Mathematical Sciences: Probability and Statistics: Analysis of Stochastic Hybrid Systems with Applications to Synthetic Biology
Abstract
Stochastic Hybrid Systems (SHS) constitute an important class of mathematical models that integrate discrete stochastic events with continuous dynamics. SHS have been successfully used for modeling stochastic phenomena and uncertainty in a variety of engineering, biological and physical systems. The probability distribution function of the SHS state space is generally computed numerically by solving the corresponding Kolmogorov equations, or by running a large number of Monte Carlo simulations at a significant computational cost. Since one is often interested in only a few statistical moments (for example, means, variances, correlations, skewness, etc.), much time and effort can be saved by directly computing these moments without actually having to solve for the probability distribution function. The key goal of this proposal is to develop computationally tractable and scalable methods based on moments and characteristic functions for capturing stochastic dynamics of SHS. These tools will be used for addressing a variety of applied problem from solving stochastic optimal control problems for SHS to design of biomolecular circuits with a prescribed stochastic dynamics. The key aims can be summarized as follows: 1. Development of approximate methods based on moment closure schemes that provide efficient and accurate predictions of the time evolution of moments for any arbitrary SHS. 2. Development of methods based on semidefinite programming that provide precise error bounds between the actual and approximated moment dynamics. 3. Development of methods for predicting characteristic functions for general classes of SHS, and using them to infer probability distributions. 4. Uncovering the fundamental limits of noise suppression in protein levels through biochemically im- plemented feedback control strategies with stochastic time-delays. An important application of project results will be the emerging interdisciplinary field of Synthetic biology, where biomolecular circuits are engineered within living cells for novel defense and medical applications. Operation of these circuits inside living cells poses a unique challenge from the noisy cellular environment compounded with low-copy numbers of molecular components. The project will provide a systematic SHS framework for mechanistic modeling of the inherently nonlinear and stochastic dynamics of circuits. Such frameworks that incorporate physiological noise mechanisms in the design and analysis process are critically needed to accelerate the field of synthetic biology, leading to new control paradigms for regulating stochastic dynamics of biomolecular systems. Mathematical techniques for modeling and analyzing developed as part of this project will be converted into Matlab packages and provided as freeware on the PI s personal website. These methods will aid several ongoing projects in the lab from designing viral phage therapy to target superbugs, designing drug-dosing schedules for cancer treatment, and improving precision of projectile impact subject to environmental noise.
Document Details
- Document Type
- DoD Grant Award
- Publication Date
- Apr 22, 2019
- Source ID
- W911NF1910243
Entities
People
- Abhyudai Singh
Organizations
- Army Contracting Command
- United States Army
- University of Delaware