The environment within living cells is incredibly noisy with biochemical species randomly bumping and reacting with each other. This inherent probabilistic nature along with low population counts of cellular species creates considerable stochastic fluctuations in protein copy numbers over time inside individual cells. Increasing evidence suggests that this stochastic dynamics plays important functional roles within cells. Moreover, many diseased states have been attributed to elevated noise levels in specific proteins. Stochastic analysis of biochemical processes relies heavily on Monte Carlo simulation techniques that come at a significant computational cost. In addition, these techniques do not provide closed-form solutions that enable a systematic understanding of how stochastic variability is regulated in these systems. This project will overcome these challenges by developing computationally tractable methodologies based on moment closure schemes for studying stochastic dynamics of gene regulatory networks. Various analytical approximations that relate statistical properties of the system to biologically relevant parameters will be investigated. Far from being a hindrance, signatures of protein noise levels can be informative of the underlying gene network topology. This project will build mathematical techniques that harness quantitative measurements of stochasticity in protein levels for inferring regulatory interactions between genes and proteins.
Biological data is being collected at a rapid rate and innovative methods for analyzing data are critically needed. Advances in experimental techniques allow measurements of fluctuations in protein levels in individual cells, which carry useful information to probe interactions between genes and proteins. In this project, tools exploiting statistical properties of these fluctuations to characterize cellular processes will be developed and will be made available for the broad scientific community to use. Stochastic variability in protein levels has been implicated in bacterial antibiotic resistance, mutation-independent selection of tumors and driving pathogenic human viruses, e.g., HIV, into a drug-resistant dormant state. This research will improve the characterizations of gene networks underlying these disease systems and thus this research will have a broader impact on medicine. Many of the results of this project will be incorporated into various courses offered across different departments providing interdisciplinary training and research experience to students at the interface of mathematical and biological sciences.
