Dynamical Modeling Resources

Xiong Y, Rangamani P, Fardin MA, Lipshtat A, Dubin-Thaler B, Rossier O, Sheetz MP, Iyengar R. Mechanisms controlling cell size and shape during isotropic cell spreading. Biophys J. 2010 May 19;98(10):2136-46.
PMID: 20483321 | PMCID: PMC2872297 | EndNote Citation

Rangamani P, Fardin MA, Xiong Y, Lipshtat A, Rossier O, Sheetz MP, Iyengar R. Signaling network triggers and membrane physical properties control the actin cytoskeleton-driven isotropic phase of cell spreading. Biophys J. 2011 Feb 16;100(4):845-57.
PMID: 21320428 | PMCID: PMC3037558 | EndNote Citation

This is the C++ code for the cell spreading model presented in Xiong et al (Biophys J 98(10):2136-46) and Rangamani et al (Biophys J 100(4):845-57). We provide brief instructions on using the program here, please contact Padmini Rangamani (padmini.rangamani@berkeley.edu) for any questions. Download and unzip the source code. Compile the release version of the code using makefile CellMotility command. The executable file CellMotility is created. In order to run simulations using this code, the following files are necessary - reactions.ini, parameters.ini and concentrations.ini. Sample files can be found in the 'Release' directory. The concentrations can be entered as a time series at equal intervals with the time step entered on the first line. For constant concentration input, similar to the simulations in Xiong et al (Biophys J 98(10):2136-46), enter a large time step (greater than simulation time) and enter the concentrations of arp2/3, capping protein and G-actin.

The output is created as .csv files; the file names can be changed in parameters.ini
The .csv files can be analyzed using MATLAB or similar programs.

Source Code: source_curvature_mar2010.zip

Rodriguez-Brenes IA, Peskin CS Quantitative theory of telomere length regulation and cellular senescence. Proc Natl Acad Sci U S A. 2010 Mar 23;107(12):5387-92.
PMID: 20207949 | PMCID: PMC2851797 | EndNote Citation

Telomere-App is an implementation of the stochastic model described in the paper

Systems requirements: Mac OS X 10.4 or higher.
Move the file "fraction_data_N.dat" found in the folder "Telomere-App" to the root directory (usually called Macintosh HD).

Running a Simulation:
To run a simulation the user must choose the values of the parameters µ, p, T0, L0 explained in the paper "Quantitative theory of telomere length regulation and cellular senescence". The other parameters used in the model cannot be changed in this application and are set to the values described in the paper.

After completing a successful "Run" of the program. Several binary files are created:

1- A file "param_matlab.dat" containing the values of the parameters used in the simulation.
2- A file "Pop_data.dat"
3- A variable number of files called "pop_doubling_N.dat" where N is the number corresponding age of the cell culture as described by Cumulative Population Doublings. These files contain the lengths of each of the 92 chromosomes of every cell in the sample. The output files while be saved in the root directory (often called Macintosh HD).

Visualizing Results:
The folder "Telomere-App" contains the file "length_vs_pd.m" and "load_telomere_data.m". Running this script in Matlab plots the results. For help in using this files type help and the name of the files in Matlab's command window.

Files: Telomere-App.zip, README.pdf, fraction_data_N.dat, length_vs_pd.m, load_telomere_data.m

Jia Z, Bien H, Entcheva E. Detecting space-time alternating biological signals close to the bifurcation point. IEEE Trans Biomed Eng. 2010 Feb;57(2):316-24.
PMID: 19695992 | EndNote Citation | Supplementary Materials

The algorithm is designed to quantify the temporal persistence of period-2 rhythms (alternans) in traces of biological signals, exhibiting such instabilities (ECG, action potentials, calcium transients etc), recorded from multiple spatial locations. The advanced version (calfSDA) analyses data traces from multiple locations, obtained under dynamic pacing - successively increasing/decreasing pacing frequencies. It performs analysis and statistics on the identified alternans over space and time, revealing evolution patterns as pacing frequency changes, and keeping track of spatial concordance/discordance. Both functions accept pre-processed data, after beat detection and extraction of a parameter of interest - peak height, duration etc.

Wang LJ, Sobie EA. Mathematical model of the neonatal mouse ventricular action potential. Am J Physiol Heart Circ Physiol. 2008 Jun;294(6):H2565-75.
PMID: 18408122 | EndNote Citation | Supplementary Materials
This paper describes a novel mathematical model of electrical signaling and calcium handling in ventricular cells from the neonatal (day 1) mouse. Neonatal mouse and rat hearts are commonly used in experimental studies, but the lack of a mathematical description of action potentials and calcium transients in these cells previously made quantitative interpretation difficult. We created the first mathematical model of the neonatal mouse myocyte by modifying, based on experimental data, the densities and/or formulations of ion transport mechanisms in an adult cell model. The new model reproduces the characteristic AP shape of neonatal cells, with a brief plateau phase and longer duration than the adult (APD80=60.8 vs. 12.6 ms). As shown in the Figure, the model correctly reproduces the responses of adult and neonatal cells to drugs that block specific potassium channels in the cell membrane.

Model Code
The two files, "wand_ode.m" and "dydt_wang.m" must be in the same directory to run the model. wang_ode.m is the master script that defines the model parameters and electrical stimulation protocol. This program then uses Matlab's ODE solvers and calls the other program to integrate the differential equations. When the simulation is complete, wang_ode.m plots the action potential and various ionic currents.

Models in VCell
Models developed in VCell can be accessed through the VCell portal. These are full models (containing all parameters and geometries) along with all the simulations shown in the published manuscripts. Parameters include both experimentally measured and estimated values. Annotated parameters can be found in the supplemental material of each paper. New users are required to register at VCell.org.

After log in, click on File -> Open -> BioModel -> Shared Models. The following models are stored in VCell:

Eungdamrong NJ, Iyengar R. Compartment-specific feedback loop and regulated trafficking can result in sustained activation of Ras at the Golgi. Biophys J. 2007 Feb 1;92(3):808-15.
PMID: 17098795 | EndNote Citation | Supplementary Materials

This is an ODE model of EGF-dependent Ras activation at different subcellular locations (plasma membrane and Golgi). Eungdamrong and Iyengar showed that multiple mechanisms, such as regulated trafficking and engagement of DAG-dependent feedback loops, operating at different time-scales, orchestrate the sustained activation of Ras. Palmitoylation dynamics can also regulate the accumulation of active Ras at the Golgi.

After log in, click on File -> Open -> BioModel -> Shared Models: Model can be found at Eungdamr -> eungdamrong and iyengar Biophys Journal

Neves SR, Tsokas P, Sarkar A, Grace EA, Rangamani P, Taubenfeld SM, Alberini CM, Schaff JC, Blitzer RD, Moraru II, Iyengar R. Cell shape and negative links in regulatory motifs together control spatial information flow in signaling networks. Cell. 2008 May 16;133(4):666-80.
PMID: 18485874 | PMCID: PMC2728678 | EndNote Citation | Supplementary Materials

This is a PDE model of beta-adrenergic induction of cAMP and MAPK activation in hippocampal neurons. The study by Neves et al., looks into the mechanisms that give rise to spatial microdomains, subregions of high concentration of signaling molecules. Signaling events that originate at the membrane and are terminated in the cytosolic compartment will give rise to cAMP microdomains in cellular regions of high surface to volume ratio such as dendrites. cAMP microdomains are conserved in downstream components.

Model can be found at Neves -> neves_cell_2008

Lipshtat A, Jayaraman G, He JC, Iyengar R. Design of versatile biochemical switches that respond to amplitude, duration, and spatial cues. Proc Natl Acad Sci U S A. 2010 Jan 19;107(3):1247-52.
PMID: 20080566 | PMCID: PMC2824311 | EndNote Citation | Supplementary Materials

This is an ODE model of receptor regulated Rap1 activation. Here Lipshtat et al., explore the ability of small GTPases, such as Rap1, to act as flexible switches leading to first-order ultrasensitive signaling. Due to the extracellular signal dependent degradation of Rap-GAP, active Rap displays an ultrasensitive response to the amplitude and duration of the extracellular signal.

Model can be found at Azilipshtat -> PNAS_switch

Bhalla US, Iyengar R. Emergent properties of networks of biological signaling pathways. Science. 1999 Jan;283(5400):381-7.
PMID: 9888852 | EndNote Citation | Supplementary Materials

Membrane Diffusion Coefficients
Partial Listing of diffusion coeffficients of integral membrane proteins provided by Suzanne Scarlata, PhD, (SBCNY Investigator).
Supplementary Materials
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