Beyond the two-state model of switching in biology and computation

Abstract

The thesis presents various perspectives on physical and biological computation. Our fundamental object of study in both these contexts is the notion of switching/erasing a bit. In a physical context, a bit is represented by a particle in a double well, whose dynamics is governed by the Langevin equation. We define the notions of reliability and erasing time-scales in addition to the work required to erase a bit for a given family of control protocols. We call bits “optimal” if they meet the required reliability and erasing time requirements with minimal work cost. We find that optimal bits always saturate the erasing time requirement, but may not saturate the reliability time requirement. This allows us to eliminate several regions of parameter space as sub-optimal. In a biological context, our bits are represented by substrates that are acted upon by catalytic enzymes. We define retroactivity as the back-signal propagated by the downstream system when connected to the upstream system. We analyse certain upstream systems that can help mitigate retroactivity. However, these systems require a substantial pool of resources and are therefore not optimal. As a consequence, we turn our attention to insulating networks called push-pull motifs. We find that high rates of energy consumption are not essential to alleviate retroactivity in push-pull motifs; all we need is to couple weakly to the upstream system. However, this approach is not resilient to cross-talk caused by leak reactions in the circuit. Next, we consider a single enzyme-substrate reaction and analyse its mechanism. Our system has two intermediate states (enzyme-substrate complexes). Our main question is “How should we choose binding energies of the intermediates to minimize sequestra- tion of substrates (retroactivity), whilst maintaining a minimum flux at steady-state?”. Choosing very low binding energies increases retroactivity since the system spends a considerable proportion of time in the intermediate states. Choosing binding energies that are very high reduces retroactivity, but hinders the progress of the reaction. As a result, we find that the the optimal binding energies are both moderate, and indeed tuned with each other. In particular, their difference is related to the free energy difference between the products and reactants.