Pedro Mendes, Multiscale hybrid differential equation and agent-based models

Abstract: Biological phenomena are notorious for crossing several temporal and spatial scales. While often it may be sufficient to focus on a single scale, it is not rare that we have to consider several scales simultaneously. Computational modeling and simulation of biological systems thus frequently requires to include diverse temporal and spatial scales. A popular approach in systems biology is to combine differential equations and agent-based models, where usually small sets of differential equations are used to represent the internal state of each cell, with the cells being represented as interacting autonomous agents on a lattice. This type of hybrid models allows for parallel solution of smaller sets of differential equations rather than the solution of a single but very large set of differential equations. At certain discrete times, the agents are allowed to communicate, and only then are the different sets of differential equations able to influence each other. This time discretization of the cell-cell interactions carries an inherent approximation error compared to the continuous interaction of these cells in the single model of a large set of coupled differential equations. Here we study this approximation error and investigate the conditions in which it becomes negligible, thus defining the domain where the multiscale approach is valid. The approach is illustrated with a classic model of Drosophila segment polarity network, where a model based on a full set of differential equations (the original version of that model) is compared with a hybrid model combining differential equations and agent-based approach (implemented with the open source software simulators Vivarium and COPASI). This study is also relevant to other hybrid simulations, such as those representing “whole-cell models”, where partitions may be done at other organizational scales.