Simulating CXCR5 Dynamics in Complex Tissue Microenvironments

Abstract

To effectively navigate complex tissue microenvironments, immune cells sense molecular concentration gradients using G-protein coupled receptors. However, due to the complexity of receptor activity, and the multimodal nature of chemokine gradients in vivo, chemokine receptor activity in situ is poorly understood. To address this issue, we apply a modelling and simulation approach that permits analysis of the spatiotemporal dynamics of CXCR5 expression within an in silico B-follicle with single-cell resolution. Using this approach, we show that that in silico B-cell scanning is robust to changes in receptor numbers and changes in individual kinetic rates of receptor activity, but sensitive to global perturbations where multiple parameters are altered simultaneously. Through multi-objective optimization analysis we find that the rapid modulation of CXCR5 activity through receptor binding, desensitization and recycling is required for optimal antigen scanning rates. From these analyses we predict that chemokine receptor signaling dynamics regulate migration in complex tissue microenvironments to a greater extent than the total numbers of receptors on the cell surface.

Keywords: B cells; G-protein coupled receptors; chemokines; mathematical modelling; systems biology.

Figure 1

In silico CXCR5 modelling: Graphical Overview of the gradient sensing algorithm (A), including receptor internalization and recycling (B) in the context of CXCL13 gradients (C) Quantification of scanning rates in wild-type and CXCR5 deficient B cells. (D) Quantifying scanning rates when perturbing total receptor numbers holding all other parameters fixed at baseline values. Median values are shown with error bars representing the I.Q.R. (E) Distributions of scanning rates observed from our global parameter perturbation analysis.

Figure 2

OAT perturbation of kinetic parameters that regulate CXCR5 signaling. (A) Perturbing kinetic parameters regulating CXCR5 activity and assessing the effect on in silico scanning rates. (B) Partial rank correlation coefficients quantifying the sensitivity of in silico scanning rates to perturbations in a given parameter, taking the influence of the other parameters into account. (C) eFAST analysis of parameter sensitivities using the CXCL13emulator Si (black) represents the fraction of output variance that can be explained by the value assigned to that parameter. STi (grey) represents the variance caused by higher order non-linear effects between that parameter and others explored. Bars represent the mean value for either Si or STi, with error bars representing the standard error over three resample curves.

Figure 3

Optimizing CXCR5 signaling in silico. (A) Pareto front of solutions representing the optimal trade off in performance between different in silico migratory behaviors and scanning rates (color coded), using the multiobjective optimization algorithm NSGA-II. (B) Parameter distributions corresponding to the Pareto optimal solutions shown in (A).

Figure 4

Single cell tracking in silico to assess the spatiotemporal dynamics of CXCR5 expression and signaling. (A) Experimentally obtained in vivo CXCL13 reporter expression from different stromal cell subsets in the CXCL13-EYFP mouse. (B) In silico scanning rates for the entire follicle using equal secretion rates for all stromal cell subsets or secretion rates representative of CXCL13 reporter expression. (C) In silico scanning rates following OAT perturbations to secretion rates in different stromal cell subsets. (D) In silico scanning rates for the subcapsular sinus using equal secretion rates for all stromal cell subsets or secretion rates representative of CXCL13 reporter expression. (E) Single-cell tracking of CXCR5 expression on the cell surface. (Top) each line represents a distinct B cell within the same simulation run and (bottom) comparison of free and receptor signaling dynamics within a single cell. (F) Spatial dependence of CXCR5 signaling within the follicle. Each dot in the diagram represents the X and Y coordinates of a B cell agent in the simulator. The top of each square diagram is the subcapsular sinus. Each agent is colored by the number of receptors (as indicated by the title of each plot) with red representing high values and blue representing low values.