Entropic Interactions Research Articles

All-Atom Perspective of the DENV-3 Methyltransferase Inhibition Mechanism.

The Dengue virus (DENV) is an enveloped, single-stranded RNA virus with several antigenically distinct serotypes (DENV-1 to DENV-5). Dengue fever, as a major public health threat transmitted by mosquitoes, affects millions of people worldwide (especially in tropical and subtropical regions). Toward drug developments of DENV, the nonstructural protein 5 methyltransferase (MTase) serves as an attractive target. The MTase transforms S-adenosyl methionine to S-adenosyl homocysteine (SAH), which is thereby selected as the target with which external drugs compete with. In this work, using alanine scanning with generalized Born and interaction entropy (ASGB-IE), we provide an all-atom perspective of the protein-ligand interactions formed by DENV-3 MTase and SAH derivatives. Residues with consistently high contributions to stabilization are summarized, and the general DENV-3 MTase inhibition mechanism is elucidated. Additionally, the mutational impact on binding thermodynamics is found to be entropy-driven. We also highlight the advantage of the ASGB-IE method for affinity estimation compared to standard end-point protocols, which is highly related to the selection of interfacial residues in free energy estimation. Finally, we performed a thorough scan of the mutational space on critical sites (saturation mutagenesis) and identified 14 mutants causing resistance to the current inhibitors.

A head-to-head comparison of MM/PBSA and MM/GBSA in predicting binding affinities for the CB1 cannabinoid ligands.

The substantial increase in the number of active and inactive-state CB1 receptor experimental structures has provided opportunities for CB1 drug discovery using various structure-based drug design methods, including the popular end-point methods for predicting binding free energies-Molecular Mechanics/Poisson-Boltzmann Surface Area (MM/PBSA) and Molecular Mechanics/Generalized Born Surface Area (MM/GBSA). In this study, we have therefore evaluated the performance of MM/PBSA and MM/GBSA in calculating binding free energies for CB1 receptor. Additionally, with both MM/PBSA and MM/GBSA being known for their highly individualized performance, we have evaluated the effects of various simulation parameters including the use of energy minimized structures, choice of solute dielectric constant, inclusion of entropy, and the effects of the five GB models. Generally, MM/GBSA provided higher correlations than MM/PBSA (rMM/GBSA = 0.433 - 0.652 vs. rMM/PBSA = 0.100 - 0.486) regardless of the simulation parameters, while also offering faster calculations. Improved correlations were observed with the use of molecular dynamics ensembles compared with energyminimized structures and larger solute dielectric constants. Incorporation of entropic terms led to unfavorable results for both MM/PBSA and MM/GBSA for a majority of the dataset, while the evaluation of the various GB models exerted a varying effect on both the datasets. The findings obtained in this study demonstrate the utility of MM/PBSA and MM/GBSA in predicting binding free energies for the CB1 receptor, hence providing a useful benchmark for their applicability in the endocannabinoid system as well as other G protein-coupled receptors. The study utilized the docked dataset (Induced Fit Docking with Glide XP scoring function) from Loo et al., consisting of 46 ligands-23 agonists and 23 antagonists. The equilibrated structures from Loo et al. were subjected to 30ns production simulations using GROMACS 2018 at 300K and 1atm with the velocity rescaling thermostat and the Parinello-Rahman barostat. AMBER ff99SB*-ILDN was used for the proteins, General Amber Force Field (GAFF) was used for the ligands, and Slipids parameters were used for lipids. MM/PBSA and MM/GBSA binding free energies were then calculated using gmx_MMPBSA. The solute dielectric constant was varied between 1, 2, and 4 to study the effect of different solute dielectric constants on the performance of MM/PB(GB)SA. The effect of entropy on MM/PB(GB)SA binding free energies was evaluated using the interaction entropy module implemented in gmx_MMPBSA. Five GB models, GBHCT, GBOBC1, GBOBC2, GBNeck, and GBNeck2, were evaluated to study the effect of the choice of GB models in the performance of MM/GBSA. Pearson correlation coefficients were used to measure the correlation between experimental and predicted binding free energies.

Transglutaminase–mucin binding dynamics in gastrointestinal mucus: Interfacial behaviour, thermodynamics and gelation mechanism

Transglutaminase, an enzyme present in epithelial cells and as a residual component in processed foods, is hypothesised to interact with gastrointestinal mucus, impacting its structure and function. To test the physical validity of this phenomenon, this study investigates the binding kinetics and thermodynamics between porcine gastric mucin (PGM) and microbial transglumatinse (TGM) in a model gastrointestinal mucus, followed by the rheological analysis of the resulting systems. At pH 7, TGM exhibited pronounced binding with the PGM interface, characterised by a high surface density (55.34 ± 1.86 µg/m−2) and a low dissociation constant (KD ∼ 4.03 ± 0.10 μM) as determined by surface plasma resonance (SPR). Conversely, at pH 3, TGM showed weak adhesion onto PGM, resulting in a less stable binding, reflected by a lower surface density (10.94 ± 0.67 µg/m−2) and a higher dissociation constant (KD ∼ 6.24 ± 0.22 μM). Regardless of the nature of interaction, the Hill coefficients (nH ≥ 1) indicated that the binding sites were markedly denser at pH 7 (1383.38 ± 46.47 pmol/m−2), than at pH 3 (273.68 ± 16.84 pmol/m−2). Fluorimetry analysis suggested temperature-dependent dynamic binding between PGM and TGM. The resulting Benesi – Hildebrand plots illustrated a linear correlation between PGM and increasing TGM concentration, suggesting a single-step interaction mechanism. The calculated thermodynamic parameters indicated spontaneous interaction between PGM and TGM (ΔG < 0) via endothermic (entropic) interactions (ΔH > 0). Notably, hydrophobic forces played a significant role in the network stabilisation of PGM−TGM complex (ΔS > 0). Rheometry analysis elucidates that the interaction maxima within TGM−PGM systems substantially elevate both shear viscosity (η), and the melting point (Tm), shifting from 6.75 ± 0.28 to 70.94 ± 2.21 (×10−3) Pa s (at 1 s−1), and 36.80 ± 0.80 to 48.20 ± 0.11 °C, respectively. Furthermore, the coexistence of these two macromolecular species results in a 3- to 4-fold dramatic increase in the viscoelastic moduli of the binary complex. These findings build a strong physicochemical basis for the interaction between TGM and PGM, with profound effects on the rhological behaviour of the latter; it also highlights the need to examine the biochemical/enzymatic aspects of said interactions, and their potential effects on mucosa and human physiology.

Morphological Transitions of Block Copolymer Micelles: Implications for Mesoporous Materials Ordering

AbstractThe design of block‐copolymer‐based functional materials, including mesoporous membranes and nanoparticles, requires a comprehensive understanding of the hierarchical assembly of block copolymers in selective solvents into micelles and subsequent ordered phases. It is hypothesized that micellar ordering and characteristic assembly can be described using a set of phase parameters that account for entropic and enthalpic interactions. Dissipative particle dynamics (DPD) simulations are used to systematically investigate the self‐assembly of semidiluted block copolymers, resembling isoporous membrane preparation conditions. The effect of Flory–Huggins interaction parameters, block lengths, and concentration on the morphology and polydispersity of the micelles is evaluated. The interaction parameters are mapped into Flory–Huggins theory by considering the block's conformation. These results reveal the effect of polymer concentration and solvent affinity on the morphological transition of the aggregates, in agreement with existing experimental evidence. It is identified that monodisperse‐spherical micelles in solution are fundamental to stabilize ordered states. Weak solvent segregation of the largest block, curvature of the core‐corona interface, and stretching of the corona‐forming one are found to be key to stabilize monodisperse assemblies. These conditions can be predicted using spherical‐micelles packing considerations and a global phase parameter from the Flory–Huggins theory. This study provides valuable insights into the self‐assembly of diblock copolymers and offers a potential way to optimize the preparation of mesoporous ordered structures and micelle ordering in semidiluted systems.

The active components of Erzhi wan and their anti-Alzheimer's disease mechanisms determined by an integrative approach of network pharmacology, bioinformatics, molecular docking, and molecular dynamics simulation

Erzhi Wan (EZW), a classic Traditional Chinese Medicine formula, has shown promise as a potential therapeutic option for Alzheimer's disease (AD), yet its mechanism remains elusive. Herein, we employed an integrative in-silico approach to investigate the active components and their mechanisms against AD. We screened four active components with blood-brain barrier permeabilities from TCMSP, along with 307 corresponding targets predicted by SwissTargetPrediction, PharmMapper, and TCMbank websites. Then, we retrieved 2260 AD-related targets from Genecards, OMIM, and NCBI databases. Furthermore, we constructed the protein-protein interaction (PPI) network of the intersected targets via the STRING database and performed the GO and KEGG enrichment analyses using the “clusterProfiler” R package. The results showed that the intersected targets were intimately related to the p53/PI3K/Akt signaling pathway, serotonergic synapse, and response to oxygen level. Subsequently, 25 core targets were found differentially expressed in brain regions by bioinformatics analyses of GEO datasets of clinical samples from the Alzdata database. The binding sites and stabilities between the active components and the core targets were investigated by the molecular docking approach using Autodock 4.2.6 software, followed by pocket detection and druggability assessment via the DoGSiteScorer server. The results showed that acacetin, β-sitosterol, and 3-O-acetyldammarenediol-II strongly interacted with the druggable pockets of AR, CASP8, POLB, and PREP. Eventually, the docking results were further cross-referenced with the literature research and validated by 100 ns of molecular dynamics simulations using GROMACS software. Binding free energies were calculated via MM/PBSA strategy combined with interaction entropy. The simulation results indicated stable bindings between four docking pairs including acacetin-AR, acacetin-CASP8, β-sitosterol-POLB, and 3-O-acetyldammarenediol–II–PREP. Overall, our study demonstrated a theoretical basis for how three active components of EZW confer efficacy against AD. It provides a promising reference for subsequent research regarding drug discoveries and clinical applications.

Biomimetic Non-ergodic Aging by Dynamic-to-covalent Transitions in Physical Hydrogels.

Hydrogels are soft materials engineered to suit a multitude of applications that exploit their tunable mechanochemical properties. Dynamic hydrogels employing noncovalent, physically cross-linked networks dominated by either enthalpic or entropic interactions enable unique rheological and stimuli-responsive characteristics. In contrast to enthalpy-driven interactions that soften with increasing temperature, entropic interactions result in largely temperature-independent mechanical properties. By engineering interfacial polymer-particle interactions, we can induce a dynamic-to-covalent transition in entropic hydrogels that leads to biomimetic non-ergodic aging in the microstructure without altering the network mesh size. This transition is tuned by varying temperature and formulation conditions such as pH, which allows for multivalent tunability in properties. These hydrogels can thus be designed to exhibit either temperature-independent metastable dynamic cross-linking or time-dependent stiffening based on formulation and storage conditions, all while maintaining structural features critical for controlling mass transport, akin to many biological tissues. Such robust materials with versatile and adaptable properties can be utilized in applications such as wildfire suppression, surgical adhesives, and depot-forming injectable drug delivery systems.

Protein Thermodynamic Properties, Crystallisation, and the Hofmeister Series.

The Hofmeister series is a series of ions ordered according to their ability to precipitate proteins. It has also been linked to a host of (bio)chemical phenomena. Several attempts over the years to correlate the series to the varying success of different salts in crystallising proteins have been largely inconclusive. A correlation, based on published data and crystallisation conditions for several proteins, is proposed here between some thermodynamic properties of proteins and the position in the Hofmeister series of the salts from which they preferentially crystallise. Namely, a high ratio between the entropic or enthalpic protein-solvent interactions contribution to thermodynamic stability and the total thermodynamic stability of a given protein, indicate the protein's high propensity to crystallise in solutions of highly kosmotropic salts. Low such ratios on the other hand, indicate that chaotropic salts can be equally successful, i. e. that the protein in question is rather indifferent to the Hofmeister character of the salt. Testing various model proteins for crystallisation against screens containing salts found at different points on the Hofmeister series, as well as further bibliographic analysis, have yielded results that appear to largely corroborate this hypothesis. These conclusions may conceivably be used as a crystallisation predictive tool.

Identification of FTY720 and COH29 as novel topoisomerase I catalytic inhibitors by experimental and computational studies

The development of novel topoisomerase I (TOP1) inhibitors is crucial for overcoming the drawbacks and limitations of current TOP1 poisons. Here, we identified two potential TOP1 inhibitors, namely, FTY720 (a sphingosine 1-phosphate antagonist) and COH29 (a ribonucleotide reductase inhibitor), through experimental screening of known active compounds. Biological experiments verified that FTY720 and COH29 were nonintercalative TOP1 catalytic inhibitors that did not induce the formation of DNA-TOP1 covalent complexes. Molecular docking revealed that FTY720 and COH29 interacted favorably with TOP1. Molecular dynamics simulations revealed that FTY720 and COH29 could affect the catalytic domain of TOP1, thus resulting in altered DNA-binding cavity size. The alanine scanning and interaction entropy identified Arg536 as a hotspot residue. In addition, the bioinformatics analysis predicted that FTY720 and COH29 could be effective in treating malignant breast tumors. Biological experiments verified their antitumor activities using MCF-7 breast cancer cells. Their combinatory effects with TOP1 poisons were also investigated. Further, FTY720 and COH29 were found to cause less DNA damage compared with TOP1 poisons. The findings provide reliable lead compounds for the development of novel TOP1 catalytic inhibitors and offer new insights into the potential clinical applications of FTY720 and COH29 in targeting TOP1.

Accurate prediction of dynamic protein-ligand binding using P-score ranking.

Protein-ligand binding prediction typically relies on docking methodologies and associated scoring functions to propose the binding mode of a ligand in a biological target. Significant challenges are associated with this approach, including the flexibility of the protein-ligand system, solvent-mediated interactions, and associated entropy changes. In addition, scoring functions are only weakly accurate due to the short time required for calculating enthalpic and entropic binding interactions. The workflow described here attempts to address these limitations by combining supervised molecular dynamics with dynamical averaging quantum mechanics fragment molecular orbital. This combination significantly increased the ability to predict the experimental binding structure of protein-ligand complexes independent from the starting position of the ligands or the binding site conformation. We found that the predictive power could be enhanced by combining the residence time and interaction energies as descriptors in a novel scoring function named the P-score. This is illustrated using six different protein-ligand targets as case studies.

One-pot strategy for the preparation of nanoparticles grafted with bimodal polymers: An in-silico insight

Polymer nanocomposites composed of polymer-grafted nanoparticles (NPs) have garnered significant interest due to their diverse functional applications in various domains. The emerging concept of bimodal polymer brushes within the grafting-nanoparticle framework offers control over interfacial entropic and enthalpic interactions. Here, we introduce a novel one-pot strategy that integrates “grafting-to” and “grafting-from” methods to create polymer-grafted bimodal NPs. Utilizing coarse-grained molecular dynamics simulations with a stochastic reaction model, we explore the factors influencing grafting density and polydispersity in these NPs. Our findings demonstrate that this one-pot strategy achieves a polydispersity similar to the two-step “grafting-from then grafting-to” process, while attaining a moderate grafting density comparable to the “grafting-to then grafting-from” approach. Consequently, we analyze factors such as “grafting-from” reaction rates, and initial feeding ratios, step-addition techniques which collectively influence the final grafting density and polydispersity index within this one-pot strategy. This comprehensive investigation enhances our understanding of the kinetics behind synthesizing bimodal polymer-grafted NPs and offers insights for designing polymer-based nanocomposites with improved performance.

Research on Case Reasoning Multi-attribute Group Decision-making Method Based on Hesitant Fuzzy Set

In this study, a hesitant fuzzy set-based case-based reasoning integration method is proposed for the multi-attribute group decision-making problem with unknown attribute weights and mixed forms of attribute values. First, from two perspectives, traditional distance measure and information theory, a multi-objective optimization model is constructed using the distance similarity measure and information entropy of each type of attributes to determine the attribute weights. Secondly, considering the hybrid and nonlinear characteristics of case data, based on the principle of symmetric interaction entropy and TOPSIS method, a global similarity measure based on symmetric interaction entropy is proposed and a case inference algorithm suitable for hesitant fuzzy environment is designed. Finally, by analyzing the arithmetic cases of the target case in the case base, the most similar historical cases to the target case are retrieved to determine the decision-making scheme, and the practicality and feasibility of the decision-making method are verified. The results show that considering hesitant fuzzy theory for case-based reasoning research will help improve the accuracy and reliability of decision-making and provide more effective support for multi-attribute group decision management.

The effects of interfacial layers on dielectric properties of an acrylic co-polymer containing polymer-grafted reduced graphene oxide

In this study, the influence of interfacial layers, in addition to other effective parameters, on the dielectric efficiency of polymer nanocomposites in the rubbery state is presented. For this purpose, reduced graphene oxide (rGO) was grafted by poly (butyl acrylate) chains (rGO-PBA) via surface-initiated atom transfer radical polymerization (SI-ATRP) and incorporated into an acrylic co-polymer matrix with the glass-transition temperature (Tg) well below room temperature. The rGO exhibited poor dispersion and uneven distribution in acrylic co-polymer, whereas polymer grafted-rGO showed excellent dispersion. The grafted chains can penetrate and form entropic interactions with the matrix chains, which results in a strong interfacial region. The immobilized interfacial layer was characterized by DSC and dielectric measurements. The dielectric measurements in different temperatures provided the means to evaluate the contribution of the interfacial layers on dielectric properties. The findings confirmed that there exists an optimum chain mobility in which the chain polarization shows a major contribution to the dielectric properties of polymer nanocomposites. Reduction of temperature to a certain degree exhibited more rise in the dielectric properties of polymer/rGO-PBA nanocomposites than pure matrix which can be correlated to the interfacial region.

An Efficient Approach to the Accurate Prediction of Mutational Effects in Antigen Binding to the MHC1.

The major histocompatibility complex (MHC) can recognize and bind to external peptides to generate effective immune responses by presenting the peptides to T cells. Therefore, understanding the binding modes of peptide-MHC complexes (pMHC) and predicting the binding affinity of pMHCs play a crucial role in the rational design of peptide vaccines. In this study, we employed molecular dynamics (MD) simulations and free energy calculations with an Alanine Scanning with Generalized Born and Interaction Entropy (ASGBIE) method to investigate the protein-peptide interaction between HLA-A*02:01 and the G9209 peptide derived from the melanoma antigen gp100. The energy contribution of individual residue was calculated using alanine scanning, and hotspots on both the MHC and the peptides were identified. Our study shows that the pMHC binding is dominated by the van der Waals interactions. Furthermore, we optimized the ASGBIE method, achieving a Pearson correlation coefficient of 0.91 between predicted and experimental binding affinity for mutated antigens. This represents a significant improvement over the conventional MM/GBSA method, which yields a Pearson correlation coefficient of 0.22. The computational protocol developed in this study can be applied to the computational screening of antigens for the MHC1 as well as other protein-peptide binding systems.

A Unified Description of Salt Effects on the Liquid-Liquid Phase Separation of Proteins.

Protein aggregation via liquid-liquid phase separation (LLPS) is ubiquitous in nature and is intimately connected to many human diseases. Although it is widely known that the addition of salt has crucial impacts on the LLPS of proteins, full understanding of the salt effects remains an outstanding challenge. Here, we develop a molecular theory that systematically incorporates the self-consistent field theory for charged macromolecules into the solution thermodynamics. The electrostatic interaction, hydrophobicity, ion solvation, and translational entropy are included in a unified framework. Our theory fully captures the long-standing puzzles of the nonmonotonic salt concentration dependence and the specific ion effect. We find that proteins show salting-out at low salt concentrations due to ionic screening. The solubility follows the inverse Hofmeister series. In the high salt concentration regime, protein continues salting-out for small ions but turns to salting-in for larger ions, accompanied by the reversal of the Hofmeister series. We reveal that the solubility at high salt concentrations is determined by the competition between the solvation energy and translational entropy of the ion. Furthermore, we derive an analytical criterion for determining the boundary between the salting-in and salting-out regimes, which is in good agreement with experimental results for various proteins and salt ions.

A Science Friction Story: Molecular Interactions in Semiflexible Polymer Networks

AbstractEstablished model theories, developed to capture the mechanical behavior of soft, complex materials composed of semiflexible polymers, assume that entropic interactions between filaments are primarily responsible for determining the mechanical response. In recent studies, the generally accepted tube model has been challenged in terms of this basic assumption about filament–filament interactions, but also because of its predictions regarding the frequency dependence of the elastic modulus in the intermediate frequency regime. A central question is how molecular interactions and friction between network constituents influence the rheological response of isotropic entangled networks of semiflexible polymers. It has been previously shown that friction forces between aligned pairs of actin filaments are not negligible. Here, the influence of friction forces and attractive interactions on network rheology is systematically investigated by means of targeted surface modification. It is shown that these forces have a qualitative and quantitative influence on the viscoelastic properties of semiflexible polymer networks and contribute to their response to nonlinear deformations. By comparing two polymer model systems with respect to their surface compositions, a possible explanation is given about the origin of acting forces on a molecular level.

Structural and thermodynamic properties of conserved water molecules in Mpro native: A combined approach by MD simulation and Grid Inhomogeneous Solvation Theory.

The new viral strains of severe acute respiratory syndrome coronavirus-2 (SARS-CoV-2) are continuously rising, becoming more virulent, and transmissible. Therefore, the development of new antiviral drugs is essential. Due to its significant role in the viral life cycle of SARS-CoV-2, the main protease (Mpro) enzyme is a leading target for antiviral drug design. The Mpro monomer consists of domain DI, DII, and DI-DII interface. Twenty-one conserved water molecules (W4-W24) are occupied at these domains according to multiple crystal structure analyses. The crystal and MD structures reveal the presence of eight conserved water sites in domain DI, DII and remaining in the DI-DII interface. Grid-based inhomogeneous fluid solvation theory (GIST) was employed on MD structures of Mpro native to predict structural and thermodynamic properties of each conserved water site for focusing to identify the specific conserved water molecules that can easily be displaced by proposed ligands. Finally, MD water W13 is emerged as a promising candidate for water mimic drug design due to its low mean interaction energy, loose binding character with the protein, and its involvement in a water-mediated H-bond with catalytic His41 via the interaction Thr25(OG)---W13---W---His41(NE2). In this context, water occupancy, relative interaction energy, entropy, and topologies of W13 are thermodynamically acceptable for the water displacement method. Therefore, the strategic use of W13's geometrical position in the DI domain may be implemented for drug discovery against COVID disease by designing new ligands with appropriately oriented chemical groups to mimic its structural, electronic, and thermodynamic properties.

Exploring transmembrane allostery in the MexB: DB08385 variant as a promising inhibitor-like candidate against Pseudomonas aeruginosa antibiotic resistance: a computational study.

Pseudomonas aeruginosa, a formidable pathogen renowned for its antimicrobial resistance, poses a significant threat to immunocompromised individuals. In this regard, the MexAB-OprM efflux pump acts as a pivotal line of defense by extruding antimicrobials from bacterial cells. The inner membrane homotrimeric protein MexB captures antibiotics and translocates them into the outer membrane OprM channel protein connected through the MexA adaptor protein. Despite extensive efforts, competitive inhibitors targeting the tight (T) protomer of the MexB protein have not received FDA approval for medical use. Over the past few years, allosteric inhibitors have become popular as alternatives to the classical competitive inhibitor-based approach because of their higher specificity, lower dosage, and reduced toxicological effects. Hence, in this study, we unveiled the existence of a transmembrane allosteric binding pocket of MexB inspired by the recent discovery of an important allosteric inhibitor, BDM88855, for the homolog AcrB protein. While repurposing BDM88855 proved ineffective in controlling the MexB loose (L) protomer, our investigation identified a promising alternative: a chlorine-containing variant of DB08385 (2-Cl DB08385 or Variant 1). Molecular dynamics simulations, including binding free energy estimation coupled with heterogeneous dielectric implicit membrane model (implicit-membrane MM/PBSA), interaction entropy (IE) analysis and potential of mean force (PMF) calculation, demonstrated Variant 1's superior binding affinity to the transmembrane pocket, displaying the highest energy barrier in the ligand unbinding process. To elucidate the allosteric crosstalk between the transmembrane and porter domain of MexB, we employed the 'eigenvector centrality' measure in the linear mutual information obtained from the protein correlation network. Notably, this study confirmed the presence of an allosteric transmembrane site in the MexB L protomer. In addition to this, Variant 1 emerged as a potent regulator of allosteric crosstalk, inducing an 'O-L intermediate state' in the MexB L protomer. This induced state might hold the potential to diminish substrate intake into the access pocket, leading to the ineffective efflux of antibiotics.

On the origin of Sanchez-Lacombe equation of state theory in hydrostatic strain energy model for rubber-like materials

To capture the volume deformation of rubber-like materials, the strain energy density (SED) function of a compressible hyperelastic model is formulated as the hydrostatic/liquid-like term from interchain interaction changes plus the compressible elastic term owing to elastic deformation of crosslinking network. Notably, the former term dominates volume responses. Although the physics of the hydrostatic term is relatively clear, to our knowledge, few physically-based models are available. However, in our previous work (Liu and Lu, 2023), we constructed a physically-based hydrostatic SED function inspired by the Flory-Orwoll-Vrij equation of state (EOS) theory for pure polymer fluids, and proposed the general strategy for developing hydrostatic functions according to the EOS theories. Sanchez-Lacombe EOS theory (note: a type of lattice-fluid EOS theory) inspired this work. We assume: (i) a rubber-like material consists of polymer segments occupying lattice sites and unoccupied/vacant lattice sites, and the compressibility of the material corresponds to changes in vacant sites fraction; (ii) the hydrostatic strain energy is associated with the interchain interaction energy change and the mixing entropy change between network and vacant sites. According to the Helmholtz free energy in Sanchez-Lacombe EOS theory and limiting our attention to the isothermal condition, another physically-based hydrostatic SED function is constructed; a specific compressible hyperelastic model is provided by further combining compressible 8-chain elastic SED function. The basic framework of this compressible model is inherently consistent with the Flory-Rehner framework for swollen elastomers. Our model provides good predictions for volume deformation data of ten different rubber-like materials in hydrostatic compression (HC), uniaxial tension (UT), and constrained uniaxial compression (CUC). The proposed model reveals that HC, CUC, or uniaxial compression correspond to the entropy-decreasing process and they all are controlled by entropy changes; while for UT, equibiaxial tension, or pure shear, the entropy first increases and then decreases, and the interchain interaction energy and entropy changes control the responses for initial small stretches and remaining large stretches, respectively. This study aims to provide a new physical insight and a valid physically-based hydrostatic SED function for the compressibility of rubber-like materials.

Boltzmann-Shannon interaction entropy: A normalized measure for continuous variables with an application as a subsample quality metric.

The recent introduction of geometric partition entropy offered an alternative to differential Shannon entropy for the quantification of uncertainty as estimated from a sample drawn from a one-dimensional bounded continuous probability distribution. In addition to being a fresh perspective for the basis of continuous information theory, this new approach provided several improvements over traditional entropy estimators including its effectiveness on sparse samples and a proper incorporation of the impact from extreme outliers. However, a complimentary relationship exists between the new geometric approach and the basic form of its frequency-based predecessor that is leveraged here to define an entropy measure with no bias toward the sample size. This stable normalized measure is named the Boltzmann-Shannon interaction entropy (BSIE)) as it is defined in terms of a standard divergence between the measure-based and frequency-based distributions that can be associated with the two historical figures. This parameter-free measure can be accurately estimated in a computationally efficient manner, and we illustrate its utility as a quality metric for subsampling in the context of nonlinear polynomial regression.

Biophysical Characterization of the Thermodynamic Basis and Binding Orientation for Factor VIII Membrane Association

After vesicular damage occurs, factor VIII (fVIII) is proteolytically activated by thrombin and binds to activated factor IX (fIX) on the surface of activated platelets during the blood coagulation cascade to form the intrinsic “tenase” complex. Once activated, fVIII dissociates from von Willebrand factor and C1 and C2 domains bind to activated platelet surfaces. Previous studies have identified that the C1 and C2 domains bind to negatively charged membranes through both surface exposed hydrophobic residues located in the beta hairpin loops and adjacent positively charged residues. The thermodynamics of fVIII lipid binding are currently uncharacterized and our current understanding of the binding orientation of the C1 and C2 domains of fVIII on lipid membranes is incomplete. In this study, we investigate the thermodynamics and binding orientation of the C domains via mutagenesis to both surface exposed hydrophobic residues and adjacent charged residues. Binding measurements between phosphatidylserine (PS) containing lipid nanodiscs and fVIII C domains have revealed that the C1 domain lipid binding is driven by enthalpic interactions, whereas the C2 domain binding is driven by entropic interactions. Binding experiments on fVIII C2 domain mutants for both surface exposed hydrophobic and positively charged residues have revealed differential disruption to lipid binding. Lastly, we have utilized molecular dynamics to perform simulations on the C1 and C2 domains binding to lipid nanodiscs to elucidate the binding orientation of the C domains and identify novel residues that interact with the membrane. Our results from these simulations agree with previous work, showing that C domain lipid binding centers on R2163 (C1) and R2320 (C2).