Characterizing emergent properties of immunological systems with multi- cellular rule-based computational modeling Arvind K. Chavali 1* , Erwin P. Gianchandani 1* , Kenneth S. Tung 2 , Michael B. Lawrence 1 , Shayn M. Peirce 1 and Jason A. Papin 1 1 Department of Biomedical Engineering, University of Virginia, Box 800759, Health System, Charlottesville, VA 22908, USA 2 Department of Pathology, University of Virginia, Box 800214, Health System, Charlottesville, VA 22908, USA The immune system is comprised of numerous com- ponents that interact with one another to give rise to phenotypic behaviors that are sometimes unexpected. Agent-based modeling (ABM) and cellular automata (CA) belong to a class of discrete mathematical approaches in which autonomous entities detect local information and act over time according to logical rules. The power of this approach lies in the emergence of behavior that arises from interactions between agents, which would otherwise be impossible to know a priori. Recent work exploring the immune system with ABM and CA has revealed novel insights into immunological processes. Here, we summarize these applications to immunology and, particularly, how ABM can help for- mulate hypotheses that might drive further experimen- tal investigations of disease mechanisms. Introduction In recent years, computational analysis, coupled with high-throughput experimental data, has facilitated the study of complex biological phenomena [1]. In particular, systems biology-based approaches are enabling the syn- thesis of vast amounts of literature through the construc- tion of computational models (see Glossary) for probing biological function [2]. Examples of these approaches in- clude genome-scale reconstructions of metabolic networks [3], differential equation-based kinetic models of signaling networks [4] and statistical inference models of cellular network organization [5]. Once constructed and validated, models can be perturbed in different ways (e.g. inputs can be altered to mimic different environments) to facilitate exploration of network features [6]. These in silico (or dry- laboratory) experiments are complementary to traditional wet-laboratory experimental approaches [7]. Moreover, computational modeling, which often requires less time and cost, aids in facilitating experiments and/or measure- ments that can be infeasible in a laboratory setting, all the while generating novel insights and hypotheses for further research and development. Review Glossary Adaptive (adapting): a property of an agent or system that exhibits behavioral changes (e.g. in response to perturbations to its surrounding environment); to display features of memory. Agent: a discrete unit with defined rules governing its behavior or response; agents can interact with other agents and their surrounding environment. Agent-based modeling (ABM): a modeling framework simulating systems in discrete time and space; agent-based models include agents, rules, time steps and environments; agents can be mobile and are characterized by asynchro- nous behaviors, that is, they update their states independently of one another. Autonomous: acting independently of others. Cellular automata (CA): a related approach to ABM; also simulates systems in discrete time and space; cells or entities are fixed in position (immobile) and change state over a time period; synchronous updating of agent states is applied in classical CA. It is important to note that the word ‘cellular’ in CA does not imply a biological cell, but, rather, signifies a discrete entity or element. Complex system: a system comprised of numerous interconnected parts without a central organizing structure; associations or interactions between parts lead to global behaviors; dynamic and non-linear. Computational model: general term used for describing a computer program that simulates a natural phenomenon such as a biological process. Continuous: describes transitions between an infinite number of states; non- discrete. Deterministic: lacking randomness; an agent or system whose future state is fully determined by the current state in which it lies. Discrete (discretization): describes transitions between a countable number of states; a set of isolated points in time and/or space; non-continuous. Dry-lab vs. Wet-lab: terms used for differentiating between in silico computa- tional work and classical experimental work with, and handling of, biological samples. Emergence: the global behaviors or patterns that arise through ‘self-organiza- tion’ and that could not have otherwise been characterized a priori. Environment: the topology of the simulation or ‘world’ space; can be 1D, 2D or 3D. Identifiable: unique and having own history of interactions, activities or states. IF-THEN-ELSE: conditional programming statement. Multi-cellular: related to a property of a biological system consisting of two or more cells. Non-linear: as in a non-linear system, in which the output does not scale according to the behaviors of components that comprise the system. Rules (rule-set): a set of logical decision heuristics which govern agents’ activities; literature-derived or based on qualitative observations of the system. Self-organizing (self-organization): the ability to exhibit organization that drives phenotype without a global organizing structure; based on component interactions of a system. Sensitivity analysis: related to quantifying the relationship between variations in input parameters and resulting effects on model outputs. Stochastic (stochasticity): random; a process that is driven by probabilistic outcomes. von Neumann or Moore neighborhoods: environment in classical 2D square- lattice CA models; von Neumann scheme refers to grid elements orthogonal (North, South, East and West) from the element of interest; Moore scheme refers to all eight grid elements (North, South, East, West, Northwest, Northeast, Southwest and Southeast) surrounding the element of interest. Corresponding author: Papin, J.A. (papin@virginia.edu) * These authors contributed equally to this article. 1471-4906/$ – see front matter ß 2008 Elsevier Ltd. All rights reserved. doi:10.1016/j.it.2008.08.006 Available online 27 October 2008 589