My research interests lie in mathematical modeling of biological processes. I use asymptotic analysis and perturbation theory to better understand biochemical processes. My projects include the following:
Hydraulic Conductance: This project sought a better understanding of the mechanisms by which hydraulic transport of water experiences resistance in bromeliads. This work, in collaboration with Professor Gretchen North at Occidental College uses a differential equation model to separate overall conductance from individual conductances in the axial (through the xylem) and radial (through intracellular space) directions. Future direction of this work seeks to better understand the effect of shade and light on the properties of hydraulic transport.
Competitive Binding: Comparison of wild-type to mutant mitochrondial DNA may give insight to pathology. Here, we worked within the framework of a competitive binding model where wild-type and mutant DNA area allowed to bind in real-time to a microarray. Exploration of different limits of the general mathematical model are useful in building intuition for mathematical approximation and reduction.
Gastric Acid Regulation: My dissertation was an investigation of acid regulation in the stomach. This research addressed the question of how acid levels are maintained across a relatively thin mucus layer (about 500 microns) at such a steep gradient (pH 2.0 to pH 7.0, five orders of magnitude in concentration). In addition, this work investigated the mechanism by which gastric acid is transported from its point of production (in the gastric pits) across the mucus layer to the lumen of the stomach, against its natural concentration gradient. This work used ordinary and partial differential equation models to investigate spatial and temporal aspects of the mechanisms regulating acid maintenance and transport, respectively.
Publications:
North GB, Lynch FH, Maharaj FD, Phillips CA, Woodside WT. “Leaf hydraulic conductance for a tank bromeliad: axial and radial pathways for moving and conserving water,” Frontiers of Plant Science: 4:78 (2013).
Lynch FH, North GB, Page BS, and Faulwell CJ. “Analysis of a Hybrid Numerical Method – Decomposing Leaf Hydraulic Conductance,” Letters in Biomathematics 5:1 (2018).
Lynch FH. “Analysis of a Mathematical Model of Real-Time Competitive Binding on a Microarray,” CODEE Journal: 15:2 (2022).
