Michaelis Menten Kinetics -Enzyme Kinetics, Binding and Cooperativity Dr. M. Vijayalakshmi School of Chemical and Biotechnology SASTRA University Joint Initiative of IITs and IISc Funded by MHRD Page 1 of 9
Table of Contents 1 INTRODUCTION... 3 2 EQUILIBRIUM BINDING... 5 2.1 BINDING CURVE... 5 3 COMPLEXITY IN BINDING... 7 4 COOPERATIVITY AND ALLOSTERY... 8 5 REFERENCE... 9 5.1 TEXT BOOK... 9 5.2 LITERATURE REFERENCES... 9 Joint Initiative of IITs and IISc Funded by MHRD Page 2 of 9
1 Introduction This module begins initially with enzyme kinetics and chemical equilibrium to make the students familiar with reaction equations that are applicable in the later part of the discussions. Enzymes are group of catalysts and biological macromolecules that have high specificity. Most of the enzymes are involved in cellular metabolism but the precise mechanisms of action of many enzymes are yet to be clearly understood. There is still a long gap in understanding the physiological behaviour of enzymes as experimental studies use only isolated and purified enzymes. Enzymes are involved in complex cascade of events with several intermediate steps. Enzymes reduce the activation energy and hence speed up the reaction without influencing the reaction equilibrium and free energy as in Fig 1. Fig 1: Free energy profile in enzyme catalysis Enzymes either catalyse a single step reaction or a set of complex reactions with several intermediate steps. For an enzymatic reaction to occur, there should be an effective interaction between the substrate and the enzyme. Enzymes bind their substrates through weak non covalent interactions that need specific orientation of the molecules to form a complex. The region of enzyme where the substrate gets Joint Initiative of IITs and IISc Funded by MHRD Page 3 of 9
bound is the active site and these are specific for different substrates of a particular enzyme. Two models were proposed to explain the specificity of the enzyme based on the conformational changes occurring in the enzyme to facilitate the binding of substrate Fig 2. i). Lock and key The enzyme s active site has a conformation matching the substrate and hence whenever it comes near the site it can be easily accommodated. ii). Induced fit Once the substrate molecule reaches the vicinity of enzymes active site, it changes its own conformation to accommodate the substrate. Fig 2: Models to support the binding of enzyme and substrate Initially, the substrate binds to the active site of the enzyme after which the conversion of substrate to product happens and finally, unaltered enzyme is detached from the product. This is a strictly physical interaction and the binding substrate, is often referred as ligand. Hence, understanding the specific binding of macromolecule (enzyme) with its ligand (substrate) is essential to analyse the functionality of an enzyme. Binding of an enzyme and substrate is simple in a single substrate reaction, but becomes more complex with the presence of two or more substrates or molecules such as inducers, inhibitors or cofactors in the biological system. Joint Initiative of IITs and IISc Funded by MHRD Page 4 of 9
2 Equilibrium Binding A simple enzymatic reaction involves binding of free enzyme (E) to the ligand (A) to form the complex (EA). The reaction is reversible and hence law of mass action can be used to define the binding event with two terms namely association constant (K a ) and dissociation constant (K d ). Where, K 1 Macromolecule (E) + Ligand (A) Macromolecule-ligand complex (EA) K -1 Both association and dissociation constants can be used to describe the equilibrium of the enzymatic reaction. In general, association constant K a is used to explain the equilibrium of the reaction and dissociation constant K d is used to explain the enzyme kinetics. The affinity of binding depends on the concentration of the substrate. Association constant K a is inversely proportional to the concentration of the substrate and hence more K a will lead to more affinity. The dissociation constant K d is directly proportional to concentration and hence lower the value of K d, strong binding affinity will be observed. 2.1 Binding curve The relationship between the fraction of free ligand to the fraction of ligand bound to macromolecule can be arrived at from the expression of K d and usually shown as a binding curve. Initially, only the total enzyme and ligand concentrations are known. So, from law of mass conservation, [E] 0 = [E] + [EA] and Joint Initiative of IITs and IISc Funded by MHRD Page 5 of 9
[A] 0 = [A] + [EA] Concentration of bound ligand can be determined through experiments. When a ligand has only one binding site for an enzyme, its concentration in bound form will be, However, in real conditions, most of the enzymes have more than one binding site for a specific ligand. For e.g., Haemoglobin (Hb) has 4 distinct binding sites for oxygen molecule. Haemoglobin present in our blood has the ability to bind oxygen and it carries it from lungs to the tissues. The partial pressure of oxygen plays important role in binding of oxygen to haemoglobin. Also, the concentration of Haemoglobin present in blood is essential to determine its binding efficiency. When all the binding sites in Hb molecules are occupied, the blood is said to be 100% saturated and cannot carry any more oxygen. Under the different partial pressures of oxygen the saturation level of haemoglobin is influenced Fig 3. Fig3: Binding curve for Haemoglobin showing the %saturation at different partial pressures of oxygen In certain situations, one of the reactant might be available at huge amount and hence we can neglect the change in concentration of that reactant throughout the reaction. Consider any hydrolysis reaction, where hydrogen ions will be present in Joint Initiative of IITs and IISc Funded by MHRD Page 6 of 9
excess amount, making it difficult to detect any change in its concentration. In these situations, the K d for excess reactant is not considered and an apparent K d will be calculated which is concentration of the reactant times K d. In biological processes, the genetic material either DNA/RNA, requires proper binding with specific proteins for their active mechanisms like transcription and translation to be executed. RNA polymerase enzyme complex should bind to DNA efficiently to initiate and proceed with transcription. In addition, binding of small molecules such as transcription factors, activators/repressors to this enzyme complex is crucial for the process to take over. This will give a clear idea on the importance of binding. 3 Complexity in Binding Binding of a single protein molecule to DNA is complex and is difficult to understand while the binding of multiple protein complexes that are non-equivalent makes the binding process much more complex Fig 4. Fig4. Complexity in analysis of protein-dna binding at equilibrium It is essential to optimise the conditions for effective binding between DNA and protein. To achieve this, we should concentrate on quantitative analysis on the Joint Initiative of IITs and IISc Funded by MHRD Page 7 of 9
binding affinity and the occupancy of the binding site (either fully or partially occupied); number of protein molecules binding to each DNA molecule; equilibrium binding constants and specificity of the binding; Cooperativity of binding in case of multiple proteins binding to same DNA molecule, etc., 4 Cooperativity and Allostery In most biological events the enzyme has the ability to bind another substrate molecule in a site different from that of the active site where the first substrate has been bound. In such conditions, binding of first substrate might have some influence over the binding of second substrate/ligand at a different site of the enzyme, where this indirect influence at a different site is called Co-operativity. The binding of another substrate at a different site apart from its active site is called allostery and enzymes showing this property are termed allosteric enzymes (allo other). Certain molecules or ligands that bind to the binding site can either be activators or inhibitors, depending on how they influence the binding at the second site when bound to the enzyme. Cooperativity of the ligands towards the enzyme can be either positive where the binding of the first ligand facilitates binding of other or negative where the condition is reverse. Whenever the number of binding sites in the enzyme is limited, the affinity of ligand is critical to determine the binding. So far, we have seen the advantages of an enzymatic reaction and the steps involved, equilibrium of the binding, its complexity and the cooperative behaviour in enzymes. We shall discuss the kinetics of a simple single substrate enzymatic reaction, in the next lecture. Joint Initiative of IITs and IISc Funded by MHRD Page 8 of 9
5 Reference 5.1 Text Book 1. Bisswanger H, Enzyme Kinetics, Principles and Methods, WILEY-VCH (2002) 5.2 Literature References 1. Rippe K et al., Analysis of protein-dna binding at equilibrium, B. I. F. Futura, (1997), 12, 20-26. 2. Athel Cornish-Bowden, Two centuries of catalysis, J. Biosci., (1997), 2, 87-92. Joint Initiative of IITs and IISc Funded by MHRD Page 9 of 9