Modeling Biochemical Interactions Controlling the Cytoskeleton of Spreading Cells

Transcription

1 Modeling Biochemical Interactions Controlling the Cytoskeleton of Spreading Cells By Mary Motz, Sophia Rick, and Dr. Magdalena Stolarska Abstract Biological cells respond to their environment. This is done in part by physical attachments through chemical bonds to surfaces with which they interact which then sets of a biochemical signal cascade within the cell. These types of biochemical reactions can be mathematically modeled by systems of differential equations that can then be solved numerically. Such a system of equations often has many parameters that are difficult to determine. However, it is important to correctly set these parameters so that the mathematical model can make accurate predictions about cellular response. In this project, students will work with a mathematical model that describes the chemical reactions that take place when a cell attaches to a surface, and use various pieces of software, including Copasi, MatLab, and ImageJ, to correctly fit parameters to this model. Introduction Cells sense their microenvironments and respond by moving. Generally, cells migrate in four distinct ways: crawling, swimming, extension, and contraction. Cell movement is vital to countless biological processes. Cellular motility is the result of a series of complex biochemical reactions. Recently it has become much clearer that the attachment of a cell to the extracellular surface is imperative to the way the cell moves. Ultimately cell movement can be paired down to the interactions of these critical components: fibronectin, integrin, actin, and myosin. Fibronectin, a binding agent that cells like to stick to, is a protein found on extracellular surfaces. Integrin is a protein found on the cell surface. Each strand of fibronectin on the surface binds with integrin on the cell. When integrin and fibronectin bind, the process of cell movement initializes. Actin, specifically F-actin, is a protein microfilament found within cells that polymerizes and interacts with myosin, the protein that allows cells to contract locally. When actin polymerizes it develops branches, or barbed ends, which push out the edge of the cell, called the leading edge. Barbed ends are typically oriented from the interior toward the cell membrane. The polymerizing, branching, and severing

2 creates more barbed ends which allow the membrane of the cell to be pushed out. Thus, barbed ends are crucial for cell spreading. Figure 1 Figure 2 Figure 1: This is an illustration of the attachments of a cell that is sitting on surface. These attachments are what allow the cell to sense and respond to mechanical properties of the surface and its surrounding microenvironment. Figure 2: Myosin and actin filaments within a cell slide over one another to affect cell movement. While there are many internal structures that affect a cell s movement, a cell s movement is a direct response to the mechanical properties of its microenvironment. Evidence of this can be found in multiple experimental papers. In 2010, Tee and collaborators (2011) did a study regarding the effects of surface stiffness on a cell. They put cells on fibronectin-coated surfaces of varying stiffnesses and found that the stiffer the surface, the more cells spread. Not only that, but they found that the cells sensed the stiffness of the surface, and adjusted their own stiffness to match accordingly. In another study by Engler, researchers found that the fate of a stem cell is dependent on the stiffness of the surface it is on. The stem cells sensed their environment s stiffness via their attachments to the surface and became different types of tissue in response to these connections. Both experiments show the relationship between a cell s attachment to a surface and the cells response. This summer, we took a deeper look at the rate of the cell s biochemical response to its environment. This biochemical response is the series of 14 reactions between 18 intracellular components, including reactants, products, and modifiers. The system initializes when the integrins on the cell bind to the extracellular fibronectin. From there, the cascading reactions activate different proteins within the cell which ultimately sever and nucleate actin. The goal is to have local concentrations of the barbed ends of actin and myosin. Then, these concentrations can be embedded into a model of a moving cell.

3 Model Figure 3: This is the reaction pathway that we studied. It begins with integrin binding to fibronectin yielding activated integrin (A = activated species). The activated integrin then acts as a catalyst in the activation reaction of Src. And the activated Src then acts as a catalyst in the Arp2/3 and Rho activation reactions. Src is also a catalyst in the deactivation of cofilin. Activated Arp2/3 causes the elongation of actin filaments, also called actin nucleation. But actin filaments are also being severed as they grow by activated cofilin. ROCK and activated Rho bind together to get activated ROCK. Finally, activated ROCK acts as a catalyst in the Myosin activation reaction.

4 Reactions The above (Fig 3) reactions can be mathematically described by the system of differential equations below. The individual terms are based on binding, decay, and enzymatic reactions. (Sheridan)

5 Methodology To best examine and analyze the biochemical network, we used a variety of mathematical software. Specifically, we utilized MatLab, Copasi (COmplex PAthway SImulator), and ImageJ. Copasi is advanced software that allowed us to not only create a model of our biological process, but then also run simulations of biochemical pathways. This works by first allowing us to input all reactions we would like to include in our model (Figure 4). Figure 4: Input of all of our reaction in Copasi. Different reactions have different kinetics, so Copasi lets us specify these differences within each reaction (Figure 5). We can choose the rate law for each reaction from a list of pre-programed laws, or, if the rate law we desire does not already exist in Copasi, we are presented with the option of creating our own. This is also where we enter in any known parameter values. Copasi then automatically generates differential equations for each species in the reaction. Figure 5: A closer look at our first reaction in Copasi, integrin and fibronectin combining to activate integrin. Here we have selected the mass action rate law and set our parameters to k_f = and k_r = 0.168

6 Figure 6: A time course graph, measuring the concentration of the species in our reactions, generated by Copasi. Copasi can take the information that we have entered into our reactions, solve the system of equations that it generates, and create a time course graph of the species in the model (Figure 6). We can choose how long we would our time course to run and how often we would like our time steps to be. Copasi then tracks the concentration at each time step and presents us with that information in a savable format after it has completed its analysis. In order for Copasi to create time course graphs that accurately predict what is happening inside the cell, all parameters need to be set to correct values. These values can be determined by matching the model to experimental data. In order to extract experimental data from the literature in a format that can be used by Copasi, we need another piece of software called ImageJ. Once we have pulled the data we need from an image, we can use the parameter fitting tool provided by Copasi. First, we upload the data we have gathered. Then we specify which parameter we would like to fit. Copasi then uses a minimization of weighted sum of squares to find the optimal parameter value (see the formula below). We are also provided with a graph that displays a line made up of the data entered with the text file, the line of best fit generated by Copasi, and the error between the two. Results The data that we obtained was found using specific concentration of each individual species, usually µm, or µmol/l. Then using Copasi s time course tool, we could observe the evolution of each species concentration in the cell (See Figure 6). We were able to obtain data for three species: integrin, Arp2/3, and Rho. To get these results, we needed to pull experimental data from other sources. But this data was not necessarily recorded in concentrations, nor was it in table form necessary for parameter

7 estimation in Copasi. So we needed to use ImageJ to not only quantify the data, but also convert the data into the kind of data we can use (concentrations). Using ImageJ, we scaled and integrated graphs to obtain three data sets that can then be individually imported into Copasi s parameter estimation tool. a. b. c. Figure 7a-c: (a) The data for integrin evolution is given in fluorescence intensities. In extracting this data from a publication by Mould and collaborators in 2014, we scaled the intensities so that their maximum was 15. We also only used the first 100 sec in our parameter fitting. (b) The Arp2/3 experimental data is taken from a study by Goode, Drubin, and Rodal in 2001, we needed to analyze a shorter time range, so we scaled it to go from 0 to 1 s. (c) Most interestingly, the data we analyzed for the activation of Rho is taken from an article by Dubash and collaborators in 2007.This came in the form of a Western Blot. ImageJ is able to integrate the intensities of darkness to obtain a fluorescence intensity such as the one shown in (a). These integrated intensities were then scaled to a maximum value of 1. Using the data-sets we obtained from ImageJ, we then used the parameter estimation tool in Copasi. On each of the following graphs the dotted line is the experimental data that we entered into Copasi, the solid line is the line of best fit generated by Copasi, and the small circles line is the error between the two. Figure 8: Integrin Results - kcat = Figure 9: Arp Results - kcat =

8 All other parameters in the model are approximated based off of earlier work. Discussion and Conclusions This summer, we had a significant number of accomplishments. We learned how to use unknown software, Copasi and ImageJ, in order to achieve our goals. And in doing so, we found three parameter values for our reaction Figure 10: Rho Results - kcat = pathway. Unfortunately, there were many times that reaching our goal was very difficult due to the lack of existing experimental data and the nonlinearity of the reaction equations. This nonlinearity of the equations had adverse effects on the analytical tools used by Copasi so that it yielded varying results at times. Moving forward, we hope to get more viable experimental data on more of the intercellular species. This would allow us to find parameter values for the remaining approximations. Ultimately, we hope that this model will be integrated into a model of a cell that moves. References Dubash, Adi D., et al. "A novel role for Lsc/p115 RhoGEF and LARG in regulating RhoA activity downstream of adhesion to fibronectin." Journal of cell science (2007): Engler, Adam J., et al. "Matrix elasticity directs stem cell lineage specification." Cell (2006): Goode, Bruce L., et al. "Activation of the Arp2/3 complex by the actin filament binding protein Abp1p." The Journal of cell biology (2001): Hoops, Stefan, et al. "COPASI a complex pathway simulator." Bioinformatics (2006): Mould, A. Paul, et al. "Disruption of integrin fibronectin complexes by allosteric but not ligand-mimetic inhibitors." Biochemical Journal (2014):

9 Sheridan, Nicholas. Modeling biochemical interactions controlling the cytoskeleton of spreading using the Finite Element Method, CAM Summer Research Report, Tania, Nessy et al. Modeling the Synergy of Cofilin and Arp2/3 in Lamellipodial Protrusive Activity Biophysical Journal, Volume Tee, Shang-You, et al. "Cell shape and substrate rigidity both regulate cell stiffness." Biophysical journal (2011): L25-L27. Appendix Given the parameter values above, here we show time course plots of all critical species of the model. Ultimately, the goal is that the attachment of the cell to the surface leads to an increase in barbed ends, which are the primary pushing machinery in the cell. Integrin and Activated Integrin Src and Activated Src Arp2/3 and Activated Arp2/3 Rho and Activated Rho

10 ROCK and Activated ROCK Myosin and Activated Myosin Cofilin and Activated Cofilin F-Actin New and F-Actin Old Barbed Ends

11 These are tables of the parameter values and intial concentrations that we used in our Copasi model. The highlighted parameters are the values obtained using Copasi s parameter estimating tool. Parameter Values used in Copasi Integrin + Fib = Integrin Active Cofilin -> Cofilin Active k_f l/(µmol*s) k_cat /s k_r /s K_M 4 µmol/l Src = Src Active Cofilin Active -> Cofilin k_cat /s k_cat /s k_cat /s K_M 4 µmol/l K_M 6.7 µmol/l Cofilin Active -> K_M2 4 µmol/l k_sev 0.01 Arp2/3 -> Arp2/3 Active Cof_0 0.1 k_cat /s n 4 K_M 2.2 µmol/l l k_f /s FActinNew -> FActinOld Arp2/3 -> k_age 0.1 1/s k_nuc 60 -> FActinNew l V_ /s K_MA 2 µmol/l J_f 0.01 µmol/(l*s) Rho -> RhoA FActinOld -> k_cat /s k_deg /s K_M 6.7 µmol/l -> BarbedEnds RhoA + ROCK = ROCKA k_cap 0 k_f 10 l/(µmol*s) kappa 106 k_r /s k_sev 0.01 Myosin -> Myosin Active n 4 k_cat 1.8 1/s l K_M 2.47 µmol/l k_nuc 60 K_MA 2 µmol/l Cof_0 0.1 Initial Concentrations Species Concentration (µmol/l) Integrin 15 IntegrinA 0 Fibronectin 0.15 Src 1 SrcA 0 Csk 0.05 Arp2/3 1 Arp2/3A 0 Rho 1 RhoA 0 ROCK 1 ROCKA 0 Myosin 1 MyosinA 0 Cofilin 1 CofilinA 0 FActinNew 1 FActinOld 1 BarbedEnds 1