Fig. 2: Mapping CXCL13 spatial distribution through simulation analysis and multiobjective optimization.

a Overview of the multiscale model platform. In this modular system stromal cells are modeled as a graph (Module 1), chemokine diffusion is modeled as a discretized partial differential equation (Module 2), while B cells are modeled as agents that can interact with their local environment through a set of coupled differential equations and vector-based calculations (Module 3). b Example structure of an artificial neural network used to emulate CXCL13Sim. The network has 13 input nodes that connect to three hidden layers, and a single output node predicting the meandering index. A distinct network is created for each simulator output. The hyperparameters of the network were determined using k-folds cross-validation. c The in silico follicular stromal network with a chemotactic landscape created for models 1 and 2 by the network. d Comparison of scanning rates in silico for models 1 and 2. Each parameter set was run 200 times with significance assessed using the Vargha−Delaney A-test⁷⁰. The test statistic (0.99) exceeds the threshold for a large effect size (0.71). Bar plots represent the median value for the emergent scanning rate and the error bars represent the IQR. e Parameter distributions for diffusion and decay rates corresponding to the Pareto optimal solutions shown in (f) with calibrated values for each parameter shown using the dotted red line. f Using a MOEA scheme we seek to address the following four objectives: minimize the root mean squared error between emulator and simulator responses for cell speed, meandering index and motility coefficient; and maximize scanning rates. The Pareto front of solutions represents the trade-off in performance between cell behaviors and scanning rates, using NSGA-II (emulation pipeline described in Supplementary Fig. 1). Source data are provided as a Source Data file.