Research Group at Shepherd  Dr. Qing Wang (Mathematics, PI), Dr. Zhijun Wang (Computer Science).
Project Mentor  Dr. David Klinke, Department of Chemical Engineering, Department of Microbiology, Immunology & Cell Biology, West Virginia University.
Experimental Data by Dr. Jonathan Bramson, Department of Pathology and Molecular Medicine, McMaster University, Hamilton, Ontario, Canada
Goal of Simulation
Find the closetooptimal, hopefully the optimal, parameter set in a highdimensional parameter space using a computationally tractable method. Please see handouts for the model. Test set comes from experimental data.
Parameter Set Optimization
Genetic Algorithm. Encode with the parameter set. Evolve using crossover and mutation. For each generation, the ODE set is solved for each individual and the fitness function value (variance here) is calculated. The top half is passed to the next generation. Note the best individual in each generation is free from mutation. Crossover point(s) and mutation rate can be dynamically adjustable parameters so the algorithm can move more efficiently in the large parameter space and hopefully not get trapped in notsogood local minimums.
Simulated Annealing + AMCMC. If applicable to the model, good estimates of initial parameter values may be calculated using simulated annealing. Then this initial parameter set is used as the starting point for a Markov chain. Please refer to the methodology article from Dr. Klinke [1].
Initial Value ODE Solvers
RungeKutta (order 4). AdamsMoulton formulas (nonstiff problems). Backward differentiation formulas (stiff problems). Any ODE solver should be implemented in the most efficient way due to the amount of calls in either the genetic or the AMCMC method. The ODE solver is the computational bottleneck of the simulation.
Please note: All variable and parameter values are equally weighted during the initial phase. The relative weights can be changed easily.
Design and Implementation Plan
Parameter ranges, initial values, and simulation parameters can be specified on the interface. Final converged or timeup parameter values and the numerical solution to ODEs are saved in a text file and used for analysis and drawing.
Please note that functional curves for variables can be drawn using the saved data file. There are quite a few variables and they have different units so they can not be drawn in the same graph on the simulation interface as before.
The simulators in the following table are hosted and tested from this page. Please note the simulation process will consume client machine's resources. Internet Explorer with .Net framework 4 and/or Visual Basic Power Pack are required to run the application.
07/04/2014  New Holiday Edition  
Equation Set Solver  Version Notes  
Blue 2 with M Sample
impulse parameter files  Impulses_LV.
Impulses_M. Please put above files on Windows Desktop. Parameters can be modified. 



Second Generation Model  Possible Future Work  
Simulator  Equation Set Solver  Version Notes  
Violet 1. Violet 1 Linear  Violet 2 



New Fitness with Separated Components  Possible Future Work  
Simulator  Equation Set Solver  Version Notes  
Indigo 1. Indigo 1 Linear  Indigo 2 



11/22/2013  First Generation Model Update  
Simulator  Equation Set Solver  Version Notes  
Blue 1. Blue 1 Linear  Blue 2 (Sample impulse parameter file) 



6/6/2013  New Fitness with Components, New Version of Equations (1.5 & 1.6), etc.  
Simulator  Equation Set Solver  Version Notes  
Green 1 Green 1 Linear 
Green 2 


Green 3 Green 3 Linear 
Green 4 
Following changes were made to Green 1 & Green 2.



12/20/2012  New Terms (last update  2/17/2013 with new fitness/variance)  
Simulator  Equation Set Solver  Version Notes  
Yellow 1  Yellow 2  Equations (1.1)  (1.4). Set fitness/variance thresholds for TE_{1} and TE_{2} respectively. TE1 or TE2 has 1. The previous fitness definition using normalized ratios (always ≥ 1). 2. The normalized (divided by the maximum of experimental data squared and the number of data points) variance (always ≥ 0). 

Yellow 3  Yellow 4  Equations (1.1)  (1.9). Not changed.  

12/7/2012  Fitting the Curves — Complete Model Edition  
Simulator for 1.11.9 (from w/o volt in eq. 1.5 versions)  Equation Set Solver  Version Notes  
Orange 1  Orange 2  LV^{2} / ( γ + LV^{2}) for all 3 terms in 1.1 and 1.2.  
Orange 3  Orange 4  LV^{3} / ( γ + LV^{3}) for all 3 terms in 1.1 and 1.2.  
Orange 5  Orange 6  LV^{power} / ( γ + LV^{power}) for all 3 terms in 1.1 and 1.2.  
For versions Orange 1  6 above, please put your experimental data file "exp_data.txt" on the desktop, or else the default experimental data file will be used. 
11/23/2012  Fitting the Curves Edition  
Simulator for 1.11.4 (from w/o volt in eq. 1.5 versions)  Equation Set Solver  Version Notes  
Red 1  Red 2  LV for all 3 terms in 1.1 and 1.2.  
Red 3  Red 4  LV / ( γ + LV) for all 3 terms in 1.1 and 1.2.  
Red 5  Red 6  LV^{2} / ( γ + LV^{2}) for all 3 terms in 1.1 and 1.2.  
Red 7  Red 8  LV^{1/2} for all 3 terms in 1.1 and 1.2.  
Red 9  Red 0  LV^{3} / ( γ + LV^{3}) for all 3 terms in 1.1 and 1.2.  
For versions Red 1  0 above, please put your experimental data file "exp_data.txt" on the desktop, or else the default experimental data file will be used. 
Simulators  11/19/2012  Version Notes  
w/o volt in eq. 1.8 ← Violet 6  Equation solver only.  LV / ( γ + LV) > LV ^ 1/2 for all equations. Others same as the last row. Updated 11/20/2012.  
w/o volt in eq. 1.8 ← Violet 5  Special version (1.11.7 only).  
w/o volt in eq. 1.8 ← Violet 4  Equation solver only.  LV / ( γ + LV) > LV for all equations. Others same as the last row. Updated 11/20/2012.  
w/o volt in eq. 1.8 ← Violet 3  Special version (1.11.7 only).  
w/o volt in eq. 1.8 ← Violet 2  Equation solver only.  LV > LV / ( γ + LV) in (1.1). Equation for T_{E1} is decomposed into 4 new equations. Terms with parameters α and a_{21} are removed from equations. T_{E1} is changed to T_{E1d} in (1.7).  
w/o volt in eq. 1.8 ← Violet 1  Special version (1.11.7 only). 
Simulators  11/13/2012  Version Notes  
w/ volt in eq. 1.5 ← Blue 7 w/o volt in eq. 1.5 ← Blue 8  Equation solvers only.  LV > LV ^ 1/2 for all 3 terms in (1.1) and (1.2). Updated 11/20/2012.  
w/ volt in eq. 1.5 ← Blue 5 w/o volt in eq. 1.5 ← Blue 6  Special versions.  
w/ volt in eq. 1.5 ← Blue 3 w/o volt in eq. 1.5 ← Blue 4  Equation solvers only.  LV > LV^{2} / ( γ + LV^{2}) for all 3 terms in (1.1) and (1.2).  
w/ volt in eq. 1.5 ← Blue 1 w/o volt in eq. 1.5 ← Blue 2  Special versions. 
Simulators  11/8/2012  Version Notes  
Version w/ volt in eq. 1.5. Version w/o volt in eq. 1.5.  Equation solvers only.  LV > LV / ( γ + LV) in the second term of (1.2). Other features same as in the table below. This is an incremental version. 

Version S w/ volt in eq. 1.5. Version S w/o volt in eq. 1.5.  Special versions.  
Version 3 w/ volt in eq. 1.5. Version 3 w/o volt in eq. 1.5 (O1).  Discussions on 10/15/2012. 
Simulators  10/26/2012  Version Notes  
Version w/ volt in eq. 1.5. Version w/o volt in eq. 1.5.  Equation solvers only.  LV > LV / (
γ + LV) in (1.1) and the first term of (1.2). Other features same as in the table below. 

Version S w/ volt in eq. 1.5. Version S w/o volt in eq. 1.5.  Special versions.  
Version 3 w/ volt in eq. 1.5. Version 3 w/o volt in eq. 1.5.  Discussions on 10/15/2012. 
Simulators  Version Notes  
Version w/ volt in eq. 1.5. Version w/o volt in eq. 1.5.  Equation solvers only.  ↑↑↑
Modified versions 

Version S w/ volt in eq. 1.5. Version S w/o volt in eq. 1.5. 
Special versions  Simplified version with equations 1.1  1.4
only. a23 and a32 are 0s. Note: The first four equations are decoupled from the others. Please ignore parameters and variables that are not in 1.1  1.4. 

Version 3 w/ volt in eq. 1.5. Version 3 w/o volt in eq. 1.5.  Discussions on 10/15/2012.
New default ranges for beta1 and beta2. Version #s added in output
files. Each simulation run will have its own folder with output files
partitioned as requested. Limit TE3, IFNg, and TNFa exp. data to first
14 days. Step size is changeable. Partitioned files are written in real time to prevent interruptions such as power outrage so they are not sorted. If a simulation finishes, the whole output file is sorted by variance. 

Version 2 w/ volt in eq. 1.5. Version 2 w/o volt in eq. 1.5.  Changes implemented from discussions on 10/3/2012. Major changes  kd1, kd2, and c1 become constants for each simulation. gp100 exp. data (Te3, C(t), IFNg, TNFa) added. Variance component option added.  
Version w/ volt in eq. 1.5. Version w/o volt in eq. 1.5.  Major changes  New 0s. Variable step size. INFg excluded from fitness. Use C(t). New kp2 and kd4.  
Version 1. Version ex1. Version ex2.  Archives. Last update  9/20/2012. See hard copy version notes. 
[1] David Klinke, "An Empirical Bayesian Approach for Modelbased Inference of Cellular Signaling Networks", BMC Bioinformatics, November 2009.
Send me Suggestions about Design and Coding of the Simulator
Reference Simulators from Previous Projects
Please note: Simulators are downloaded and run on clients. Parameters are adjusted on GUIs of SARS and H1N1 simulators since their values are easily determined. For the cancer cell dynamics simulation, optimal parameter values need to be computed using approximation methods which either "walk" or "jump" in a huge highdimensional parameter space until a good point is found or a preset running time is up.