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Understanding natural protein evolution and designing novel proteins are motivating interest in development of high-throughput methods to explore large sequence spaces. In this work, we demonstrate the application of multisite λ dynamics (MSλD), a rigorous free energy simulation method, and chemical denaturation experiments to quantify evolutionary selection pressure from sequence-stability relationships and to address questions of design. This study examines a mesophilic phylogenetic clade of ribonuclease H (RNase H), furthering its extensive characterization in earlier studies, focusing on E. coli RNase H (ecRNH) and a more stable consensus sequence (AncCcons) differing at 15 positions. The stabilities of 32,768 chimeras between these two sequences were computed using the MSλD framework. The most stable and least stable chimeras were predicted and tested along with several other sequences, revealing a designed chimera with approximately the same stability increase as AncCcons, but requiring only half the mutations. Comparing the computed stabilities with experiment for 12 sequences reveals a Pearson correlation of 0.86 and root mean squared error of 1.18 kcal/mol, an unprecedented level of accuracy well beyond less rigorous computational design methods. We then quantified selection pressure using a simple evolutionary model in which sequences are selected according to the Boltzmann factor of their stability. Selection temperatures from 110 to 168 K are estimated in three ways by comparing experimental and computational results to evolutionary models. These estimates indicate selection pressure is high, which has implications for evolutionary dynamics and for the accuracy required for design, and suggests accurate high-throughput computational methods like MSλD may enable more effective protein design.

We consider the 2-spin spherical Sherrington–Kirkpatrick model without external magnetic field where the interactions between the spins are given as random variables with heavy-tailed distribution. We show that the free energy exhibits a sharp phase transition depending on the location of the largest eigenvalue of the interaction matrix. We also prove the order of the limiting free energy and the limiting distribution of the fluctuation of the free energy for both regimes. [ABSTRACT FROM AUTHOR]

The presence of bound water in clay has a significant impact on the physical and chemical properties of clay, particularly its strength, permeability, and creep behavior. In this paper, the bound water in clay has been studied from the perspective of water potential. Initially, the adsorption isotherms of powders and consolidated samples for Na- and Ca-bentonite and illite were measured, and the bound water content was determined by subtracting the capillary water in the isotherms, with the capillary water being calculated by mercury intrusion porosimetry tests. The results indicated that bound water is independent of the void ratio and pore structure of clay, which is consistent with previous studies. Then, metadynamics was conducted to determine the adsorption free energy landscapes of the three clays, and the lowest suctions of the three clay minerals were determined to be −1.7 , −5.4 , and −2.1 GPa , respectively. Finally, through a comparison of the simulations and experiments in this study and in the literature, three important conclusions were drawn. Firstly, the lowest water potential for montmorillonite exhibits a linear relationship with the hydration free energy of exchangeable cations. Secondly, the critical water potential for tightly bound water is determined as the first inflection point in the relationship between water potential and water content, and the critical value of montmorillonite is found to be correlated to the valence of exchangeable cations. Lastly, the boundary between loosely bound water and capillary water is determined as the starting point of capillary water formation. Overall, this research highlights the importance of considering water potential as a key factor in understanding the behavior of bound water in clay. [ABSTRACT FROM AUTHOR]

Synthetic dyes, such as Alizarin Red S, contribute significantly to environmental pollution. This study investigates the biosorption potential of Alhagi maurorum biosorbent for the removal of Alizarin Red S (ARS) from aqueous solutions. Fourier transform infrared spectroscopy (FTIR) was used to analyze the biosorbent's adsorption sites. Various parameters were optimized to maximize dye adsorption. An optimal removal efficiency of 82.26% was attained by employing 0.9 g of biosorbent with a 25 ppm dye concentration at pH 6 and 60 °C over 30 min. The data were modeled using various isothermal and kinetic models to understand the adsorption behavior. Thermodynamic parameters indicated that the adsorption process was spontaneous and endothermic. The pseudo-second-order kinetic model best described the data, indicating chemisorption as the rate-limiting step. The data matched best to the Langmuir model, indicating that the adsorption occurs as a monolayer on uniform surfaces with a finite number of binding sites. The model showed a strong correlation (R² = 0.991) and a maximum adsorption capacity (qmax) of 8.203 mg/g. Principal component analysis (PCA) identified temperature as the dominant factor, with the primary component, PC1 capturing 100% of its effect. The mechanisms involved in ARS biosorption on A. maurorum include electrostatic interactions, hydrogen bonding, hydrophobic interactions, dipole-dipole interactions, and π-π stacking. Alhagi maurorum showed promising potential for biosorbing toxic dyes from contaminated water, suggesting further investigation for practical applications. [ABSTRACT FROM AUTHOR]

Computational methods such as molecular dynamics (MD) have illuminated how single‐atom ions permeate membrane channels and how selectivity among them is achieved. Much less is understood about molecular permeation through eukaryotic channels that mediate the flux of small molecules (e.g. connexins, pannexins, LRRC8s, CALHMs). Here we describe computational methods that have been profitably employed to explore the movements of molecules through wide pores, revealing mechanistic insights, guiding experiments, and suggesting testable hypotheses. This review illustrates MD techniques such as voltage‐driven flux, potential of mean force, and mean first‐passage‐time calculations, as applied to molecular permeation through wide pores. These techniques have enabled detailed and quantitative modeling of molecular interactions and movement of permeants at the atomic level. We highlight novel contributors to the transit of molecules through these wide pathways. In particular, the flexibility and anisotropic nature of permeant molecules, coupled with the dynamics of pore‐lining residues, lead to bespoke permeation dynamics. As more eukaryotic large‐pore channel structures and functional data become available, these insights and approaches will be important for understanding the physical principles underlying molecular permeation and as guides for experimental design. [ABSTRACT FROM AUTHOR]

This study showed that the predictor in logistic regression can be applied to estimating the Gibbs free energy of tRNAs' recognition of and binding to their aminoacyl-tRNA synthetases. Then, 24 linear logistic regression models predicting different classes of tRNAs loaded with a corresponding amino acid were trained in a machine learning classification method, reducing the misclassification error to zero. The models were based on minimal subsets of Boolean explanatory variables describing the favorite presence of nucleotides or nucleosides localized in the different parts of the tRNA. In 90% of cases, they agree with the components of the consensus strand in a class of tRNAs loaded by a given amino acid. According to the proposed theoretical model, the values of the free energy for the entry of the recognition state in the process of tRNA charging were obtained, and the inputs from identity nucleotides and the tRNA strand backbone were distinguished. Almost all the resulting models indicated leading anticodon tandems defining the first and second positions of the anticodon (positions 35 and 36 of the tRNA strand) and the small sets (up to six positions) of the other nucleotides as the natural identity nucleotides most influential in the free energy balance. The magnitude of their input to this energy depends on the position in the strand, favoring positions −1, 35, and 36. The role of position 34 is relatively smaller. These identity attributes may not always be fully arranged in a real single adaptor molecule but were comprehensively present in a given tRNA class. A detailed analysis of the resulting models showed that the absolute value of the energy of binding the tandem 35–36 decreases with the number of identity positions, as well as with the decreasing number of possible hydrogen bonds. On the other hand, in these conditions, the absolute value of the energy of binding of other identity nucleotides increases. All the models indicate that the nucleotide-independent energy of the repulsion tRNA backbone decreases with the number of identity nucleotides. It was also shown that the total free energy change in entering the recognition state increases with the amino acid mass, making this process less spontaneous, which may have an evolutionary reference. [ABSTRACT FROM AUTHOR]

We investigate the inhibition mechanism between pomotrelvir and the SARS‐CoV‐2 main protease using molecular mechanics and quantum mechanics/molecular mechanics simulations. Alchemical transformations where each Pi group of pomotrelvir was transformed into its counterpart in nirmatrelvir were performed to unravel the individual contribution of each group to the binding and reaction processes. We have shown that while a γ‐lactam ring is preferred at position P1, a δ‐lactam ring is a good alternative for the design of inhibitors for variants presenting mutations at position 166. For the P2 position, tertiary amines are preferred with respect to secondary amines. Flexible side chains at the P2 position can disrupt the preorganization of the active site, favouring the exploration of non‐reactive conformations. The substitution of the P2 group of pomotrelvir by that of nirmatrelvir resulted in a compound, named as C2, that presents a better binding free energy and a higher population of reactive conformations in the Michaelis complex. Analysis of the chemical reaction to form the covalent complex has shown a similar reaction mechanism and activation free energies for pomotrelvir, nirmatrelvir and C2. We hope that these findings could be useful to design better inhibitors to fight present and future variants of the SARS‐CoV‐2 virus. [ABSTRACT FROM AUTHOR]

This study explores the interactions between hexanal Schiff bases and a B12N12 nanocage, employing density functional theory (DFT) calculations to deepen our understanding of noncovalent bonds. Hexanal, a key component in tea, plays a vital role in prolonging the shelf-life of various plant-based products by inhibiting phospholipase-D. Our research initially focused on synthesizing Schiff bases through the condensation of hexanal with nucleobases and an amino acid. We then conducted a series of DFT calculations, including geometry optimizations, frontier molecular orbital (FMO), natural bond orbital (NBO) and noncovalent interactions (NCI) assays, using Gaussian 16 and ORCA 5.0.2 software packages. This study reveals that hexanal Schiff bases form stable complexes with the B12N12 nanocage, exhibiting notable dative coordinate bonding. The FMO analysis indicates a significant energy gap variation among the complexes, with CSB2 showing the lowest energy gap, hinting at its high reactivity. In the LED assay, CSB2 demonstrates the lowest decomposition energy, highlighting its potential stability. The AIMD simulations provide insights into the electronic motions of these complexes, underscoring their dynamic nature. Our NBO analysis offers a comprehensive view of the electron distribution within these complexes, emphasizing the significance of nitrogen and boron atoms in the bonding process. The NCI assay sheds light on the predominant van der Waals and steric interactions contributing to the stability of the complexes. This investigation provides a detailed account of the NCI between hexanal Schiff bases and the B12N12 nanocage. The findings not only contribute to the field of noncovalent bonding in inorganic-fullerene structures but also open avenues for future applications in material science and molecular engineering. The intermolecular interactions between Schiff's bases and nanocage through noncovalent dative bonds. The reaction energy of the formation of CSB3 is more facile than the other two complexes. CBS2 has a low band gap is more active than the other two, and has less local decomposition energy. [ABSTRACT FROM AUTHOR]

• Atrazine migrates from ice to water during the freezing process. • The migration of herbicide atrazine is related to binding energy. • The migration ability of herbicide atrazine is related to free energy. • Temperature is the key to determine the magnitude of the free energy. Atrazine causes concern due to its resistant to biodegradation and could be accumulated in aquatic organisms, causing pollution in lakes. This study measured the concentration of atrazine in ice and the water under ice through a simulated icing experiment and calculated the distribution coefficient K to characterize its migration ability in the freezing process. Furthermore, density functional theory (DFT) calculations were employed to expatiate the migration law of atrazine during icing process. According to the results, it could release more energy into the environment when atrazine staying in water phase (-15.077 kcal/mol) than staying in ice phase (-14.388 kcal/mol), therefore it was beneficial for the migration of atrazine from ice to water. This explains that during the freezing process, the concentration of atrazine in the ice was lower than that in the water. Thermodynamic calculations indicated that when the temperature decreases from 268 to 248 K, the internal energy contribution of the compound of atrazine and ice molecule (water cluster) decreases at the same vibrational frequency, resulting in an increase in the free energy difference of the compound from -167.946 to -165.390 kcal/mol. This demonstrated the diminished migratory capacity of atrazine. This study revealed the environmental behavior of atrazine during lake freezing, which was beneficial for the management of atrazine and other pollutants during freezing and environmental protection. [ABSTRACT FROM AUTHOR]

Mainstream economics describes virtual wealth with theory that is at odds with the physical laws that govern a nation's physical resources. This confusion fundamentally prevents the realization of "sustainable" economies. The relation between debt and the metabolism of a country (measured by GDP or power consumption) appears to follow a diffusion relationship, in which debt encodes the temporal evolution of an economic potential. Debt enables the production of resources and the realization of a country's economic wealth potential (the sum of its environmental, geological, and societal endowments, among others). Any economic scheme dependent on finite stocks of free energy for growth must eventually collapse, and as such cannot be considered sustainable. Our simple debt–diffusion model is shown to closely match the trajectories of 44 different economies. [ABSTRACT FROM AUTHOR]

We present Einstein coefficient spectra and a detailed-balance derivation of generalized Einstein relations between them that is based on the connection between spontaneous and stimulated emission. If two broadened levels or bands overlap in energy, transitions between them need not be purely absorptive or emissive. Consequently, spontaneous emission can occur in both transition directions, and four Einstein coefficient spectra replace the three Einstein coefficients for a line. At equilibrium, the four different spectra obey five pairwise relationships and one lineshape generates all four. These relationships are independent of molecular quantum statistics and predict the Stokes' shift between forward and reverse transitions required by equilibrium with blackbody radiation. For Boltzmann statistics, the relative strengths of forward and reverse transitions depend on the formal chemical potential difference between the initial and final bands, which becomes the standard chemical potential difference for ideal solutes. The formal chemical potential of a band replaces both the energy and degeneracy of a quantum level. Like the energies of quantum levels, the formal chemical potentials of bands obey the Rydberg-Ritz combination principle. Each stimulated Einstein coefficient spectrum gives a frequency-dependent transition cross-section. Transition cross-sections obey causality and a detailed-balance condition with spontaneous emission, but do not directly obey generalized Einstein relations. Even with an energetic width much less than the photon energy, a predominantly absorptive forward transition with an energetic width much greater than the thermal energy can have such an extreme Stokes' shift that its reverse transition cross-section becomes predominantly absorptive rather than emissive. [ABSTRACT FROM AUTHOR]

The current study was conducted by introducing a narrow bandgap semiconductor, ZnIn 2 S 4 , with the goal of addressing the inefficiency of hydrolysis dissociation and the limited visible light absorption capacity faced by TiO 2 as a hydrogen evolution reaction (HER) catalyst due to its low conduction band position and wide bandgap. Using a one-step hydrothermal process, ZnIn 2 S 4 nanosheet/TiO 2 nanorod heterostructures were built on nickel foam substrates. The nanosheet structure of ZnIn 2 S 4 is shaped like a flower, which greatly increased the roughness of the TiO 2 surface and revealed additional active sites. The ZnIn 2 S 4 /TiO 2 heterostructure demonstrates quick reaction kinetics and effective electron transport capability, as demonstrated by the electrochemical test results. An overpotential of just 195 mV is required to obtain a current density of 10 mA cm−2. In addition, the overpotential is further decreased to 160 mV under simulated solar radiation. Furthermore, ZnIn 2 S 4 addition minimizes the free energy of hydrogen adsorption on the TiO 2 surface and optimizes the position of its Fermi energy level, improving the usage of photogenerated carriers, according to density functional theory (DFT) calculations. This work validates the prospective use of ZnIn 2 S 4 /TiO 2 heterostructures in photoelectrocatalysis and offers a fresh viewpoint for developing high-performance HER catalysts. • Composite of TiO 2 with ZnIn 2 S 4 exposes more active sites and improves HER performance. • Changes in d-band center and free energy explain catalytic performance enhancement. • Formation of interfacial electric field improves HER performance of TiO 2. [ABSTRACT FROM AUTHOR]

The serotonin transporter (SERT) is a member of the Solute Carrier 6 (SLC6) family and is responsible for maintaining the appropriate level of serotonin in the brain. Dysfunction of SERT has been linked to several neuropsychiatric disorders, including depression, anxiety and obsessive‐compulsive disorder. Therefore, an in‐depth understanding of the mechanism on an atomistic level, coupled with a quantification of transporter dynamics and the associated free energies is required. Here, we constructed Markov state models (MSMs) from extensive unbiased molecular dynamics simulations to quantify the free energy profile of serotonin (5HT) triggered SERT occlusion and explored the driving forces of the mechanism of occlusion. Our results reveal that SERT occludes via multiple intermediate conformations and show that the motion of occlusion is energetically downhill for the 5HT‐bound transporter. Force distribution analyses show that the interactions of 5HT with the bundle domain are crucial. During occlusion, attractive forces steadily increase and pull on the bundle domain, which leads to SERT occlusion. Some interactions become repulsive upon full occlusion, suggesting that SERT creates pressure on 5HT to promote its movement towards the cytosol. [ABSTRACT FROM AUTHOR]

A fully discrete semi-convex-splitting finite-element scheme with stabilization for a Cahn–Hilliard cross-diffusion system is analyzed. The system consists of parabolic fourth-order equations for the volume fraction of the fiber phase and solute concentration, modeling pre-patterning of lymphatic vessel morphology. The existence of discrete solutions is proved, and it is shown that the numerical scheme is energy stable up to stabilization, conserves the solute mass, and preserves the lower and upper bounds of the fiber phase fraction. Numerical experiments in two space dimensions using FreeFem illustrate the phase segregation and pattern formation. [ABSTRACT FROM AUTHOR]

In thermodynamic theory, free energy (i.e., available energy) is the concept facilitating the combined applications of the theory's two fundamental laws, the first and the second laws of thermodynamics. The critical step was taken by Kelvin, then by Helmholtz and Gibbs—that in natural processes, free energy dissipates spontaneously. With the formulation of the second law of entropy growth, this may be referred to as the dissymmetry proposition manifested in the spontaneous increase of system/environment entropy towards equilibrium. Because of Kelvin's pre-entropy law formulation of free energy, our concept of free energy is still defined, within a framework on the premise of primacy of energy, as "body's internal energy or enthalpy, subtracted by energy that is not available". This primacy of energy is called into question because the driving force to cause a system's change is the purview of the second law. This paper makes a case for an engineering thermodynamics framework, instead, to be based on the premise of the primacy of dissymmetry over free energy. With Gibbsian thermodynamics undergirded with dissymmetry proposition and engineering thermodynamics with a dissymmetry premise, the two branches of thermodynamics are unified to become classical thermodynamics. [ABSTRACT FROM AUTHOR]

Abstract Synthetic dyes, such as Alizarin Red S, contribute significantly to environmental pollution. This study investigates the biosorption potential of Alhagi maurorum biosorbent for the removal of Alizarin Red S (ARS) from aqueous solutions. Fourier transform infrared spectroscopy (FTIR) was used to analyze the biosorbent’s adsorption sites. Various parameters were optimized to maximize dye adsorption. An optimal removal efficiency of 82.26% was attained by employing 0.9 g of biosorbent with a 25 ppm dye concentration at pH 6 and 60 °C over 30 min. The data were modeled using various isothermal and kinetic models to understand the adsorption behavior. Thermodynamic parameters indicated that the adsorption process was spontaneous and endothermic. The pseudo-second-order kinetic model best described the data, indicating chemisorption as the rate-limiting step. The data matched best to the Langmuir model, indicating that the adsorption occurs as a monolayer on uniform surfaces with a finite number of binding sites. The model showed a strong correlation (R² = 0.991) and a maximum adsorption capacity (qmax) of 8.203 mg/g. Principal component analysis (PCA) identified temperature as the dominant factor, with the primary component, PC1 capturing 100% of its effect. The mechanisms involved in ARS biosorption on A. maurorum include electrostatic interactions, hydrogen bonding, hydrophobic interactions, dipole-dipole interactions, and π-π stacking. Alhagi maurorum showed promising potential for biosorbing toxic dyes from contaminated water, suggesting further investigation for practical applications.

Background: The loss-of-function (LOF) classification of most missense variants in tumor suppressor breast cancer genes BRCA1, BRCA2, PALB2, and RAD51C remains unclassified and confounds clinical actionability. Classifying these variants is challenging due to their rarity, leading clinicians to rely on in silico predictive methods. Protein stability changes are associated with function, making stability predictors valuable. Stability predictions upon missense variant perturbations require high-resolution protein structures. However, the availability of these high-resolution structures is lacking. This study explores using generative AI to predict high-resolution protein structures, which can then be analyzed with in silico protein stability prediction methods to assess LOF activity in ordered regions of the protein. This study also determines the appropriate in silico protein stability and dedicated in silico missense prediction methods in dbNSFP v4.7 database to predict LOF activity in ordered regions of these four genes. Functional classifications from homology recombination DNA repair (HDR) assays and variant classifications from the ClinVar database provide a reliable dataset for evaluating the performance of these in silico prediction methods. Results: Complex AlphaFold2 structures of the BRCA1-C terminal (BRCT) domain and the DNA-binding (DB) domain of BRCA2, analyzed using protein stability tool FoldX predicts LOF activity from missense variants significantly better than experimentally-derived structures in ordered regions. The BRCT domain achieved an Area Under the Curve (AUC)= 0.861 (95 % CI:0.858–0.863) and AUC= 0.842 (95 % CI:0.840–0.845), while the DB domain achieved an AUC= 0.836 (95 % CI:0.8322–0.841), compared to AUC= 0.847 (95 % CI:0.844–0.850) and AUC= 0.835 (95 % CI:0.832–0.837) from the BRCT domain, and AUC= 0.830 (95 % CI:0.821–0.8320) from the DB domain from experimentally-derived structures. Protein stability does not predict LOF activity from missense variants better than dedicated in silico missense predictors. Overall, we find that AlphaMissense ranks highly, with an average AUC= 0.890 (95 % CI 0.886–0.895) from ordered regions across these four cancer genes, compared to all other in silico missense predictors present in the dbNSFP database. Conclusions: The study reveals that generative AI protein predicted structures can outperform experimentally-derived structures in evaluating LOF activity from predicted protein stability in ordered regions of genes BRCA1, BRCA2, PALB2 and RAD51C. The study also highlights the predictive performance of AlphaMissense as the premier in silico missense prediction method to predict LOF activity from missense variants in these four tumor suppressor breast cancer genes. The code for this study can be downloaded for free on GitHub (https://github.com/rohandavidg/CarePred)

[Display omitted] There is a relationship between the static contact angle of droplets and soap bubbles on flat homogeneous surfaces, therefore, it should be possible to derive a relationship between the static contact angle of a soap bubble on a periodic topographic surface and a droplet on a flat homogeneous surface. A free energy model of the static contact angle of soap bubbles on a topographic surface in the Cassie-Baxter state was derived. Polydimethylsiloxane surfaces of varying area fraction (0.125, 0.250, 0.500, 0.750, and 1.00) and periodic topographies (lined and pillared) were fabricated using 3D printed moulds for pattern transfer. A bubble goniometer was developed to accommodate bubbles of 40,000 ± 5,000 mm3 and 50,000 ± 5,000 mm3 volumes. Then, the static contact angle of bubbles of both volumes were measured on the varying topographic surfaces. The derived predictions imply that the relationship between the static contact angle for bubbles on a flat homogeneous surface and on a composite surface, has the same form as the Cassie-Baxter equation for a droplet. The experimental results for the measured static contact angle for both bubble volumes on the varying surfaces had good agreement with the predicted trends. [ABSTRACT FROM AUTHOR]

In thermodynamic theory, free energy (i.e., available energy) is the concept facilitating the combined applications of the theory’s two fundamental laws, the first and the second laws of thermodynamics. The critical step was taken by Kelvin, then by Helmholtz and Gibbs—that in natural processes, free energy dissipates spontaneously. With the formulation of the second law of entropy growth, this may be referred to as the dissymmetry proposition manifested in the spontaneous increase of system/environment entropy towards equilibrium. Because of Kelvin’s pre-entropy law formulation of free energy, our concept of free energy is still defined, within a framework on the premise of primacy of energy, as “body’s internal energy or enthalpy, subtracted by energy that is not available”. This primacy of energy is called into question because the driving force to cause a system’s change is the purview of the second law. This paper makes a case for an engineering thermodynamics framework, instead, to be based on the premise of the primacy of dissymmetry over free energy. With Gibbsian thermodynamics undergirded with dissymmetry proposition and engineering thermodynamics with a dissymmetry premise, the two branches of thermodynamics are unified to become classical thermodynamics.

Hydraulic oil leaks during mechanical maintenance, resulting in flushing wastewater contaminated with dispersed nano-oil droplets. In this study, 75 mg L−1 of polysilicate aluminum ferric (PSAF) was stirred at 350 rpm and the optimal chemical oxygen demand (COD) removal was 71%. The increase of PSAF led to more hydrolysis of Fe, and 1,175 cm−1 hydroxyl bridged with negative oil droplets. At the same molar concentration, PSAF hydrolyzes cationic metals more rapidly than polymeric aluminum chloride (PAC). PSAF forms flocs of smaller complex structures with greater bridging. The Al–O and Si–O peaks occurred at 611 and 1,138 cm−1, indicating the formation of Si–O–Fe and Si–O–Al bonds on the flocs surface. Higher stirring speeds did not change the free energy of the flocs surface γTot, mainly because the decrease in the van der Waals force (γLW) offset the increase of Lewis acid–base force (γAB). Preserving the non-polar surface, in summary, owing to its bridging abilities and affinity for non-polar surfaces, PSAF demonstrates superior efficiency over PAC in capturing and removing oil droplets. HIGHLIGHTS 75 mg L−1 of PSAF was stirred at 350 rpm and the optimal COD removal was 71%.; PSAF bridging was superior to PAC in terms of Si–O–Fe and Si–O–Al bonds.; PSAF forms flocs of smaller complex structures with greater bridging.; Higher stirring speeds did not change the non-polar surface of PSAF flocs to have good adsorption.;

Bacterial cellulose (BC)/kappa carrageenan (κ-C) hydrogel was synthesized via in-situ method by inoculating the κ-C into the Acetobacter xylinum cell culture medium. The structural features of the hydrogel was characterized using Fourier Transform Infrared Spectroscopy. The presence of both biopolymers in the hydrogel was confirmed by the O–H stretching of BC at 3390 cm−1 and the sulfate group (-SO3) of κ-C at 1226 cm−1. Scanning electron microscope images of the hydrogel showed A 3-D network of fibrils with high porosity. The enhanced swelling capacity of the hydrogel in water at pH 7 is due to the combined number of hydrophilic groups from BC and κ-C. The conductivity of the hydrogel increased with increasing κ-C due to the increased number of sulfate groups (-SO3). The hydrogel had the ability to adsorb organic dyes; Congo red, Crystal violet and Methylene blue from neutral water at 27 °C. All the dyes fitted the pseudo second order kinetic model and followed both the Langmuir and the Freundlich adsorption isotherms indicating monolayer adsorption on heterogeneous surfaces. The ΔGoad was negative indicating spontaneous physisorption for the three dyes. The prepared hydrogel being environmentally friendly also showed an improved ability to adsorb the organic dyes. [ABSTRACT FROM AUTHOR]

Drying involves the evaporation of moisture, accompanied by simultaneous heat transfer, mass transfer, and momentum transfer. While the diffusion law is considered an applicable model for explaining the drying phenomenon, the actual drying process cannot be accurately predicted using an analytical solution with a constant diffusion coefficient. Energy efficiency in the drying process is low due to an insufficient understanding of the mechanisms governing moisture migration from solids to air. The development of drying theory has stalled due to an unsolvable discrepancy between experimental results and analytical results. This study analyzes the effect of the binding energy of moisture in paddy rice on the diffusion coefficient. The theoretical relationship between water activity and drying rate in paddy rice was investigated, and the drying process was successfully explained by analyzing free energy transfer and transition theory. The mechanism of rice grain drying was described using a new theoretical solution for the drying process. These results provide new insights into the development of a scientific evaluation standard for assessing the efficiency of actual drying processes. [ABSTRACT FROM AUTHOR]

This paper studies spin glass to paramagnetic transition in the Spherical Sherrington–Kirkpatrick model with ferromagnetic Curie-Weiss interaction with coupling constant J and inverse temperature β . The disorder of the system is represented by a general Wigner matrix. We confirm a conjecture of Baik and Lee (Stat Phys 165(2):185–224, 2016; Ann Henri Poincaré 18(6):1867–1917, 2017), that the critical window of temperatures for this transition is β = 1 + b N - 1 / 3 log N with b ∈ R . The limiting distribution of the scaled free energy is Gaussian for negative b and a weighted linear combination of independent Gaussian and Tracy–Widom components for positive b. In the special case where the Wigner matrix is from the Gaussian Orthogonal or Unitary Ensemble, we describe the triple point transition between spin glass, paramagnetic, and ferromagnetic regimes in a critical window for (β , J) around the triple point (1, 1): the Tracy–Widom component is replaced by the one parameter family of deformations described by Bloemendal and Virág [9]. [ABSTRACT FROM AUTHOR]

We study the well-posedness of an infinite-dimensional Hamilton--Jacobi equation posed on the set of nonnegative measures and with a monotonic nonlinearity. Our results will be used in a companion work to propose a conjecture and prove partial results concerning the asymptotic mutual information in the assortative stochastic block model in the sparse regime. The equation we consider is naturally stated in terms of the Gateaux derivative of the solution, unlike previous works in which the derivative is usually of transport type. We introduce an approximating family of finite-dimensional Hamilton--Jacobi equations and use the monotonicity of the nonlinearity to show that no boundary condition needs to be prescribed to establish well-posedness. The solution to the infinite-dimensional Hamilton--Jacobi equation is then defined as the limit of these approximating solutions. In the special setting of a convex nonlinearity, we also provide a Hopf--Lax variational representation of the solution. [ABSTRACT FROM AUTHOR]

In this article, we would like to pay tribute to Gabor Kalman, outlining his contribution to a model widely used in dense plasma physics: the high‐temperature Thomas–Fermi model. The approach of Ruoxian Ying and Kalman relies on the separation of the bound and free electrons, a physically reasonable definition of the bound electrons, a description of the source density in the Poisson equation through the electron–ion and ion–ion pair correlation functions and a determination of the degree of ionization from the minimization of the total free energy. We also report on different approximations of the function Φ$$ \varPhi $$, which is a cornerstone of the original Thomas‐Femi model. [ABSTRACT FROM AUTHOR]

In the current work, the analyti cal static gravimetric technique was used to assess the solubilities of DL-α-amino butyric acid and DL-valine in an aqueous binary solvent mixture of sodium sulfate (Na2SO4) under equilibrium saturation conditions in between temperature range 288.15 and 308.15 K. Different thermodynamic factors along with transfer Gibbs energetics and entropies under standard conditions were estimated by using computational as well as theoretical method by using the experimental solubilities. Several modes of interactions that occur during solvation were also explained. The manner that solvent molecules of solute amino acids are surrounded in the aforementioned medium employed during the process is taken into consideration. Amino acids become more soluble as the temperature rises. The study also helps us to reach the conclusion that physical properties of electrolyte (Na2SO4), mixed solvent, and the size of the amino acids' molecules are the main governing factors for the chemical stability as well as other thermodynamic and physical property like solubility of solute amino acids. [ABSTRACT FROM AUTHOR]

Understandings of how visual hallucinations appear have been highly influenced by generative approaches, in particular Friston's Active Inference conceptualization. Their core proposition is that these phenomena occur when hallucinatory expectations outweigh actual sensory data. This imbalance occurs as the brain seeks to minimize informational free energy, a measure of the distance between predicted and actual sensory data in a stationary open system. We review this approach in the light of old and new information on the role of environmental factors in episodic hallucinations. In particular, we highlight the possible relationship of specific visual triggers to the onset and offset of some episodes. We use an analogy from phase transitions in physics to explore factors which might account for intermittent shifts between veridical and hallucinatory vision. In these triggered forms of hallucinations, we suggest that there is a transient disturbance in the normal one-to-one correspondence between a real object and the counterpart perception such that this correspondence becomes between the real object and a hallucination. Generative models propose that a lack of information transfer from the environment to the brain is one of the key features of hallucinations. In contrast, we submit that specific information transfer is required at onset and offset in these cases. We propose that this transient one-to-one correspondence between environment and hallucination is mediated more by aberrant discriminative than by generative inference. Discriminative inference can be conceptualized as a process for maximizing shared information between the environment and perception within a self-organizing nonstationary system. We suggest that generative inference plays the greater role in established hallucinations and in the persistence of individual hallucinatory episodes. We further explore whether thermodynamic free energy may be an additional factor in why hallucinations are temporary. Future empirical research could productively concentrate on three areas. Firstly, subjective perceptual changes and parallel variations in brain function during specific transitions between veridical and hallucinatory vision to inform models of how episodes occur. Secondly, systematic investigation of the links between environment and hallucination episodes to probe the role of information transfer in triggering transitions between veridical and hallucinatory vision. Finally, changes in hallucinatory episodes over time to elucidate the role of learning on phenomenology. These empirical data will allow the potential roles of different forms of inference in the stages of hallucinatory episodes to be elucidated. [ABSTRACT FROM AUTHOR]

We investigate the molecular mechanism underlying the liquid‐phase exfoliation of graphene in aqueous/N‐methyl‐2‐pyrrolidone (NMP) solvent mixtures and calculate the associated free energies, considering different NMP concentrations and exfoliation temperatures. We employ steered molecular dynamics to establish a path for the exfoliation of a graphene sheet from graphite within each solvent environment. Then, we conduct umbrella sampling simulations throughout the created paths to compute the potential of mean force (PMF) of the graphene sheet. As the exfoliated nanosheet disperses into the liquid, it becomes fully covered by an adsorbed solvent monolayer. We analyze the composition of the monolayer by measuring the direct contacts of either NMP or water molecules with the carbon surface. The carbon surface exhibits a preference for adsorbing NMP over water. The NMP molecules form a hydrophobic compact monolayer structure, effectively protecting the carbon interface from unfavorable interactions with water. The creation of the hydrophobic monolayer is a key factor in the exfoliation process, as it effectively inhibits the restacking of exfoliated nanosheets. An adequate level of graphene solubility is achieved through the addition of 20 % to 30 % water by weight to the NMP solvent. This finding holds significant importance for improving production efficiency and reducing dependence on organic solvents in the industrial manufacturing of graphene. [ABSTRACT FROM AUTHOR]

Neurodegenerative diseases lead to a gradual decline in cognitive and motor functions due to the progressive loss of neurons in the central nervous system. The role of dual leucine zipper kinase (DLK) in regulating stress responses and neuronal death pathways highlights its significance as a target against neurodegenerative diseases. The non-availability of FDA-approved drugs emphasizes a need to identify novel DLK-inhibitors. We screened NPAtlas (Natural products) and MedChemExpress (FDA-approved) libraries to identify potent ATP-competitive DLK inhibitors. ADMET analyses identified four compounds (two natural products and two FDA-approved) with favourable features. Subsequently, we performed molecular dynamics simulations to examine the binding-stability and ligand-induced conformational dynamics. Molecular mechanics Poisson Boltzmann surface area (MM-PBSA) calculations demonstrated CID139591660, dithranol, and danthron having greater affinity, while CID156581477 showed lower affinity than control sunitinib. PCA and network analysis results indicated structural and network alteration post-ligand binding. Furthermore, we identified an analogue of CID156581477 using the deep learning-based web server DeLA Drug which demonstrated a higher affinity than its parent compound and the control and identified several crucial interacting residues. Overall, our study provides significant theoretical guidance for designing potent novel DLK inhibitors and compounds that could emerge as promising drug candidates against DLK following laboratory validation. [ABSTRACT FROM AUTHOR]

A continuous bundle of C ∗ -algebras provides a rigorous framework to study the thermodynamic limit of quantum theories. If the bundle admits the additional structure of a strict deformation quantization (in the sense of Rieffel) one is allowed to study the classical limit of the quantum system, i.e. a mathematical formalism that examines the convergence of algebraic quantum states to probability measures on phase space (typically a Poisson or symplectic manifold). In this manner, we first prove the existence of the classical limit of Gibbs states illustrated with a class of Schrödinger operators in the regime where Planck's constant ℏ appearing in front of the Laplacian approaches zero. We additionally show that the ensuing limit corresponds to the unique probability measure satisfying the so-called classical or static KMS-condition. Subsequently, we conduct a similar study on the free energy of mean-field quantum spin systems in the regime of large particles, and discuss the existence of the classical limit of the relevant Gibbs states. Finally, a short section is devoted to single site quantum spin systems in the large spin limit. [ABSTRACT FROM AUTHOR]

Geological evidence and atmospheric and climate models suggest habitable conditions occurred on early Mars, including in a lake in Gale crater. Instruments aboard the Curiosity rover measured organic compounds of unknown provenance in sedimentary mudstones at Gale crater. Additionally, Curiosity measured nitrates in Gale crater sediments, which suggests that nitrate-dependent Fe2+ oxidation (NDFO) may have been a viable metabolism for putative martian life. Here, we perform the first quantitative assessment of an NDFO community that could have existed in an ancient Gale crater lake and quantify the long-term preservation of biological necromass in lakebed mudstones. We find that an NDFO community would have the capacity to produce cell concentrations of up to 106 cells mL−1, which is comparable to microbes in Earth's oceans. However, only a concentration of <104 cells mL−1, due to organisms that inefficiently consume less than 10% of precipitating nitrate, would be consistent with the abundance of organics found at Gale. We also find that meteoritic sources of organics would likely be insufficient as a sole source for the Gale crater organics, which would require a separate source, such as abiotic hydrothermal or atmospheric production or possibly biological production from a slowly turning over chemotrophic community. [ABSTRACT FROM AUTHOR]

In the present review work, it is proposed to carry out a bibliographic analysis about the thermal behaviour of the dolomitic mineral. The state of the art of dolomite currently indicates a growing use as a refractory material due to the cheaper alternative it represents compared to other materials such as magnesium oxide. The importance of dolomite apart from its application in the steel industry lies in the fact that it has expanded to other industrial fields such as the production of catalysts, catalyst supports, and industrial effluent purification materials. In these and other applications, understanding the thermal behaviour of the material is necessary to evaluate the feasibility of application. In this review, the different experimental proposals developed over time in terms of thermal behaviour are studied, emphasizing the reaction mechanisms that have been proposed in different investigations. [ABSTRACT FROM AUTHOR]

In the present paper, we construct new Gibbs measures for the Ising model on the Cayley tree of order two. Moreover, we find the free energy corresponding to the found measures and compare it with the known ones. [ABSTRACT FROM AUTHOR]

Background: Liquid crystal (LC) mesophases have an orientational and positional order that can be found in both synthetic and biological materials. These orders are maintained until some parameter, mainly the temperature or concentration, is changed, inducing a phase transition. Among these transitions, a special sequence of mesophases has been observed, in which priority is given to the direct smectic liquid crystal transition. The description of these transitions is carried out using the Landau–de Gennes (LdG) model, which correlates the free energy of the system with the orientational and positional order. Methodology: This work explored the direct isotropic-to-smectic A transition studying the free energy landscape constructed with the LdG model and its relation to three curve families: (I) level-set curves, steepest descent, and critical points; (II) lines of curvature (LOC) and geodesics, which are directly connected to the principal curvatures; and (III) the Casorati curvature and shape coefficient that describe the local surface geometries resemblance (sphere, cylinder, and saddle). Results: The experimental data on 12-cyanobiphenyl were used to study the three curve families. The presence of unstable nematic and metastable plastic crystal information was found to add information to the already developed smectic A phase diagram. The lines of curvature and geodesics were calculated and laid out on the energy landscape, which highlighted the energetic pathways connecting critical points. The Casorati curvature and shape coefficient were computed, and in addition to the previous family, they framed a geometric region that describes the phase transition zone. Conclusion and significance: A direct link between the energy landscape’s topological geometry, phase transitions, and relevant critical points was established. The shape coefficient delineates a stability zone in which the phase transition develops. The methodology significantly reduces the impact of unknown parametric data. Symmetry breaking with two order parameters (OPs) may lead to novel phase transformation kinetics and droplets with partially ordered surface structures. [ABSTRACT FROM AUTHOR]

Lateral predictive coding is a recurrent neural network that creates energy-efficient internal representations by exploiting statistical regularity in sensory inputs. Here, we analytically investigate the trade-off between information robustness and energy in a linear model of lateral predictive coding and numerically minimize a free energy quantity. We observed several phase transitions in the synaptic weight matrix, particularly a continuous transition that breaks reciprocity and permutation symmetry and builds cyclic dominance and a discontinuous transition with the associated sudden emergence of tight balance between excitatory and inhibitory interactions. The optimal network follows an ideal gas law over an extended temperature range and saturates the efficiency upper bound of energy use. These results provide theoretical insights into the emergence and evolution of complex internal models in predictive processing systems. [ABSTRACT FROM AUTHOR]

Genome editing based on the CRISPR-Cas9 system has paved new avenues for medicine, pharmaceutics, biotechnology, and beyond. This article reports the role of first-principles (ab-initio) molecular dynamics (MD) in the CRISPR-Cas9 revolution, achieving a profound understanding of the enzymatic function and offering valuable insights for enzyme engineering. We introduce the methodologies and explain the use of ab-initio MD simulations to characterize the two-metal dependent mechanism of DNA cleavage in the RuvC domain of the Cas9 enzyme, and how a second catalytic domain, HNH, cleaves the target DNA with the aid of a single metal ion. A detailed description of how ab-initio MD is combined with free-energy methods - i.e., thermodynamic integration and metadynamics - to break and form chemical bonds is given, explaining the use of these methods to determine the chemical landscape and establish the catalytic mechanism in CRISPR-Cas9. The critical role of classical methods is also discussed, explaining theory and application of constant pH MD simulations, used to accurately predict the catalytic residues' protonation states. Overall, first-principles methods are shown to unravel the electronic structure of the Cas9 enzyme, providing valuable insights that can serve for the design of genome editing tools with improved catalytic efficiency or controllable activity.

In order to study the effect of typical transition metal ions on coal spontaneous combustion under low temperature oxidation conditions, the transition metal ions of lignite (HM), gas coal (QM) and fertilizer coal (FM) were determined, and Fe (Ⅲ), Mn (Ⅲ) and Cu (Ⅱ), which are abundant in transition metal ions and have strong oxidation, were selected as the research objects. The charge distribution, frontier orbitals and Laplacian bond levels were analyzed by the quantum chemistry calculation method, and the existence of active sites was proved. Two reaction processes of Ar—CH2—CH3 to Ar—CO—CH3 with or without transition metal ions were investigated, and the thermodynamic parameters were obtained by model optimization, transition state calculation and IRC verification. The calculation results show that the activation energy barrier is 164.18 kJ/mol without transition metal ion and 158.72 kJ/mol with transition metal ion. The effect of transition metal ion on the total reaction rate is not significant. With the participation of Fe (Ⅲ), Mn (Ⅲ) and Cu (Ⅱ), the total heat releases of the reaction are 1535.52, 1834.97 and 365.93 kJ/mol, respectively, which are higher than the heat release from the oxidation of aliphatic hydrocarbons by oxygen molecules (319.93 kJ/mol). The free energy barriers of C—H in oxidized aliphatic hydrocarbons are 42.79, 4.30 and 117.29 kJ/mol, respectively, which are all lower than the activation energies of C—H oxidation by oxygen molecules (146.38 kJ/mol). The order of C—H oxidation capacity of transition metal ions from high to low is Mn (Ⅲ), Fe (Ⅲ) and Cu (Ⅱ). During the reaction process, the formation of ·OH and H+ is accompanied by further reaction with the coal structure to accelerate the spontaneous combustion process of coal. In order to verify the accuracy of the simulation results, the time and concentration of CO gas products in four different coal samples were measured by temperature programmed gas chromatography. It was found that the temperature points of CO gas products in four coal samples were similar. The coal samples with manganese ion added produced CO gas products at 90 ℃, while the other three coal samples produced CO gas products at 100 ℃. The concentration of CO gas products from large to small is Mn (Ⅲ), Fe (Ⅲ), Cu (Ⅱ) and raw coal sample, which is consistent with the calculated results. With the increase of temperature, the effect of Mn (Ⅲ) on increasing the rate of CO production gradually weakens, and the effect of iron and copper ions on catalytic coal spontaneous combustion is gradually significant. The experimental results have a certain correlation with the simulation results. Compared with oxygen molecules, transition metal ions in coal are more likely to oxidize C—H, which not only causes the free radical chain reaction to occur earlier, but also increases the heat release of the reaction and the production of ·OH and H+, thus promoting spontaneous combustion of coal. This has reference significance for the mechanism of spontaneous combustion of transition metal catalyzed coal.

Abstract In the current study, we utilized molecular modeling and simulation approaches to define putative potential molecular targets for Burdock Inulin, including inflammatory proteins such as iNOS, COX-2, TNF-alpha, IL-6, and IL-1β. Molecular docking results revealed potential interactions and good binding affinity for these targets; however, IL-1β, COX-2, and iNOS were identified as the best targets for Inulin. Molecular simulation-based stability assessment demonstrated that inulin could primarily target iNOS and may also supplementarily target COX-2 and IL-1β during DSS-induced colitis to reduce the role of these inflammatory mechanisms. Furthermore, residual flexibility, hydrogen bonding, and structural packing were reported with uniform trajectories, showing no significant perturbation throughout the simulation. The protein motions within the simulation trajectories were clustered using principal component analysis (PCA). The IL-1β–Inulin complex, approximately 70% of the total motion was attributed to the first three eigenvectors, while the remaining motion was contributed by the remaining eigenvectors. In contrast, for the COX2–Inulin complex, 75% of the total motion was attributed to the eigenvectors. Furthermore, in the iNOS–Inulin complex, the first three eigenvectors contributed to 60% of the total motion. Furthermore, the iNOS–Inulin complex contributed 60% to the total motion through the first three eigenvectors. To explore thermodynamically favorable changes upon mutation, motion mode analysis was carried out. The Free Energy Landscape (FEL) results demonstrated that the IL-1β–Inulin achieved a single conformation with the lowest energy, while COX2–Inulin and iNOS–Inulin exhibited two lowest-energy conformations each. IL-1β–Inulin and COX2–Inulin displayed total binding free energies of − 27.76 kcal/mol and − 37.78 kcal/mol, respectively, while iNOS–Inulin demonstrated the best binding free energy results at − 45.89 kcal/mol. This indicates a stronger pharmacological potential of iNOS than the other two complexes. Thus, further experiments are needed to use inulin to target iNOS and reduce DSS-induced colitis and other autoimmune diseases.

Silver nanoparticles (AgNPs) can be of various shapes such as spherical, nanorod, cylindrical, cubic, irregular, etc on textile materials. However, there is a huge scarcity of literature on the mechanisms of different shapes of AgNPs. In this study, 3 sets of fabric samples were prepared by pretreating with sodium hydroxide (NaOH), citric acid, and non-ionic detergent (span-80). To investigate the diverse shape mechanism green synthesized AgNPs by Calendula arvensis leaves, Citrus reticulate peel, and Cucumis sativus peel extracts were incorporated into the fabric samples. The samples were characterized by UV-VIS Spectroscopy, X-ray Diffraction (XRD), and Scanning Electron Microscopy (SEM). The UV-VIS spectra confirmed successful AgNP synthesis for Calendula arvensis and Citrus reticulata, but Cucumis sativus failed AgNP synthesis. The AgNPs were incorporated into the treated fabrics by padding and in-situ method. Then the SEM and XRD images were analyzed meticulously to delve into the nanoparticle shape-building mechanism in light of pH, incorporation methods, and crystallography. It was seen, that pH was the core factor in shape diversity. A pH lower than 7.0 produced predominately closed-pack crystals (111) and due to the low pH, the Gibbs free energy (GFE) was weaker and hence resulted in spherical nanoparticles. Again, the pH range from 7.1 to 8.0 produced cubic shapes due to a high number of open-pack crystals (110) and moderate Gibbs free energy (GFE). On the other hand, pH greater than 8.0 provided high Gibbs free energy, which expedited the reaction and led the nanoparticle shapes to anisotropy.

Retinoblastoma is a kind of cancer that mostly affects children's eyes, and this study intends to find drugs that can suppress the protein kinase cyclin-dependent kinase 4 (CDK4). CDK4 overexpression leads to the hyper-phosphorylation of RB tumor suppressor protein, which ultimately results in uncontrolled cell division. Aberration of cell cycle regulation, specifically the excessive expression of transcription factors responsible for uncontrolled cell division causes retinoblastoma progression. Hence, we screened 25,000 kinase-targeted small molecules against CDK-4 by Glide in Maestro, the top 11 were chosen based on docking scores, binding modes, chemical variety, and other parameters. We ran molecular dynamics (MD) simulations of top hits found in the docking studies and determined their free binding energy. This helped us to understand their thermodynamic and dynamic properties, as well as confirm the docking results, finally the two most promising ligands (3396 and 960) were obtained. As a result of our research, we have identified promising new compounds for treating retinoblastoma. To validate the possible therapeutic and preventative effects of this ligand, rigorous experimental validation, animal studies as well as clinical trials would be required.