Delays in biological networks and feedback design
Gene regulatory networks lie at the crux of life and, despite rapidly evolving tools in synthetic biology, our ability to replicate the robustness of these systems remains a challenge. We have not been able to fully understand and, hence, design effective feedback mechanisms. I present work towards said challenge through extensions in control and dynamical systems lending to an effective network design in the presence of delays, an adversarial facet of biology.
In this talk I focus on the role of delays in biological networks. I show how understanding the effects of delays and stochastic processes on gene expression dynamics can be used to design effective controllers for stability. First, I present a stability condition for stochastic linear systems with identically, independently, distributed stochastic delays. In an application to a single gene oscillator, I demonstrate the stabilizing effects of increasing the relative variance of the delay uncertainty. Using the insight gained from this analysis along with inspiration from nature, I present a stabilizing controller for the single gene oscillator based on adding a larger delay in parallel. A generalized delay-based feedback design approach shows this architecture to be near optimal. In summary, through a deeper understanding of the effects of delays on dynamics, I arrive at an effective stabilizing controller in a system with large delays, where traditional methods in controls cannot be used for feedback design.
Marcella M. Gomez is currently a postdoctoral fellow at the University of California, Berkeley in Electrical Engineering and Computer Science. She received her bachelors from UC Berkeley in 2008 and her PhD from the California Institute of Technology in 2015, both in Mechanical Engineering. Her research interests lie in developing synergistic methods combining control and dynamical systems with synthetic biology for the advancement in understanding and designing of complex genetic networks.