Computational Molecular Biology 2024, Vol.14, No.2, 45-53 http://bioscipublisher.com/index.php/cmb 47 3.2 Agent-based modeling 3.2.1 Principles and applications Agent-based modeling (ABM) is a flexible computational approach used to simulate the interactions of individual agents within a system, capturing the emergent behavior of complex biological networks. ABMs are particularly useful in fields ranging from molecular biology to ecology, where they can model phenomena such as cell migration, molecular dynamics, and disease spread (Hinkelmann et al., 2010; Nardini et al., 2020). These models are typically specified through protocols like the ODD protocol, which standardizes model descriptions and facilitates their analysis (Grob et al., 2019). 3.2.2 Strengths and limitations The strengths of ABM include its ability to model heterogeneous agents and capture stochastic behaviors, making it suitable for simulating real-world biological systems. However, ABMs often require extensive computational resources due to their complexity and the need for numerous simulations to explore parameter spaces. This computational demand can be mitigated by using neural networks to emulate ABMs, significantly improving efficiency while maintaining accuracy (Wang et al., 2019). Despite these advancements, challenges remain in accurately predicting model dynamics in certain parameter regimes, which can sometimes be addressed by integrating differential equation models learned from ABM simulations (Nardini et al., 2020). 3.2.3 Case studies in biological systems Several case studies highlight the application of ABM in biological systems. For example, ABMs have been used to model cell biology experiments, such as birth-death-migration processes, and epidemiological models like the susceptible-infected-recovered (SIR) model. These studies demonstrate the utility of ABM in predicting system dynamics and exploring biological phenomena. Additionally, the integration of ABM with other computational frameworks, such as equation learning, has shown promise in enhancing the predictive power and applicability of these models in various biological contexts. 3.3 Differential equation-based approaches Differential equation-based approaches are fundamental in modeling the dynamic behavior of biological networks. These methods use mathematical equations to describe the rate of change of system variables over time, providing insights into the underlying mechanisms of biological processes. For instance, control-theoretic approaches using differential equations have been applied to drug delivery systems, while other methods have been used to infer biochemical network dynamics and predict system behavior under different conditions (Mochizuki, 2016). Additionally, multi-scale probabilistic models, such as ProbRules, combine differential equations with logical rules to represent network dynamics across different scales, offering robust predictions of gene expression and molecular interactions (Grob et al., 2019). These approaches are crucial for understanding the complex interactions within biological networks and developing effective interventions. 4 Dynamic Modeling of Gene Regulatory Networks 4.1 Boolean networks 4.1.1 Basic concepts and applications Boolean networks are a fundamental approach to modeling gene regulatory networks (GRNs) due to their simplicity and intuitive nature. They represent genes as nodes and regulatory interactions as edges, with each gene being in one of two states: active or inactive. This binary representation allows for the construction of dynamic models that can predict the behavior of genetic networks under various conditions. Boolean networks are particularly useful for understanding the overall structure and dynamics of GRNs, making them a popular choice for initial modeling efforts (Saadat and Albert, 2013; Tyson et al., 2019). 4.1.2 Modeling gene regulation The process of modeling gene regulation using Boolean networks involves several key steps. First, experimental data is used to infer the network structure, identifying which genes regulate which others. This is followed by the application of graph-theoretical measures to analyze the network's properties. The network is then converted into a
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