MBioTS Projects and Mentors

Species living in the natural world experience complex, spatially-structured environments. From bacteria growing and moving around in a small chunk of soil, to gorillas living and interacting in a montane cloud forest, organisms living in structured environments interact more often with other individuals that are nearby and may experience a range of different conditions depending on their specific location within their habitat. In this project, the biological members will use microbial experiments to quantify the effects of spatial structure and heterogeneity on ecological and evolutionary dynamics. Data from experiments will be utilized by the mathematical members to both formulate and calibrate mathematical models of bacterial movement. Evolutionary changes will be simulated by manipulating growth rates and diffusion coefficients in a time dependent manner, with the goal of comparing experimental results with those in the simulated environment. The proposed microbial experimental set up, along with simulations, will be used to gain insight into the impacts of environmental heterogeneity on invasion dynamics.

Cell migration plays a critical role in a number of biological processes such as embryonic development, wound healing, and immune response. Altered cell movement can also be characteristic of pathological conditions, for example, cancer cells invasion to healthy tissue. Motility is determined by both properties of the cells and the extracellular environment. Traditional assays struggle with evaluating cell phenotypes over time and correlating time-dependent responses with changes in the extracellular environment. An alternate approach is to track the dynamics of live cells through time-lapse imaging and utilize knowledge based data-driven modeling to understand the individual and collective behavior of cells at high spatio-temporal precision.   Biological members will be involved in image acquisition and analysis of time-lapse images of cultured cells.  Mathematical members will utilize both mechanistic principles and individual cell data to discover interaction rules in many-particle biological systems that depend on both local interactions and environmental factors.  A main goal will be to use both mathematical modeling and learning techniques to understand fundamental scientific principles by which cells interact, and how this interaction depends on the local microenvironment.

Repeating patterns, such as hair follicles and bristles, are important for epithelia that sense the environment. Optimized organization contributes to normal tissue function, and can give animals spatially mapped input of environmental stimuli. Although many local signaling mechanisms that drive the formation of repeating patterns are understood, how these local signals upscale into tissue-wide patterns remains unclear. A genetically tractable system for the study of repeating patterns are the sensory bristles in the fruit fly Drosophila melanogaster. In this project, biological members will work to generate in vivo confocal imaging data of the developing spot pattern, as well as generate pupae that express RNAi targeting modiers in the dorsal thorax. Students will sort pupae by genotype using visible markers, age to the appropriate stage, and prepare samples for live imaging on a confocal microscope. Mathematical members will be responsible for implementing clustering algorithms to quantify bristle pattern data and detect pattern differences. Repeated spot patterns will be characterized based on three measures of spatial distribution, relative sensory area, relative cluster distance and relative cluster size. By combining these measures to define a sensory pattern score, the team member will test the efficacy of this sensory pattern score using data on fully developed sensory bristle patterns from the fruit flies. These scores will give precise quantitative measures for comparison between fruit flies with different gene knockdowns throughout different stages of development, and allow for a better understanding of the processes and mechanisms driving repeated pattern formation in this system.

An important component of research in mathematical biology relies on the acquisition, analysis, and integration of existing publicly available data into mathematical models. This project aims to introduce a team to utilizing publicly available data sets which would otherwise be impossible to collect during a 10-week program. Members will use open-source clinical pharmaceutical data to retrieve clinical data and employ both statistical and theoretical models to test hypotheses. Biological members will focus on understanding the details of the clinical data set and the approaches used to generate these data. A possible data set is published data from a clinical trial studying the efficacy of adjuvant chemotherapy in combination with a monoclonal antibody for resected non-small-cell lung cancer (NSCLC) patients. Here biological team members will obtain a detailed understanding of the mechanisms of action of the therapies, so that the team may hypothesize causes for the improved efficacy of combination therapies. The biological team will also be responsible for retrieving,processing, and analyzing the data set. The mathematical members will utilize the retrieved and processed data through information visualization. Qualitative patterns will guide the construction of models, and quantitative data will be used to identify model-specific parameters and possibly their distributions. The team will employ validated models to both evaluate previous as well as propose novel hypotheses; in the NSCLC case, we may hypothesize mechanisms as to the reason bevacizumab is ineffective when applied in early-stage disease, but improves outcome with respect to disease-free progression in advanced-stage NSCLC.