Emphasis: Mathematical Biology, Advisor: Sam Walcott (WPI)
Most broadly, I'm interested in using mathematical tools to answer compelling about biology. My Ph.D. research has focused on developing a theory of muscle contraction that is able to replicate muscle measurements from the single molecule to whole-muscle levels. In the future, I hope to extend my quantitative skills to a wide range of biological applications, specifically with a focus on using mathematics to connect small scale mechanisms to larger biological function.
A summary of my past and current research is detailed below.
Biological Background and Relevance
Muscle contraction is a fundamental biological process that drives essential processes from heart contraction to locomotion. Some muscle types, like those in the heart and lungs, perform functions that are vital to sustain life, and thus muscular fatigue can cause devastating effects.
At the molecular level, muscle contraction is a result of an ATP-dependent interaction between two proteins, actin and myosin. These micro-level interactions scale up to cause changes at the sub-cellular and cellular levels, resulting in what we know as muscle contraction. The field of muscle contraction is well-studied experimentally, however there is still much that is unknown about the mechanisms behind contraction. In particular, developing a comprehensive theory of muscle contraction is challenging, given that there is unique behavior at each size scale. To have a complete understanding of muscle contraction, we must successfully model the connections across these scales.
Figure 1: Sketch illustrating the various size scales in the physiology of muscle. My modeling work is focused at the level of actin and myosin, with emphasis on developing a model that scales to the larger fiber level.
Molecular Mechanism for Muscle Fatigue
In collaboration with the Debold Lab (University of Massachusetts, Amherst)
There are likely many contributing factors that play a role in fatigue, including calcium dynamics, activation and regulation of contraction, molecular level effects, and more. It has been shown experimentally that these agents of fatigue include acidosis and increase phosphate (Pi) levels, which have been linked with loss of contractile function in muscle fibers (Nelson et al 2014, Debold et al 2011, Pate et al 1995). However, the exact mechanisms behind how these factors affect myosin's interaction with actin remain unclear, in part because the individual effects of Pi and pH are unique to each size scale. For example, single molecule measurements show pH, but no Pi-dependence (Debold et al 2008). Larger ensembles of myosin experience a decrease in actin speed with acidosis, but this effect is partially reversed by increased Pi levels (Debold et al 2011). In fatigued fibers, a decrease in pH and an increase in Pi occur simultaneously, and thus we must develop a model that captures these concurrent effects.
With this project, I developed a minimal mathematical model of the actomyosin interaction under conditions of acidosis and high phosphate that accurately predicts cellular level measurements of fatigue. Further information and full references can be found in Jarvis et al (2018).
Effect of Weakly-Bound Cross-Bridges in Modeling Muscle Measurements
In collaboration with the Swank Lab (Rensselaer Polytechnic Institute)
Muscle measurements of the actomyosin interaction are well-described by a four-state mechanochemical model which includes two bound states, where myosin and actin are actively producing force, and two unbound states, where myosin and actin are not interacting (Walcott et al 2012). Fiber level measurements, however, suggest there is another weakly-bound interaction between actin and myosin. Given this discrepancy across scales, it is of interest to explore this weakly-bound actomyosin interaction.
Additionally, muscle fibers elicit a complex force response to a quick stretch, and a simple four-state model is unable to reproduce the unique behavior. Experimentally, when muscle fibers are activated, held isometrically, and then stretched a rapid small amplitude stretch, the force response can be described by four phases. First, there is a peak in force with stretch (phase I), followed by a rapid decay in force (phase II), a delayed increase in force (phase III), and a slower recovery period (phase IV). Phase III of this response is alternatively known as stretch-activation, and the molecular mechanism of this phenomenon is unknown.
With this work, I aim to understand the necessity of this weakly-bound state in consistently modeling muscle measurements across scales, as well as the overall effect of weak binding at the cellular level of muscle contraction.