Nonequilibrium Thermodynamics in Biochemical Systems and Its Application

Living systems are open systems, where the laws of nonequilibrium thermodynamics play the important role. Therefore, studying living systems from a nonequilibrium thermodynamic aspect is interesting and useful. In this review, we briefly introduce the history and current development of nonequilibrium thermodynamics, especially that in biochemical systems. We first introduce historically how people realized the importance to study biological systems in the thermodynamic point of view. We then introduce the development of stochastic thermodynamics, especially three landmarks: Jarzynski equality, Crooks’ fluctuation theorem and thermodynamic uncertainty relation. We also summarize the current theoretical framework for stochastic thermodynamics in biochemical reaction networks, especially the thermodynamic concepts and instruments at nonequilibrium steady state. Finally, we show two applications and research paradigms for thermodynamic study in biological systems.     

Two-cell stochastic model of the Schlögl reaction with small diffusional coupling

We study a stochastic theory of the two-cell model of the Schlögl reaction beyond the bistability threshold. We restrict ourselves to the case of a small diffusional coupling, where inhomogeneous steady states occur, and where a nucleationlike behavior is expected. Our analysis agrees with the deterministic analysis in the thermodynamic limit, and permits to calculate the long time evolution of the probability distribution function. We compare our results with a recent Monte Carlo simulation of this problem.     

Lattice Boltzmann model for combustion and detonation

In this paper we present a lattice Boltzmann model for combustion and detonation. In this model the fluid behavior is described by a finite-difference lattice Boltzmann model by Gan et al. [Physica A, 2008, 387: 1721]. The chemical reaction is described by the Lee-Tarver model [Phys. Fluids, 1980, 23: 2362]. The reaction heat is naturally coupled with the flow behavior. Due to the separation of time scales in the chemical and thermodynamic processes, a key technique for a successful simulation is to use the operator-splitting scheme. The new model is verified and validated by well-known benchmark tests. As a specific application of the new model, we studied the simple steady detonation phenomenon. To show the merit of LB model over the traditional ones, we focus on the reaction zone to study the non-equilibrium effects. It is interesting to find that, at the von Neumann peak, the system is nearly in its thermodynamic equilibrium. At the two sides of the von Neumann peak, the system deviates from its equilibrium in opposite directions. In the front of von Neumann peak, due to the strong compression from the reaction product behind the von Neumann peak, the system experiences a sudden deviation from thermodynamic equilibrium. Behind the von Neumann peak, the release of chemical energy results in thermal expansion of the matter within the reaction zone, which drives the system to deviate the thermodynamic equilibrium in the opposite direction. From the deviation from thermodynamic equilibrium, Δ _m *, defined in this paper, one can understand more on the macroscopic effects of the system due to the deviation from its thermodynamic equilibrium.     

Theory of oxidation/reduction-induced valence transformations of metal ion dopants in oxide crystals mediated by oxide-vacancy diffusion: I. Thermodynamic analysis

We consider theoretically valence transformations of doping metal ions in oxide crystals induced by oxidation and reduction obtained by changes in the ambient oxygen partial pressure. Three types of oxygen vacancies are assumed to mediate transformations: neutral, singly ionized, and doubly ionized. We provide thermodynamic equilibrium analyses, yielding concentration relations among the oxygen vacancy, metal ions, holes and electrons as functions of the ambient oxygen pressure. The results suggest that experimental study of different species concentrations at thermodynamic equilibrium as functions of pressure and temperature should allow assessment of various reversible reaction constants controlling the process. In the Part II companion paper, the kinetic (diffusion) characteristics are considered in detail.     

柚皮苷二氢查尔酮抗氧化活性的构效关系研究

采用DPPH自由基清除实验和Materials Studio 软件中的DmoL3程序对柚皮苷二氢查尔酮的DPPH自由基清除率、几何结构和性质（振动频率、反应活性及热力学性质）进行了理论研究,得到了分子的抗氧化活性数据、稳定几何构型、各原子上的电荷分布、热力学性质、Fukui指数和前线分子轨道参数,计算结果表明柚皮苷二氢查尔酮具有较高的反应活性,分子中酚羟基上的氧原子是影响其反应活性的主要部位,也是发生亲电反应的活性位点,表现出较强的抗氧化性,当柚皮苷二氢查尔酮浓度为0.3mg•mL-1时,DPPH自由基清除率达到86.49%。     

柚皮苷二氢查尔酮抗氧化活性的构效关系研究

采用DPPH自由基清除实验和Materials Studio 软件中的DmoL3程序对柚皮苷二氢查尔酮的DPPH自由基清除率、几何结构和性质（振动频率、反应活性及热力学性质）进行了理论研究,得到了分子的抗氧化活性数据、稳定几何构型、各原子上的电荷分布、热力学性质、Fukui指数和前线分子轨道参数,计算结果表明柚皮苷二氢查尔酮具有较高的反应活性,分子中酚羟基上的氧原子是影响其反应活性的主要部位,也是发生亲电反应的活性位点,表现出较强的抗氧化性,当柚皮苷二氢查尔酮浓度为0.3mg•mL-1时,DPPH自由基清除率达到86.49%。     

柚皮苷二氢查尔酮抗氧化活性的构效关系研究

采用DPPH自由基清除实验和Materials Studio软件中的DmoL~3程序对柚皮苷二氢查尔酮的DPPH自由基清除率、几何结构和性质(振动频率、反应活性及热力学性质)进行了理论研究,得到了分子的抗氧化活性数据、稳定几何构型、各原子上的电荷分布、热力学性质、Fukui指数和前线分子轨道参数,计算结果表明柚皮苷二氢查尔酮具有较高的反应活性,分子中酚羟基上的氧原子是影响其反应活性的主要部位,也是发生亲电反应的活性位点,表现出较强的抗氧化性,当柚皮苷二氢查尔酮浓度为0.3mg·mL~(-1)时,DPPH自由基清除率达到86.49%.     

费托合成工艺热力学性质的计算化学研究

本文采用高精度的G4方法,全面计算了不同反应条件下费托合成工艺中可能的1287个产物的热力学数据,然后用这些数据得到的热力学量用于分析实际化工生产的热力学和分析费托合成的产物分布.结果表明:降温、加压和增大氢碳比(H_2/CO)时,热力学上可能生成的产物数目增多.在低温、高压和高碳氢比下,很多产物都在热力学上可以生成,其中产物的选择性主要由动力学因素控制.另一方面,升温或者降压可以提高小分子产物的选择性.值得注意的是在降温、加压和增大碳氢比到一定条件时,产物的平衡产率会达到最大值并且不随条件改变而变化,这说明优化条件改变产率是有一定限度的.热力学分析同样对设计和评价费托合成的反应机理有重大意义,其中甲醛的平衡产率很低,可以排除含有甲醛的反应路径.近期有一些采用金属氧化物-分子筛双功能催化剂高选择性获得C_(2-4)烯烃和芳烃的报道,其中有很多可能进入分子筛孔道的中间体,分析结果显示乙烯酮、甲醇和二甲醚是可能的中间体.     

Adsorption and catalysis: The effect of confinement on chemical reactions

Confinement within porous materials can affect chemical reactions through a host of different effects, including changes in the thermodynamic state of the system due to interactions with the pore walls, selective adsorption, geometrical constraints that affect the reaction mechanism, electronic perturbation due to the substrate, etc. In this work, we present an overview of some of our recent research on some of these effects, on chemical equilibrium, kinetic rates and reaction mechanisms. We also discuss our current and future directions for research in this area.     

Non-equilibrium Dynamics of an Infinite Range XY Model in an External Field

We study the XY model with infinite range interactions in an external magnetic field. The simulations show that in the thermodynamic limit this model does not relax to the thermodynamic equilibrium—instead it becomes trapped in a non-ergodic out-of-equilibrium state. We show how the relaxation towards this non-equilibrium state can be studied using the properties of the collisionless Boltzmann (Vlasov) equation.     

A Markov Model for Kinesin

We investigate the validity of a Markov approach for the motility of kinesin. We show in detail how the various mechanochemical states and reaction rates that are experimentally measured, can be used to create a Markov-chain model. We compare the performance of this model to motility data and we find global similarities in the load and ATP-concentration dependency of speed and mean run length. We also discuss the relation between the experimentally found stalling behavior and thermodynamic expectations. Finally, the Markov chain modelling provides a way to calculate the mean entropy production and the (power) efficiency.     

Temperature dependences of dual fluorescence as criterion for determining character of photoreactions

We performed comparative studies of the temperature quenching of dual fluorescence of acetonitrile solutions of several molecular probes with proton transfer reaction in an excited singlet state of 4′-(dieth-ylamino)-3-hydroxyflavone (FET), 1-methyl-2-(4-methoxy)phenyl-3-hydroxy-4(1H)-quinolone (QMOM), and 3-hydroxyflavone (3HF) parent molecule at different energies of excitation quanta. In accordance with expressions obtained from balance equations for photoreactions of the kinetic and thermodynamic character, the intensity ratios of fluorescence bands as functions of the degree of quenching behave differently. Namely, the quenching increases the relative intensity of bands normal form/tautomer for reactions of the kinetic type, retaining this ratio unchanged for reactions of the thermodynamic character. Our experimental studies showed that, for fluorescent probes with the kinetic reaction (3HF and QMOM), the intensity ratio fluorescence bands increases almost linearly with the degree of quenching, whereas, in the thermodynamic case (FET), this ratio is independent of this parameter. Conclusions about the character of reactions that we obtained in this work agree well with data of independent investigations of these molecules by laser spectroscopy with high time resolution, and the obtained relations allow us also to judge the mechanism of temperature quenching in the case of the reaction of the kinetic type. The method can be used for comparatively simple express selection of molecular probes, candidate for new applications.     

Field-theoretical treatment of the liquid-vapor phase transition in nuclear systems

The liquid-vapor phase transition in hot nuclear matter is investigated in a field-theoretical approach employing euclidean-space (imaginary time) path-integral techniques. This approach allows us to study the nucleation due to both quantum and thermodynamic fluctuations. The bubbles of the new phase appear as instanton solutions of the euclidean-space field equations. The critical bubble sizes and associated transition probabilities are calculated. We examine the temperature and density values for which a phase transition may develop in hot nuclear matter produced in the course of a heavy-ion reaction.     

The density of states for an antiferromagnetic Ising model on a triangular lattice

The Wang-Landau algorithm is an efficient Monte Carlo approach to the density of states of a statistical mechanics system. The estimation of state density would allow the computation of thermodynamic properties of the system over the whole temperature range. We apply this sampling method to study the phase transitions in a triangular Ising model. The entropy of the lattice at zero temperature as well as other thermodynamic properties is computed. The calculated thermodynamic properties are explained in the context of the magnetic phase transition.      

Liquid Phase Kinetic and Thermodynamic Studies on Promoted Nickel Catalysts used for H/D Exchange

Successful choice of the suitable catalyst composition for hydrogen/deuterium exchange reaction between hydrogen and water requires understanding of chemical kinetics as well as surface properties and activity in both liquid- and vapour phases. The present study deals with the thermodynamic and kinetic behaviour of a simple liquid phase reaction on the surface of nickel catalyst promoted with zirconium oxide used for the H/D exchange. This study helps understand the condensation of water on the catalyst surface during operation which leads to its poisoning. In this specific case water molecules are responsible for selective poisoning of this type of catalysts. The reaction rate constant, the increase in Gibb,s free energy, the enthalpy, the entropy of activation and the energy of activation were calculated.     

Thermal Global Expansion Coefficient Measurement for a Harmonic Trapped Gas Across Bose-Einstein Condensation

We report the measurement of the global thermal expansion coefficient of a confined Bose gas of ⁸⁷Rb in a harmonic potential around the Bose-Einstein condensation transition temperature. We use the concept of global thermodynamic variable, previously introduced and appropriated for a non-homogeneous system. We observe the behavior of the thermal expansion coefficient above and below the critical temperature showing the lambda-like shape present in superfluid helium. The study demonstrates the potentiality of global thermodynamic variables for the investigation of properties across the critical temperature, and a new way to study the thermodynamic properties of the quantum systems.     

Vibrational temperature of the adlayer in the ‘hot-atom’ reaction mechanism

The hot-atom reaction mechanism brings about reaction rates several orders of magnitude higher than those expected in the case of adatoms which have thermalized with the surface. This paper addresses the issue of a possible thermodynamic characterization of the adlayer under reactive conditions and at the steady state. In turn, this implies having to determine the temperature of the adatoms. This is done by means of a nonequilibrium statistical thermodynamic approach, by exploiting a suitable definition of the entropy. The interplay between reaction rate, vibrational temperature of the adatoms and adsorbed quantities is highlighted. This paper shows that the vibrational temperature depends on reaction rate, logarithmically and exhibits a non-linear scaling on physical quantities linked to the energetics of the reaction, namely the adsorption energy and the binding energy of the molecule. The present modeling is also discussed in connection with response equations of nonequilibrium thermodynamics.     

How Does Pressure Fluctuate in Equilibrium?

We study fluctuations of pressure in equilibrium for classical particle systems. In equilibrium statistical mechanics, pressure for a microscopic state is defined by the derivative of a thermodynamic function or, more mechanically, through the momentum current. We show that although the two expectation values converge to the same equilibrium value in the thermodynamic limit, the variance of the mechanical pressure is in general greater than that of the pressure defined through the thermodynamic relation. We also present a condition for experimentally detecting the difference between them in an idealized measurement of momentum transfer.     

Quantum mechanical free energy barrier for an enzymatic reaction

We discuss problems related to in silico studies of enzymes and show that accurate and converged free energy changes for complex chemical reactions can be computed if a method based on a thermodynamic cycle is employed. The method combines the sampling speed of molecular mechanics with the accuracy of a high-level quantum mechanics method. We use the method to compute the free energy barrier for a methyl transfer reaction catalyzed by the enzyme catechol O-methyltransferase at the level of density functional theory. The surrounding protein and solvent are found to have a profound effect on the reaction, and we show that energies can be extrapolated easily from one basis set and exchange-correlation functional to another. Using this procedure we calculate a barrier of 69 kJ/mol, in excellent agreement with the experimental value of 75 kJ/mol.