Krešimir Josić

Bionote:

Krešimir Josić is currently John and Rebecca Moores Professor of Mathematics in the University of Houston. He is an applied mathematician who works closely with experimental biologists to understand how the structure of neural and genetic circuits is related to their function. His background is in the theoretical and computational analysis of stochastic biological systems. He uses mathematical and computational modeling to provide a mechanistic understanding of the dynamical patterns in biological systems observed in vivo and in vitro. Prof. Josić is the recipient of several awards, including a Simons Foundation Fellowship, and the Bellman Prize. He is on the editorial boards of the journals SIAM Dynamical Systems, SIAM Review, and Mathematical Biosciences.  He was the chair of the SIAM Activity Group on the Life Sciences from 2021 until 2023.

The Spatio-Temporal Dynamics of Synthetic Microbial Consortia

Abstract

Modeling is essential in the design of genetic circuits with desired properties. I will review several examples where mathematical models have been central to the development and understanding of the dynamic of synthetic organisms. I will start with a discussion of synthetic bacterial consortia that exhibit emergent oscillatory behavior - when co-cultured, the interaction between two bacterial strains results in population-level transcriptional oscillations. The spatio-temporal dynamics of such consortia, including synchrony between distant parts of the population, depend sensitively on the architecture of the underlying genetic circuits. I will then describe how oscillations, and other spatiotemporal patterns can arise in consortia of cells that individually exhibit bistable dynamics. I will show how simplified mathematical models can help us understand how order emerges in these systems, how robust oscillations and other patterns can arise, and how they are maintained. 

Bayesian Inference of Biochemical Reaction Rates 

Abstract

Parameter inference using experimental observations of biochemical reaction processes is a key problem in systems biology.  However, biochemical data are intrinsically stochastic, and observations are noisy. I will describe different Bayesian approaches that can be used to infer rate parameters in such situations. While conceptually straightforward, the main difficulty in implementing such methods is the need for the numerical computation of high-dimensional integrals to find the estimates of interest. I will describe how Markov Chain Monte Carlo (MCMC) methods can be used to achieve this.  I will also briefly describe approximate Bayesian methods, and Hamiltonian Monte Carlo techniques. Experimental data is frequently obtained using discrete-time sampling systems. This means that we can at best observe the state of the system at discrete intervals, and the exact timing of reactions is unknown.  This provides a challenge to a direct implementation of classical methods.  I will discuss algorithms that can be applied in such situations.

I will provide Python code to both generate synthetic time series of some simple biochemical reaction processes, as well as implement the different inference techniques described in the lecture.