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. 2015 Nov;4(11):615-29.
doi: 10.1002/psp4.12018. Epub 2015 Nov 13.

Agent-Based Modeling in Systems Pharmacology

J Cosgrove  1 , J Butler  1 , K Alden  2 , M Read  3 , V Kumar  4 , L Cucurull-Sanchez  5 , J Timmis  6 , M Coles  7
Affiliations

Agent-Based Modeling in Systems Pharmacology

J Cosgrove et al. CPT Pharmacometrics Syst Pharmacol. 2015 Nov.

Abstract

Modeling and simulation (M&S) techniques provide a platform for knowledge integration and hypothesis testing to gain insights into biological systems that would not be possible a priori. Agent-based modeling (ABM) is an M&S technique that focuses on describing individual components rather than homogenous populations. This tutorial introduces ABM to systems pharmacologists, using relevant case studies to highlight how ABM-specific strengths have yielded success in the area of preclinical mechanistic modeling.

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Figures

Figure 1
Figure 1
Structure of an ABM: Agents (shown as blue and orange spheres) are individual entities capable of maintaining their associated attributes with respect to their local environment and governing rules. The environment in which an agent exists provides a context for their interactions. The aggregate behaviors of the agents can then lead to the emergence of complex patterns and behaviors.
Figure 2
Figure 2
Microglia modeled as agents using the UML. The modeling of microglia in ARTIMMUS. Microglia exist only in the CNS. The only MHC:peptide complex that they present is MHC‐II:MBP. This presentation requires the phagocytosis of a neuron and is probabilistic. A small proportion of microglia expresses MBP immediately, represented by λ(basal expression). This is to reflect the fact that the physiological turnover of neurons (which is not in itself represented in the domain model) will result in their phagocytosis by microglia and the presentation of MHC‐II:MBP complexes. Microglia exist in immature and mature states. While immature they are more phagocytic than when mature. Maturation occurs some time into their lifespan, represented by λ(maturation), but may also be induced through perception of a sufficient concentration of type 1 cytokine. Perception of sufficient concentration of type 1 cytokine induces TNF‐α secretion in microglia. Both immature and mature microglia are able to express MHC‐II molecules. Microglia do not exist indefinitely, and expire after some period of time, represented by λ(expire). Figure adopted from Read et al.39
Figure 3
Figure 3
The capacity for various types of model to capture spatial resolution and cellular heterogeneity: When determining the appropriate modeling technique to employ it is important to consider the spatiotemporal scales relevant to the system and the heterogeneity of the entities of interest. Ordinary Differential Equations (ODEs) and Physiologically Based Pharmacokinetic (PBPK) models cannot capture systems with explicit spatial resolution (although compartmentalized systems are possible), relying on the abstract notion of well‐mixed space. Partial Differential Equations (PDEs), and thereby, coupled systems of ODEs, are capable of spatial resolution, but to capture heterogeneous cellular phenotypes is often intractable. State‐based modeling approaches enable heterogeneous phenotypes among cell populations but cannot in themselves capture spatial resolution (although they can model multiple, spatially disconnected compartments). ABMs incorporate state‐based systems in spatial environments; as such, ABMs can capture both heterogeneous cell populations with an explicit notion of space and time.
Figure 4
Figure 4
Capturing the emergent phenomena of EAE: An expected behaviors diagram sets the research context of the ABM. This is achieved by depicting the phenomena observed in the murine EAE model, and the behaviors manifesting from cellular interactions hypothesized to be responsible for them. Figure adopted from Read et al.40
Figure 5
Figure 5
Spatial compartments within ARTIMMUS: The spatial compartments of the domain model, and the manner in which cells may migrate between them. Figure adopted from Read et al.40
Figure 6
Figure 6
In silico anti‐CD3 treatment result in a lower rate of neuronal death, but a higher number of total neurons killed for some efficacies greater than 80%: (a) EAE was induced at day 0 followed by administration of anti‐CD3 at day 4. (b) The number of neurons killed per hour. (c) Cumulative count of neurons killed for varying efficacies of anti‐CD3 treatment. 100% efficacy blocks all TCR:MHCpeptide bindings, 50% blocks half of all binding events, and 0% represents the control. Figure adopted from Read et al.41
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