Characterizing emergent properties of immunological systems with multi-cellular rulebased computational modeling Arvind K. Chavali, Erwin P. Gianchandani, Kenneth S. Tung, Michael B. Lawrence, Shayn M. Peirce, and Jason A. Papin : Specifics of multi-cellular rule-based computational modeling In this supplement, we describe additional details about agent-based modeling (ABM) and cellular automata (CA) approaches not presented in the manuscript. We present other important features of these modeling techniques while providing concrete immunological examples. ABM vs. classical CA: deterministic rule-sets In Box 1, we provided specific differences between ABM and CA. We mentioned that classical CA models contain deterministic rule-sets. Here, we present a related example in immunology. Specifically, in a CA model simulating human immunodeficiency virus (HIV) infection dynamics, a healthy element (representing a CD4 + T cell or monocyte) was allowed to change its state to infected stage 1 only if the healthy element had at least one infected stage 1 element in its surrounding vicinity [1]. This is an example of a deterministic rule as the new state of the element at the subsequent time-step will always be the same (for the entire duration of the simulation) if any one of the initial configurations defined by the rule-set exists at the current time-step. Furthermore, as described in Box 1, modified CA models include probabilistic rule-sets. Several immunological CA models that we catalog in Table 1 (and Supplementary Material II online) fall under the category of modified CA (see [2-6]). Model construction: defining global and local variables In Box 2, we presented an overview of steps involved in the model-building process. As part of the step involved in formulating a comprehensive rule-set during model development, global and local variables are assigned to an agent-based model. While global variables affect all compo-
nents, local variables are specific to agents or micro-compartments within the system [7,8]. For example, when simulating naïve CD4 + T cell activation in a lymph node (LN) consisting of dendritic cells (DCs) (i.e. T cells are represented as agents; DCs are stationary and part of the LN environment), the affinity of interaction between T cell receptors (TCRs) and peptide-major histocompatibility complexes (pmhcs) (on the surface of DCs) can be modeled as a global or local variable. Global control over affinity would be analogous to experimenting with C57 Black/6 (C57BL/6) mice infected with lymphocytic choriomeningitis virus (LCMV) and containing adoptively transferred TCR transgenic CD4 + T cells from SMARTA mice specific for a particular epitope of LCMV [9]. This mouse model would effectively normalize the affinity of TCR and pmhc interactions for all CD4 + SMARTA T cells. By contrast, local control over affinity in an agent-based model would provide each T cell the ability to interact with DCs with varying degrees of affinity, hence mimicking the initial endogenous CD4 + T cell response in C57BL/6 mice infected with LCMV. Model refinement: modification of rule-sets As new experimental findings are reported, rule-sets can be easily modified (following an iterative cycle of model construction/validation between computation and experiments [10,11]; see Box 2). For example, agent-based models that have characterized effector T H responses should consider the dynamics associated with the recently discovered T-helper 17 (T H 17) subtype [12,13]. Similarly, in the agent-based model of granuloma formation during Mycobacterium tuberculosis infection (see Table 1 in the manuscript), T cell movement toward granulomas was strongly correlated with granuloma size or amount of extracellular bacteria [14]. Recently, twophoton intravital microscopy demonstrated that T cells are withheld by restricted migration immediately upon entering granuloma regions [15]. Therefore, the parameter or set of parameters influencing T cell movement in the agent-based model can be updated to capture T cell dynamics around granulomas accurately and further simulate host defense mechanisms to M. tuberculosis. Importantly, however, restricted T cell migration might be an emergent behavior that is observed in the agent-based simulation. In such cases, these new experimental findings serve as validation to the agent-based model. 2
Advantages of the ABM approach: local interactions, spatial compartmentalization and resolving discrepancies in literature through systems analysis In the section titled Expanding upon features of agent-based models and in Box 3 within the manuscript, we highlight several aspects of ABM that make the approach particularly suitable for simulating immunological systems. Here we describe in greater detail a few of these advantages. First, local interactions between cells play a pivotal rule in the organization of an immune response (e.g. macrophage stimulation by T cells at peripheral sites of infection in the tissue [16]). The decision-making ability of each agent (at any given time-step) centers on the presence of other agents in the nearby vicinity and the composition of the immediate surroundings. With a discrete representation of agents or cells, reproducing local cell-cell and cell-environment interactions is possible with ABM [17]. Global emergent patterns arising as a result of the collective outcome of the decisions made by all agents following localized communication can therefore be characterized. Accounting for spatial compartmentalization with ABM is also a straightforward process. Rulesets can dictate spatial restrictions for individual agents, thereby restricting movement of agents within the simulation space. For example, the LN is divided into T cell and B cell zones with different types of cell-cell interactions occurring within each compartment and between compartments [18]. Keeping these zones spatially segregated would be crucial to reproducing the system dynamics accurately. Relaxing the assumption that cell populations at a site of infection are spatially well-mixed results in very different viral infection dynamics [19]. The complexity of the immune system, including associated processes and mechanisms, is often compounded by conflicting data [20]. A systems biology-based approach that attempts to synthesize the vast amount of literature on a particular topic and integrate heterogeneous data sets can assist in clarification of these discrepancies and lead to the formulation of new experimentally testable hypotheses [21,22]. As an example, the question of whether naïve T cells seeking cognate interactions with DCs in LNs pursue a random migration strategy or one based on chemotaxis was addressed recently using an agent-based model [23]. The analysis concluded that, to 3
increase the efficiency of T cell scanning within the LN, a random migration strategy is warranted [23]. Disadvantages of the ABM approach: overcoming computational limitations As we describe in Box 3, a limitation of computational modeling in general is that the finetuning of model parameters can be tedious if the parameter space is very large. Changing one parameter can have a drastic impact on the global properties of the entire system. Although optimization procedures have been developed to explore the parameter space efficiently [24], they are not necessarily applicable to the types of systems modeled by ABM, in which the dynamics are studied rather than particular endpoint values. Additionally, systems-level properties cannot always be described quantitatively and instead require visual characterization (e.g. the flocking behavior of birds discussed previously) [24]. Nevertheless, a method for performing sensitivity analysis, in which the parameter space of a given agent-based model is explored to quantitatively evaluate how sensitive model outputs are to variations in input parameters, was recently proposed [25]. In Box 3, we also highlighted that the ABM approach can be computationally intensive for immunological models due to large numbers of agents and rules associated with immune-related processes. A few models of immune responses have been developed using parallel computing architectures in order to increase simulation efficiency in terms of computational time and memory (e.g. PARIMM) [6,26]. In addition, it is possible to incorporate simplifying assumptions to decrease overall system complexity for better computational performance of the agent-based model [7]. Importantly, these assumptions have to be reasonable so that the system being modeled computationally is realistic and retains characteristics of the real biological system of interest. Furthermore, limitations associated with the complexity of the systems being modeled are being addressed in other disciplines such as ecology through the use of pattern-oriented modeling (POM) of agent-based systems [27]. POM is an approach in which multiple patterns present in nature serve to help define the rule-set of the agent-based model simulating the particular system 4
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