Dimensionality of Motion and Binding Valency Govern Receptor-Ligand Kinetics As Revealed by Agent-Based Modeling.

Teresa Lehnert,Marc Thilo Figge

doi:10.3389/fimmu.2017.01692

Abstract

Mathematical modeling and computer simulations have become an integral part of modern biological research. The strength of theoretical approaches is in the simplification of complex biological systems. We here consider the general problem of receptor–ligand binding in the context of antibody–antigen binding. On the one hand, we establish a quantitative mapping between macroscopic binding rates of a deterministic differential equation model and their microscopic equivalents as obtained from simulating the spatiotemporal binding kinetics by stochastic agent-based models. On the other hand, we investigate the impact of various properties of B cell-derived receptors—such as their dimensionality of motion, morphology, and binding valency—on the receptor–ligand binding kinetics. To this end, we implemented an algorithm that simulates antigen binding by B cell-derived receptors with a Y-shaped morphology that can move in different dimensionalities, i.e., either as membrane-anchored receptors or as soluble receptors. The mapping of the macroscopic and microscopic binding rates allowed us to quantitatively compare different agent-based model variants for the different types of B cell-derived receptors. Our results indicate that the dimensionality of motion governs the binding kinetics and that this predominant impact is quantitatively compensated by the bivalency of these receptors.

Highlights

In recent decades, computational biology has developed into an autonomous scientific discipline that has become indispensable for contemporary biological research
The population kinetics can be straightforwardly described by a coupled system of ordinary differential equations (ODE), whereas agent-based models (ABM) resolve spatial structures of receptors and ligands and account for the dimensionality of the spatial environment in which these molecules diffuse and interact
While ligands are throughout considered as being in solution and as having spherical shape, the four combinations of receptor properties give rise to four different ABM variants that are denoted by their receptor properties, respectively, as O-SOL, O-membrane anchored (MEM), Y-SOL, and Y-MEM

Summary

Introduction

Computational biology has developed into an autonomous scientific discipline that has become indispensable for contemporary biological research. Models based on ordinary differential equations (ODE) are presumably most frequently applied in biological research, even though this modeling approach is only valid if the system under consideration consists of large amounts of constituents, e.g., molecules, that are homogeneously distributed or well stirred in some spatial environment [1] This is because ODE models do not explicitly account for any spatial aspects of a system and changes in system variables, e.g., concentrations of molecules, are described by functions of time that are continuous and deterministic. These assumptions, which may be typically appropriate for chemical systems, are for biological systems at best applicable from a macroscopic point of view. Albeit more detailed than deterministic ODE models, all these approaches have in common that a macroscopic viewpoint on the system is taken

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