Classical thermodynamics is aimed at quantifying the efficiency of thermodynamic engines by bounding the maximal amount of mechanical energy produced compared to the amount of heat required under quasi-static operation. While this was accomplished early on, by Carnot and Clausius, the more practical problem of quantifying limits of output power remained elusive due to the fact that quasi-static processes require infinitely slow cycling, resulting in a vanishing power. Recent insights, drawn from stochastic thermodynamics, bridge the gap between theory and practice by presenting fresh approaches that lead to general laws applicable to the non-equilibrium system. Remarkably, the problem of minimizing dissipation over a finite time window can be expressed as a stochastic control problem leading to physically meaningful expressions for the dissipation cost in thermodynamic engines.

Building on the framework of stochastic thermodynamics, we derive bounds on the maximal power that can be drawn by cycling an overdamped ensemble of particles via a time-varying potential while alternating contact with heat baths of different temperature (Tc cold, and Th hot). The previous work focused on the setting where the potential is quadratic andthe distributions are Gaussian. Our analysis relaxes this assumption and asks about fundamental bounds on the power under arbitrary distribution. Specifically, first by casting the optimization problem of the power into the Benamou-Brenier formulated Optimal mass transport problem, we show that the power output is bounded by the Fisher information of the boundary distribution, which can become unbounded with complicated and irregular control. However, it is unreasonable to expect technological solutions to such demands, and therefore, a constraint on the complexity of the potential seems meaningful. Assuming a suitable bound M on the spatial gradient of the controlling potential, we show that the maximal achievable power is bounded by M/8(Th/Tc-1). Moreover, we show that this bound can be reached to within a factor of (Th/Tc-1)/(Th/Tc+1) by operating the cyclic thermodynamic process with a quadratic potential.

While the majority of works in the literature are concerned with thermodynamic engines operating in the setting of Carnot's cyclic contact with alternating heat baths, the natural processes in living organisms do not follow this setting. Instead, it is the periodic fluctuations in chemical concentrations in conjunction with the variability of electrochemical potentials that provide the universal source of cellular energy. Thus, energy exchange is often mediated by continuous processes and energy differentials, whereas the Carnot cycle reflects the switching mechanics of an idealized engine. We herein propose to consider thermodynamic processes driven by a heat bath with periodic and continuous temperature profile, and study questions of maximal power and efficiency at maximal power. Our results state that themaximal power satisfies a bound proportional to the average fluctuations in the temperature profile. Moreover, we show the surprising result that the efficiency at maximal power does not depend on the specific temperature profile, only the maximum and minimum.

The zinc finger protein Tristetraprolin (TTP) promotes translation repression and degradation of mRNAs containing AU-rich elements (AREs). While much attention has been directed towards understanding the decay process and the machinery involved, the translation repression role of TTP has remained poorly understood. My thesis research identified the cap-binding translation repression 4EHP-GYF2 complex as a co-factor of TTP. Immunoprecipitation and in vitro pulldown assays demonstrate that TTP associates with the 4EHP-GYF2 complex via direct interaction with GYF2, and mutational analyses show that this interaction occurs via conserved tetraproline motifs of TTP. Mutant TTP with diminished 4EHP-GYF2 binding is impaired in its ability to repress a luciferase reporter ARE-mRNA. 4ehp knockout mouse embryonic fibroblasts (MEFs) display increased induction and slower turnover of TTP target mRNAs as compared to wild-type MEFs. This work highlights the function of the conserved tetraproline motifs of TTP and identifies 4EHP-GYF2 as a co-factor in translational repression and mRNA decay by TTP.

The human genome encodes for two TTP homologs, BRF1 and BRF2, both of which are capable of ARE binding and decay activation. I observed that TTP family proteins are differentially regulated during serum-activated G0-G1-S transition in NIH 3T3 cells. The G0-G1-S cell cycle transition is regulated at multiple levels to avoid erroneous or mistimed cell proliferation. Transition over the G0-G1-S cell cycle requires repression of Retinoblastoma (RB) proteins, which are central components of the CDK-RB-E2F checkpoint pathway controlling in this transition. I identified ARE-containing Rb, Rbl1 and Rbl2 mRNAs encoding retinoblastoma proteins as targets of degradation by TTP family proteins. Depletion of TTP family proteins results in reduced expression of E2F transcription targets, and slower transition out of quiescence compared to control conditions. Together, this work demonstrates the involvement of mRNA decay in cell cycle progression.