Stochastic simulation of multiscale complex systems with PISKaS: A rule-based approach.

Computational simulation is a widely employed methodology to study the dynamic behavior of complex systems. Although common approaches are based either on ordinary differential equations or stochastic differential equations, these techniques make several assumptions which, when it comes to biological processes, could often lead to unrealistic models. Among others, model approaches based on differential equations entangle kinetics and causality, failing when complexity increases, separating knowledge from models, and assuming that the average behavior of the population encompasses any individual deviation. To overcome these limitations, simulations based on the Stochastic Simulation Algorithm (SSA) appear as a suitable approach to model complex biological systems. In this work, we review three different models executed in PISKaS: a rule-based framework to produce multiscale stochastic simulations of complex systems. These models span multiple time and spatial scales ranging from gene regulation up to Game Theory. In the first example, we describe a model of the core regulatory network of gene expression in Escherichia coli highlighting the continuous model improvement capacities of PISKaS. The second example describes a hypothetical outbreak of the Ebola virus occurring in a compartmentalized environment resembling cities and highways. Finally, in the last example, we illustrate a stochastic model for the prisoner's dilemma; a common approach from social sciences describing complex interactions involving trust within human populations. As whole, these models demonstrate the capabilities of PISKaS providing fertile scenarios where to explore the dynamics of complex systems.

Rule-Based Models and Applications in Biology.

Complex systems are governed by dynamic processes whose underlying causal rules are difficult to unravel. However, chemical reactions, molecular interactions, and many other complex systems can be usually represented as concentrations or quantities that vary over time, which provides a framework to study these dynamic relationships. An increasing number of tools use these quantifications to simulate dynamically complex systems to better understand their underlying processes. The application of such methods covers several research areas from biology and chemistry to ecology and even social sciences.In the following chapter, we introduce the concept of rule-based simulations based on the Stochastic Simulation Algorithm (SSA) as well as other mathematical methods such as Ordinary Differential Equations (ODE) models to describe agent-based systems. Besides, we describe the mathematical framework behind Kappa (κ), a rule-based language for the modeling of complex systems, and some extensions for spaßtial models implemented in PISKaS (Parallel Implementation of a Spatial Kappa Simulator). To facilitate the understanding of these methods, we include examples of how these models can be used to describe population dynamics in a simple predator-prey ecosystem or to simulate circadian rhythm changes.