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The second law of thermodynamics and the concept of positive entropy generation are analyzed following classical statistical mechanics methods. Previously, using the generalized Boltzmann–Gibbs entropy and its associated general entropy conservation relation, positive entropy generation expressions were obtained in agreement with phenomenological results and the work of Boltzmann and Gibbs. In this study, using the general approach, we formally and explicitly trace the specific entropy generation expressions to truncations in the full N-body description of the entropy state to a lower s-body description. Using higher-order superposition approximations, it is formally shown that the generalized Boltzmann–Gibbs entropy in the s-order state is always less than the corresponding Boltzmann–Gibbs entropy in the lower (s − 1)-order state. Using the general form of the entropy conservation equation, entropy generation is shown to be a required compensatory effect to ensure that all physical variables and physical processes associated with heat, work, temperature, etc., are independent of the particular entropy definition state.

The Omicron variant and its sub-lineages are the only current circulating SARS-CoV-2 viruses worldwide. In this study, the conformational stability of the isolated Receptor Binding Domain (RBD) of Omicron’s spike protein is examined in detail. The parent Omicron lineage has over ten mutations in the ACE2 binding region of the RBD that are specifically associated with its β hairpin loop domain. It is demonstrated through biophysical molecular computations that the mutations in the β hairpin loop domain significantly increase the intra-protein interaction energies of intra-loop and loop–RBD interactions. The interaction energy increases include the formation of new hydrogen bonds in the β hairpin loop domain that help stabilize this critical ACE2 binding region. Our results also agree with recent experiments on the stability of Omicron’s core β barrel domain, outside of its loop domain, and help demonstrate the overall conformational stability of the Omicron RBD. It is further shown here through dynamic simulations that the unbound state of the Omicron RBD remains closely aligned with the bound state configuration, which was not observed for the wild-type RBD. Overall, these studies demonstrate the significantly increased conformational stability of Omicron over its wild-type configuration and raise a number of questions on whether conformational stability could be a positive selection feature of SARS-CoV-2 viral mutational changes.

Abstract The SARS-CoV-2 prefusion spike protein is characterized by a high degree of flexibility and temporal transformations associated with its multifunctional behavior. In this study, we have examined the dynamics of the Receptor Binding Domain (RBD) of the SARS-CoV-2 spike protein in detail. Its primary, binding subdomain with human Angiotensin Covering Enzyme II includes a highly conspicuous flap or loop that is part of a beta hairpin loop structural motif. Dynamic details of the RBD obtained through RMSF and Order Parameter calculations are consistent with structural details including the stability of “glue” points or dominant interaction energy residues of the RBD in the Up and Down states with its neighboring N-terminal domain (NTD) protomer. The RBD flap in the Up state protomer periodically obstructs the binding site on an approximate 70 ns time interval and is reminiscent of an HIV-1 protease polypeptide flap that opens and closes to modulate that enzymes activity. No claim is made here regarding the possible modulating role of the flap; however, the flap may be a potential site for therapeutic targeting aimed at keeping it in the closed state, as previously demonstrated in the inhibition of the HIV-1 protease polypeptide. The RBD primary binding subdomain is further shown to have not only similar dynamics but, also, an approximate 30% sequence similarity to the HIV-1 protease polypeptide.

Equilibrium, canonical based expressions of entropy are known to exhibit non-local effects that can complicate statistical mechanical formulations and applications. Here, we demonstrate that proper normalization of the underlying probability density functions can remove non-local effects in entropy. Our analysis is carried out through third order in density function expansions and lead to results consistent with macroscopic thermodynamics, as required. In addition, we provide complete expressions for smaller dimensional systems that may not conform to the thermodynamic limit.

ABSTRACT Monitoring and strategic response to variants in severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) represent a considerable challenge in the current pandemic and for future viral outbreaks. Mutations/deletions of the virion’s prefusion Spike protein may have significant impact on vaccines and therapeutics that utilize this key structural protein in their mitigation strategies. In this study, we have demonstrated how dominant energetic landscape mappings (“glue points”) based on ab inito all-atom force fields coupled with phylogenetic sequence alignment information can identify key residue mutations and deletions associated with variants. We also found several examples of excellent homology of stabilizing residue glue points across the lineages of betacoronavirus Spike proteins that we have called “sequence homologous glue points.” SARS-CoV-2 demonstrates the least number of stabilizing glue points associated with interchain interactions among Down-state protomers across lineages. Additionally, we computationally studied variants among the trimeric Spike protein of SARS-CoV-2 using all-atom molecular dynamics to ascertain structural and energetic changes among variants. We examined both a theoretically based triple mutant and the UK or B.1.1.7 variant. For the theoretical triple mutant, we demonstrated through alanine substitutions that three key residues could cause the transition of Down-to-Up protomer states, where the transition is characterized by the “arm” length of the receptor-binding domain (RBD) rather than the hinge angle. For the B.1.1.7 variant, we demonstrated the critical importance of mutations D614G and N501Y on the structure and binding, respectively, of the Spike protein. We note that these same two key mutations are also found in the South African B.1.351 variant. IMPORTANCE Viral variants represent a major challenge to monitoring viral outbreaks and formulating strategic health care responses. Variants represent transmitting viruses that have specific mutations and deletions associated with their genome. In the case of SARS-CoV-2 and other related viruses (betacoronaviruses), many of these mutations and deletions are associated with the Spike protein that the virus uses to infect cells. Here, we have analyzed both SARS-CoV-2 variants and related viruses, such as Middle Eastern respiratory syndrome coronavirus (MERS-CoV), in order to understand not only differences, but also key similarities between them. Understanding similarities can be as important as differences in determining key functional features of a class of viruses, such as the betacoronaviruses. We have used both phylogenetic analysis, which traces genetic similarities and differences, along with independent biophysics analysis, which adds function or behavior, in order to determine possible functional differences and hence possible transmission and infection differences among variants and lineages.

Nonequilibrium statistical mechanics or molecular theory has put the transport equations of mass, momentum and energy on a firm or rigorous theoretical foundation that has played a critical role in their use and applications. Here, it is shown that those methods can be extended to nonequilibrium entropy conservation. As already known, the “closure” of the transport equations leads to the theory underlying the phenomenological laws, including Fick’s Law of Diffusion, Newton’s Law of Viscosity, and Fourier’s Law of Heat. In the case of entropy, closure leads to the relationship of entropy flux to heat as well as the Second Law or the necessity of positive entropy generation. It is further demonstrated how the complete set of transport equations, including entropy, can be simplified under physically restrictive assumptions, such as reversible flows and local equilibrium flows. This analysis, in general, yields a complete, rigorous set of transport equations for use in applications. Finally, it is also shown how this basis set of transport equations can be transformed to a new set of nonequilibrium thermodynamic functions, such as the nonequilibrium Gibbs’ transport equation derived here, which may have additional practical utility.

In this study, we generalize our previous methods for obtaining entropy generation in gases without the need to carry through a specific expansion method, such as the Chapman–Enskog method. The generalization, which is based on a scaling analysis, allows for the study of entropy generation in gases for any arbitrary state of the gas and consistently across the conservation equations of mass, momentum, energy, and entropy. Thus, it is shown that it is theoretically possible to alter specific expressions and associated physical outcomes for entropy generation by changing the operating process gas state to regions significantly different than the perturbed, local equilibrium or Chapman–Enskog type state. Such flows could include, for example, hypersonic flows or flows that may be generally called hyper-equilibrium state flows. Our formal scaling analysis also provides partial insight into the nature of entropy generation from an informatics perspective, where we specifically demonstrate the association of entropy generation in gases with uncertainty generated by the approximation error associated with density function expansions.

In this study, we propose a mesh-free (particle-based) Smoothed Particle Hydrodynamics model for simulating a Rayleigh collapse. Both empty and gas cavities are investigates and the role of heat diffusion is also accounted for. The system behaves very differently according to the ratio between the characteristic time of collapse and the characteristic time of thermal diffusion. This study identifies five different possible behaviours that range from isothermal to adiabatic.

Following Irving and Kirkwood’s (J. Chem. Phys.1950, 18, 817) classical approach to the statistical mechanics of transport processes and the conservation equations for mass, momentum, and energy, we introduce a particular dynamical variable for entropy and derive the general nonequilibrium entropy conservation equation. This particular formalism is shown to encompass both Boltzmann’s and Gibbs’ entropy definitions as special cases. Entropy generation is shown to follow from phase-space dimensionality loss and truncations or approximations in higher-order space, the latter of which is consistent with the thesis of Jaynes (Am. J. Phys.1965, 33, 391). The general approach to entropy conservation given here not only completes Irving and Kirkwood’s treatment of the transport equations but also allows for a consistent analysis of all transport equations for any given system. Following standard perturbation expansion methods about local equilibrium states, we derive the closed form of the entropy conservation equation for isolated systems, which is shown to be in agreement with well-known phenomenological results and the principles of irreversible thermodynamics. In addition, the generalized nonequilibrium entropy developed here is fully consistent with its equilibrium counterpart. As an example, our formalism allows the analysis of entropy changes in dense gases and liquids through the introduction of a nonequilibrium Green’s entropy. This study provides a firm molecular basis of entropy conservation by consistent methods across the transport equations, allowing ready extensions to complex systems. Such foundations are of contemporary importance in designing energy-efficient or minimum entropy generating engineering systems. [ABSTRACT FROM AUTHOR]

Predicting the long-time, nonequilibrium dynamics of receptor-ligand interactions for structured proteins in a host fluid is a formidable task, but of great importance to predicting and analyzing cell-signaling processes and small molecule drug efficacies. Such processes take place on timescales on the order of milliseconds to seconds, so “brute-force” real-time, molecular or atomic simulations to determine absolute ligand-binding rates to receptor targets and over a statistical ensemble of systems are not currently feasible. In the current study, we implement on real protein systems a previously developed 3–5 hybrid molecular dynamics/Brownian dynamics algorithm, which takes advantage of the underlying, disparate timescales involved and overcomes the limitations of brute-force approaches. The algorithm is based on a multiple timescale analysis of the total system Hamiltonian, including all atomic and molecular structure information for the system: water, ligand, and receptor. In general, the method can account for the complex hydrodynamic, translational-orientational diffusion aspects of ligand-docking dynamics as well as predict the actual or absolute rates of ligand binding. To test some of the underlying features of the method, simulations were conducted here for an artificially constructed spherical protein “made” from the real protein insulin. Excellent comparisons of simulation calculations of the so-called grand particle friction tensor to analytical values were obtained for this system when protein charge effects were neglected. When protein charges were included, we found anomalous results caused by the alteration of the spatial, microscopic structure of water proximal to the protein surface. Protein charge effects were found to be highly significant and consistent with the recent hypothesis of Hoppert and Mayer (Am Sci 1999;87:518–525) for charged macromolecules in water, which involves the formation of a “water dense region” proximal to the charged protein surface followed by a “dilute water region.” We further studied the algorithm on a D-peptide/HIV capside protein system and demonstrated the algorithms utility to study the nonequilibrium docking dynamics in this contemporary problem. In general, protein charge effects, which alter water structural properties in an anomalous fashion proximal to the protein surface, were found to be much more important than the so-called hydrodynamic interaction effects between ligand and receptor. The diminished role of hydrodynamic interactions in protein systems allows for a much simpler overall dynamic algorithm for the nonequilibrium protein-docking process. Further studies are now underway to critically examine this simpler overall algorithm in analyzing the nonequilibrium protein-docking problem. Proteins 2003;52:339–348. © 2003 Wiley-Liss, Inc. [ABSTRACT FROM AUTHOR]

The SARS-CoV-2 virion responsible for the current world-wide pandemic COVID-19 has a characteristic Spike protein (S) on its surface that embellishes both a prefusion state and fusion state. The prefusion Spike protein (S) is a large trimeric protein where each protomer may be in a so-called Up state or Down state, depending on the configuration of its receptor binding domain (RBD) within its distal, prefusion S1 domain. The Up state is believed to allow binding of the virion to ACE-2 receptors on human epithelial cells, whereas the Down state is believed to be relatively inactive or reduced in its binding behavior. We have performed detailed all-atom, dominant energy landscape mappings for noncovalent interactions (charge, partial charge, and van der Waals) of the SARS-CoV-2 Spike protein in its static prefusion state based on two recent and independent experimental structure publications. We included both interchain interactions and intrachain (domain) interactions in our mappings in order to determine any telling differences (different so-called "glue" points) between residues in the Up and Down state protomers. The S2 proximal, fusion domain demonstrated no appreciable energetic differences between Up and Down protomers, including interchain as well as each protomer's intrachain, S1-S2 interactions. However, the S1 domain interactions across neighboring protomers, which include the RBD-NTD cross chain interactions, showed significant energetic differences between Up-Down and Down-Down neighboring protomers. This included, for example, a key RBD residue ARG357 in the Up-Down interaction and a three residue sequence ALA520-PRO521-ALA522, associated with a turn structure in the RBD of the Up state protomer, acting as a stabilizing interaction with the NTD of its neighbor protomer. Additionally, our intra chain dominant energy mappings within each protomer, identified a significant "glue" point or possible "latch" for the Down state protomer between the S1 subdomain, SD1, and the RBD domain of the same protomer that was completely missing in the Up state protomer analysis. Ironically, this dominant energetic interaction in the Down state protomer involved the backbone atoms of the same three residue sequence ALA520-PRO521-ALA522 of the RBD with the amino acid R-group of GLN564 in the SD1 domain. Thus, this same three residue sequence acts as a stabilizer of the RBD in the Up conformation through its interactions with its neighboring NTD chain and a kind of latch in the Down state conformation through its interactions with its own SD1 domain. The dominant interaction energy residues identified here are also conserved across reported variations of SARS-CoV-2, as well as the closely related virions SARS-Cov and the bat corona virus RatG13. We conducted preliminary molecular dynamics simulations across 0.1 μ seconds to see if this latch provided structural stability and indeed found that a single point mutation (Q564G) resulted in the latch releasing transforming the protomer from the Down to the Up state conformation. Full trimeric Spike protein studies of the same mutation across all protomers, however, did not exhibit latch release demonstrating the critical importance of interchain interactions across the S1 domain, including RBD-NTD neighboring chain interactions. Therapies aimed at disrupting these noncovalent interactions could be a viable route for the physico-chemical mitigation of this deadly virion.