Reaction Network Dynamics

One of my favorite pieces is "Can a Biologist Fix a Radio?"  In it, Lazebnik suggests that interactions in biological systems are just as important as the components themselves when trying to understand the system as a whole. Cells operate far from equilibrium - oftentimes they need the capacity to adapt to signals to maintain homeostasis over time. This is much easier to understand as a consequence of dynamic interacting components rather than an outcome of any single component. We can formally analyze these interactions and their dynamics to develop an understanding of the "decision-making" processes of cells. These formalizations may not be 100% accurate, but as George Box said, "all models are wrong, but some are useful."

In my work, I tend to think of differential equations as a formal description of the dynamics of interacting components. Interestingly, without even invoking exotic regulatory mechanisms, just a few interacting molecules can accomplish potentially useful dynamics. One of the core model behaviors that has been well described using this approach is that of biochemical adaptation. 

Biochemical adaptation occurs when a signaling system responds transiently to a perturbation, but returns to a baseline state. It enables a system to respond to changes in an input rather than in the absolute magnitude of the input. One familiar example of this is the human visual system. When we move into brighter or darker environments, our visual sensitivity adapts to the new environment. This enables us to distinguish light and dark objects in areas with different lighting. 

In cells, adaptation is especially associated with bacterial chemotaxis. This enables cells to read whether the local concentration of sensed molecules is increasing or decreasing over time. If the molecule is an attractant like a sugar, the cells "tumble" less frequently when the concentration is rising. This causes them to randomly reorient less frequently, causing them to take advantage of correct guesses. 

How do the cells accomplish this? And how hard is it to design a biochemical circuit capable of adaptation? This is a great place to start playing around with our model "radio" to understand how the interacting parts can achieve our behavior of interest. Ma et al. took a computational screening approach to this question. They asked, "what if we modeled the biochemical dynamics of many different three component systems? Can we discover principles underlying the rare three component systems that can achieve adaptation?" 

For a project in a graduate course at the University of Arizona in 2016 or so (just before starting my PhD at UCSF), I dove into the Ma paper and reproduced many of their results here.