Simulate microscopic and macroscopic models of cell migration

LorenziEtAl2026ModellingMatlab code used to simulate the microscopic and macroscopic models in "Phenotype-structuring of non-local kinetic models of cell migration driven by environmental sensing" (2026), by Tommaso Lorenzi, Nadia Loy, Chiara Villa Generalities Public gitlab repository LorenziEtAl2026Modelling This repository provides Matlab files to simulate the microscopic and macroscopic models in Tommaso Lorenzi, Nadia Loy, Chiara Villa (2026) Phenotype-structuring of non-local kinetic models of cell migration driven by environmental sensing Available on ArXiv [2412.16258] and HAL [hal-04851469] For details we refer the interested reader to this publication. AuthorsNadia Loy (Politecnico di Torino) and Chiara Villa (CNRS, MAP5, Université Paris Cité) CitationLoy, N. and Villa, C. (2026). Matlab code to simulate microscopic and macroscopic models of collective cell migration on phenotypically heterogeneous cell populations. DOI 10.5281/zenodo.14552670 If you use this software in your work then please cite the above named paper. Copyright noticeMatlab code to simulate microscopic and macroscopic models of collective cell migration on phenotypically heterogeneous cell populations. Copyright (C) 2026 N. Loy & C. Villa Repository content and how to use The code is set up to simulate the microscopic model (2.1)-(2.2) described in Section 2 of LorenziEtAl2026Modelling, to simulate the PDE (3.48) and the reduced model (4.15) in LorenziEtAl2026Modelling, under the numerical setup detailed in Section 4.1 of LorenziEtAl2026Modelling. To change the model set up:- 'Parameters.m' : the main parameter values of the simulations can be modified here, including the value of the first order correction coefficient 'epsilon'. This does not include numerical scheme-specific parameters, which can be modified in the respective files for simulating the macroscopic (SimPDE) and microscopic (SimMC) models. This function is called from the files: MICRO_SimMC_1D.m, MICRO_SimMC_2D.m, MACRO_SimPDE_1D.m, MACRO_SimPDE_2D.m and 'MACRO_Sim_2D_SIM.m'. To simulate the microscopic model:- 'MICRO_SimMC_1D.m' : file to run Monte Carlo simulations of the microscopic model in 1D, with Kappa = Dirac delta, including interactions in which both phenotypic switching and directional changes occur (results shown in Section 4.3.1), and effect of order Dt^2. In our model set up it yields the same results as in the absence of such interactions (this was thoroughly checked), because phenotypic changes only depend on phenotype and not on velocity, thus simulating the phenotypic switch before the change in velocity accounts for both particles only switching phenotype and those switching both phenotype and velocity. - 'MICRO_SimMC_2D.m' : file to run Monte Carlo simulations of the microscopic model in 2D (results shown in Section 4.3.1), with Kappa = Dirac delta or Kappa = Von Mises. To run simulations for Kappa given as a Von Mises distributions, first download the function 'vmrand'* by Dylan Muir (2024) and add it to the folder. * Dylan Muir (2024). vmrand(fMu, fKappa, varargin) (https://www.mathworks.com/matlabcentral/fileexchange/37241-vmrand-fmu-fkappa-varargin), MATLAB Central File Exchange. Retrieved October 22, 2024. To simulate the macroscopic model:- 'MACRO_SimPDE_1D_DD.m' : file to run for simulations of the macroscopic model in 1D with Kappa = Dirac delta (results shown in Section 4.3.1) - 'MACRO_SimPDE_2D.m' : file to run for simulations of the macroscopic model in 2D (results shown in Section 4.3.2) - 'MACRO_SimPDE_2D_SIM.m' : file to run for simulations of the simplified (SIM) macroscopic model given by equation (4.15) in 2D (results shown in Section 4.3.3) - 'Nonlocal_advection_1D_DD.m' : function called from within the 'MACRO_Sim_1D_DD.m' file to calculate the advection velocity U_T^eps and the variance-covariance matrix D_T^eps appearing in PDE (3.50) in 1D with Kappa = Dirac delta - 'Nonlocal_advection_2D_DD.m' : function called from within the 'MACRO_Sim_2D.m' file to calculate the advection velocity U_T^eps and the variance-covariance matrix D_T^eps appearing in PDE (3.50) in 2D with Kappa = Dirac delta - 'Nonlocal_advection_2D_VM.m' : function called from within the 'MACRO_Sim_2D.m' file to calculate the advection velocity U_T^eps and the variance-covariance matrix D_T^eps appearing in PDE (3.48) in 2D with Kappa = Von Moses - 'Nonlocal_advection_2D_SIM.m' : function called from within the 'MACRO_Sim_2D_SIM.m' file to calculate the advection velocity U_T^eps and the variance-covariance matrix D_T^eps appearing in PDE (3.48) in 2D - 'MUSCL_GP.m' : function called from within 'MACRO_Sim_1D_DD.m', 'MACRO_Sim_2D.m' and 'MACRO_Sim_2D_SIM.m' files to compute the numerical approximation of the flux of PDE (3.48) using the MUSCL scheme. Go to this function to change the flux-limiter to use for the simulation. Reproducing plots from LorenziEtAl2026Modelling The data produced by simulations that is used to obtain the plots in LorenziEtAl2026Modelling was stored in a folder 'Saved data'. Due to data file sizes, these are not uploaded in the repository. We detail how to reproduce the figures from scratch and note that the files below to create plots call data files stored in a folder 'Saved data', which may need to be adapted if produced data is stored elsewhere (or with different file names). To reproduce the figures in Section 4.3 of LorenziEtAl2026Modelling:- 'Plot_comparison_1D_eps.m' : file to reproduce figure 2. One must first run 'MICRO_SimMC_1D.m' and 'MACRO_SimPDE_1D_DD.m' for the different values of 'epsilon' that should be plot and save the data.- 'Plot_comparison_2D.m' : file to reproduce figure 3. One must first run 'MICRO_SimMC_2D.m' and 'MACRO_SimPDE_2D.m', selecting Kappa = 'DD', for the chosen value of 'epsilon' that should be plot and save the data.- 'Plot_stripes.m' : function to reproduce figures 4, 5, 6 and 7. This function is called from within 'MACRO_Sim_2D.m' and 'MACRO_Sim_2D_SIM.m' to plot results, so just run that file with the chosen set up.