Synthetic biology holds the promise of allowing us to engineer living beings. However, the underlying processes are complex. Modeling will therefore be essential in the design of genetic circuits with desired properties. I will start by reviewing examples where mathematical models helped in the development of synthetic organisms: The first is a synthetic gene circuit in Escherichia coli that exhibits robust temperature compensation – it maintains a constant period over a range of ambient temperatures. The second is a synthetic bacterial microconsortium that exhibits emergent oscillatory behavior – when co-cultured, the interaction between two bacterial strains results in population-level transcriptional oscillations. In both cases mathematical models predicted and experiments confirmed a number of properties of the systems.
Such successes are encouraging. But how far can modeling take us? I will argue that our models are still fairly coarse, and do not adequately describe important properties of genetic signaling networks. For instance, “transcriptional delay” – the delay between the start of protein production and the time a mature protein finds a downstream target – can have a significant impact on the dynamics of gene circuits. These effects can be described by reduced, non-Markovian models that are quite different from established ones. I will also discuss work with experimental collaborators to characterize the distribution of this delay.
Kresimir Josic is a Professor in the Department of Mathematics at the University of Houston. He is a member of the Mathematical Biology group, the Symmetry and Dynamics group, as well as the Center for Neuro-Engineering and Cognitive Sciences at the University of Houston, as well as the Gulf Coast Consortium for Theoretical and Computational Neurosciences. He is interested in a number of topics in applied mathematics, most of which concern applications of the theory of deterministic and stochastic dynamical systems to problems in neuroscience, systems biology and evolution. Currently Professor Josic is working on multiple projects with his students, including Quantifying the impact of correlated on the information that neural tissue carries about a stimulus.
