Mathematics Research

SMATA Pipeline

Often, the series of events for establishing a model, building a simulator, selecting which control strategies to implement, and validating results can be fragmented and inefficient. For this reason, we set out to provide a cohesive strategy for developing and analyzing dynamic models. The modeling pipeline my collaborators and I have developed (Synergistic Model Acquisition and Target Analysis Pipeline, referred to as the SMATA pipeline) includes equation learning (to develop network topology and regulatory functions), attractor analysis, application of control theory, simulation of suggested targets, and subsequent model modification as needed. More details on the components of this pipeline can be found in my doctoral thesis, linked below.

Stochastic Modeling

Discrete models of gene regulatory networks can incorporate stochastic processes depending on the update scheme used. Synchronous update schemes produce deterministic dynamics, in which all nodes are updated simultaneously. In contrast, asynchronous update schemes produce stochastic dynamics, where a randomly selected node is updated at each time step. Within the stochastic discrete dynamical systems (SDDS) framework, separate propensities are defined for state transitions that increase or decrease node activity (e.g., OFF to ON versus ON to OFF). This framework leverages Markov chain theory to study long-term system behavior. These propensities serve as parameters governing node and pathway activation or deactivation, providing a biologically interpretable mechanism for modeling regulatory dynamics.

(Cancer) Systems Biology 

Systems biology, particularly in the context of cancer, is an increasingly important field that requires multidisciplinary collaboration to achieve a holistic understanding of complex biological systems. Rather than relying solely on traditional experimental approaches in vivo or in vitro, this field leverages in silico models informed by clinical data and prior literature to study system-level behavior and generate testable hypotheses. There are a wide range of mathematical frameworks available to construct such models, often classified by how they represent time and population states. Continuous population models with continuous time include ordinary differential equations, while discrete population models with continuous time include stochastic approaches such as the Gillespie algorithm. Discrete population models with discrete time include Boolean networks, logical models, and their stochastic counterparts. These approaches enable the integration of interactions across multiple biological scales, allowing for the simulation of clinically relevant spatiotemporal dynamics and the evaluation of therapeutic intervention strategies.

In cancer systems biology specifically, these models are used to uncover general principles of tumor progression and to identify potential targets for intervention. When combined with patient-derived data and modern control techniques, in silico models have the potential to predict clinically relevant endpoints and optimize treatment strategies. However, predictive models remain limited, in part due to data availability and the inherent complexity of the system. A key limitation of many existing models is their focus on single-cell type dynamics, often neglecting interactions between cancer cells and their local microenvironment. It is well established that the tumor microenvironment plays a critical role in regulating cancer cell behavior, and models that omit these interactions may lead to incomplete or confounded conclusions. Additionally, although recent efforts have expanded toward multiscale modeling, reconciling dynamics across varying temporal and spatial scales remains a significant challenge. While multiscale models may offer more realistic representations, control methods that directly apply to such systems are still limited. As a result, discrete-state models (e.g., Boolean networks) are often used as a mechanistic and computationally tractable alternative. These models avoid extensive parameter estimation while still capturing key system dynamics, making them particularly useful for studying complex regulatory networks in cancer.