Research

To realize the promise of personalized medicine, modelers need to be able to integrate different types of data collected from a patient into a computational framework that enables decision-making about optimal interventions to help the patient to either maintain or regain health. A fundamental problem that currently does not have a widely applicable solution is how to calibrate a generic computational model of human biology to a given patient at a given time. In joint work with members of the Laboratory for Systems Medicine and the Mehrad Lab at the University of Florida,  I am working on data assimilation algorithms to address this issue.

In a recent manuscript [Knapp et al 2025], my coauthors and I present an algorithm to address the problem above for the agent-based model framework, commonly used to capture stochastic and spatially heterogeneous biological processes, such as tumor growth or immune system dynamics. This algorithm addresses the key challenge of bridging the gap between the clinically measurable quantities (the macro-state) and the fine-grained data at different physiological scales which are required to run the model (the micro-state).

The differentiation of stem cell colonies into specified tissue types is possible through local and long-distance intercellular communication; however, it is unclear which local mechanisms take priority in context-specific situations as the fates of cell colonies are established. In joint work with Elena Dimitrova, Melissa Kemp, Eunbi Park, and Jack Toppen, we consider human induced pluripotent stem cells (hiPSCs) whose therapeutic potential arises from their ability to differentiate into all germ layers. Prior work in the literature [Guye et al 2016] suggests that both cell-autonomous and non-autonomous (e.g. positional) mechanisms determine cell fate during the differentiation of hiSPCs, producing patterns and other system-level features in the process.

Informed by experimental data, we have focused our work on three interrelated projects:

• The development of a general-use, computational pipeline to quantitatively examine the multicellular organization and pattern formation of hiPSC colonies using topological data analysis [Hartsock et al 2025].

• The development of an agent-based model (ABM) of early hiPSC differentiation in which agents (i.e. cells) are equipped with a Boolean network model of a target pathway serving as a potential mechanism for intercellular communication [Park et al 2025, in preparation].

• The generalization of a mathematical framework [Yereniuk & Olson 2019] which formalizes ABMs for the purpose of estimating long-term behavior of biologically-inspired ABMs without simulations, specifically changes in agent population densities over time [Cruz et al 2025, in preparation].

With the above, we aim to ascertain which modes of intercellular communication determine cell fate by studying both local interactions and emergent colony behaviors.

A double occurrence word (DOW) is a word (i.e., a sequence of symbols) in which every symbol appears exactly twice. In some instances, DNA rearrangement processes can be modeled using DOWs. It was discovered that over 95% of the scrambled genome of Oxytricha trifallax could be described using the so called repeat (aa) and return (aa^R) patterns, with gaps allowed between the a's [Burns et al 2016]. A pattern is said to "appear" in a DOW w if a can be uniquely associated with a sequence of distinct symbols in w.

The proposed unscrambling process in [Burns et al 2016] involves removing repeat/return words from a given DOW one at a time; this removal process was studied formally in [Jonoska et al 2017]. In order to understand how so much scrambling may have arisen within the genome of Oxytricha trifallax, my collaborators and I studied the insertion of repeat and return words into DOWs in [Cruz et al 2020] and characterized the structure of a given DOW w which allows two distinct insertions to yield equivalent DOWs. The characterization introduces a method to generate families of words recursively.

From the molecular to the microbiological scale and beyond, the organization of elementary "building blocks" may not only be influenced by local interactions but by environmental changes and other external controls. A system of interactive molecular arrangement (SIMA) is a model which utilizes the aforementioned dynamics and is based on experimental design [Jonoska & Seeman 2015]. In this model, two types (species) of floating molecular (DNA) tiles attach to a predesigned array in an alternating manner according to an external control. The array consists of neighboring tiles which "communicate" and which are complementary to the floating tiles. The synchronous attachment of a single species of floating tiles makes the SIMA model similar to the cellular automaton (CA) model. My collaborators and I formally described the SIMA model in [Braun et al 2017] and explored some of its computational capabilities, but several questions remain unanswered.