Simulation programs
All codes presented here are freely available, courtesy of their author, Michael I. Monine (email)
Brownian Dynamics model of enzyme-mediated reactions at cell membranes
Spatial coupling model for pathway crosstalk
More references on spatial simulation methods
Cell population-based model
This is a simulation program for a hybrid model of dermal wound invasion. The model accounts for the platelet-derived growth factor (PDGF) gradient sensing mechanism in fibroblasts mediated by cell surface receptors and the phosphoinositide 3-kinase (PI3K) signal transduction pathway. The hybrid model treats fibroblasts as discrete objects endowed with heterogeneous properties, such as receptor, PI3K and 3' phosphoinositide phosphatase expression levels.
The algorithm is implemented in the C language. Note: the program uses an X11 library of Xt Widgets, which is typically available on basic Unix, Linux or Mac platforms. To run this program on Mac, make sure that X11 is installed (this package can be found on the Mac OS installation DVD).
References
Haugh J.M. (2006).
Deterministic model of dermal wound invasion incorporating receptor-mediated signal transduction and spatial gradient sensing.
Biophysical Journal, 90:2297-2308. (doi:10.1529/biophysj.105.077610)Monine M.I., Haugh J.M. (2008).
Cell population-based model of dermal wound invasion with heterogeneous intracellular signaling properties.
Cell Adhesion & Migration, 2:137-145. (link)
Program files
Source code: wound_model.c
Input parameters: wound.data
Makefile (required for compilation): makefile
Place all these files in the same directory. To compile the source code, simply type
"make wound_model".
If you see errors, verify paths in makefile.
Running the program
In a command line, type "./wound_model input.data OUTDIR",
where "input.data" is the name of an input parameter file (e.g., wound.data), and "OUTDIR" is the name of the output directory.
Input parameters
DISTR_rmax, DISTR_pmax, DISTR_emax: denote distribution types for parameters rmax, pmax and emax. For each parameter, DISTR=0 corresponds to a constant value, 1 to the normal distribution, 2 to the log-normal distribution and 3 to the uniform distribution. Note that DISTR_* should be integer.
MEAN_rmax, MEAN_pmax, MEAN_emax: mean values of the normal and log-normal distributions for the corresponding parameters, rmax, pmax and emax.
Model: cane be 1, 2 or 3 (integer); this value sets up the model type.
SIGMA_rmax, SIGMA_pmax, SIGMA_emax: standard deviation of the normal and log-normal distributions for the corresponding parameters, rmax, pmax and emax.
constant_rmax, constant_pmax, constant_emax: can be 0 or 1; 0 indicates that values of rmax, pmax or emax are distributed, 1 indicates that no distribution is used (DISTR, MEAN, SIGMA values are ignored).
rmax_0, pmax_0, emax_0: values of rmax, pmax and emax for a case when these parameters are kept constant (not distributed, DISTR=0, constant=1).
For detailed description of other parameters, see Haugh, Biophys J 2006, 90:2297 and Monine and Haugh, CAM 2008, 2:137.
Screenshot of the program
Spatial profiles of basic model characteristics and x-positions of cells with different levels of receptor expression. Sampling is done according to the Model 2. Files containing time courses for each observable value are saved in the specified ouput directory.
Brownian Dynamics model of enzyme-mediated reactions at cell membranes
This program implements a 2D Brownian Dynamics (BD) simulation method, which is sometimes referred to as a method of Green's function. We use this cumputational method to build a model of enzyme-mediated activation/deactivation of a substrate (a memebrane-attached molecule, e.g., Ras). We specifically consider reaction versus diffusion limitation, the effect of increasing enzyme density, and the spontaneous membrane association/dissociation of enzyme molecules. The main observable value of the model is an effective enzymatic rate constant (alpha). The simulation results have been verified vs. various continuum theories. This algorithm may be readily adapted for the stochastic simulation of more complex cell signaling systems.
The algorithm is implemented in the C language. Note: the program uses an X11 libriry of Xt Widgets, which is typically available on basic Unix, Linux or Mac platforms. To run this program on Mac, make sure that X11 is installed (this package can be found on the Mac OS installation DVD).
References
Monine M.I., Haugh J.M. (2005).
Reactions on cell membranes: Comparison of continuum theory and Brownian dynamics simulations.
Journal of Chemical Physics, 123:074908. (doi:10.1063/1.2000236)Haugh J.M. (2002).
A unified model for signal transduction reactions in cellular membranes.
Biophysical Journal, 82:591-604. (link)
Program files
Source code: membr.c
Input parameters: membr.data
Data required for evaluation of the error function: ERF.dat and ERFCX.dat
Makefile (required for compilation): makefile
Place all these files in the same directory. To compile the source code, simply type
"make membr".
If you see errors, verify paths in makefile.
Running the program
In a command line, type "./membr membr.data membr.out",
where "membr.data" is the name of an input parameter file, and "membr.out" is the name of the output file.
Input parameters
eta_Rec: dimensionless receptor density.
N_Rec: number of receptors per simulated area.
S: effective radius of receptor-enzyme complex.
N_Ras: number of Ras molecules per simulated area.
enzyme_on_off: 0 or 1. In simulations with stable (non-dissociating) enzymes, enzyme_on_off=0. For enzymes with final lifetime, enzyme_on_off=1.
k_r_on: rate constant of cytosolic enzyme binding (pseudo-first-order reaction).
k_r_off: enzyme dissociation rate constant.
Da: Damkohler number.
Diff: Ras diffusion coefficient.
kappa: dimensionless rate constant of Ras activation (second-order reaction).
TSTEP: timestep, if a particle reaches the activation layer surrounding an enzyme-receptor complex.
dS: thickness of the activation layer.
t_out: time interval for output values.
For detailed description of the parameters, see Haugh, Biophys J 2002, 82:591 and Monine and Haugh, J Chem Phys 2005, 123:074908.
Screenshots of the program
Formation of an active substrate zone surrounding the receptor-enzyme complex at equilibrium. Simulation conditions are the same as in Fig. 4 of Monine and Haugh, J Chem Phys 2005, 123:074908. Here is an input file for this simulation. 5000 substrate particles and only one stable receptor-enzyme complex were used. The plot to the right shows relaxation of the enzymatic rate constant to its equilibrium value, which corresponds to the data point obtained at eta_RE=eta_E=10-3 and Da=1 in Fig. 4 (alpha~9). Note that a spatial distribution of enzymes is not important at these parameter values. A receptor-bound enzyme is shown by a blue disk, inactive substrate particles are shown by green dots, and active substrate particles are indicated by red dots. The CPU time required to get a reasonable amount of data at equilibrium was about 10 min on Mac G5.
Simulation of an array of receptors with unstable enzymes. The conditions are similar to those used to generate Fig. 6 of Monine and Haugh, J Chem Phys 2005, 123:074908. The numbres of substrate particles and receptors were adjusted to make this simulation more tracktable for demostration purpose. Here is an input file. In the screenshot, yellow disks denote single receptors and blue disks indicate receptor-bound enzymes. Dynamical plots to the right show the number of enzymes bound to receptors (per simulation area), NRE, and the enzymatic rate constant, alpha. The value of NRE was averaged over small time steps. Fluctuations of NRE occur near the equilibrium level given by konNR/(koff+kon). The CPU time required to get these results was about 40 min on Mac G5.
Spatial coupling model for pathway crosstalk
This model is based on our previously developed BD method for simulating enzyme-mediated substrate activation/deactivation (Monine and Haugh, J Chem Phys 2005, 123:074908). Here, the algorithm has been extended to include more complex interactions.
The program is written in the C language. Right now it does not have GUI.
References
Monine M.I., Haugh J.M. (2008).
Signal transduction at point-blank range: analysis of a spatial coupling mechanism for pathway crosstalk.
Biophysical Journal, 95:2172-2182. (doi:10.1529/biophysj.108.128892)The algorithm is described in Supporting material for this paper.
Program files
Source code: Ras_model.c
Input parameters: Ras_model.data
Data required for evaluation of the error function: ERF.dat and ERFCX.dat
Makefile (required for compilation): makefile
Place all these files in the same directory. To compile the source code, simply type
"make Ras_model".
If you see errors, verify paths in makefile.
Running the program
In a command line, type "./Ras_model".
Simulation produces a bunch of *.out files.
Input parameters
N_Rec: number of receptors per simulated area.
N_Ras: number of Ras particles per simulated area.
S: effective radius of receptor-enzyme complex.
dS: thickness of the activation layer.
eta_R dimensionless receptor density.
TSTEP: timestep, if a particle reaches the activation layer surrounding an enzyme-receptor complex.
Diff: Ras diffusion coefficient.
phi_RE: affinity of receptor interaction with GEF
tau_RE: lifetime of receptor/GEF complex
tau_SE: lifetime of Ras/GEF complex
kci_E: ratio of Ras/receptor rates for GEF binding
kappa_RE: 2D rate constant for association of Ras/GEF complex with receptor
phi_act: GEF catalytic efficiency
tau_GAP: Ras-GTP lifetime
phi_RP: affinity of receptor interaction with PI3K
tau_RP: lifetime of receptor/PI3K complex
tau_SP: lifetime of Ras/PI3K complex
kci_P: ratio of Ras/receptor rates for PI3K binding
kappa_RP: 2D rate constant for association of Ras/PI3K complex with receptor
t_end: simulation time.
t_print: time interval for output values.
For detailed description of the parameters, see Monine and Haugh, Biophys J 2008, 95:2172.
More references on spatial simulation methods
Here are a few more recent papers describing Brownian dynamics and Green's function approach:
Morelli M.J., P.R. ten Wolde (2008). Reaction Brownian Dynamics and the effect of spatial fluctuations on the gain of a push-pull network. arXiv:0804.4125v1 [q-bio.QM] (recommended) (link)
J.S. van Zon, P. R. ten Wolde (2005). Simulating Biochemical Networks at the Particle Level and in Time and Space: Green's Function Reaction Dynamics. Phys. Rev. Lett., 94:128103 (link)
Batsilas L., et al. (2003). Stochastic model of autocrine and paracrine signals in cell culture assays. Biophys. J., 85:3659-3665 (see in Appendix) (link)
Ridgway D., et al. (2008). Coarse-Grained Molecular Simulation of Diffusion and Reaction Kinetics in a Crowded Virtual Cytoplasm. Biophys. J., 94:3748-3759 (link)
Hsieh M., et al. (2008). Stochastic simulations of ErbB homo and heterodimerisation: potential impacts of receptor conformational state and spatial segregation. IET Systems Biology, 2:256-272 (link)
Andrews S.S., Bray D. (2004). Stochastic simulation of chemical reactions with spatial resolution and single molecule detail. Physical Biology, 1:137-151 (link)
