Classifying general nonlinear force laws in cell-based models via the continuum limit

though discrete cell-based frameworks are now commonly used to simulate a whole range of biological phenomena, it is typically not obvious how the numerous different types of model are related to one another, nor which one is most appropriate in a given context. Here we demonstrate how individual cell movement on the discrete scale modeled using nonlinear force laws can be described by nonlinear diffusion coefficients on the continuum scale. A general relationship between nonlinear force laws and their respective diffusion coefficients is derived in one spatial dimension and, subsequently, a range of particular examples is considered. For each case excellent agreement is observed between numerical solutions of the discrete and corresponding continuum models. Three case studies are considered in which we demonstrate how the derived nonlinear diffusion coefficients can be used to (a) relate different discrete models of cell behavior; (b) derive discrete, intercell force laws from previously posed diffusion coefficients, and (c) describe aggregative behavior in discrete simulations

Neural criticality from effective latent variables

Observations of power laws in neural activity data have raised the intriguing notion that brains may operate in a critical state. One example of this critical state is "avalanche criticality," which has been observed in a range of systems, including cultured neurons, zebrafish, and human EEG. More recently, power laws have also been observed in neural populations in the mouse under a coarse-graining procedure, and they were explained as a consequence of the neural activity being coupled to multiple latent dynamical variables. An intriguing possibility is that avalanche criticality emerges due to a similar mechanism. Here, we determine the conditions under which dynamical latent variables give rise to avalanche criticality. We find that a single, quasi-static latent variable can generate critical avalanches, but that multiple latent variables lead to critical behavior in a broader parameter range. We identify two regimes of avalanches, both of which are critical, but differ in the amount of information carried about the latent variable. Our results suggest that avalanche criticality arises in neural systems in which there is an emergent dynamical variable or shared inputs creating an effective latent dynamical variable, and when this variable can be inferred from the population activity.Comment: 18 pages, 5 figure

Tuneable resolution as a systems biology approach for multi-scale, multi-compartment computational models

The use of multi-scale mathematical and computational models to study complex biological processes is becoming increasingly productive. Multi-scale models span a range of spatial and/or temporal scales and can encompass multi-compartment (e.g., multi-organ) models. Modeling advances are enabling virtual experiments to explore and answer questions that are problematic to address in the wet-lab. Wet-lab experimental technologies now allow scientists to observe, measure, record, and analyze experiments focusing on different system aspects at a variety of biological scales. We need the technical ability to mirror that same flexibility in virtual experiments using multi-scale models. Here we present a new approach, tuneable resolution, which can begin providing that flexibility. Tuneable resolution involves fine- or coarse-graining existing multi-scale models at the user's discretion, allowing adjustment of the level of resolution specific to a question, an experiment, or a scale of interest. Tuneable resolution expands options for revising and validating mechanistic multi-scale models, can extend the longevity of multi-scale models, and may increase computational efficiency. The tuneable resolution approach can be applied to many model types, including differential equation, agent-based, and hybrid models. We demonstrate our tuneable resolution ideas with examples relevant to infectious disease modeling, illustrating key principles at work. WIREs Syst Biol Med 2014, 6:225–245. doi:10.1002/wsbm.1270 How to cite this article: WIREs Syst Biol Med 2014, 6:289–309. doi:10.1002/wsbm.127

Learning differential equation models from stochastic agent-based model simulations

Agent-based models provide a flexible framework that is frequently used for modelling many biological systems, including cell migration, molecular dynamics, ecology, and epidemiology. Analysis of the model dynamics can be challenging due to their inherent stochasticity and heavy computational requirements. Common approaches to the analysis of agent-based models include extensive Monte Carlo simulation of the model or the derivation of coarse-grained differential equation models to predict the expected or averaged output from the agent-based model. Both of these approaches have limitations, however, as extensive computation of complex agent-based models may be infeasible, and coarse-grained differential equation models can fail to accurately describe model dynamics in certain parameter regimes. We propose that methods from the equation learning field provide a promising, novel, and unifying approach for agent-based model analysis. Equation learning is a recent field of research from data science that aims to infer differential equation models directly from data. We use this tutorial to review how methods from equation learning can be used to learn differential equation models from agent-based model simulations. We demonstrate that this framework is easy to use, requires few model simulations, and accurately predicts model dynamics in parameter regions where coarse-grained differential equation models fail to do so. We highlight these advantages through several case studies involving two agent-based models that are broadly applicable to biological phenomena: a birth-death-migration model commonly used to explore cell biology experiments and a susceptible-infected-recovered model of infectious disease spread