Statistical Thermodynamic Model Research Articles

Energetic driving force for LHCII clustering in plant membranes.

Plants capture and convert solar energy in a complex network of membrane proteins. Under high light, the luminal pH drops and induces a reorganization of the protein network, particularly clustering of the major light-harvesting complex (LHCII). While the structures of the network have been resolved in exquisite detail, the thermodynamics that control the assembly and reorganization had not been determined, largely because the interaction energies of membrane proteins have been inaccessible. Here, we describe a method to quantify these energies and its application to LHCII. Using single-molecule measurements, LHCII proteoliposomes, and statistical thermodynamic modeling, we quantified the LHCII-LHCII interaction energy as ~-5 kBT at neutral pH and at least -7 kBT at acidic pH. These values revealed an enthalpic thermodynamic driving force behind LHCII clustering. Collectively, this work captures the interactions that drive the organization of membrane protein networks from the perspective of equilibrium statistical thermodynamics, which has a long and rich tradition in biology.

An integrated statistical-thermodynamic model for fission gas release and swelling in nuclear fuels

We propose a new model for burst fission gas release induced by microcracking in ceramic nuclear fuels such as uranium dioxide. The model stipulates that the densities of defects in the fuel material, such as microcracks and fission gas bubbles on grain boundaries, evolve in accordance with the second law of thermodynamics. Central to the model is the notion of an effective temperature, conjugate to the configurational entropy of the fuel material, and directly linked to the burnup. The model predicts that microcracking, driven by the internal stress state of the fuel material, reduces the bubble storage capacity of grain boundaries, and accounts for burst fission gas release during rapid temperature transients that simulate power transients, reactor startup, and loss-of-coolant accident conditions.

Accurate description of gas hydrates of carbon dioxide and hydrogen for storage and transportation

This paper reports theoretical study of stability zones and composition of “H2 + CO2” clathrate hydrates of cubic structure I (sI) and II (sII) in dependence on pressure and temperature for different gas phase composition using extended van der Waals and Platteeuw statistical thermodynamic model. It was found that rising of CO2 content in H2 + CO2 gas mixture phase makes formation of sI hydrate more thermodynamically preferable rather than sII hydrate, and in the same time CO2 content increasing reduces formation pressure of the resulting hydrate. Observed difference between gas phase composition and gas molecules trapped in hydrate phase allows to consider these hydrates as a gas separation medium. We believe that presented results could be applicable for improvements of hydrate technology for CO2 utilization as a greenhouse gas, and hydrogen obtained from natural gas refinement transportation.

Thermal analysis of integrated hydrate-based desalination system with intermediate fluid type LNG vaporizer

With a growing population, excessive industrial activities, and limited freshwater resources, water scarcity is considered a prime global risk. Desalination of seawater is essential to overcome former challenges, however, energy-intensive water desalination processes have pushed the water community towards sustainable and economical seawater desalination techniques. This study presents a hydrate-based desalination (HyDesal) system where liquefied natural gas (LNG) is suggested to be used as a source of cooling energy and hydrate former. The study's novel use of an intermediate fluid type LNG vaporizer (IFV) is a prime objective. Detailed analysis of the complex heat transfer processes of the LNG vaporizer is conducted to estimate the thermal performance of the LNG vaporizer using a model based on the heat transfer analysis of each of the three sub-components of the IFV. The analysis for each sub-component is coupled as a set of linear equations in matrix form. An algorithm was also designed and developed to assess the thermal parameters of the IFV in an iterative procedure. The former algorithm is suggested to evaluate the performance of the complex heat transfer processes of the IFV. Furthermore, the effect of various operating parameters of the LNG vaporizer on its performance is investigated. Besides, a general thermal analysis of the suggested hydrate-based desalination system is investigated. Design parameters of the desalination system, such as the required mass flow rate of the seawater, mass flow rate of the hydrate former, and operating conditions are evaluated. In addition, a statistical thermodynamics model (modified van der Waals and Platteeuw) was also employed to trace the hydrate phase boundary in the presence and absence of inhibitors. The coupled thermodynamic model provides an accurate update of process T or P conditions along with fractional cage occupancies.

Small gas adsorption on 2D material SnSe: a first-principles study

SnSe not only has a large surface-to-volume ratio, but also provides enough space to adsorb small-molecule gases owing to its unique wrinkled structure, so it exhibits great application prospects in gas sensing. In this study, we have comprehensively investigated the adsorption properties of H2, N2, CO, CO2, H2S, H2O, NH3, NO, SO2, and NO2 on SnSe by the first-principles density functional theory, and have analyzed the sensing potential of SnSe for these small gas molecules. It is found that only NO and SO2 have suitable adsorption energies, showing that they can be stably adsorbed on the SnSe substrate and easily desorbed under certain conditions. Moreover, NO adsorption introduces a magnet moment that can be differentiated from SO2 and NO2. Additionally, according to the calculation results of the statistical thermodynamics model and nonequilibrium Green’s function method, SO2 possesses enormous adsorption density and larger current than NO under the same condition. Therefore, SnSe is promising for reversible SO2 sensing.

Short-Range Order Modeling in Alloys

The short and long-range orders in alloys can be assessed based on a new expression for the combinatorial factor, which is more convenient and intuitive than the traditionally used form. This novel expression can be directly applied to reproduce the results of several well-known statistical-thermodynamic models that are typically considered independent or even inconsistent. The short list of models includes Quasichemical Theory, Associated Solution Model, Surrounded Atom Model, and Cluster Site Approximation. As a result, the formalism and interpretation of these models are significantly clarified, allowing us to identify and fix several long-standing errors that might otherwise have gone unnoticed. Multicomponent generalization of these models is also greatly simplified. For systems undergoing a phase transition, an extended version of the theory provides a mechanism that allows the correct critical temperature of phase transition to be reproduced, as well as a significant increase in the accuracy of thermodynamic functions. In the case of order–disorder transformations, the new theory ensures an integrated description of short and long-range orders, which has long been considered an important and difficult problem.

Determination of Hydrogen’s Thermophysical Properties Using a Statistical Thermodynamic Method

Accurate determination of the thermophysical properties of hydrogen is a crucial issue in hydrogen system design. By developing computational programs, a statistical thermodynamic model based on fundamental equations of state was implemented to determine hydrogen’s thermophysical properties, including the ortho-hydrogen fraction in equilibrium hydrogen, para-ortho hydrogen conversion heat, isobaric heat capacities and enthalpies. The deviations of calculated para-hydrogen enthalpies from REFPROP data were within 2.22%, ranging from 20 K to 300K at 0.1 MPa, and within 2.32% between 100 K and 1500 K at pressures from 0.1 MPa to 20 MPa. To quantitatively assess the convenience of the statistical thermodynamic method, the running speeds of programs with different methods for determining hydrogen’s thermophysical properties were compared. The time required for statistical thermodynamic calculation was 7.95% that required for treading REFPROP data when the performance of the variable density multilayer insulation combined with a one vapor-cooled shield and para-ortho hydrogen conversion was calculated. The programs developed based on the statistical thermodynamic method can be used to determine the thermophysical properties of hydrogen or other fluids.

Macromolecular crowding impact on anti-CRISPR AcrIIC3/NmeCas9 complex: Insights from scaled particle theory, molecular dynamics, and elastic networks models

The coupling of Cas9 and its inhibitor AcrIIC3, both from the bacterium Neisseria meningitidis (Nme), form a homodimer of the (NmeCas9/AcrIIC3)2 type. This coupling was studied to assess the impact of their interaction with the crowders in the following environments: (1) homogeneous crowded, (2) heterogeneous, and (3) microheterogeneous cytoplasmic. For this, statistical thermodynamic models based on the scaled particle theory (SPT) were used, considering the attractive and repulsive protein-crowders contributions and the stability of the formation of spherocylindrical homodimers and the effects of changes in the size of spherical dimers were estimated. Studies based on models of dynamics, elastic networks, and statistical potentials to the formation of complexes NmeCas9/AcrIIC3 using PEG as the crowding agent support the predictions from SPT. Macromolecular crowding stabilizes the formation of the dimers, being more significant when the attractive protein-crowder interactions are weaker and the crowders are smaller. The coupling is favored towards the formation of spherical and compact dimers due to crowding addition (excluded-volume effects) and the thermodynamic stability of the dimers is markedly dependent on the size of the crowders. These results support the experimental mechanistic proposal of inhibition of NmeCas9 mediated by AcrIIC3.

Translation initiation consistency between in vivo and in vitro bacterial protein expression systems.

Strict on-demand control of protein synthesis is a crucial aspect of synthetic biology. The 5'-terminal untranslated region (5'-UTR) is an essential bacterial genetic element that can be designed for the regulation of translation initiation. However, there is insufficient systematical data on the consistency of 5'-UTR function among various bacterial cells and in vitro protein synthesis systems, which is crucial for the standardization and modularization of genetic elements in synthetic biology. Here, more than 400 expression cassettes comprising the GFP gene under the regulation of various 5'-UTRs were systematically characterized to evaluate the protein translation consistency in the two popular Escherichia coli strains of JM109 and BL21, as well as an in vitro protein expression system based on cell lysate. In contrast to the very strong correlation between the two cellular systems, the consistency between in vivo and in vitro protein translation was lost, whereby both in vivo and in vitro translation evidently deviated from the estimation of the standard statistical thermodynamic model. Finally, we found that the absence of nucleotide C and complex secondary structure in the 5'-UTR significantly improve the efficiency of protein translation, both in vitro and in vivo.

Experimental analysis and modeling of the molecular architecture influence on the solid-liquid transition of ethylene/1-octene copolymer solvent systems

The knowledge of solid-liquid equilibria of polymer-solvent systems is particularly important for further clarifying and understanding polymer crystallization. The molecular architecture in terms of molecular weight and branching related to the semicrystallinity of the polymer plays a key role in solid-liquid equilibria in polyethylene-solvent systems. Recently, a new thermodynamic model based on the Lattice Cluster Theory and continuous thermodynamics was developed, which can capture the influence of molecular weight distribution and degree of branching on solid-liquid equilibria. The model was applied to ethylene/1-hexene copolymer-solvent systems. However, the experimental database for solid-liquid equilibria of polymer solvent systems, where comprehensive molecular information of the polymer is connected with morphological quantities, e.g., semicrystallinity, and solid-liquid phase equilibria, is scarcely available in the literature. Therefore, herein a concept for this structure-property relationship is developed for ethylene/1-octene copolymer-solvent systems. The experimentally determined structure-property relationships are then used for determining the parameters of the statistical thermodynamics model and for model validation. The thermodynamic model allows the investigation of the transition zone from branching to molecular weight-induced solid-liquid equilibrium in dependence on the polydisperse nature of ethylene/1-octene copolymers.

Polymer Wrapping onto Nanoparticles Induces the Formation of Hybrid Colloids

Polymers stabilize the nanoparticles onto which they wrap, avoiding coagulation and undesired phase separation processes. Wrapping gives rise to hybrid colloids, and is useful in bio-intended applications. In non-covalent interaction modes, polymers physically adsorb onto the nanoparticles’ surface, NPs, and some of their portions protrude outside. Both their non-interacting parts and the free polymers are in contact with the solvent, and/or are dispersed in it. Wrapping/protruding ratios were forecast with a simple statistical thermodynamic model, and the related energy calculated. The wrapping efficiency is controlled by different contributions, which stabilize polymer/NP adducts. The most relevant ones are ascribed to the NP-polymer, polymer–polymer, and polymer–solvent interaction modes; the related energies are quite different from each other. Changes in the degrees of freedom for surface-bound polymer portions control the stability of adducts they form with the NPs. The links between wrapped, free, and protruding states also account for depletion, and control the system’s properties when the surface adsorption of hosts is undesired. Calculations based on the proposed approach were applied to PEO wrapping onto SiO2, silica, and nanoparticles. The interaction energy, W, and the changes in osmotic pressure associated with PEO binding onto the NPs have been evaluated according to the proposed model.

Complex Physical Properties of an Adaptive, Self-Organizing Biological System

Physical modeling of the functioning of the adaptive immune system, which has been thoroughly characterized on genetic and molecular levels, provides a unique opportunity to define an adaptive, self-organizing biological system in its entirety. This paper describes a configuration space model of immune function, where directed chemical potentials of the system constitute a space of interactions. A mathematical approach is used to define the system that couples the variance of Gaussian distributed interaction energies in its interaction space to the exponentially distributed chemical potentials of its effector molecules to maintain its steady state. The model is validated by identifying the thermodynamic and network variables analogous to the mathematical parameters and by applying the model to the humoral immune system. Overall, this statistical thermodynamics model of adaptive immunity describes how adaptive biological self-organization arises from the maintenance of a scale-free, directed molecular interaction network with fractal topology.

A Statistical Perspective on Microsolvation.

The lack of a procedure to determine equilibrium thermodynamic properties of a small system interacting with a bath is frequently seen as a weakness of conventional statistical mechanics. A typical example for such a small system is a solute surrounded by an explicit solvation shell. One way to approach this problem is to enclose the small system of interest in a large bath of explicit solvent molecules, considerably larger than the system itself. The explicit inclusion of the solvent degrees of freedom is obviously limited by the available computational resources. A potential remedy to this problem is a microsolvation approach where only a few explicit solvent molecules are considered and surrounded by an implicit solvent bath. Still, the sampling of the solvent degrees of freedom is challenging with conventional grand canonical Monte Carlo methods, since no single chemical potential for the solvent molecules can be defined in the realm of small-system thermodynamics. In this work, a statistical thermodynamic model based on the grand canonical ensemble is proposed that avoids the conventional system size limitations and accurately characterizes the properties of the system of interest subject to the thermodynamic constraints of the bath. We extend an existing microsolvation approach to a generalized multibath "microstatistical" model and show that the previously derived approaches result as a limit of our model. The framework described here is universal and we validate our method numerically for a Lennard-Jones model fluid.

Model of inverse “dry” micelles with coexisting spherical, globular and cylindrical aggregates

A new statistical thermodynamic model of inverse nonionic aggregates of surfactant molecules in nonpolar solvents is considered. This model admits the fluctuation coexistence of inverse spherical, globular, and spherocylindrical aggregates without activation barriers between them. The model is based on the assumption of a uniform bulk density of the number of molecular groups inside the core of an aggregate that can continuously transform into a sphere, a globule, and a spherocylinder. In this model, for any aggregation numbers, the work of aggregation depends not only on the aggregation numbers and the concentration of surfactant monomers, but also on two independent geometric parameters characterizing, at the same aggregation numbers, the deviation from the spherical form of the aggregate towards globular and spherocylindrical forms. Even in the range of small aggregation numbers, this fact leads to a significant difference between the equilibrium distribution function of aggregates, which depends on the aggregation number and two form parameters, and the one-dimensional distribution function in terms of aggregation numbers. It is shown that the optimal values of the form parameters, which minimize the work of aggregation, are in good agreement for spherocylindrical aggregates with the predictions of a purely geometric model of such aggregates under the additional assumption of a uniform surface density of molecular groups at the micelle core. The predictions of a new molecular thermodynamic model for the degrees of surfactant micellization in inverse aggregates of various forms at different surfactant concentrations are considered.

Coordination Changes in Densified Aluminate Glass upon Compression up to 65 GPa: A View from Solid-State Nuclear Magnetic Resonance.

Deciphering the structural evolution in irreversibly densified oxide glasses is crucial for fabricating functional glasses with tunable properties and elucidating the nature of pressure-induced anomalous plastic deformation in glasses. High-resolution NMR spectroscopy quantifies atomic-level structural information on densified glasses; however, its application is limited to the low-pressure range due to technical challenges. Here, we report the first high-resolution NMR spectra of oxide glass compressed by diamond anvil cells at room temperature, extending the pressure record of such studies from 24 to 65 GPa. The results constrain the densification path through coordination transformation of Al cations. Based on a statistical thermodynamic model, the stepwise changes in the Al fractions of oxide glasses and the effects of network polymerization on the densification paths are quantified. These results extend the knowledge on densification of the previously unattainable pressure conditions and contribute to understanding the origin of mechanical strengthening of the glasses.

Computing grain boundary “phase” diagrams

AbstractGrain boundaries (GBs) can be treated as two‐dimensional (2‐D) interfacial phases (also called “complexions”) that can undergo interfacial phase‐like transitions. As bulk phase diagrams and calculation of phase diagram (CALPHAD) methods serve as a foundation for modern materials science, we propose to extend them to GBs to have equally significant impacts. This perspective article reviews a series of studies to compute the GB counterparts to bulk phase diagrams. First, a phenomenological interfacial thermodynamic model was developed to construct GB lambda diagrams to forecast high‐temperature GB disordering and related trends in sintering and other properties for both metallic and ceramic materials. In parallel, an Ising‐type lattice statistical thermodynamic model was utilized to construct GB adsorption (segregation) diagrams, which predicted first‐order GB adsorption transitions and critical phenomena. These two simplified thermodynamic models emphasize the GB structural (disordering) and chemical (adsorption) aspects, respectively. Subsequently, hybrid Monte Carlo and molecular dynamics atomistic simulations were used to compute more rigorous and accurate GB “phase” diagrams. Computed GB diagrams of thermodynamic and structural properties were further extended to include mechanical properties. Moreover, machine learning algorithms were combined with atomistic simulations to predict GB properties as functions of four independent compositional variables and temperature in a 5‐D space for a given GB in high‐entropy alloys or as functions of five GB macroscopic (crystallographic) degrees of freedom plus temperature and composition for a binary alloy in a 7‐D space. Other relevant studies are also examined. Future perspective and outlook, including two emerging fields of high‐entropy grain boundaries (HEGBs) and electrically (or electrochemically) induced GB transitions, are discussed.

Three-component 1,1,3,3-tetramethylguanidine based CO2-binding organic liquids: Statistical solvent design and thermodynamic modeling of CO2 solubility by LJ-Global TPT2 EoS

In this study, three-component CO2-binding organic liquids (CO2BOLs) are introduced for high pressure CO2 absorption. The non-aqueous, green solvents consist of a superbase (1,1,3,3-tetramethylguanidine (TMG)), a tertiary alkanolamine (Dimethylethanolamine (DMEA), Diethylethanolamine (DEEA) and N-methyldiethanolamine (MDEA)) and an alcohol (MeOH, n-BuOH, sec‑BuOH, tert‑BuOH and 1-HexOH). The best combination of solvent components was determined to be the TMG/DMEA/n-BuOH BOL (molar ration:1/1/1) based on both CO2 loading (αeq= 0.431 mol CO2/mol solvent) and absorption rate (αR= 0.225 mol CO2/mol solvent within 20 min) by implementing screening experiments. The mixture design approach was applied for the design of experiments, modeling and investigating the effect of components’ proportion on αeq and αR at the constant temperature of 35.0 °C and initial CO2 pressure of 25.0 bar. The highest αeq (0.573 mol CO2/mol BOL) and αR (0.362 mol CO2/mol solvent) were obtained using TMG/n-butanol (1/1) and DMEA BOLs, respectively. The CO2 solubility data in the two-component BOLs: TMG/n-BuOH, TMG/DMEA and DMEA/n-BuOH as well as the three-component TMG/DMEA/n-BuOH BOL were gathered at 25.0, 35.0 and 45.0 °C and the pressures up to 35.0 bar using equimolar solvent mixtures. The LJ-Global TPT2 EoS was used in the simultaneous VLE and chemical equilibrium calculation algorithm for the thermodynamic modeling of CO2 solubility in the BOLs. The AAD% in the modeling of TMG/n-BuOH, TMG/DMEA, DMEA/n-BuOH and TMG/DMEA/n-BuOH BOLs were calculated to be 11.5%, 12.4%, 10.5 and 12.9%, respectively. The enthalpies of CO2 absorption in BOLs and the speciation of the system components were predicted from reaction equilibrium constants and using LJ-Global TPT2 EoS.

Thermodynamic coupling between neighboring binding sites in homo-oligomeric ligand sensing proteins from mass resolved ligand-dependent population distributions.

Homo‐oligomeric ligand‐activated proteins are ubiquitous in biology. The functions of such molecules are commonly regulated by allosteric coupling between ligand‐binding sites. Understanding the basis for this regulation requires both quantifying the free energy ΔG transduced between sites, and the structural basis by which it is transduced. We consider allostery in three variants of the model ring‐shaped homo‐oligomeric trp RNA‐binding attenuation protein (TRAP). First, we developed a nearest‐neighbor statistical thermodynamic binding model comprising microscopic free energies for ligand binding to isolated sites ΔG 0, and for coupling between adjacent sites, ΔG α . Using the resulting partition function (PF) we explored the effects of these parameters on simulated population distributions for the 2 N possible liganded states. We then experimentally monitored ligand‐dependent population shifts using conventional spectroscopic and calorimetric methods and using native mass spectrometry (MS). By resolving species with differing numbers of bound ligands by their mass, native MS revealed striking differences in their ligand‐dependent population shifts. Fitting the populations to a binding polynomial derived from the PF yielded coupling free energy terms corresponding to orders of magnitude differences in cooperativity. Uniquely, this approach predicts which of the possible 2 N liganded states are populated at different ligand concentrations, providing necessary insights into regulation. The combination of statistical thermodynamic modeling with native MS may provide the thermodynamic foundation for a meaningful understanding of the structure–thermodynamic linkage that drives cooperativity.

Statistical thermodynamics of DNA with open states

The study in the open states plays an important role in understanding the laws of DNA biological activity. The techniques of statistical thermodynamics are potentially able of providing a general framework for understanding the influence of the open states on DNA functionality. In this paper, we develop statistically based DNA thermodynamics with the open states. There were ascertained the internal variables related to the DNA open states which were introduced for determining nucleotides interaction. Besides, there was found the free energy form corresponding to the structural-scaling parameter playing the role of the ≪effective temperature≫ of the open state’s induced thermodynamics. Following the open state statistical thermodynamic model, the DNA dynamics was studied as compared with the Peyrard–Bishop–Dauxois model. The ≪critical≫ dynamics was ascertained in characteristic ranges of the structural-scaling parameter as a form of the open states collective modes, providing the functionality of the DNA dynamics.

Solvation Thermodynamics of Solutes in Water and Ionic Liquids Using the Multiscale Solvation-Layer Interface Condition Continuum Model.

Molecular assembly processes are generally driven by thermodynamic properties in solutions. Atomistic modeling can be very helpful in designing and understanding complex systems, except that bulk solvent is very inefficient to treat explicitly as discrete molecules. In this work, we develop and assess two multiscale solvation models for computing solvation thermodynamic properties. The new SLIC/CDC model combines continuum solvent electrostatics based on the solvent layer interface condition (SLIC) with new statistical thermodynamic models for hydrogen bonding and nonpolar modes: cavity formation, dispersion interactions, combinatorial mixing (CDC). Given the structures of 500 solutes, the SLIC/CDC model predicts Gibbs energies of solvation in water with an average accuracy better than 1 kcal/mol, when compared to experimental measurements, and better than 0.8 kcal/mol, when compared to explicit-solvent molecular dynamics simulations. The individual SLIC/CDC energy mode values agree quantitatively with those computed from explicit-solvent molecular dynamics. The previously published SLIC/SASA multiscale model combines the SLIC continuum electrostatic model with the solvent-accessible surface area (SASA) nonpolar energy mode. With our new, improved parametrization method, the SLIC/SASA model now predicts Gibbs energies of solvation with better than 1.4 kcal/mol average accuracy in aqueous systems, compared to experimental and explicit-solvent molecular dynamics, and better than 1.6 kcal/mol average accuracy in ionic liquids, compared to explicit-solvent molecular dynamics. Both models predict solvation entropies, and are the first implicit-solvation models capable of predicting solvation heat capacities.