MATLAB Code Description

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1 MATLAB Code Description 17 October 2016 Predictive analysis of mechanistic triggers and mitigation strategies for pathological scarring in skin wounds by Sridevi Nagaraja, Lin Chen, Jian Zhou, Yan Zhao, David Fine, Luisa A. DiPietro, Jaques Reifman, Alexander Y. Mitrophanov Correspondence about modeling- and software-related technical questions to Sridevi Nagaraja: 1

2 CONTENTS Overview... 3 System Requirements... 3 MATLAB Code Description... 4 Normal Scar Formation Model... 6 Local Sensitivity Analysis... 8 Sampling-based Global Sensitivity Analysis (randomized parameter sets)... 8 Variance-based Global Sensitivity Analysis (randomized parameter sets)... 9 Identification of Critical Model Parameters

3 Overview The MATLAB code for the wound healing model was developed at the DoD Biotechnology High Performance Computing Software Applications Institute (BHSAI), Ft. Detrick, Maryland, to study the mechanistic triggers of pathological scarring and to identify promising molecular targets to reduce pathological scarring in wounds. The software currently implements a set of 27 ordinary differential equations (ODEs) and a delay differential equation (DDE) to simulate normal and pathological scarring in wounds. Sampling-based and variance-based global sensitivity analysis methods were implemented to identify the mechanistic triggers of pathological scarring and the molecular targets for the reduction of pathological (i.e., excessive) scarring in wounds. The inputs for the wound healing model and the sensitivity analyses are embedded in the code. The user can directly change parameter values inside some of the provided MATLAB files. The System Requirements Section of this document contains the details about the computer system that we used to develop and run the code. The rest of this document provides information about using the code for the three different types of analysis described in the paper (wound healing time course modeling and sampling- or variance-based global sensitivity analysis for 40,000 parameter sets). System Requirements We used the following software and hardware components: Software Operating System: Windows 7 Enterprise (64-bit operating system) MATLAB version (R2015a) (64-bit operating system) MATLAB Statistics Toolbox, Version 8.0 (R2015a) Microsoft (MS) Excel 2010 for plotting the figures in the paper Hardware Intel Core(TM) 2 Duo CPU 3.00 GHz and 4.00 GB RAM Disk space: 3-4 GB is recommended for a typical installation For extended sensitivity analysis, we used two server computers with the following specifications: CPU: 2x Intel Xeon X5650 ( GHz) RAM: MHz Disk space: 4x ,000 RPM 3

4 MATLAB Code Description The code was developed in MATLAB R2015a. The MATLAB files used in the code can be divided into three parts. The first part of the code comprises the MATLAB files that were developed by our group and are listed below. Main.m inflammation_delay_prolif_mech.m Parameters.m Graphs_main.m Param_var_local.m Global_local.m prcccalculation.m prccclustering.m CCfigure.m Latinhypercube.m efastclustering.m commonclustering.m simulation routine that runs the normal scarring model function comprising model equations, as well as chemotaxis, mechanical stress, and cytokine feedback functions script containing parameter values and initial conditions (also contains the program s main input) script that performs basic plotting of all model variables function for calculating the logarithmic local sensitivity values for a given parameter set simulation routine for sampling-based global sensitivity analysis (in the vicinities of 40,000 random parameter sets) function for calculating the partial rank correlation coefficients (PRCCs) between each of the 31 model variables and each of the 108 model parameters at 41 simulation time points function for dividing the PRCC values into three clusters using k-means clustering function for plotting the results of the PRCC analysis function that generates a user-defined number of random parameter sets function for dividing the efast sensitivity values into three clusters using k-means clustering function to find the model parameters common to the top cluster (cluster #1) of PRCC and efast analysis 4

5 The second part of the code comprises the MATLAB files originally developed by Marino et al. (1). We downloaded these files and performed slight modifications to them in order to suit the purpose of our study. The MATLAB files included in the second part of the code are listed below. Model_efast_modified ODE_efast_modified Parameter_settings_EFAST _ efast_sd_modified.m _ simulation routine for variance-based efast analysis (contains the number of samples per curve and resamples) function comprising model equations, as well as chemotaxis, mechanical stress, and cytokine feedback functions script that initializes the parameter values, initial conditions, and timing parameters for efast analysis function for calculating the efast sensitivity values for each model variable with respect to each model parameter from 40,500 simulations Note: The original MATLAB files and their descriptions can be found at the following link: The third part of the code comprises third-party MATLAB files that were downloaded and used in our simulations in their unmodified form. The following list gives the names of those MATLAB files and the source from where they can be downloaded. PRCC.m parameterdist.m _ SETFREQ.m padcat.m padcat-varargin-/content/padcat.m formatticks.m format-tick-labels/content//format_ticks.m parforprogress.m _ progress-monitor--progress-bar--that-works-with-parfor Note: The first three files on this list were developed by Marino et al. (1) 5

6 Instructions for downloading and saving the MATLAB files. The files are currently available in the.txt format. In order to run them in MATLAB, the files need to be converted in.m format. Please follow the instructions given below: 1. Download all the files into your current working folder in MATLAB. 2. Open each file one at a time in notepad and click File> Save As and change the.txt extension at the end of the file name to.m and then click Save. 3. MATLAB may ask you to specify the filename one more time. Please use the same file name as in the.txt file. Normal Scar Formation Model 1. The INPUT to the model is the initial concentration of platelets, which reflects the severity of an injury. The default value of this parameter is platelets/ml. This value is defined in the Parameters.m file under Initial conditions. To increase or decrease the severity of an injury, increase or decrease the value of the parameter P_init in this file. Note: any additional simulation of interest, e.g., pathological scarring induced by a 1.5-fold higher collagen production rate by fibroblasts and by a 2-fold reduction in fibroblast apoptosis rate, will need to be initiated by changing the respective parameters in the Parameters.m file. 2. To run the model, open Main.m and click the Run icon or type Main in the MATLAB command window. 3. After the routine is executed, the kinetic curves of some of the model variables will be displayed in two separate figures, as shown below. Figures for other model variables are commented. Please uncomment them to obtain plots for all model variables. Figure 1: kinetics of the total neutrophil, total macrophage, fibroblast, and myofibroblast concentrations Figure 2: kinetics of the total collagen and collagen fiber concentrations 6

7 These output figures show the raw values calculated by the model. The raw values of all model variables, as well as simulation time points, are stored in the output variable g in the MATLAB workspace. The normalized values of all model variables are stored in the output variable gnorm in the MATLAB workspace. Note: the raw values of all model variables were imported into MS Excel, normalized, and plotted along with normalized experimental data, as shown in Figure 2, Figure 3, Figure 6, and Supplemental Figure 2 of the paper. Note: pathological scarring simulations shown in Figure 6 of the paper were performed by executing the file Main.m after simultaneously increasing the parameter kprod_f by 1.5- fold of its default value and decreasing the parameter k_apop_f by 2-fold of its default value in the Parameters.m file. 7

8 Local Sensitivity Analysis Simulation: to calculate the local sensitivity values in the vicinity of the default parameter set, open the file Main.m and uncomment the last two lines under Local sensitivity analysis (lines 43-44). Then, click on the Run icon or type Main in the MATLAB command window. Output: the raw sensitivity values for all the model variables at 41 simulated time points for each of the 108 main model parameters are stored in the output variable Gsen_local (a structure of size 1 108, where each element represents the simulation for a particular parameter variation) in the MATLAB workspace. Note: for a complete list of the parameter identifying numbers, check the file Parameters.m. Each parameter is assigned an identifying number shown in the comment next to its initialization. Sampling-based Global Sensitivity Analysis (randomized parameter sets) For the sampling-based sensitivity analysis, we calculated the partial rank correlation coefficient (PRCC) between each model variable and each model parameter for 41 time points representing day 0 to day 40 of the simulation using simulated data from 40,000 simulations. Simulation: to calculate the time courses for all the model variables for a number of random parameter sets, follow the instructions given below. 1. Open Global_local.m. 2. Change the value of the parameter iter to choose the number of randomly generated parameter sets (default value used in the paper: 40,000). 3. Change the value of the parameter rangefactor to increase or decrease the uniform distribution sampling range for the extended sensitivity analysis [default value used in the paper: 2, i.e., the parameter values in the generated sets are chosen randomly from a 4-fold range (2-fold higher and 2-fold lower than the default value)]. Note: to simulate the time courses for all model variables with one parameter set using one compute node takes ~1 minute. Therefore, to compute the sensitivity values for 40,000 parameter sets, we used 12 parallel nodes, and the simulation took approximately 48 hours to complete. The user is advised to start with smaller values of iter (e.g., 50 or 100). If using parallel processing, replace the for command in Global_local.m, line 35, by parfor and specify the number of nodes that will be used in the parpool command right before using parfor. 8

9 4. Click on the Run icon or type Global_local in the MATLAB command window. 5. To calculate the PRCCs between each model variable and each model parameter for the 40,000 simulations, uncomment the line 71 in Global_local.m. Output: the kinetic trajectories for all the 31 model variables for each of the randomly generated 40,000 parameter sets are stored in the output variable Y_main_global in the MATLAB workspace. The PRCCs and the associated p-values are stored in the output variable M. M is a structure with 6 fields, and each field has 41 elements representing the respective PRCC values and p-values for each simulation time point. The PRCC values and the p-values are stored in field 5 and field 6 of the output variable M in the MATLAB workspace, respectively. 6. To plot the PRCC values at a given time point, open CCfigure.m. Enter the time point for which the PRCCs need to be plotted in line 2 (default value is 41, i.e., the final time point of the simulation). To run the script, click the Run icon or type CCfigure in the MATLAB command window. Sample output is shown in the figure below. Variance-based Global Sensitivity Analysis (randomized parameter sets) For the variance-based sensitivity analysis, we calculated the individual and total efast sensitivity values between each model variable and each model parameter for 41 simulation time points representing day 0 to day 40 of the simulation. 9

10 Simulation: to calculate the time courses for the model variables for a number of random parameter sets, follow the instructions given below. 1. Open Model_efast_modified.m. 2. Change the value of the parameter NR to choose the number of resampling to be performed (default value used in the paper: 5). 3. Change the value of the parameter k to the number of parameters in the model (value used in the paper: 108). 4. Change the value of the parameter NS to choose the number of samples per search curve (default value used in the paper: 75, minimal number of samples for efast analysis is 65). 5. To run the model, click the Run icon or type Model_efast_modified in the MATLAB command window. Output: the kinetic trajectories for all the 31 model variables for each of the randomly generated 40,500 (108 parameters 75 samples 5 resampling) simulations are stored in the output variable Y in the MATLAB workspace. The individual and total sensitivity values for each model variable with respect to each parameter at 41 simulation time points are stored in the output variables Si and Sti in the MATLAB workspace, respectively. Identification of Critical Model Parameters To identify the model parameters whose modulation drives pathological scarring, we performed clustering analysis to divide the 108 PRCCs and the 108 individual efast sensitivity values into three groups. Model parameters with high PRCCs and efast sensitivity values were assigned to cluster #1. We specifically looked at the model parameters in cluster #1 for the model variables representing fibroblast concentration and total collagen concentration. However, we performed the clustering analysis for all model variables. Simulation: to perform the clustering analysis follow the instructions given below. 1. Call the function prccclustering.m by typing the following in the MATLAB command window: [M2 Var_prccparam Var_prcc] = prccclustering(m,var) 2. Call the function efastclustering.m by typing the following in the MATLAB command window: 10

11 [Var_efastSiparam Var_efastSi Var_efastStiparam Var_efastSti N2] = efastclustering1(si,sti,var) Note: in both these functions, the input parameter var specifies the number assigned to each model variable for which the clustering needs to be performed. In our simulations, we performed the analysis for all model variables. Therefore, the default value of var is an array of numbers 1 to Open commonclustering.m. Click on the Run icon or type commonclustering in the MATLAB command window. Output: the parameter numbers and the corresponding PRCCs belonging to cluster #1 for all the 31 model variables at 40 simulation time points (representing day 1 to day 40 of the simulation) are stored in the output variable M2 in the MATLAB workspace. The parameter numbers and the corresponding efast sensitivity values belonging to cluster #1 for all the 31 model variables at 40 simulation time points are stored in the output variable N2 in the MATLAB workspace. The model parameter numbers and the corresponding PRCC and efast sensitivity values for the model parameters common to the cluster #1 of both the PRCC and efast analysis are stored in the output variable O in the MATLAB workspace. Note: the values of the critical PRCCs and efast sensitivity values were imported into MS Excel, and plotted using a bar graph (Figure 4 of the paper). References 1. Marino, S., I. B. Hogue, C. J. Ray, and D. E. Kirschner A methodology for performing global uncertainty and sensitivity analysis in systems biology. J Theor Biol 254: