The methods which can actually measure mechanical characteristics such as elastic modulus (G') and viscous modulus (G'') are the most important issues in the next section. Bulk rheology, one of the best known methods, using a cone and plate rheometer with oscillatory stress was applied to study the viscoelastic properties of the fibrin clots and will be studied in detail in the current thesis. 3.2 Rheology The time dependent elastic responses of materials are called viscoelasticity which is typical of all polymeric materials. Biorheology provides theoretical and experimental concepts to understand how biological materials store and dissipate energy. As a first step, two dimensionless numbers, the Peclet number and the Deborah number, are introduced to understand the flow behaviour qualitatively. The Peclet number (P e ) determines when the microstructure is deformed significantly by applying stresses. The diffusion coefficient (D) is related to the dissipating force with the Einstein relationship, and is expressed as where kt is the thermal energy and f is the frictional coefficient. With the assumption of nonslip boundary conditions, from the Navier-Stokes equations, the frictional coefficient (f) can be calculated as by Stoke s relationship, where η is the viscosity of the solution and a is the particle radius. So that the diffusion coefficient (D) of the constituent particles is given by the Stoke s-einstein relationship as 52

53 . (3-10) In addition, the relaxation time (t a ) associated with the diffusive motion of the particles is (the time for the colloids to diffuse their own radius). The characteristic time (t s ) during which these spherical particles experience the applied stress (σ) for shear flow is. The Peclet number (P e ) is thus defined as, (3-11) which follows the requirement of undisturbed microstructure. The time scale (τ) of a structural relaxation by diffusion must be less than the measurement time (t) for a linear viscosity experiment, so that the Deborah number (D) can be stated as by definition (, solid-like;, liquid-like). Both conditions of the Peclet and Deborah numbers have to be satisfied for a linear viscoelasticity experiment. Steady state shear experiments always probe non-linear viscoelasticity, while oscillatory experiments are sensitive to linear viscoelasticity in the limit of small amplitude Linear viscoelasticity Through inspection, the ratio of the maximum stress to the maximum strain is found to be constant in a linear viscoelastic material. For example, this rheological behaviour could be modelled with a Hookean spring or a dashpot containing a Newtonian oil (figure 3-2). For a spring, the constitutive equation has the response of a purely elastic solid, where σ is shear stress due to the applied strain with the shear modulus G. On the other hand, the shear stress σ is proportion to the shear strain rate with the viscosity η as for a Newtonian 53

54 liquid. Using these mechanical models as analogues enables us to describe a wide range of deformations. The two simplest arrangements that help us to understand biological materials are the models in series or parallel. When a stress is applied to the parallel elements of a Kelvin-Voigt model in figure 3-3b, both elements will respond and a linear addition of the stresses is described by the constitutive equation. For a model arranged with a dashpot and spring in series, the Maxwell model in figure 3-3a, then the strain rates add linearly and are described as. Figure 3-2: The left model shows a Hookean spring with modulus G, and the right model shows a Newtonian dashpot containing a Newtonian oil of viscosity η. 66 Figure 3-3: (a) The Maxwell model has a dashpot and a spring in series. (b) The Kelvin-Voigt model has a dashpot and a spring in parallel. 66 For an elastic material symbolized by a spring, the stress will remain constant all the time as a strain is applied. If the strain is applied to a Maxwell model, giving rise to a stress via the 54

55 instantly responding spring, there then follows a gradual reduction in stress with time as the piston slowly moves through the fluid in the dashpot. Using a first-order rate expression to describe the decay of stress, the equation is given as constant. After a rearrangement, the expression becomes where k describes the rate. Integration of this expression gives. Evaluating this expression gives, thus the rate constant k has the dimensions of reciprocal time and can be replaced by a time constant τ m. Therefore, the exponential of both sides of the expression gives an equation to describe the decay of the stress with time when a rapid strain applied to a Maxwell model which is. (3-12) Applying the decay time constant in equation 3-12, the shear modulus relaxation function is illustrated as. The exponential decay equation (3-13) describes the decay of shear modulus with time which, for example, is clearly seen in data from polydimethylsioxane sample. 67 We can consider the exponential relaxation characterizing the response of a Maxwell model as an example of Boltzmann (1876) superposition integral that is. (3-14) If the strain is supposed to be applied at time t 0 which increases over a time ν to a maximum γ, no strain is applied at times less than t 0 ν and the strain is constant at times greater than t 0. This gives limits to the Boltzmann superposition integral and we can get 55

56 . (3-15) We substitute q, which lies between t 0 and t 0 ν, to express the superposition integral to give so that. If we choose t 0 = 0, we know it occurs at t + gν where g lies between 0 and 1, and we can get. For a viscoelastic liquid,, we obtain (3-16) When a linear viscoelastic material is deformed sinusodially, the stress develops in direct response to the applied strain after an initial start-up period. The strain oscillates at the same frequency with a shift of phase angle (δ) with respect to the strain wave (ω). By decomposing the stress wave into two waves of the same frequency, one in phase with strain (γ) and one 90 out of phase with strain, the strain can be written as, thus. (3-17) The elastic modulus is now (in-phase) and the viscous (or loss) modulus is, also given from the decomposition of the stress wave. Trigonometry shows, so that we can observe. (3-18) This characterises the linear viscoelasticity of a polymer as the ratio of loss modulus (G'') to elastic modulus (G'). Using the prime and double prime notation in a complex number ( ), γ can be represented as γ 0 e iωt, and now and. Hence we can define (3-19) 56

57 where G * is a complex number with (3-20) or. (3-21) In order to describe the material properties as a function of frequency for a body that behaves as a Maxwell model, an applied sinusoidal wave is expressed in the exponential form. Therefore, we have the complex strain, the complex strain rate. The stress response lags by the phase angle δ, which leads to and. So, applying the complex stress and strain relationship to the constitutive equation for a Maxwell fluid we have the resulting relationship. (3-22) We may rearrange equation 3-22 and apply the decay time constant to give the complex modulus and the frequency as ω ωτ, which can be further rearranged to give an expression. (3-23) We achieve separation of the real and imaginary components by multiplying through, we have. (3-24) These equations describe the frequency dependence of the stress with respect to the strain. As the frequency increases, the loss modulus first increases from zero to G/2 and then reduces to 57

58 zero, which gives a bell-shape curve shown in figure 3-4. The complex and storage moduli equals a constant when the frequency tends to infinity, and the crossover point between the storage and loss moduli occurs at τ m. Figure 3-4: The frequency response of the dynamic viscosity in a Maxwell model. 66 The gel point (GP) 68 defines the rheological transition between an elasticoviscous fluid and solid. The complex shear modulus G* from equation 3-20 can be classically described by the relation 69,70, (3-25) where is the relative distance to the gel point. Here p is the reaction extent, p c is the reaction extent at the gel point. is the characteristic frequency associated with the slowest relaxation process, where s and t are the exponents which govern the power law behaviours of the steady-state vicoelastic properties. 58

59 Before the gel point ( ) and, the material behaves as viscous liquid and we have which leads to. (3-26) After the gel point ( ), we have which leads to. (3-27) For, we have at any reaction extent, which leads to (3-28) Where δ is the loss angle defined in equation At the gel point, ω * tends to zero and the following power law is predicted in all the frequency ranges below :. (3-29) Consider a polymer of fractal dimension d f, which relates the molecular weight M of the polymer to its relative distance as. The value of d f is calculated from analysis of the viscoelastic data at the gel point by use of the established relationship 71 : (3-30) Where d is the space dimension (d = 3 herein). 59

60 3.2.2 Cone-and-Plate rheometer Mooney and Ewart (1934) suggested the first cone-and-plate rheometer to measure viscosity of materials and Russell s (1946) studies ultimately led to the development of the Weissenberg Rheometer (Jobling and Roberts, 1959; Lammiman and Roberts, 1961) and the Ferranti Shirley instrument (McKennell, 1954). 67 Nowadays, the cone-and-plate rheometer is often used to study non-newtonian effects and it is used to understand rheological properties of the fibrin clots in the current study. (a) (b) Figure 3-5: (a) Schematic diagram of a cone-and-plate rheometer. (b) The shear flow geometry of a cone-and-plate rheometer. 67 According to the sketch of the cone-and-plate rheometer, spherical coordinates are the proper shear flow geometries for its dynamic problems (fig 3-5). Assuming the flow is steady, laminar and isothermal, the flow has only a single component, while, and is smaller than 0.10 rad ( 6 ). The body force is negligible and liquid boundary is spherical, so that the equation of motion can be obtained as 60

61 (3-24) (3-25) (3-26) The boundary conditions of equation 3-24 are and. Since within 1% for, we will get. (3-27) By integrating equation 3-26, the shear stress can be written as. (3-28) Introducing from a torque balance on the plate to a note from equation 3-28 which is, we can obtain. (3-29) However, as rad, the relationship can be found, so that the shear stress through the flow 67 is fundamentally a constant given by. (3-30) From a symmetric matrix in a spherical coordinates (figure 3-5b), a homogeneous shear strain can be written as 61

62 . (3-31) B is known as a Finger deformation tensor from for stretching and R for rotation. According to that F is the tensor product of V rewritten as since and an approximation as β is small, the velocity profile can be presented as. Applying the approximation into the rate of deformation tensor (2D) of a spherical coordinate which is, the shear rate is given by. (3-32) Therefore, the velocity gradient at any point on the plate is calculated from the tangential velocity at that point divided by the separation between the surfaces, and what we measure experimentally at a given shear rate is the moment of force on the cone. Through equations 3-30, 3-31 and 3-32, we can obtain the complex, storage and loss moduli of experimental samples. 62

63 Chapter 4 Materials and Methods 4.1 Sample preparation Tris (Hydroxymethyl) aminomethane (C 4 H 11 NO 3 ), highly purified for use in molecular biology applications (ph ph 11.5, moisture < 0.2 %, heavy metals < 5 ppm (as Pb), insoluble matter < 50 ppm) was acquired from Melford Laboratories Ltd. (Cat# B2005, Suffolk, UK). EDTA (Ethlenediaminetetraacetic acid dipotassium salt, C 10 H 14 K 2 N 2 O 8 ) purified to approximately 98 % was purchased from Sigma-Aldrich (CAS# , ST. Louis, USA). Salt (Sodium Chloride, NaCl) ready for laboratorial use (Assay: 99.1 %, heavy metal < 5 ppm (as Pb)) was bought from Calbiochem (Cat #567440, an affiliate of Merck KGaA, Darmstadt, Germany). Tris-EDTA buffer (0.01 M pure Tris, M EDTA, ph 7.4) is made from Tris and EDTA dissolved in deionised water and ph corrected by the addition of HCl with a total solution volume of 500 ml. Tris-EDTA plus NaCl buffer (0.01 M pure Tris, M EDTA, 0.15 M NaCl, ph 7.4) is made from Tris and EDTA with additional salt dissolved in deionised water. The ph was again corrected by the addition of HCl with a total solution volume of 500 ml. Buffer solutions were prepared in a 500 ml bottle, sealed by 63

64 parafilm, stored at 4 C and used within 2 months. Human fibrinogen [lyophilized, plasminogen depleted, homogeneously purified by SDS-PAGE, clottability > 95%, solubility (in H 2 O) : 25 mg/ml] was purchased from Calbiochem (Cat# , an affiliate of Merck KGaA, Darmstadt, Germany) and was diluted to 5 mg/ml in Tris-EDTA buffer (0.01 M pure Tris, M EDTA, ph 7.4) or Tris-EDTA plus NaCl buffer (0.01 M pure Tris, M EDTA, 0.15 M NaCl, ph 7.4) over a water bath maintained at 37 C for approximately one hour. Following reconstitution, aliquots with Tris-EDTA buffer or Tris-EDTA plus NaCl buffer were prepared in 10 ml tubes, sealed by parafilm and stored at 80 C for six months. Stock solutions stored at -80 C were thawed in a 37 C water bath. For the experiments, fibrinogen solutions were stored at 4 C and used within two weeks. Thrombin from human plasma (lyophilized, complete activation from homogeneous prothrombin by SDS-PAGE, activity 1000 NIH-units/mg protein, solubility (aqueous buffer or H 2 O): 1 mg/ml) was bought from Calbiochem (Cat# , an affiliate of Merck KGaA, Darmstadt, Germany) and was reconstituted to 20 IU/ml in Tris-EDTA buffer (0.01 M pure Tris, M EDTA, ph 7.4) or Tris-EDTA plus NaCl buffer (0.01 M pure Tris, M EDTA, NaCl 0.15 M, ph 7.4) in 10 ml tubes, sealed by parafilm and stored at - 80 C for 2 months. For experiments, aliquots at 2 IU/ml have been prepared and stored at 4 C and used within one week. The two different existing units for thrombin in widespread international use are the International Unit (IU) for the WHO International Standard (IS) and the US unit (NIH unit) for the US Standard. The current WHO International Standard (IS) for thrombin was established in 1991, but the National Institute of Health (NIH) standard is generally used in calibration of commercial thrombin reagents as 1 NIH unit =. Thrombin units reported in this study are defined by the WHO International Standard (IS). One NIH unit is equivalent to IU of thrombin depending on the influence of PEG in 64

65 the assay. 72 One unit of commercial thrombin is determined by comparison with a standard curve prepared using the Bureau of Biologics standard thrombin. Reaction constituents for rheometry experiments were prepared in a 2-ml Eppendorf centrifuge tube at 20 C with enough Tris-EDTA buffer (10 mm pure Tris, 1 mm EDTA, ph 7.4) or Tris-EDTA plus NaCl buffer (10 mm pure Tris, 1 mm EDTA, 150 mm NaCl, ph 7.4) to bring the total volume to 1 ml. The corresponding amounts and concentrations of the individual reagents were calculated beforehand. The accurate amount of fibrinogen was mixed with the appropriate buffer in the Eppendorf centrifuge tube first. After the last step for initiating coagulation, the addition of thrombin, the resulting mixtures were mildly orbital shaken and the total amount of mixture was quickly transferred from tube to the stainless steel rheometer cone and plate fixture, which has a 1 cone and 50 mm diameter. The clots from a fixed combination of 1.2 mg/ml fibrinogen with 0.3 IU/ml thrombin in Tris-EDTA buffer (10 mm pure Tris, 1 mm EDTA, ph 7.4) were made for the experiments to study the gel point. Reaction mixtures for the experiments of time-dependent rheological properties were made of fibrinogen (1.2 mg/ml) with varying thrombin (0.25, 0.3, 0.4, 0.9 IU/ml) in Tris-EDTA buffer (10 mm pure Tris, 1 mm EDTA, ph7.4) or in Tris-EDTA plus NaCl buffer (10 mm pure Tris, 1 mm EDTA, 0.15M NaCl, ph 7.4), and thrombin (0.5 IU/ml) with varying fibrinogen (1.0, 1.5, 2.0, 2.5 mg/ml) in Tris-EDTA buffer (10 mm pure Tris, 1 mm EDTA, ph 7.4) or in Tris-EDTA plus NaCl buffer (10 mm pure Tris, 1 mm EDTA, 0.15M NaCl, ph 7.4). Consistent with the data from experiments of time-dependent rheological properties, for analysis of clotting time and concentration, additional concentrations of the clots were made from mixtures of 1.2 mg/ml fibrinogen with 1 IU/ml thrombin, or 0.5 IU/ml thrombin with 4.0 or 4.5 mg/ml fibrinogen in Tris-EDTA buffer (10 mm pure Tris, 1 mm 65

66 EDTA, ph 7.4), that brought the reacting concentrations sufficiently high to expect an asymptote for clotting time. For micrographs, which were designed for comparison with rigidity measurements, mixtures were prepared in a 0.5-ml Eppendorf centrifuge tube at 20 C with enough Tris-EDTA buffer (10 mm pure Tris, 1 mm EDTA, ph 7.4) or Tris-EDTA plus NaCl buffer (10 mm pure Tris, 1 mm EDTA, 150 mm NaCl, ph 7.4) to bring the total volume to 0.1 ml. Concentrations of the reaction mixtures were fibrinogen (1.2 mg/ml) with varying thrombin (0.3, 0.4, 0.9 IU/ml) in Tris-EDTA buffer (10 mm pure Tris, 1 mm EDTA, ph 7.4) or in Tris-EDTA plus NaCl buffer (10 mm pure Tris, 1 mm EDTA, 0.15M NaCl, ph 7.4), and thrombin (0.5 IU/ml) with varying fibrinogen (1.0, 1.5, 2.0 mg/ml) in Tris-EDTA buffer (10 mm pure Tris, 1 mm EDTA, ph 7.4). The accurate amount of fibrinogen was mixed with the appropriate buffer in the Eppendorf centrifuge tube first, and the resulting mixture with additional thrombin for initiating coagulation was mildly orbital shaken in the tube. Around 40 μl of the final sample solution were transferred immediately onto a single cavity microscope slide (Jencons (Scientific) Limited, Leighton Buzzard, UK, size mm, 15mm wide depression), covered with a conventional cover slip (size mm) and sealed with commercial nail polish. All samples were labelled and stored at room temperature until tested. 4.2 Rheometer All studies of the rheological properties of fibrin clots were performed on a Bohlin Gemini HR Nano Rheometer (Malvern Instruments Ltd, Malvern, UK). The clot rigidity was 66

67 measured and calculated by the software of the Bohlin GEMINI 150 HR NANO version (Malvern Instruments Ltd, Malvern, UK). The rheometer was isolated from interfering vibrations with a passive anti-vibration table. Measuring procedures were maintained isothermally at the controlling temperature with a TCU (temperature control unit) which is connected to cooling bottles in circulation (figure 4-1).The air bearing maintains an air pressure of 3 bar to give the rheometer an ultra-low friction for the sensitivity required. The action of indexing (zeroing) should be done every time after the 1 / 50 mm cone-andplate is attached and before loading the sample. It is important when loading the sample not to over load or under fill (figure 4-2a). A flat ended spatula is ideal to remove excess sample. Any process involved in changing the structure such as the use of a syringe, which might shear the sample, should be avoided when loading the sample. After finishing the experiments, methanol was used to clean the cone and plate surfaces. Gap panel Normal force sensors Air bearing tube Temperature control units Figure 4-1: The instrument configuration of a Bohlin Gemini HR Nano Rheometer (Malvern Instruments Ltd, Malvern, UK). The gap panel allows the local control of bearing position. The normal force sensors measure any upward thrust on the geometry. The air bearing tube contains bearing, motor and position sensors, which is the heart of the rheometer. The temperature control unit (TCU) maintains the sample at constant temperature. 67

68 The Malvern Bohlin Gemini rheometer is part of an advanced range of modular and compact rheometers with 'fluids to solids' capability. According to the Malvern Bohlin Gemini rheometer s specifications, the torque range is 3 nnm to 200 mnm with a resolution > 1 nnm for controlled stress or strain oscillation, the frequency range is 1 μhz to 150 Hz with controlled speed (CR mode) 0.01 mrad/sec 600 rad/sec and measurable speed (CS mode) 10 nrad/sec 600 rad/sec and the normal force (NI) measurement range is N 20 N (50 N option). Moreover, the position resolution is 50 nano radians, the step change in strain is less than 10 ms and temperature range is from -150 C to 550 C. The sinusoidal deformation parameters of viscoelastic properties are explained in section 3.2 comprehensively. Figure 4-2b illustrates the mechanical geometries of the oscillatory test on the rheometer. Figure 4-2: (a) Illustrates over loaded, correct and under filled loading. Incorrect loading might cause differences > 30% for the same sample. (b) Explains the oscillation test performed mechanically on a sample in the rheometer. The top plate or cone oscillates back and forth instead of rotating on the sample. 102 Cone-and-plate is defined as a cone on a flat bottom plate and was used as the measuring geometry for this study. The advantages of cone and plate geometry are that it is easy to 68

69 clean, a small sample volume is required, and it allows the study of very low viscosities (10 times less than water). The gap between the cone-and-plate geometry is fixed depending on the cone angle size. For example, 150 μm is for a 4 cone, 70 μm is for a 2 cone and 30 μm is for a 1 cone which has to be ten times larger than the average particle size of the sample. 73 Table 4-1 shows the expected errors from oscillation tests with various cone-and-plate angles. 74 A CP 1/50 cone-and-plate, with an angle of 1 with a 50 mm diameter was used for the measurements in this study. Consequently, the gap between the cone-and-plate fixtures was 30 μm and the expected errors from work with a cone-and-plate would be 0.03 % across the gap giving data with an error of around 0.02 %. Cone Angle ( ) Variation of Shear Rate across Gap (%) Typical Error in Shear Rate Calculation (%) Table 4-1: Expected errors from work with a cone-and-plate geometry during the oscillation tests. It shows that for a 1 cone the shear rate will vary by 0.03% across the gap giving data with around 0.02% error. According to this table, smaller angles produce smaller shear distribution errors than larger angles. According to previous studies, fibrin clots are defined as semi-flexible polymers in the linear viscosity region (LVR), the behaviours of which were described in chapter 3. Experiments were designed to study the time dependent rheological properties of fibrin clot, and the single 69

70 frequency sweep oscillation was therefore chosen as the main measurement strategy, while the frequency was selected from the gel point experiment. For the gel point experiment, single frequency sweep oscillations of the clot from a fixed combination were taken at a range of various frequencies (0.03, 0.04, 0.06, 0.07, 0.08, 0.1 and 0.2 Hz) under an imposed strain of On the other hand, for the measurements of time dependent rheological properties, the frequency 0.1 Hz and strain were fixed so that the viscoelastic properties of various concentrations of clots could be calculated from the evolution of stress with time, and the total measuring time was designed to be 16 hours. Measuring processes and data are detailed in chapter Microscopy All observations of the appearances of the fibrin fibre and network have been made with an Olympus IX71 inverted microscope (Olympus UK Ltd., London, UK) using differential interference contrast (DIC), a coolled pe-100 single-wavelength LED illuminator (coolled limited, Andover, UK) and a Photron FASTCAM-X 1024 PCI digital CCD camera (Photron (Europe) Ltd., Bucks, UK). Standing on an inadequately damped optical table, the microscope was further isolated from interfering vibrations with an active anti-vibration table (Halcyonics, Göttingen, Germany). Images at the clotting time 2 hr, 8 hr and 14 hr of the clots from mixtures that contained fibrinogen 1.2, 1.5, 2.0 or 2.5 mg/ml, thrombin 0.3, 0.4, 0.5 or 0.9 IU/ml, 0 or 150 mm NaCl, and Tris EDTA (10 mm Tris, 1 mm EDTA, ph7.4) were regarded to compare with their rheological properties measured by rheometer in chapter 4.2. The samples were analysed using a 100 oil immersion objective with a DIC condenser of N A DIC-C =

71 The basic principle of differential interference contrast (DIC) microscopy is the enhancement of image contrast by amplifying the optical path difference between two polarised rays of light as they are transmitted through objects and their surroundings within a sample. To enable DIC microscopy needs four additional components to be mounted in the optical path on the microscope frame, that are the polariser (before the condenser) for linearly polarising the incoming light, the beam-splitting prism called a Wollaston or Nomarski prism at the condenser, the objective Wollaston/Nomarski prism for recombining the two rays after they traversed the sample and the analyser before the light reaches the detector. Olympus offers objective DIC prisms in three versions, each suitable for different types of applications. As the work on living fibrin networks conducts both thin and thick specimens, a DIC 40 prism had to be used. The LED illuminator coolled pe-100 used in the OLYMPUS IX71 microscope is a fully configured unit which is supplied with a fixed LED of wavelength 525 nm. 75 The digital CCD camera Photron FASTCAM-X 1024 PCI employs a light sensitive 10-bit (grey scale of 1024 steps) CMOS sensor (Complementary Metal Oxide Semiconductor), and the size of the individual quadratic pixels is reported to be μm 2. The CCD camera also utilizes a high-speed global electronic shutter down to 1.5 μs independent of the frame rate, which is available up to 1000 fps at full resolution ( ). The image or pixel scale was found to be uniform in both directions and was calibrated with a 0.1 mm calibration grating to be ± 0.03 nm/ pixel. 76,77 71

72 Chapter 5 Results and Data Analysis 5.1 Gel point The key point in the perspective of blood coagulation is that the blood clot is required to perform a haemostatic function and the properties of a viscoelastic solid are necessary in order to perform this function. Thus, it is important to consider the rheological significance of the gel point as it defines the transition between a viscoelastic fluid and solid. The oscillatory shear measurements over a range of frequency in recent researches provide an appropriate basis for detecting incipient clot formation in samples of whole blood. 78 A criterion of gel point which is independent of the oscillatory frequency introduced by later studies 79 recognises that both G and G scale as power-laws in frequency (see chapter 3.2). Due to rheometrical constraints, which are the rapidity of gelation and the strain sensitivity, the evolution of viscoelasticity during fibrin-thrombin gelling course was monitored by sequential single frequency sweeps under controlled strain 0.15 at frequencies 0.03, 0.04, 0.06, 0.07, 0.08, 0.1 and 0.5 Hz. With data collected over only 1 period, a total of 32 points were taken in order to minimise the experimental time. A Bohlin Gemini HR Nano 72

73 Rheometer (Malvern Instruments Ltd, Malvern, UK) was used to examine the gel point of fibrin clots. Reaction components were premixed in a 2ml Emppendorf centrifuge tube with enough Tris-EDTA buffers to bring the fibrinogen concentration to 1.2 mg/ml and the total solution volume to 1000 μl. After the addition of 0.3 IU/ml thrombin, the last step for initiating coagulation, the reaction components were thoroughly mixed by gently rocking the tube, and 1ml of the clotting mixture was quickly transferred from the tube to the middle of the lower stainless steel rheometer plate (less than 60 seconds). The cone-and-plate (1 / 50mm) was then lowered onto the sample with a gap of 30μm (refer to CH.4 for details). The time-dependent storage modulus (G ), loss modulus (G ) and phase angle (δ ), which is from loss tangent (tan δ = G /G ), were calculated by Bohlin Gemini HR Nano Rheometer software GEMINI 150 HR NANO version (Malvern Instruments Ltd, Malvern, UK). (a.) (b.) Figure 5-1: Screenshots of the storage modulus (red symbols) and loss modulus (blue symbols) and phase angle (green symbols) at (a) 0.1 and (b) 0.5 Hz directly from the GEMINI 150 HR NANO rheometer. 73

74 Figure 5-1 shows screenshots of fibrin gelation at 0.1 and 0.5 Hz from the rheometer. At 0.1 Hz, the loss modulus G (Pa) and phase angle (δ ) show a few oscillations in figure 5-1a, however, the storage modulus G (Pa) increased gradually and the crossing point of G and G is predictable. Nevertheless, figure 5-1b shows frequent oscillations of G (Pa), G (Pa) and phase angle (δ ) at 0.5 Hz. Both results show that the range of frequencies to measure the gel point for strain-sensitive gel formation of 1.2 mg/ml fibrinogen and 0.3 IU/ml thrombin is 0.1 Hz. Therefore, in order to satisfy a more accurate phase angle (δ ) at the gel point, these results were not included in the following analysis. The time-dependent storage modulus G (Pa), loss modulus G (Pa) and phase angle (δ ) were calculated by Origin (OriginPro SR6, v8.0988, OriginLab Corporation, Northampton, USA) as functions of frequencies (0.3, 0.4, 0.6, 0.7 and 0.8 Hz) in figure 5-2 and 5-3. Figure 5-2: Results of phase angle (δ ) at the sequential frequencies 0.03 (black solid square symbols), 0.04 (red solid circle symbols), 0.06 (blue solid up triangle symbols), 0.07 (pink solid down triangle symbols) and 0.08 (green solid rhombus symbols) Hz calculated via frequency sweep measurements of fibrin gel formed with 1.2 mg/ml fibrinogen and 0.3 IU/ml. δ = tan -1 (G /G ). 74

75 The initial time-dependent phase angle (δ ) of each measuring frequency was frequencyindependent at the start, rapidly decreased and then achieved a plateau after the gel point (figure 5-2). Figure 5-3a shows a rapid increase in G (Pa), but at higher frequencies, 0.08 or 0.07 Hz, it slowed down soon after to a gradual rise and then reached a plateau characteristic of a viscoelastic solid. On the other hand, G (Pa) at each frequency in figure 5-3b increased progressively from the beginning to accomplish a plateau. After the gel point, phase angle (δ ), G (Pa) and G (Pa) increased as sweep frequency increased. A visual inspection of the data shows that the gel point was attained at gel time of approximately 70 s, with an estimated frequency independent phase angle (δ ) of 55.3 (± 0.5 ). This value of δ corresponds to α = (see equation 3-29) which is related to fractal dimension d f = 1.86 (see equation 3-30). These values are in agreement with previous studies 80,81 which support a recent confocal microscopy study. 82 According to recent studies 80, the criterion of gel time must be at least an order of magnitude larger than the time taken to perform each frequency sweep in order to obtain an accurate measure of α at the gel point. But, the levels of the fibrinogen and thrombin concentrations selected from the combinations of main experiments (chapter 5.2 and 5.3), which were close to the circulating concentrations in human plasma, produced fibrin gelation in a very short time ( 100 s). However, from the results of figure 5-1, 5-2 and 5-3, the observable gel point demonstrates that the following time-dependent rigidity experiments as functions of fibrin mixture concentrations were progressed in a viscoelstic solid phase at 0.1 Hz, which is required to perform a haemostasis function. In addition, a feature of many studies is the employment of a typically single frequency 0.1 Hz of oscillation throughout the coagulation process, 83, 84 and this frequency is chosen to mimic the operation of TEG (Thromboelastography) in some instances

76 Figure 5-3: Results of (a) G (Pa) and (b) G (Pa) at the sequential frequencies 0.03 (black solid square symbols), 0.04 (red solid circle symbols), 0.06 (blue solid up triangle symbols), 0.07 (pink solid down triangle symbols) and 0.08 (green solid rhombus symbols) Hz calculated via frequency sweep measurements of fibrin gel formed with 1.2 mg/ml fibrinogen and 0.3 IU/ml. 76

77 5.2 Rheological behaviours and clotting times According to the same procedures of detecting gel point (section 5.1), after the addition of thrombin, 1ml of the clotting mixture was quickly transferred to the stainless steel rheometer and operated with a gap of 30 μm at 25 C (refer to CH.4). A Bohlin Gemini HR Nano Rheometer (Malvern Instruments Ltd, Malvern, UK) and a 1 / 50mm cone-and-plate were used here to examine the viscoelastic properties of fibrin clots. Oscillatory measurements were taken at 0.1 Hz (verified in section 5.1) under an imposed strain of For measuring purposes, the rheometer was operated in an oscillatory mode, with data collected over 10 periods. A total of 2048 points were taken with an integration time of 100 s, a wait time of 306 s and a delay time of 2 s. Clot Fibrinogen (mg/ml) Thrombin (IU/ml) NaCl (M) A X B X C X D X E F G H X I X J X K X L M N O Table 5-1: The concentration compositions of the clots (A.-O.). The clots A-D and clots H-K were prepared with Tris-EDTA buffer. The clots E-F and L-O were prepared with Tris-EDTA plus NaCl buffer. Materials, sample preparations and methods are described in detail in chapter 4. 77

78 The storage modulus (G ), a measure of the elastic energy stored during the deformation imposed by one oscillation of the rheometer, was calculated by Bohlin Gemini HR Nano Rheometer software GEMINI 150 HR NANO version (Malvern Instruments Ltd, Malvern, UK) and used as a measure of clot rigidity. The loss modulus (G ), which reflects the energy dissipated by the clot during deformation, and the phase angle (δ ) were also recorded. Table 5-1 summarizes the combinations of concentrations for all the clots analysed in section 5.2 and 5.3. Reaction mixtures comprised of fibrinogen and thrombin with either of two different buffers, Tris-EDTA buffer (0.01M pure Tris, 0.001M EDTA, ph7.4) or Tris- EDTA plus NaCl buffer (0.01M pure Tris, 0.001M EDTA, 0.15M NaCl, ph7.4). Figure 5-4: Screenshot of completed rheometer measurements for fibrinogen 1.2 mg/ml and thrombin 0.3 IU/ml with Tris-EDTA buffer at 25 C. The phase angle δ (green symbols) dropped dramatically between s and increased back to plateau values. The storage modulus G' (red symbols) and the loss modulus G'' (blue symbols) both significantly increased before 10,000 s and then rose slowly to plateau values. 78

79 Figure 5-5: (a) Shows that values of the elastic modulus G' were bigger than values of the viscous modulus G'' from the clots of fibrinogen 1.2 mg/ml and thrombin 0.3 IU/ml in Tris- EDTA buffer. Plateau values of G' were Pa and G'' were Pa. Plateau values of the phase angle were (b) Reveals that values of the phase angle from the clots of fibrinogen 1.2 mg/ml and thrombin 0.3 IU/ml in Tris-EDTA buffer were smaller than 45 during the whole process. 79

80 A clotting time of 16 hours was necessary to cause a full development of the clot stiffness. Figure 5-4 is an example screenshot from a rheometer measurement and is also represented in figure 5-5 with Origin (OriginPro SR6, v8.0988, OriginLab Corporation, Northampton, USA). The primary result from the screen shot is that it provides an estimate of fibrin s rheological behaviour. Both the loss and storage moduli increased significantly from the beginning of the test, but went to plateau values after 30,000 seconds. Nonetheless, the phase angle decreased dramatically from 0 to 3,000 seconds and then rose up back to a plateau value of about 15 afterwards. The data analysed in Origin shows the real values of G, G and δ in figure 5-5 which are characterized in three clear time regions. The phase angle decreased dramatically from 0-5,000 s and increased sharply from 5,000 s to 10,000 s in the first phase, then stayed at plateau from 10,000 to 25,000 s and jumped to another plateau after 26,000 s. The loss modulus G (Pa) and the storage modulus G (Pa) of fibrin as a function of clotting time displays three characteristic regimes; Phase I (Newtonian plateau), Phase II (shear thickening) and Phase III (Newtonian plateau). The values of the elastic modulus were bigger than values of the viscous modulus and the values of the phase angles were thus smaller than 45 for the duration of the test. Figure 5-6 and 5-7 shows the analysis of varying elastic moduli G' (Pa) with clotting time(s) as a function of fibrinogen and thrombin concentrations in Tris-EDTA buffer or Tris-EDTA plus NaCl buffer at 25 C. Samples were measured over 16 hours to present full development structural transformations of clot from fibrinogen monomers before clotting, showing the transformation of fibrin fibres into fibrin networks. The rigidities for clots in Tris-EDTA 80

81 buffer made of fibrinogen (1.2 mg/ml) and altering thrombin (0.25, 0.3, 0.4 or 0.9 IU/ml) were shown in figure 5-6a, and for clots made of thrombin (0.5 IU/ml) and altering fibrinogen (1.0, 1.5, 2.0 or 2.5 mg/ml) were shown in figure 5-6b. At the thrombin concentration 0.25 IU/ml, there was a low initial stiffness with duration of 25,000 s, and then the rigidities rose up sharply from 25,000 s to reach the plateau value at the end of experiment time. The rigidities at the thrombin concentration 0.4 IU/ml had a similar outcome that increased with a steep slope for 35,000 s and then accomplished a plateau. In fig 5-6a, the values of G' (Pa) at the thrombin concentrations 0.3 and 0.9 IU/ml were twice or three times greater than those that were at the thrombin concentrations 0.25 and 0.4 IU/ml, and oscillations were more significant at 0.3 and 0.9 IU/ml thrombin. Similar phenomena as the clot with 0.25 IU/ml thrombin in figure 5-6a were seen in figure 5-6b, that the rigidities for solutions of 0.5 IU/ml thrombin and fibrinogen at the concentration 1.0, 1.5 or 2.0 mg/ml increased slowly at the beginning and rose up rapidly from 25,000 s until they approached the final plateau. On the other hand, mixtures made of 0.5 IU/ml and 2.5 mg/ml fibrinogen had much higher elastic modulus, which mounted with a gentle slope before 15,000 s, had a sharp increase from 15,000 to 30,000 s, and approached final plateau values with a slower increase in the end. Solutions of fibrinogen (1.2 mg/ml) with varying thrombin concentrations (0.25, 0.3 or 0.4 IU/ml) achieved higher values of elastic modulus (10-75 Pa) in comparison with the final values of G (6-18 Pa) from thrombin (0.5 IU/ml) and fibrinogen (1.0, 1.5 or 2.0 mg/ml) in Tris-EDTA buffer (figure 5-6). 81

82 Figure 5-6: (a) Shows the clotting time and the elastic modulus G (Pa) of clots formed with fibrinogen 1.2 mg/ml and thrombin 0.25 IU/ml (black solid square symbols), 0.3 IU/ml (red solid circle symbols), 0.4IU/ml (blue solid up triangle symbols), 0.9 IU/ml (pink solid down triangle symbols) in Tris-EDTA buffer at 25 C. (b) Shows the clotting time and the elastic modulus G (Pa) of clots formed with thrombin 0.5 IU/ml and fibrinogen 1.0 mg/ml (black solid square symbols), 1.5 mg/ml (red solid circle symbols), 2.0 mg/ml (blue solid up triangle symbols), 2.5 mg/ml (pink solid down triangle symbols) in Tris-EDTA buffer at 25 C. 82

83 Figure 5-7: (a) Shows the clotting time and the elastic modulus G (Pa) of clots formed with fibrinogen 1.2 mg/ml and thrombin 0.3 IU/ml (red solid circle symbols), 0.4 IU/ml (blue solid up triangle symbols), 0.9 IU/ml (pink solid down triangle symbols) in Tris-EDTA plus NaCl buffer at 25 C. (b) Shows the clotting time and the elastic modulus G (Pa) of the clots formed with thrombin 0.5 IU/ml and fibrinogen 1.0 mg/ml (black solid square symbols), 1.5 mg/ml (red solid circle symbols), 2.0 mg/ml (blue solid up triangle symbols), 2.5 mg/ml (pink solid down triangle symbols) in Tris-EDTA plus NaCl buffer at 25 C. 83

84 The dependence of clots, stiffness over sixteen hours with varying fibrinogen or thrombin concentrations in Tris-EDTA plus NaCl buffer are presented in figure 5-7. Rigidities of clots formed with 0.3 and 0.4 IU/ml thrombin exhibited a steady increase before 5,000 s, then increased sharply from 5,000 to 25,000 s, and went onto plateau values after 25,000 s. With the thrombin concentration 0.9 IU/ml, the elastic modulus G (Pa) increased from 0 to 17,000 s, had a slow rise after a short-term sharp expansion in the next region and finished with a rapid decay from 43,000 s (figure 5-7a). A similar decline in the final phase was also observed on the clots with higher fibrinogen concentration 2.5 mg/ml in figure 5-7b, that rigidities steadily increased before 35,000 s, followed by a dramatic increase from 35,000 to 40,000 s and dropped sharply after 40,000 s. The rigidities for clots of 1.5 and 2.0 mg/ml fibrinogen with salt, built up quickly from the start and achieved plateau values after the 35,000 s, while clots of 1.0 mg/ml fibrinogen increased with a slow slope and gradually approached plateau values after 30,000 s (figure 5-7b). Due to the interaction of thrombin with sodium and potassium, values of G (Pa) from clots in Tris-EDTA buffer with salt were times larger than those from clots only in Tris-EDTA buffer. According to previous studies 84, clots begin to form when the average G value is Pa. For this reason, clotting time was defined as the time when the rigidity of the test sample was detected at the value of G = Pa. Figure 5-8a presents the measuring times to form fibrin clot of fibrinogen 1.2 mg/ml and thrombin (0.25, 0.3, 0.4, 0.9 or 1 IU/ml) in Tris- EDTA buffer and figure 5-8b shows the clotting times for mixtures of thrombin 0.5 IU/ml and fibrinogen (1.0, 1.5, 2.0, 2.5, 4.0 or 4.5 mg/ml) in Tris-EDTA buffer. The points of both graphs were fitted to a power law equation ( ) using Origin s (OriginPro SR6, v8.0988, OriginLab Corporation, Northampton, USA) power fitting 84

85 capability, where y represents the measuring clotting time (at G = Pa), x is the varying concentration, A is the initial value and R is the rate. The fitting result of clots formed with fibrinogen 1.2 mg/ml and thrombin (0.25, 0.3, 0.4, 0.9 IU/ml) shows that the clotting time attains a plateau value as the thrombin concentration increases ( 1 IU/ml), and the clotting time will tend to infinity when thrombin concentration approaches 0 IU/ml. A similar result can be observed from clots of fibrinogen (1.0, 1.5, 2.0, 2.5, 4.0 or 4.5 mg/ml) with thrombin 0.5 IU/ml, in that the clotting time will achieve a plateau with rising fibrinogen concentration ( 4.5 mg/ml) and approach an infinite value when fibrinogen concentration is reduced to 0 mg/ml. The asymptotes of the fitting curves show that no fibrin clot will be observed in the absence of thrombin or fibrinogen, and a boundary time is necessary for any mixed concentration. From the fitting results, this value of the boundary time is 1990 ± 6 seconds for the clots with varying thrombin concentrations, and is 2330 ± 6 seconds for the clots with varying fibrinogen concentrations. Figure 5-8 illustrates that solutions of lower thrombin or fibrinogen concentration took longer times to form fibrin clots. A wider range of the thrombin or fibrinogen concentrations were taken for collection of clotting time following other research which suggested the normal concentration for fibrinogen in circulation for an adult is 2-4 mg/ml 86,31 and is 1.1 IU/ml 87 for thrombin. On the other hand, according to the interaction between thrombin and sodium ion (Na + ) 88, the clotting times of clots in Tris-EDTA plus NaCl buffer from fibrinogen 1.2 mg/ml with varying thrombin, and from thrombin 0.5 IU/ml with varying fibrinogen were too short ( 306 seconds, which is the start measuring point) to be detected. 85

86 Figure 5-8: (a) Symbols show the clotting times of clots made from fibrinogen 1.2 mg/ml and thrombin (0.25, 0.3, 0.4, 0.9 IU/ml) in Tris-EDTA buffer, and (b) Shows symbols for the clotting times of clots made from thrombin 0.5 IU/ml and fibrinogen (1.0, 1.5, 2.0, 2.5 mg/ml) in Tris- EDTA buffer. Both graphs were fitted in the equation, where (red solid curves). 86

87 5.3 Fibrin structures, rigidities and concentrations For thrombin or fibrinogen concentrations, the correlation between rigidity and component concentrations was no longer observed after 2 hours. In some cases, the rigidity of solutions with a higher concentration was lower than the rigidity of those with lower concentration. In accordance with this finding, zoomed-in data of figures 5-6 and 5-7 is displayed in figures 5-9 and 5-10 with the intention of discussing the relation between concentrations, rigidities and clotting time. The ranges of G (Pa) were set to observe variation of rigidity in the clotting time zone 0-40,000 s. In figure 5-9a, the clots of fibrinogen 1.2 mg/ml and thrombin (0.25, 0.3, 0.4 or 0.9 IU/ml) in Tris-EDTA buffer had a higher rigidity for a higher thrombin concentration before 10,000 s. Conversely, after 10,000 s, the value of G (Pa) dropped from the thrombin concentration 0.4 IU/ml to 0.3 IU/ml. G (Pa) for clots of 0.5 IU/ml thrombin and fibrinogen (1.0, 1.5, 2.0 or 2.5 mg/ml) in Tris-EDTA buffer. The rigidities for clots of 1.5 and 2.0 mg/ml fibrinogen decreased less than those for clot of 1.0 mg/ml fibrinogen after 8,000 s, but G (Pa) for the clot of fibrinogen 2.0 mg/ml grew bigger than G (Pa) at the fibrinogen concentration 1.0 mg/ml again after 24,000 s. 87

88 Figure 5-9: Zoomed-in results obtained from data of figure 5-6 in the adjusted time zone 0 40,000 s with the rigidity values. (a) The values of G (Pa) were larger as thrombin concentrations increased at the beginning, but G (Pa) for clot of 0.3 IU/ml thrombin (red solid circle symbols) became larger than clot of 0.4 IU/ml thrombin (blue solid up triangle symbols) after 10,000 s. (b) The values of G (Pa) increased with fibrinogen concentration before 8,0000 s. G (pa) for clot of fibrinogen 1.5 (red solid circle symbols) and 2.0 mg/ml (blue solid up triangle symbols) dropped lower than the clot made with fibrinogen 1.0 mg/ml (black solid square symbols) after 8,000 s, although rigidities at the fibrinogen concentration 2.0 mg/ml became larger than those at the fibrinogen concentration 1.0 mg/ml after 24,000 s. 88

89 Figure 5-10: Zoomed-in results obtained from data of figure 5-6 in adjusted time zone 0 40,000 s showing the rigidity values. (a) The values of G (Pa) were higher when thrombin concentrations increased at the beginning, but G (Pa) of 0.4 IU/ml thrombin (blue solid up triangle symbols) dropped sless than 0.3 IU/ml thrombin (red solid circle symbols) after 13,000s. (b) The values of G (Pa) increased with fibrinogen concentrations, but G (Pa) for clot of fibrinogen 1.5 mg/ml (red solid circle symbols) decreased lower than clot of fibrinogen 1.0 mg/ml (black solid square symbols) after 6,000 s. 89

90 A similar phenomenon was found in figure 5-10, that the values of G (Pa) for clots made of varying thrombin concentrations with additional salt increased with thrombin concentrations, although after 13,000 s, G (Pa) at the thrombin concentration 0.4 IU/ml, it then decreased to be lower than at the thrombin concentration 0.3 IU/ml. G (Pa) at the fibrinogen concentration 1.5 mg/ml decreased lower than at the fibrinogen concentration 1.0 mg/ml after 6,000 s (figure 5-10b). Furthermore, consistent with the results above, the values of G (Pa) for clots of varying fibrinogen or thrombin concentrations with or without salt at 2 hr, 8 hr and 14 hr clotting time were compared in figure 5-11 and Data points of G (Pa) at 2 hr for clots were fitted with the power law ( ), using Origin s (OriginPro SR6, v8.0988, OriginLab Corporation, Northampton, USA) power fitting capability where A 1. B = 0.91 ± for rigidities at 2 hr of the clots with varying thrombin concentrations (figure 5-11a) is in agreement with the result of Glover et al. (1975), who reported that the concentration dependence of G for platelet free plasma clots is c (G ~ c). 89 In figure 5-11b, B = 1.40 ± for clots with varying fibrinogen concentrations consistent with the results demonstrated by Ferry and Morrison (1947) 90, Roberts et al. (1974) 91, and Nelb et al. (1976) 92, that had measured the concentration dependence of G for unligated fibrin clots to be varying between c 1.5 and c

91 Figure 5-11: (a) Shows values of G (Pa) for the clots formed from fibrinogen 1.2 mg/ml with thrombin (0.25, 0.3, 0.4 or 0.9 IU/ml), and (b) shows values of G (Pa) for the clots formed from thrombin 0.5 IU/ml with fibrinogen (1.0, 1.5, 2.0 or 2.5 mg/ml) in Tris-EDTA buffer at 2 hr (solid black square symbols), 8 hr (solid orange circle symbols) and 14 hr (solid blue triangle symbols). The values of G (Pa) at 2 hr were fitted with the power law (red dash line). 91

92 Figure 5-12: (a) Shows values of G (Pa) for the clots formed from fibrinogen 1.2 mg/ml with thrombin (0.25, 0.3, 0.4 or 0.9 IU/ml), and (b) shows values of G (Pa) for the clots formed from thrombin 0.5 IU/ml with fibrinogen (1.0, 1.5, 2.0 or 2.5 mg/ml) in Tris-EDTA plus NaCl buffer at 2 hr (solid black square symbols), 8 hr (solid orange circle symbols) and 14 hr (solid blue triangle symbols). The values of G (Pa) at 2 hr were fitted with the power law (red dash line). 92

93 The values of B for clots with varying thrombin and fibrinogen concentrations in figure 5-12a and 5-12b are 0.74 ± and 0.64 ± 0.015, which were not reported previously yet. On the other hand, the relationships G ~ c 2 (fibrin clots formed with mg/ml fibrinogen; Shen et al., 1975) 93 ; and G ~ c 2.1 (fibrin clots formed with 5-20 mg/ml fibrinogen; Fukada and Kaibara, 1973) 94 were established by earlier researchers. Overall, the fitting results show that rigidities of fibrin clots after 2 hr are correlated with their concentrations with or without salt. Nevertheless, G (Pa) at 8 hr and 14 hr of the clots in Tris-EDTA buffer and Tris-EDTA plus NaCl buffer did not increase as the concentrations of thrombin or fibrinogen built up with time. At 8 hr and 14 hr, the values of G (Pa) raised as the thrombin concentration increased from 0.25 IU/ml (the lowest point of each graph) to 0.3 IU/ml, then reduced as the thrombin concentration increased to 0.4 IU/ml, and raised up again as the thrombin concentration increased to 0.9 IU/ml (figure 5-11a). Figure 5-12a shows a similar reduction between 0.3 and 0.4 IU/ml with additional salt. In figure 5-11b and 5-12b, for the clots made in Tris- EDTA buffer and Tris-EDTA plus NaCl buffer, G (Pa) at 8 hr and 14 hr decreased as the fibrinogen concentration increased from 1.0 to 1.5 mg/ml, and increased as the fibrinogen concentration increased from 1.5 to 2.5 mg/ml. Furthermore, rigidities for the clots with varying thrombin concentrations in Tris-EDTA plus NaCl buffer represented lower values at 14 hr than at 8 hr. Along with the relation between the rigidity and concentration of fibrin, optical micrographs of clots formed with varying mixtures at 2 (A), 8 (B) and 14 (C) hr clotting time were taken for studying comparisons between clot structures and rigidities. Figure 5-13 and 5-14 show 93

94 the changes as thrombin and fibrinogen concentrations were varied, and figure 5-15 presented the differences with additional NaCl in the mixture. Reaction mixtures were comprised of fibrinogen (1.2 mg/ml) and varying thrombin [0.3 (a), 0.4 (b) or 0.9 (c) IU/ml] in Tris-EDTA buffer or in Tris-EDTA plus NaCl buffer, and thrombin (0.5 IU/ml) with varying fibrinogen [1.0 (d), 1.5 (e) or 2.0 (f) mg/ml] in Tris-EDTA buffer. In figure 5-13A, the overall appearances of clots consisted of 0.3, 0.4 and 0.9 IU/ml thrombin at 2 hr were uniform meshes of very fine fibres or protofibrils, and few branch points were shown at the thrombin concentrations 0.4 and 0.9 IU/ml. However, at 8 hr, fibre lengths increased as the thrombin concentration increased from 0.3 to 0.4 IU/ml, and decreased as the thrombin concentration increased from 0.4 to 0.9 IU/ml. The fibre and branching densities were decreased as the thrombin concentration increased from 0.3 to 0.4 IU/ml, and increased as the thrombin concentration raised from 0.4 to 0.9 IU/ml. According to the images, the fibrin network at the thrombin concentration 0.9 IU/ml had much more branching points and fibres than at the thrombin concentration 0.3 IU/mg (Figure 5-13B). At 14 hr, clear branching points and bending fibres were observed from structures of fibrin clots with thrombin concentrations 0.3 and 0.9 IU/ml. The fibre and branching densities of clots at the thrombin concentration 0.3 and 0.9 IU/ml were higher than those at the thrombin concentration 0.4 IU/ml. Conversely, the fibrin network at the thrombin concentration 0.4 IU/ml had thicker fibres than at the thrombin concentration 0.3 and 0.9 IU/ml (Figure 5-13C). 94

95 A B C Figure 5-13: Brightfield optical microscopy images of clots formed from the mixtures of fibrinogen 1.2 mg/ml and thrombin [(a) 0.3, (b) 0.4 or (c) 0.9 IU/ml] in Tris-EDTA buffer at the (A) 2 hour, (B) 8 hour or (C) 14 hour. Bar, 16 pixels ( 2.68 μm). 95

96 Figure 5-14D shows increasing fibrinogen concentration from 1.0 to 2.0 mg/ml at 2 hr led to lengthening of the node to node distances, larger liquid spaces, less fibre density and thinner fibres. The decrease in fibre diameter and the increase in branching density at 2 hr with increasing fibrinogen concentration may be attributed to higher rates of monomer formation due to higher substrate concentrations. At 8 hr, the increase of fibre length and thickness was due to decreased thrombin-to-fibrinogen ratios when the fibrinogen concentration increased. The fibrin fibre thickness increased and the branch points decreased as the fibrinogen concentration inceased from 1.0 to 1.5 mg/ml. Conversely, the fibrin fibre thickness decreased and the number of branch points increased as the fibrinogen concentration inceased from 1.5 to 2.0 mg/ml (figure 5-14E). At the fibrinogen concentrations 1.0 and 2.0 mg/ml, three dimentional networks of both thick and thin fibrin fibre bundles at 14 hr were clearly observed, which was not observed in the clot with 1.5 mg/ml fibrinogen. Moreover, the clot structure at the fibrinogen concentration 1.0 mg/ml was more porous than at the fibrinogen concentration 2.0 mg/ml. Similar results are seen in figure 5-14E, at 14 hr, fibre thickness, length and branching points decreased as the fibrinogen concentration increased from 1.0 to 1.5 mg/ml and increased as the fibrinogen concentration increased from 1.5 to 2.0 mg/ml (figure 5-14F). At 8 hr and 14 hr, the structure for the clot made of 1.5 mg/ml fibrinogen lacked a three dimentional network. Figure 5-13 and 5-14 both demonstrate that fibre thickness, length, density and branch points ceased increasing or decreasing at 8 hr and 14 hr as the thrombin or fibrinogen concentration increased. These results correlate with the previous rigidity measurements. 96

97 D E F Figure 5-14: Brightfield optical microscopy images of clots formed from the mixtures of thrombin 0.5 IU/ml and fibrinogen [(d) 1.0, (e) 1.5 or (f) 2.0 mg/ml] in Tris-EDTA buffer at (D) 2 hour, (E) 8 hour or (F) 14 hour. Bar, 16 pixels ( 2.68 μm). 97

98 A B C Figure 5-15: Brightfield optical microscopy images of fibrin clots in the presence of NaCl. The experimental mixtures were combined fibrinogen 1.2 mg/ml with thrombin [0.3 (a), 0.4 (b) or 0.9 (c) IU/ml] in Tris-EDTA plus NaCl buffer at (A) 2 hour, (B) 8 hour or (C) 14 hour. 98