Nonequilibrium Thermodynamics in Biochemical Systems and Its Application

Distilling dynamical knowledge from stochastic reaction networks

Stochastic reaction networks are widely used in the modeling of stochastic systems across diverse domains such as biology, chemistry, physics, and ecology. However, the comprehension of the dynamic behaviors inherent in stochastic reaction networks is a formidable undertaking, primarily due to the exponential growth in the number of possible states or trajectories as the state space dimension increases. In this study, we introduce a knowledge distillation method based on reinforcement learning principles, aimed at compressing the dynamical knowledge encoded in stochastic reaction networks into a singular neural network construct. The trained neural network possesses the capability to accurately predict the state conditional joint probability distribution that corresponds to the given query contexts, when prompted with rate parameters, initial conditions, and time values. This obviates the need to track the dynamical process, enabling the direct estimation of normalized state and trajectory probabilities, without necessitating the integration over the complete state space. By applying our method to representative examples, we have observed a high degree of accuracy in both multimodal and high-dimensional systems. Additionally, the trained neural network can serve as a foundational model for developing efficient algorithms for parameter inference and trajectory ensemble generation. These results collectively underscore the efficacy of our approach as a universal means of distilling knowledge from stochastic reaction networks. Importantly, our methodology also spotlights the potential utility in harnessing a singular, pretrained, large-scale model to encapsulate the solution space underpinning a wide spectrum of stochastic dynamical systems.

Theoretical Improvements in Enzyme Efficiency Associated with Noisy Rate Constants and Increased Dissipation

Previous studies have revealed the extraordinarily large catalytic efficiency of some enzymes. High catalytic proficiency is an essential accomplishment of biological evolution. Natural selection led to the increased turnover number, kcat, and enzyme efficiency, kcat/KM, of uni-uni enzymes, which convert a single substrate into a single product. We added or multiplied random noise with chosen rate constants to explore the correlation between dissipation and catalytic efficiency for ten enzymes: beta-galactosidase, glucose isomerase, β-lactamases from three bacterial strains, ketosteroid isomerase, triosephosphate isomerase, and carbonic anhydrase I, II, and T200H. Our results highlight the role of biological evolution in accelerating thermodynamic evolution. The catalytic performance of these enzymes is proportional to overall entropy production-the main parameter from irreversible thermodynamics. That parameter is also proportional to the evolutionary distance of β-lactamases PC1, RTEM, and Lac-1 when natural or artificial evolution produces the optimal or maximal possible catalytic efficiency. De novo enzyme design and attempts to speed up the rate-limiting catalytic steps may profit from the described connection between kinetics and thermodynamics.

Synergy among Pausing, Intrinsic Proofreading, and Accessory Proteins Results in Optimal Transcription Speed and Tolerable Accuracy

Cleavage of dinucleotides after the misincorporational pauses serves as a proofreading mechanism that increases transcriptional elongation accuracy. The accuracy is further improved by accessory proteins such as GreA and TFIIS. However, it is not clear why RNAP pauses and why cleavage-factor-assisted proofreading is necessary despite transcriptional errors in vitro being of the same order as those in downstream translation. Here, we developed a chemical-kinetic model that incorporates most relevant features of transcriptional proofreading and uncovers how the balance between speed and accuracy is achieved. We found that long pauses are essential for high accuracy, whereas cleavage-factor-stimulated proofreading optimizes speed. Moreover, in comparison to the cleavage of a single nucleotide or three nucleotides, RNAP backtracking and dinucleotide cleavage improve both speed and accuracy. Our results thereby show how the molecular mechanism and the kinetic parameters of the transcriptional process were evolutionarily optimized to achieve maximal speed and tolerable accuracy.

Nonequilibrium Steady State in a Large Magneto-Optical Trap

Considering light-mediated long-range interactions between cold atoms in a magneto-optical trap (MOT), we present numerical evidence of a nonequilibrium steady state (NESS) for sufficiently large number of atoms (>108). This state manifests itself as the appearance of an anisotropic distribution of velocity when a MOT approaches the threshold beyond which self-oscillating instabilities occur. Our three-dimensional (3D) spatiotemporal model with nonlocal spatial dependencies stemming from the interatomic interactions has recently been compared successfully to predict different instability thresholds and regimes in experiments with rubidium atoms. The behavior of the NESS is studied as a function of the main MOT parameters, including its spatiotemporal characteristics.

The rate of thermodynamic cost against adiabatic and nonadiabatic fluctuations of a single gene circuit in Drosophila embryos

We study the stochastic dynamics of the externally regulating　gene circuit as an example of eve-skipped gene stripe in the development of Drosophila. Three gene regulation regimes are　considered: adiabatic phase when the switching rate of the gene from the OFF to the ON state is faster than the rate of mRNA degradation; nonadiabatic phase when the switching rate from the OFF to the ON state is slower than that of the mRNA degradation; the bursting phase when the gene switching is fast and transcription is very fast, while the ON state probability is very low. We found that the rate of　thermodynamic cost quantified by the entropy production rate can suppress the fluctuations of the gene circuit. Higher(lower) rate of thermodynamic cost leads to reduced (increased) fluctuations on the number of gene products in the adiabatic (nonadiabatic) regime. We also found that higher thermodynamic cost is often required to sustain the emergence of more gene states and therefore more heterogeneity coming from genetic mutations or epigenetics. We also study the stability of the gene state using the mean first passage time from one state to another. We found the monotonic decrease in time, i.e. on the stability of the state, in the transition from the nonadiabatic to the adiabatic regimes. Therefore, as the higher rate of thermodynamic cost suppresses the fluctuations, higher stability requires higher thermodynamics cost to maintain.