Identifying Essential Mechanisms for Cortical Actomyosin Contractions with Computational Modeling

My dissertation work centered around how filamentous actin (f-actin, red rods in the above image) was organized by non-muscle myosin II (NMM II, green circles) within cells (left-hand column) to lead to cellular shape changes over the course of development (center column), which resulted in highly organized tissues for organ development (right-hand column). I approached this project with experimental studies in quantifying durations and locations of actin organizations (to a mathematician they looked like contractions, so the engineer in me needed to determine forces and mechanics in order to conclude they were contractions), and developing mathematical models in MATLAB and image analysis techniques in ImageJ to simulate emergent actomyosin structures.

There were multiple tenants of my dissertation work, all of which have been published, but I'll highlight the most interesting ones. First, developing an emergent, agent-based model for the interaction of rod-like f-actin and spring-like NMM II in MATLAB, then creating time-lapses in ImageJ that I could analyze with image analysis techniques that could be applied to experimental images. The interesting phenomena that emerged was the prevalence of f-actin to organize into aster structures.

Through a thorough parametric analysis, I was able to destroy, bolster, or rescue the aster morphology of the model by affecting model parameters for f-actin or NMM II that mimic drug studies previously done in the lab on live cells.

Another project, in collaboration with Adam Martin's group at MIT, looked at how forces present in the cell could alter the emergent morphology from the model. Our research questions centered around the cylindrical shape of the Drosophila embryo and an emergent strip structure of NMM II versus spherical embryo mutants with a ring-like structure of NMM II. We hypothesized that there were isotopic forces in the tissue for the spherical embryos versus anisotropic forces in the wild type, cylindrical embryos. Through adding in force "transferring" f-actin to the model, we were able to simulate and verify that isotropic conditions resulted in a ring organization of NMM II whereas anisotropic conditions resulted in a strip organization of NMM II.

I built on the model to consider roles of different actin binding proteins (such as alpha actinin) to try to produce highly aligned and bundled groups of f-actin, but found that additional assumptions or elements would be needed in the model to capture this type of morphology.

I used image analysis techniques to quantify the locations and durations of actomyosin puncta in the epithelial layer of Xenopus laevis embryos when subjected to different temperatures to discover that at lower temperature cells exhibit longer duration contractions but also bursts of short duration contracts, versus shorter contractions at higher temperatures. We hypothesized that the viscoelasticity of the tissue changes with temperature changes resulting in the need for short bursts of contractions in addition to the longer duration contractions when subjected to colder temperatures. Developmentally, from a macro scale, Xenopus laevis development speeds up as temperature increases, leading to a nice benefit from the biology side where you can "time" the stage of the embryo based on the temperature in the incubator.