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This work aimed to synthesize the aluminium oxide nanoparticles using Ixoro coccinea leaf extract. Furthermore, the synthesized Ixoro coccinea aluminium oxide nanoparticles (I–Al2O3-NPs) and nanocomposites (I–Al2O3-NC), including them as the fillers in a chitosan matrix were characterized, and I–Al2O3-NC was applied to remove the toxic metals (TMs) including Cd, Ni, and Pb from water. Optimization of different batch experimental adsorption parameters (pH, concentration of TMs, dose of I–Al2O3-NC, temperature, and time of contact) was done to check the feasibility of I–Al2O3-NC for maximum removal of TMs from water. The extreme adsorption capacities using nanocomposites for Cd, Ni, and Pb were 66.0, 60.0, and 66.4 mg g−1, respectively. The I–Al2O3-NC followed the Freundlich isotherm model for removing Cd and Ni while showing the monolayer surface coverage for the removal of Pb. For this process, the best-fitted kinetic model was the pseudo-second-order equation. The enthalpy, entropy, and free energy of metal ion adsorption, among other parameters of thermodynamics, were estimated. The process was found to be exothermic, advantageous, and spontaneous. Kinetic studies show that intra-particle diffusion is essential for eliminating TMs. In addition, I–Al2O3-NC was applied for the adsorption of TMs from surface water and determined to be effective in removing these contaminants up to an acceptable drinking water standard. Regeneration of adsorbent suggested that green synthesized I–Al2O3-NC may be an active tool for removing Cd, Ni, and Pb ions from contaminated water. © 2023 Elsevier Ltd and Techna Group S.r.l.

Актуальность. Одним из приоритетных направлений нефтегазового сектора отечественной экономики является повышение эффективности и рентабельности процессов подготовки товарной нефти, однако научные результаты, полученные в данной области, являются недостаточными для современных технологических требований. Не решены вопросы недостатка данных для разработки достоверных математических моделей процессов разрушения нефтяной эмульсии, а также входных сигналов для регулирования процессов управления технологическим оборудованием для подготовки нефти. Нефть, добываемая на месторождениях, представляет собой водомасляную эмульсию прямого или обратного типа с уникальным дисперсным составом для каждой скважины. В настоящее время анализ размеров капель нефтяной эмульсии на промысле проводят с помощью классического лабораторного метода, имеющего низкую скорость получения результатов анализа, тогда как распределение глобул по размерам несет информацию о таких свойствах дисперсной системы, как скорость деградации, долговременная стабильность, вязкость и другие. Зная распределение капель по размерам конкретной нефтяной эмульсии, можно подобрать наиболее рациональные способы её разрушения, необходимые технические параметры устройств, используемых для реализации этих способов. В частности, при воздействии на каплю с частотой, близкой к её собственной, возможны интенсификация разрушения или синтез эмульсии. В связи с этим актуальным и необходимым является вывод аналитического выражения для резонансной частоты капли эмульсии и уравнений свободных колебаний. Цель: заключается в определении резонансных частот шаровой капли воды в масляной среде и оценки воздействия демпфирующих свойств среды на колебания поверхности капли. Объект: водомасляная эмульсия. Методы: математическое моделирование, ортогональные разложения, термодинамические потенциалы. Результаты. Получено аналитическое выражение для резонансной частоты водной капли, а также уравнение свободных колебаний капли в виде неконсервативной системы. The relevance. Increasing the efficiency and profitability of commercial oil preparation is one of the priority tasks of the oil and gas sector of the domestic economy, but the scientific achievements in this area require further development. The issues of lack of data for the development of reliable mathematical models of oil emulsion destruction, as well as input signals for regulating the control processes of oil preparation apparatuses, have not been resolved. The oil produced in the fields is a water-oil emulsion with a unique dispersion composition for each well. Today, the analysis of the disperse composition in the field is carried out using a classic laboratory method that has a low speed of obtaining analysis results, while the distribution of droplets by size carries information about the properties of the emulsion in such aspects as degradation rate, long-term stability, viscosity, and others. Knowing the droplets size distribution of a particular oil emulsion, it is possible to choose the most rational methods for its destruction, as well as the necessary technical settings for the devices used in these methods. In particular, when a drop is exposed to a frequency close to its own, destruction can be intensified or an emulsion can be synthesized. In this regard, the derivation of an analytical expression for the resonant frequency of an emulsion drop and the equations of free vibrations are relevant and necessary. The main aim consists in determining the resonant frequencies of a spherical water drop in an oily medium and assessing the effect of the damping properties of the medium on oscillations of the drop surface. Results. The authors obtained the analytical expression for a water drop resonant frequency, as well as an equation of a drop free oscillations presented as a non-conservative system.

Temperature dependences of the free energy (F), entropy (S) and the heat capacity (C_v) are calculated (P=0) for the organic compounds (solid benzene, naphthalene and anthracene) by using the quasiharmonic approximation. Contributions to those thermodynamic functions due to the Raman frequencies of lattice modes (solid benzene), librational modes (naphthalene), phonons and vibrons (anthracene) are taken into account in our calculations. We obtain that similar linear increase of F and nonlinear increase of S and C_v, occur with the increasing temperature in benzene and naphthalene. This linear (F) and nonlinear (S, C_v) increase is rather different for anthracene as the molecular structure becomes complex (benzene-naphthalene-anthracene), as expected. Our calculations by the quasiharmonic approximation can be compared with the experiments for those organic compounds.

Ab-initio molecular dynamics enables following the dynamics of biological systems from the first principles, describing the electronic structure and offering the opportunity to “watch” the evolution of biochemical processes with unique resolution, beyond the capabilities of state-of-the-art experimental techniques. This article reports the role of first-principles (ab-initio) molecular dynamics (MD) in the CRISPR-Cas9 genome editing 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 establish 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 and reveal the catalytic mechanism of the Cas9 enzyme, providing valuable insights that can serve for the design of genome editing tools with improved catalytic efficiency or controllable activity.

Temperature-dependent correlations for equilibrium constants (ln K) and heat of absorption (ΔHabs) of different reactions (i.e., deprotonation, double deprotonation, carbamate formation, protonated carbamate formation, dicarbamate formation) involved in the piperazine (PZ)/CO2/H2O system have been calculated using computational chemistry based ln K values input to the Gibbs–Helmholtz equation. This work also presents an extensive study of gaseous phase free energy and enthalpy for different reactions using composite (G3MP2B3, G3MP2, CBS-QB3, and G4MP2) and density functional theory [B3LYP/6-311++G(d,p)] methods. The explicit solvation shell (ESS) model and SM8T solvation free energy coupled with gaseous phase density functional theory calculations give temperature-dependent reaction equilibrium constants for different reactions. Calculated individual and overall reaction equilibrium constants and enthalpies of different reactions involved in CO2 absorption in piperazine solution are compared against experimental data, where available, in the temperature range 273.15–373 K. Postcombustion CO2 capture (PCC) is a temperature swing absorption–desorption process. The enthalpy of the solution directly correlates with the steam requirement of the amine regeneration step. Temperature-dependent correlations for ln K and ΔHabs calculated using computational chemistry tools can help evaluate potential PCC solvents’ thermodynamics and cost-efficiency. These correlations can also be employed in thermodynamic models (e.g., e-UNIQUAC, e-NRTL) to better understand postcombustion CO2 capture solvent chemistry.

Bayesian estimation in cognitive dynamics is explored through a standard subliminal priming paradigm where trained and novel targets are either preceded by an unexpected (and novel) signal in masked conditions or are presented by themselves. We challenge the assumption that predictions are generated solely upon an above-threshold activation which has travelled through the cortical hierarchy, hence has approached values similar to the authentic distribution of a stimulus via prediction error minimization. Simulations of an agent sensitive to subthreshold signal exhibit greater interference on the computational level due to the large statistical discrepancy between the expected target and the perceptual inference of a novel subthreshold activation. A competing model which bases its estimation solely upon conscious signal gives incompatible results. Our experiment follows our first model's predictions.

Jackiw-Teitelboim dilaton-quantum-gravity localizes on a double-scaled random-matrix model, whose perturbative free energy is an asymptotic series. Understanding the resurgent properties of this asymptotic series, including its completion into a full transseries, requires understanding the nonperturbative instanton sectors of the matrix model for Jackiw-Teitelboim gravity. The present work addresses this question by setting-up instanton calculus associated to eigenvalue tunneling (or ZZ-brane contributions), directly in the matrix model. In order to systematize such calculations, a nonperturbative extension of the topological recursion formalism is required -- which is herein both constructed and applied to the present problem. Large-order tests of the perturbative genus expansion validate the resurgent nature of Jackiw-Teitelboim gravity, both for its free energy and for its (multi-resolvent) correlation functions. Both ZZ and FZZT nonperturbative effects are required by resurgence, and they further display resonance upon the Borel plane. Finally, the resurgence properties of the multi-resolvent correlation functions yield new and improved resurgence formulae for the large-genus growth of Weil-Petersson volumes., Comment: 63 pages, 52 plots in 16 figures, jheppub-nosort.sty

Alzheimer’s disease represents one of the greatest medical concerns for today’s population and health services. Its multifactorial inherent nature represents a challenge for its treatment and requires the development of a broad spectrum of drugs. Recently, the cysteine protease gingipain RgpB has been related to neurodegenerative diseases, including Alzheimer’s disease, and its inhibition appears to be a promising neuroprotective strategy. Given these features, a computational study that integrates molecular dynamics (MD) simulations with classical and hybrid quantum mechanics/molecular mechanics (QM/MM) potentials was carried out to unravel the atomistic details of RgpB activity. First, a preliminary study based on principal component analysis (PCA), determined the protonation state of the Cys/His catalytic dyad, as well as the crucial role of a flexible loop that favors reactive interactions of the catalytic residues and the peptide in the precatalytic state in its closed conformation. Then, different mechanisms were explored by means of QM/MM MD simulations. The most favorable mechanism consists of two stages. First is an acylation stage that takes place in two steps where, initially, the sulfur atom of the C244 residue attacks the carbonylic carbon of the peptide and the proton of the C244 residue is transferred to the amino group of the peptide in a concerted manner. Subsequently, the peptide bond is broken, and a fragment of the peptide is released. After that, the deacylation stage takes place in a single step where a water molecule attacks the carbonylic carbon of the peptide and a proton of the water is transferred to the C244 residue. The free energy barrier of the rate limiting step is in very good agreement with available experimental data. The mechanism exhibits an unusual role of H211 residue compared with other cysteine proteases but a crucial role of the peptide in triggering the catalysis. Notably, the atomic and energetic particularities found represent a significant contribution to the comprehension of the reaction mechanism and a great opportunity for the design of efficient inhibitors of gingipain RgpB.

International audience We analyze and propose variants of the Adaptive Biasing Force method. First, we prove the convergence of a version of the algorithm where the biasing force is estimated using a weighted occupation measure, with an explicit asymptotic variance. Second, we propose a new flavour of the algorithm adapted to high dimensional reaction coordinates, for which the standard approaches suffer from the curse of dimensionality. More precisely, the free energy is approximated by a sum of tensor products of one-dimensional functions. The consistency of the tensor approximation is established. Numerical experiments on 5-dimensional reaction coordinates demonstrate that the method is indeed able to capture correlations between them.

We study generalizations of the Gross--Witten--Wadia unitary matrix model for the special orthogonal and symplectic groups. We show using a standard Coulomb gas treatment -- employing a path integral formalism for the ungapped phase and resolvent techniques for the gapped phase with one coupling constant -- that in the large $N$ limit, the free energy normalized modulo the square of the gauge group rank is twice the value for the unitary case. Using generalized Cauchy identities for character polynomials, we then demonstrate the universality of this phase transition for an arbitrary number of coupling constants by linking this model to the random partition based on the Schur measure., 18 pages, minor correction post-publication

The emergence of immune-evading variants of SARS-CoV-2 further aggravated the ongoing pandemic. Despite the deployments of various vaccines, the acquired mutations are capable of escaping both natural and vaccine-induced immune responses. Therefore, further investigation is needed to design a decisive pharmacological treatment that could efficiently block the entry of this virus into cells. Hence, the current study used structure-based methods to target the RBD of the recombinant variant (Deltacron) of SARS-CoV-2, which was used as a model variant. From the virtual drug screenings of various databases, a total of four hits were identified as potential lead molecules. Key residues were blocked by these molecules with favorable structural dynamic features. The binding free energies further validated the potentials of these molecules. The TBE for MNP was calculated to be −32.86 ± 0.10 kcal/mol, for SANC00222 the TBE was −23.41 ± 0.15 kcal/mol, for Liriodenine the TBE was −34.29 ± 0.07 kcal/mol, while for Carviolin the TBE was calculated to be −27.67 ± 0.12 kcal/mol. Moreover, each complex demonstrated distinct internal motion and a free energy profile, indicating a different strategy for the interaction with and inhibition of the RBD. In conclusion, the current study demands further in vivo and in vitro validation for the possible usage of these compounds as potential drugs against SARS-CoV-2 and its variants.

The poor performance of many existing nonpolarizable ion force fields is typically blamed on either the lack of explicit polarizability, the absence of charge transfer, or the use of unreduced Coulomb interactions. However, this analysis disregards the large and mostly unexplored parameter range offered by the Lennard-Jones potential. We use a global optimization procedure to develop water-model-transferable force fields for the ions K+, Na+, Cl���, and Br��� in the complete parameter space of all Lennard-Jones interactions using standard mixing rules. No extra-thermodynamic assumption is necessary for the simultaneous optimization of the four ion pairs. After an optimization with respect to the experimental solvation free energy and activity, the force fields reproduce the concentration-dependent density, ionic conductivity, and dielectric constant with high accuracy. The force field is fully transferable between simple point charge/extended and transferable intermolecular potential water models. Our results show that a thermodynamically consistent force field for these ions needs only Lennard-Jones and standard Coulomb interactions.

Most biological events occur on time scales that are difficult to access using conventional all-atom molecular dynamics simulations in explicit solvent. Implicit solvent techniques offer a promising solution to this problem, alleviating the computational cost associated with the simulation of large systems and accelerating the sampling compared to explicit solvent models. The substitution of water molecules by a mean field, however, introduces simplifications that may penalize accuracy and impede the prediction of certain physical properties. We demonstrate that existing implicit solvent models developed using a transfer free energy approach, while satisfactory at reproducing the folding behavior of globular proteins, fare less well in characterizing the conformational properties of intrinsically disordered proteins. We develop a new implicit solvent model that maximizes the degree of accuracy for both disordered and folded proteins. We show, by comparing the simulation outputs to experimental data, that in combination with the a99SB-disp force field, the implicit solvent model can describe both disordered (aβ40, PaaA2, and drkN SH3) and folded ((AAQAA)

Ligand and structure-based computational screenings were carried out to identify flavonoids with potential anticancer activity. Kushenol E, a flavonoid with proven anticancer activity and, at the same time, an allosteric site binder of the enzyme indoleamine 2,3-dioxygenase-1 (IDO1), was used as the reference compound. Molecular docking and molecular dynamics simulations were performed for the screened flavonoids with known anticancer activity. The following two of these flavonoids were identified as potential inhibitors of IDO1: dichamanetin and isochamanetin. Molecular dynamics simulations were used to assess the conformational profile of IDO1-flavonoids complexes, as well as for calculating the bind-free energies.

The accurate and efficient calculation of protein-protein binding affinities is an essential component in antibody and antigen design and optimization, and in computer modeling of antibody affinity maturation. Such calculations remain challenging despite advances in computer hardware and algorithms, primarily because proteins are flexible molecules, and thus, require explicit or implicit incorporation of multiple conformational states into the computational procedure. The astronomical size of the amino acid sequence space further compounds the challenge by requiring predictions to be computed within a short time so that many sequence variants can be tested. In this study, we compare three classes of methods for antibody/antigen (Ab/Ag) binding affinity calculations: (i) a method that relies on the physical separation of the Ab/Ag complex in equilibrium molecular dynamics (MD) simulations, (ii) a collection of 18 scoring functions that act on an ensemble of structures created using homology modeling software, and (iii) methods based on the molecular mechanics-generalized Born surface area (MM-GBSA) energy decomposition, in which the individual contributions of the energy terms are scaled to optimize agreement with the experiment. When applied to a set of 49 antibody mutations in two Ab/HIV gp120 complexes, all of the methods are found to have modest accuracy, with the highest Pearson correlations reaching about 0.6. In particular, the most computationally intensive method, i.e., MD simulation, did not outperform several scoring functions. The optimized energy decomposition methods provided marginally higher accuracy, but at the expense of requiring experimental data for parametrization. Within each method class, we examined the effect of the number of independent computational replicates, i.e., modeled structures or reinitialized MD simulations, on the prediction accuracy. We suggest using about ten modeled structures for scoring methods, and about five simulation replicates for MD simulations as a rule of thumb for obtaining reasonable convergence. We anticipate that our study will be a useful resource for practitioners working to incorporate binding affinity calculations within their protein design and optimization process.

A quantitative description of the excited electronic states of point defects and impurities is crucial for understanding materials properties, and possible applications of defects in quantum technologies. This is a considerable challenge for computational methods, since Kohn-Sham density-functional theory (DFT) is inherently a ground state theory, while higher-level methods are often too computationally expensive for defect systems. Recently, embedding approaches have been applied that treat defect states with many-body methods, while using DFT to describe the bulk host material. We implement such an embedding method, based on Wannierization of defect orbitals and the constrained random-phase approximation approach, and perform systematic characterization of the method for three distinct systems with current technological relevance: a carbon dimer replacing a B and N pair in bulk hexagonal BN (C$_{\text{B}}$C$_{\text{N}}$), the negatively charged nitrogen-vacancy center in diamond (NV$^-$), and an Fe impurity on the Al site in wurtzite AlN ($\text{Fe}_{\text{Al}}$). For C$_{\text{B}}$C$_{\text{N}}$ we show that the embedding approach gives many-body states in agreement with analytical results on the Hubbard dimer model, which allows us to elucidate the effects of the DFT functional and double-counting correction. For the NV$^-$ center, our method demonstrates good quantitative agreement with experiments for the zero-phonon line of the triplet-triplet transition. Finally, we illustrate challenges associated with this method for determining the energies and orderings of the complex spin multiplets in $\text{Fe}_{\text{Al}}$., Comment: 19 pages, 14 figures. Supplemental material: 7 pages

Computational drug design is increasingly becoming important with new and unforeseen diseases like COVID‐19. In this study, we present a new computational de novo drug design and repurposing method and applied it to find plausible drug candidates for the receptor binding domain (RBD) of SARS‐CoV‐2 (COVID‐19). Our study comprises three steps: atom‐by‐atom generation of new molecules around a receptor, structural similarity mapping to existing approved and investigational drugs, and validation of their binding strengths to the viral spike proteins based on rigorous all‐atom, explicit‐water well‐tempered metadynamics free energy calculations. By choosing the receptor binding domain of the viral spike protein, we showed that some of our new molecules and some of the repurposable drugs have stronger binding to RBD than hACE2. To validate our approach, we also calculated the free energy of hACE2 and RBD, and found it to be in an excellent agreement with experiments. These pool of drugs will allow strategic repurposing against COVID‐19 for a particular prevailing conditions., Schematic diagram of atom‐by‐atom molecule generation, followed by repurposed molecule selection and validation using fre‐energy calculations.

The main aim of the study was to assess the acetylcholinesterase-inhibitory potential of triterpenoid saponins (astragalosides) found in the roots of Astragalus mongholicus. For this purpose, the TLC bioautography method was applied and then the IC50 values were calculated for astragalosides II, III and IV (5.9 μM; 4.2 μM, and 4.0 μM, respectively). Moreover, molecular dynamics simulations were carried outto assess the affinity of the tested compounds for POPC and POPG-containing lipid bilayers, which in this case are the models of the blood-brain barrier (BBB). All determined free energy profiles confirmed that astragalosides exhibit great affinity for the lipid bilayer. A good correlation was obtained when comparing the logarithm of n-octanol/water partition coefficient (logPow) lipophilicity descriptor values with the smallest values of free energy of the determined 1D profiles. The affinity for the lipid bilayers changes in the same order as the corresponding logPow values, i.e.,: I > II > III~IV. All compounds exhibit a high and also relatively similar magnitude of binding energies, varying from ca. −55 to −51 kJ/mol. Apositive correlation between the experimentally-determined IC50 values and the theoretically-predicted binding energies expressed by the correlation coefficient value equal 0.956 was observed.

Non-equilibrium work switching simulations and Jarzynski’s equation are a reliable method for computing free energy differences, ΔAlow→high, between two levels of theory, such as a pure molecular mechanical (MM) and a quantum mechanical/molecular mechanical (QM/MM) description of a system of interest. Despite the inherent parallelism, the computational cost of this approach can quickly become very high. This is particularly true for systems where the core region, the part of the system to be described at different levels of theory, is embedded in an environment such as explicit solvent water. We find that even for relatively simple solute–water systems, switching lengths of at least 5 ps are necessary to compute ΔAlow→high reliably. In this study, we investigate two approaches towards an affordable protocol, with an emphasis on keeping the switching length well below 5 ps. Inserting a hybrid charge intermediate state with modified partial charges, which resembles the charge distribution of the desired high level, makes it possible to obtain reliable calculations with 2 ps switches. Attempts using step-wise linear switching paths, on the other hand, did not lead to improvement, i.e., a faster convergence for all systems. To understand these findings, we analyzed the solutes’ properties as a function of the partial charges used and the number of water molecules in direct contact with the solute, and studied the time needed for water molecules to reorient themselves upon a change in the solute’s charge distribution.

The retro-aldolase mechanism of methodol catalysed by the catalytic antibody 33F12 is described based on the exploration of the free energy landscape obtained with QM/MM methods. The amino acids involved in the reaction have been identified, as well as their specific role played in the active site and in the flexibility of the loops. Finally, the comparison with a de novo enzyme RA95.5-8F provides a deeper understanding of catalytic differences between such different protein scaffolds.

The economic conceptualization of Freudian metapsychology, based on an energetics model of the psyche's workings, offers remarkable commonalities with some recent discoveries in neuroscience, notably in the field of neuroenergetics. The pattern of cerebral activity at resting state and the identification of a default mode network (DMN), a network of areas whose activity is detectable at baseline conditions by neuroimaging techniques, offers a promising field of research in the dialogue between psychoanalysis and neuroscience. In this article we study one significant clinical application of this interdisciplinary dialogue by looking at the role of the DMN in the psychopathology of schizophrenia. Anomalies in the functioning of the DMN have been observed in schizophrenia. Studies have evidenced the existence of hyperactivity in this network in schizophrenia patients, particularly among those for whom a positive symptomatology is dominant. These data are particularly interesting when considered from the perspective of the psychoanalytic understanding of the positive symptoms of psychosis, most notably the Freudian hypothesis of delusions as an “attempt at recovery.” Combining the data from research in neuroimaging of schizophrenia patients with the Freudian hypothesis, we propose considering the hyperactivity of the DMN as a consequence of a process of massive reassociation of traces occurring in schizophrenia. This is a process that may constitute an attempt at minimizing the excess of free energy present in psychosis. Modern models of active inference and the free energy principle (FEP) may shed some light on these processes.

Free energy evaluation in molecular simulations of both classical and quantum systems is computationally intensive and requires sophisticated algorithms. This is because free energy depends on the volume of accessible phase space, a quantity that is inextricably linked to the integration measure in a coordinate representation of a many-body problem. In contrast, the same problem expressed as a field theory (auxiliary field or coherent states) isolates the particle number as a simple parameter in the Hamiltonian or action functional and enables the identification of a chemical potential field operator. We show that this feature leads a “direct” method of free energy evaluation, in which a particle model is converted to a field theory and appropriate field operators are averaged using a field-theoretic simulation conducted with complex Langevin sampling. These averages provide an immediate estimate of the Helmholtz free energy in the canonical ensemble and the entropy in the microcanonical ensemble. The method is illustrated for a classical polymer solution, a block copolymer melt exhibiting liquid crystalline and solid mesophases, and a quantum fluid of interacting bosons.

The SAMPL series of challenges aim to focus the community on specific modeling challenges, while testing and hopefully driving progress of computational methods to help guide pharmaceutical drug discovery. In this study, we report on the results of the SAMPL8 host–guest blind challenge for predicting absolute binding affinities. SAMPL8 focused on two host–guest datasets, one involving the cucurbituril CB8 (with a series of common drugs of abuse) and another involving two different Gibb deep-cavity cavitands. The latter dataset involved a previously featured deep cavity cavitand (TEMOA) as well as a new variant (TEETOA), both binding to a series of relatively rigid fragment-like guests. Challenge participants employed a reasonably wide variety of methods, though many of these were based on molecular simulations, and predictive accuracy was mixed. As in some previous SAMPL iterations (SAMPL6 and SAMPL7), we found that one approach to achieve greater accuracy was to apply empirical corrections to the binding free energy predictions, taking advantage of prior data on binding to these hosts. Another approach which performed well was a hybrid MD-based approach with reweighting to a force matched QM potential. In the cavitand challenge, an alchemical method using the AMOEBA-polarizable force field achieved the best success with RMSE less than 1 kcal/mol, while another alchemical approach (ATM/GAFF2-AM1BCC/TIP3P/HREM) had RMSE less than 1.75 kcal/mol. The work discussed here also highlights several important lessons; for example, retrospective studies of reference calculations demonstrate the sensitivity of predicted binding free energies to ethyl group sampling and/or guest starting pose, providing guidance to help improve future studies on these systems.

Through brain-inspired modeling studies, cognitive neurorobotics aims to resolve dynamics essential to different emergent phenomena at the level of embodied agency in an object environment shared with human beings. This article is a review of ongoing research focusing on model dynamics associated with human self-consciousness. It introduces the free energy principle and active inference in terms of Bayesian theory and predictive coding, and then discusses how directed inquiry employing analogous models may bring us closer to representing the sense of self in cognitive neurorobots. The first section quickly locates cognitive neurorobotics in the broad field of computational cognitive modeling. The second section introduces principles according to which cognition may be formalized, and reviews cognitive neurorobotics experiments employing such formalizations. The third section interprets the results of these and other experiments in the context of different senses of self, both “minimal” and “narrative” self. The fourth section considers model validity and discusses what we may expect ongoing cognitive neurorobotics studies to contribute to scientific explanation of cognitive phenomena including the senses of minimal and narrative self.

We present a multistep protocol, combining Monte Carlo and molecular dynamics simulations, for the estimation of absolute binding free energies, one of the most significant challenges in computer-aided drug design. The protocol is based on an initial short enhanced Monte Carlo simulation, followed by clustering of the ligand positions, which serve to identify the most relevant states of the unbinding process. From these states, extensive molecular dynamics simulations are run to estimate an equilibrium probability distribution obtained with Markov State Models, which is subsequently used to estimate the binding free energy. We tested the procedure on two different protein systems, the Plasminogen kringle domain 1 and Urokinase, each with multiple ligands, for an aggregated molecular dynamics length of 760 μs. Our results indicate that the initial sampling of the unbinding events largely facilitates the convergence of the subsequent molecular dynamics exploration. Moreover, the protocol is capable to properly rank the set of ligands examined, albeit with a significant computational cost for the, more realistic, Urokinase complexes. Overall, this work demonstrates the usefulness of combining enhanced sampling methods with regular simulation techniques as a way to obtain more reliable binding affinity estimates. This work has been funded by Spanish projects CTQ2016-79138-R and RTC-2017-6295-1.

Most recently, an outbreak of severe pneumonia caused by the infection of SARS-CoV-2, a novel coronavirus first identified in Wuhan, China, imposes serious threats to public health. Upon infecting host cells, coronaviruses assemble a multi-subunit RNA-synthesis complex of viral non-structural proteins (nsp) responsible for the replication and transcription of the viral genome. Therefore, the role and inhibition of nsp12 are indispensable. A cryo-EM structure of RdRp from SARs-CoV-2 was used to identify novel drugs from Northern South African medicinal compounds database (NANPDB) by using computational virtual screening and molecular docking approaches. Considering Remdesivir as the control, 42 compounds were shortlisted to have docking score better than Remdesivir. The top 5 hits were validated by using molecular dynamics simulation approach and free energy calculations possess strong inhibitory properties than the Remdesivir. Thus, this study paved a way for designing novel drugs by decoding the architecture of an important enzyme and its inhibition with compounds from natural resources. This disclosing of necessary knowledge regarding the screening and the identification of top hits could help to design effective therapeutic candidates against the coronaviruses and design robust preventive measurements. Graphic abstract

We show how two-species models, already proposed for the rheology of networks of associative polymer solutions, can be derived from nonequilibrium thermodynamics using the generalized bracket formalism. The two species refer to bridges and (temporary) dangling chains, both of which are represented as dumbbells. Creation and destruction of bridges in our model are accommodated self-consistently by assuming a two-way reaction characterized by a forward and a reverse rate constant. Although the final set of evolution equations for the microstructure of the two species and the expression for the stress tensor are similar to those of earlier models based on network kinetic theory, nonequilibrium thermodynamics sets specific constraints on the form of the attachment/detachment rates appearing in these equations, which, in some cases, deviate significantly from previously reported ones. We also carry out a detailed analysis demonstrating the capability of the new model to describe various sets of rheological data for solutions of associative polymers. ISSN:0148-6055

A new continuous multi-phase transformation field model was established for liquid-solid-eutectoid transformation. Taking Fe-C alloy as an example, the model was used to simulate the evolution of the micro-morphology of the liquid-solid phase transition, and the effects of temperature, solute and free energy on the nucleation of pearlite after the liquid-solid phase transition were analyzed. The micro-morphology of pearlite was simulated. The simulation results show that the austenite structure has hereditary effect on the pearlite, the morphology of pearlite structure was similar to that of the parent austenite. The eutectoid structure at the front of pearlite grows toward the interior of austenite grains in a bifurcation manner and in the spherical coronal shape. In addition, the growth rate of pearlite was related to the shape of concave-convex interface at the nucleation site, and the growth rate at the convex interface was faster than that at the concave interface.

Energy entropy is the "highest" indicator of the state of an organization, developing the ideas of efficiency and value. The integrity of energy entropy implies taking into consideration the level of order in an organization (information entropy) along with the ability to "release" effectively the energy for useful work. Versatility is ensured by the independence on a kind of activity of an organization. The formalization of energy entropy of organizations was proposed. According to the proposed approach, energy entropy is determined by an increase in total energy and its comparison with the "ideal" option; the level of free energy and information entropy that reflects the ability of the organization’s structure to ensure certain results. Incoming and outgoing (free) energy are considered as the main parameters of the organization’s state. Their combination determines the growth of energy, a set of possible combinations – information entropy. The scheme of changes in time of the main "energy parameters" of an organization (total energy, free energy, incoming energy) was identified. Two main variants of energy increase dynamics – uniform growth and growth with acceleration (slowdown) were represented. Experimental studies, which involved considering the most possible variants of dynamics of influencing parameters, were carried out. The effect of different combinations of their dynamics (simultaneous growth/decrease, growth/decrease at different rates) on the dynamics of energy entropy was analyzed. It was established that an increase in a share of free energy does not provide an outflow of energy entropy without reducing a degree of uncertainty of the results expressed in a decrease in information entropy. Conclusions about the necessary dynamics of influencing parameters to ensure the vital activity of an organization according to the energy entropy concept were made

The notions of degeneracy and redundancy are important constructs in many areas, ranging from genomics through to network science. Degeneracy finds a powerful role in neuroscience, explaining key aspects of distributed processing and structure–function relationships in the brain. For example, degeneracy accounts for the superadditive effect of lesions on functional deficits in terms of a “many-to-one” structure–function mapping. In this paper, we offer a principled account of degeneracy and redundancy, when function is operationalized in terms of active inference, namely, a formulation of perception and action as belief updating under generative models of the world. In brief, “degeneracy” is quantified by the “entropy” of posterior beliefs about the causes of sensations, while “redundancy” is the “complexity” cost incurred by forming those beliefs. From this perspective, degeneracy and redundancy are complementary: Active inference tries to minimize redundancy while maintaining degeneracy. This formulation is substantiated using statistical and mathematical notions of degenerate mappings and statistical efficiency. We then illustrate changes in degeneracy and redundancy during the learning of a word repetition task. Finally, we characterize the effects of lesions—to intrinsic and extrinsic connections—using in silico disconnections. These numerical analyses highlight the fundamental difference between degeneracy and redundancy—and how they score distinct imperatives for perceptual inference and structure learning that are relevant to synthetic and biological intelligence.

We investigate the coupling between the proton transfer (PT) energetics and the protein-solvent dynamics using the intra-molecular PT in wild type (wt) human carbonic anhydrase II and its ten-fold faster mutant Y7F/N67Q as a test case. We calculate the energy variation upon PT, and from that we also calculate the PT reaction free energy, making use of a hybrid quantum mechanics/molecular dynamics approach. In agreement with the experimental data, we obtain that the reaction free energy is basically the same in the two systems. Yet, we show that the instantaneous PT energy is on average lower in the mutant possibly contributing to the faster PT rate. Analysis of the contribution to the PT energetics of the solvent and of each protein residue, also not in the vicinity of the active site, provides evidence for electrostatic tuning of the PT energy arising from the combined effect of the solvent and the protein environment. These findings open up a way to the more general task of the rational design of mutants with either enhanced or reduced PT rate.

Solubility of oxygen and silicon in the iron-alloying liquids is important for constraining the core composition over the Earth's history. In this study, we systematically simulated the free energies of Fe-O-Si ternary liquids from 3000 K, 55 GPa to 6000 K, and 330 GPa. We found that temperature and pressure have remarkable influences on the free energies, and the nonideality of mixing is important for the chemical potentials even at high temperatures. Equilibrating with SiO$_{2}$ phase, Fe-O-Si liquids significantly enhance the solubility of Si and O simultaneously with increasing temperature. Considering the secular cooling of the Earth's core, this leads to high precipitation rates of SiO$_{2}$ once it was saturated, which would efficiently drive ancient geodynamo. If the evolution of Earth's core started from an oxygen-poor composition, later incorporations of oxygen seem to be needed to reach a core composition compatible with geophysical observations.

In the article discussed in this chapter, the authors describe a framework of neuroaesthetics for architectural experiences that considers sensory feedback stemming from movement central for the experience of the built environment. As we move through space when experiencing architecture, our sensory impressions change, rendering the body and the brain as nondissociable agents of aesthetic experience. This interaction is described by the term affordance. The authors cast the human experience of the built environment to be predicated on the functional relation between action and perception and developed a neuroscientific experiment on architectural transitions to investigate how the human brain reflects architectural affordances. They found that varying sizes of transitions, reflecting different affordances, impact early perceptual processes, suggesting that our perception is indeed colored by the action potentials afforded by the composed space. In conclusion, the shape of space resonates with our embodied predictions regarding movement.

The prevailing current view of protein folding is the thermodynamic hypothesis, under which the native folded conformation of a protein corresponds to the global minimum of Gibbs free energy G. We question this concept and show that the empirical evidence behind the thermodynamic hypothesis of folding is far from strong. Furthermore, physical theory-based approaches to the prediction of protein folds and their folding pathways so far have invariably failed except for some very small proteins, despite decades of intensive theory development and the enormous increase of computer power. The recent spectacular successes in protein structure prediction owe to evolutionary modeling of amino acid sequence substitutions enhanced by deep learning methods, but even these breakthroughs provide no information on the protein folding mechanisms and pathways. We discuss an alternative view of protein folding, under which the native state of most proteins does not occupy the global free energy minimum, but rather, a local minimum on a fluctuating free energy landscape. We further argue that ΔG of folding is likely to be positive for the majority of proteins, which therefore fold into their native conformations only through interactions with the energy-dependent molecular machinery of living cells, in particular, the translation system and chaperones. Accordingly, protein folding should be modeled as it occurs in vivo, that is, as a non-equilibrium, active, energy-dependent process.

Within the bottom-up approach to holography, we construct a class of six-dimensional gravity models, and discuss solutions that can be interpreted, asymptotically in the far UV, in terms of dual five-dimensional conformal field theories deformed by a single scalar operator. We treat the scaling dimension of such operator, related to the mass of the one scalar field in the gravity theory, as a free parameter. One dimension in the regular geometry is compactified on a shrinking circle, hence mimicking confinement in the resulting dual four-dimensional theories. We study the mass spectrum of bosonic states. The lightest state in this spectrum is a scalar particle. Along the regular (confining) branch of solutions, we find the presence of a tachyonic instability in part of the parameter space, reached by a smooth deformation of the mass spectrum, as a function of the boundary value of the background scalar field in the gravity theory. In a region of parameter space nearby the tachyonic one, the lightest scalar particle can be interpreted as an approximate dilaton, sourced by the trace of the stress-energy tensor, and its mass is parametrically suppressed. We also compute the free energy, along several branches of gravity solutions. We find that both the dilatonic and tachyonic regions of parameter space, identified along the branch of confining solutions, are hidden behind a first-order phase transition, so that they are not realised as stable solutions, irrespectively of the scaling dimension of the deforming field-theory operator. The (approximate) dilaton, in particular, appears in metastable solutions. Yet, the mass of the lightest state, computed close to the phase transition, is (mildly) suppressed. This feature is amplified when the (free) parameter controlling the scaling dimension of the deformation is 5/2, half the dimension of space-time in the field theory., Comment: 40 pages, 11 figures; Version accepted for publication

We propose a quantum-mechanical framework to describe the dynamics of human decision making, where the interactions between the open quantum system of decision makers and its surrounding environment at given temperature are relevantly taken into account. The temporal evolution of quantum system is described in terms of the time-dependent density matrix, from which we can evaluate those thermodynamic functions such as internal energy, (von Neumann) entropy and (Helmholtz) free energy. In this study we rely on the symmetrical quasi-classical (SQC) windowing approach to numerically solve the non-adiabatic quantum dynamics. We then consider the Hamiltonians to formulate the Prisoner’s Dilemma (PD) problem and calculate the population dynamics of the quantum states of two players’ decisions, where some quantum coherence or interference effects are observed. The evaluated free energy tends to decrease toward the thermodynamic equilibrium value, thus driving the dynamics of quantum system between the Nash equilibrium and Pareto optimum states. The calculated entropy often shows a tendency of temporal decrease, thus indicating the emergence of order in the quantum system. We have also applied the present scheme to the issue of the violation of the sure thing principle and found its occurrence through explicit numerical simulations for the PD problem. The present study may provide a theoretical basis to connect the dynamics of quantum decision making to the free energy principle in cognitive science.

Copper is a trace element vital to many cellular functions. Yet its abnormal levels are toxic to cells, provoking a variety of severe diseases. The high affinity Copper Transporter 1 (CTR1), being the main in-cell copper (Cu(I)) entry route, tightly regulates its cellular uptake via a still elusive mechanism. Here, all-atoms simulations unlock the molecular terms of Cu(I) transport in eukaryotes disclosing that the two Methionine triads, forming the selectivity filter, play an unprecedented dual role both enabling selective Cu(I) transport and regulating its uptake-rate thanks to an intimate coupling between the conformational plasticity of their bulky side chains and the number of bound Cu(I) ions. Namely, the Met residues act as a gate reducing the Cu(I) import-rate when two ions simultaneously bind to CTR1. This may represent an elegant autoregulatory mechanism through which CTR1 protects the cells from excessively high, and hence toxic, in-cell Cu(I) levels. Overall, these outcomes resolve fundamental questions in CTR1 biology and open new windows of opportunity to tackle diseases associated with an imbalanced copper uptake.Abstract Figure

We introduce a classical algorithm to approximate the free energy of local, translation-invariant, one-dimensional quantum systems in the thermodynamic limit of infinite chain size. While the ground state problem (i.e., the free energy at temperature T = 0) for these systems is expected to be computationally hard even for quantum computers, our algorithm runs for any fixed temperature T > 0 in subpolynomial time, i.e., in time O((1/ε)^c) for any constant c > 0 where ε is the additive approximation error. Previously, the best known algorithm had a runtime that is polynomial in 1/ε where the degree of the polynomial is exponential in the inverse temperature 1/T. Our algorithm is also particularly simple as it reduces to the computation of the spectral radius of a linear map. This linear map has an interpretation as a noncommutative transfer matrix and has been studied previously to prove results on the analyticity of the free energy and the decay of correlations. We also show that the corresponding eigenvector of this map gives an approximation of the marginal of the Gibbs state and thereby allows for the computation of various thermodynamic properties of the quantum system., LIPIcs, Vol. 251, 14th Innovations in Theoretical Computer Science Conference (ITCS 2023), pages 49:1-49:6

Electrostatic phenomena, like lightning in a thunderstorm or a balloon sticking to our hair, are everywhere in our day-to-day life. These phenomena are based on forces exerted by electric charges described by Coulomb's law. Developed for macroscopic objects, Coulomb's law even holds on the nanoscale with astonishing accuracy describing the interactions of atoms, molecules, and ions, the building blocks of all matter. Understanding their behavior is essential for all-natural sciences. One molecule of utmost importance in natural science is water. An exact electrostatic description of liquid water and its interaction with other dissolved molecules or ions is impossible due to the complex structure of the liquid. Therefore, we are usually content with a continuum description by treating water as an unstructured homogenous - dielectric - material, already explaining several phenomena like ion solvation or colloid precipitation. However, it is known that at interfaces the isotropy and homogeneity of the water's dielectric properties break down. In fact, any modification of the dielectric constant at interfaces or in confined space fundamentally influences all electrostatic interactions including equilibria of chemical reactions or particle distributions. This thesis aims to understand how the electrostatic interactions are modified in aqueous nanosystems and how well a dielectric continuum description performs. The dielectric properties of water and ions are quantified using classical force field atomistic simulations as well as using novel anisotropic linear continuum descriptions. and compared to recent experiments. For an accurate comparison between the simulations and the continuum description we develop a new simulation force field describing the physics of several monovalent ions in water with higher accuracy compared to previous parametrizations. During the subsequent study of the water properties at planar interfaces and in narrow planar channels, we find that dielectric effects differ in perpendicular and parallel surface direction but decay to the bulk value within 1 ��� 2 nm away from the surface. This universal scaling exists regardless of the studied surface type. For water-filled carbon nanotubes, we show that the dielectric tensor becomes, due to curvature effects, even more, anisotropic compared to planar systems. Based on the dielectric properties extracted from our simulations we analytically calculate interactions of charges with surfaces and between other charges in planar and cylindrical geometry on a linear response level applying previously derived solutions of Poisson's equation. Comparing the analytic predictions to explicit simulations we quantify the breakdown of linear response theory at interfaces and reveal that interactions in confinement are drastically enhanced compared to non confined systems. The findings of this work have an impact for the understanding of the transport, adsorption and evaporation properties of atoms, molecules, and ions which is not only relevant in biological systems but also for technical applications like water purification or energy storage., Elektrostatische Ph��nomene wie Blitze in einem Gewitter oder ein Luftballon, der an den Haaren haftet, sind uns allgegenw��rtig. Diese Erscheinungen beruhen auf Kr��ften, die durch elektrische Ladungen hervorgerufen und durch das Coulomb Gesetz beschrieben werden. Entwickelt f��r makroskopische Objekte, gilt dieses Gesetz bis zur Nanoskala und beschreibt dort die Wechselwirkungen zwischen Atomen, Molek��len sowie Ionen, den Bausteinen aller Materie. Das Verhalten dieser Wechselwirkungen zu verstehen, ist essentiell f��r alle Naturwissenschaften. Ein Molek��l von besonderer Bedeutung ist Wasser. Die exakte elektrostatische Beschreibung von fl��ssigem Wasser und seiner Wechselwirkung mit anderen Molek��len oder Ionen ist aufgrund seiner komplexen Struktur unm��glich. Daher begn��gen wir uns meist mit einer Kontinuumsbeschreibung, bei der Wasser als ein unstrukturiertes homogenes - dielektrisches - Material behandelt wird. Diese Vereinfachung erkl��rt bereits Ph��nomene wie Solvatation oder F��llung. Es ist jedoch bekannt, dass an Grenzfl��chen die Isotropie und Homogenit��t der dielektrischen Eigenschaften von Wasser zusammenbrechen. Die damit verbundene ��nderung der Dielektrizit��tskonstanten, beinflusst grunds��tzlich alle elektrostatischen Wechselwirkungen, mit Einfluss auf die Gleichgewichte von chemischen Reaktionen sowie Teilchenverteilungen. Diese Dissertation behandelt elektrostatische Wechselwirkungen in w��ssrigen Nanosystemen und wie gut eine dielektrische Kontinuumsbeschreibung funktioniert. Die dielektrischen Eigenschaften von Wasser und Ionen werden sowohl mit klassischen atomistischen Simulationen als auch mit einer neuartigen anisotropen linearen Kontinuumsbeschreibung quantifiziert und mit aktuellen Experimenten verglichen. F��r einen genauen Vergleich zwischen den Simulationen und der Kontinuumsbeschreibung entwickeln wir ein neues Simulationskraftfeld, das die Physik von einwertigen Ionen in Wasser mit h��herer Genauigkeit im Vergleich zu fr��heren Parametrisierungen beschreibt. Bei der anschlie��enden Untersuchung der Wassereigenschaften an planaren Grenzfl��chen und in nanometer gro��en planaren Poren finden wir, dass unterschiedliche dielektrische Eigenschaften in senkrechter und parallelen Richtung zu der Oberfl��che vorherrschen. Diese Anisotropie verschwindet aber innerhalb von 1 bis 2 nm von der Oberfl��che, unabh��ngig vom untersuchten Oberfl��chentyp. Weiterhin zeigen wir, dass f��r wassergef��llte Kohlenstoff-Nanor��hren der dielektrische Tensor aufgrund von Kr��mmungseffekten sogar noch anisotroper wird als im Vergleich zu planaren Systemen. Basierend auf den aus unseren Simulationen extrahierten dielektrischen Eigenschaften berechnen wir analytisch mit linearer Antworttheorie die Wechselwirkungen von Ladungen mit Oberfl��chen und mit anderen Ladungen in planarer und zylindrischer Geometrie unter Zuhilfenahme von bereits bekannten L��sungen der Poisson Gleichung. Durch den Vergleich der analytischen Vorhersagen mit expliziten Simulationen quantifizieren wir den Zusammenbruch der linearen Antworttheorie an Grenzfl��chen und zeigen, dass die Wechselwirkungen in Nanosystemen im Vergleich zu nicht-begrenzten Systemen drastisch erh��ht sind. Die Ergebnisse dieser Arbeit haben Auswirkungen auf das Verst��ndnis der Transport-, Adsorptions- und Verdampfungseigenschaften von Atomen, Molek��len sowie Ionen, was nicht nur f��r biologische Systeme, sondern auch f��r technische Anwendungen wie Wasseraufbereitung oder Energiespeicherung relevant ist.

In this work, we revisit the question of the linear stability of superfluid phases of matter. Famously, Landau predicted superfluid Helium would become unstable for large enough superfluid velocities. We demonstrate that this instability simply follows from a thermodynamic argument, by showing that its onset corresponds to a change of sign of one of the eigenvalues of the matrix of second derivatives of the free energy. Turning on dissipation and without any particular assumption on invariance under boosts, we show that a linear dynamical instability also develops, leading to exponential growth in time of perturbations around equilibrium. Specializing to Galilean superfluids and assuming the existence of quasiparticles, our criterion matches Landau's critical velocity. We also verify that it correctly reproduces the onset of the instability in relativistic superfluids constructed using gauge/gravity duality. Our work provides a simple, comprehensive and unified description of the Landau instability for superfluids independently of the microscopic details of the system., Comment: v1: 5 pages + appendices, 2 figures

An exploration of representations of free energies and associated rates of dissipation for a broad class of nonlinear viscoelastic materials is presented in this work. Also included are expressions for the stress functions and work functions derivable from such free energies. For simplicity, only the scalar case is considered. Certain standard formulae are generalized to include higher power terms.It is shown that the correct initial procedure in this context is to specify the rate of dissipation as a positive semi-definite functional and then to determine the free energy from this, rather than the other way around, which would be the traditional approach.Particularly detailed versions of these formulae are given for the model with two memory contributions in the free energy, the first being the well-known quadratic functional leading to constitutive relations with linear history terms, while the second is a quartic functional yielding a cubic term for the stress function memory dependence. Also, the discrete spectrum model, for which each memory kernel is a sum of exponentials, is generalized from the quadratic functional representation for the free energy to that with the quartic functional included.Finally, a model is considered, allowing functional power series with an infinite number of terms for the free energy, rate of dissipation and stress function.

The density of states of a quantum system can be calculated from its definition but, in some cases, this approach is quite cumbersome. Alternatively, the density of states can be deduced from the microcanonical entropy or from the canonical partition function. After discussing the relationship among these procedures, we suggest a simple numerical method, which is equivalent in the thermodynamic limit to perform a Legendre transformation, to obtain the density of states from the Helmholtz free energy. We apply this method to determine the many-body density of states of the unitary Fermi gas, a very dilute system of identical fermions interacting with divergent scattering length. The unitary Fermi gas is highy symmetric due to the absence of any internal scale except for the average distance between two particles and, for this reason, its equation of state is called universal. In the last part of the paper, by using the same thermodynamical techniques, we review some properties of} the density of states of a Schwarzschild black hole, which shares with the unitary Fermi gas the problem of finding the density of states directly from its definition., 10 pages, 6 figures, invited paper (short review) for the Special Issue "Cooperative Effects in Finite Systems" of the journal Symmetry (MDPI)

Дослiдженi термодинамiчнi властивостi рiдкого металiчного гелiю в другому порядку теорiї збурень за псевдопотенцiалом електрон-iонної взаємодiї. При цьому використано псевдопотенцiал, знайдений з перших принципiв. Цей псевдопотенцiал є нелокальним i нелiнiйним. Нелокальнiсть псевдопотенцiалу приводить до того, що у розвиненнi внутрiшньої енергiї, вiльної енергiї i тиску рiдкого металiчного гелiю в ряд за псевдопотенцiалом присутнiй член першого порядку. Його дiагональний матричний елемент виявляється того ж порядку величини, що i член нульового порядку. В результатi цей член дає важливий внесок у внутрiшню i вiльну енергiю, а залежнiсть їх вiд густини i температури стає суттєвiшою. Вiдповiдно зростає i тиск, при якому може реалiзовуватись рiдка металiчна фаза гелiю. Цей тиск на порядок перевищує вiдповiдний тиск у металiчному воднi i на сьогоднi є недосяжним на експериментi. Аналiз ентропiї дозволив з’ясувати область iснування рiдкої металiчної фази i з’ясувати умови її кристалiзацiї. Порiвняння з густинами, тисками i температурами всерединi газових гiгантiв Юпiтера i Сатурна дозволило зробити висновок про те, що в центральних частинах цих планет не лише водень, а i гелiй перебувають у металiчному станi. Проте тиск в надрах планет є недостатнiм для кристалiзацiї гелiю., Thermodynamic properties of liquid metallic helium have been studied in the framework of perturbation theory of the second-order in the electron-ion interaction pseudopotential. The latter was determined from the first principles and was found to be nonlocal and nonlinear. The pseudopotential nonlocality leads to the appearance of the first-order terms in the series expansions of the internal energy, free energy, and pressure of liquid metallic helium in the pseudopotential. The diagonal matrix element of this term is of the same order of magnitude as that in the zero-order term. As a result, the first-order term makes a substantial contribution to the internal and free energies, so that their dependences on the density and the temperature become stronger. Accordingly, the pressure at which the liquid phase of metallic helium can be realized increases. This pressure is an order of magnitude higher than the corresponding pressure in metallic hydrogen and is currently unattainable experimentally. The analysis of the entropy made it possible to determine the region of existence for the liquid metallic helium phase and the conditions for its crystallization. A comparison between the densities, pressures, and temperatures inside such gas giants as Jupiter and Saturn allowed us to conclude that not only hydrogen but also helium are in the metallic state in the central parts of those planets. However, the pressure in their interiors is insufficient for helium to crystallize.

Fluorodeoxyglucose (FDG), marked with the most used Positron Emission Tomography (PET) radiopharmaceutical Fluorine-18 (F-18), is a glucose analog and is taken to living cells through membrane glucose carriers. F-18 FDG involvement in tissue is proportional to glucose use. In many cancers, there is increased glucose use due to increased gluten expression and hexokinase activity. F-18 FDG PET is a proven method for diagnosis, staging, re-staging, and evaluation of treatment response in oncology. The purpose of this study is to find the effect of ionizing radiation on proteins in the mechanism of action of FDG and determine to Molecular mechanisms of F-18 FDG accumulation in metabolism. In the study, two different models were used together, the first method, the study was Molecular Docking method for modeling molecules deconstructed and the structure of FDG was energy minimized by utilizing the density functional theory, and the B3LYP functional was used with 6-311G basis set. The second method was the Monte Carlo method for modeling ionizing radiation interactive with the potential routes of FDG metabolism within the cell. It was determined that the Gibbs free energy (?G) change was compatible with the ionizing radiation factors for binding of FDG to the aphthous regions of Glucose-6-phosphate isomerase (G1), hexokinase (G2), and glucose transporter-1 (G3) were selected. In this study, the strong binding of FDG to protein influences the effect of radiation on the active site of enzymes. The G1 and G3 shown in the study interacted with only one charged amino acid FDG, and the absence of an aromatic residue around it can be considered among the results of this study as the cause of the low protective effect against ionizing radiation. © 2022 Elsevier Ltd, None.

We use molecular dynamics to compute the free energy of carbon nanoparticles crossing a hydrophobic–hydrophilic interface. The simulations are performed on a biphasic system consisting of immiscible solvents (i.e., cyclohexane and water). We solvate a carbon nanoparticle into the cyclohexane layer and use a pull force to drive the nanoparticle into water, passing over the interface. Next, we accumulate a series of umbrella sampling simulations along the path of the nanoparticle and compute the solvation free energy with respect to the two solvents. We apply the method on three carbon nanoparticles (i.e., a carbon nanocone, a nanotube, and a graphene nanosheet). In addition, we record the water-accessible surface area of the nanoparticles during the umbrella simulations. Although we detect complete wetting of the external surface of the nanoparticles, the internal surface of the nanotube becomes partially wet, whereas that of the nanocone remains dry. This is due to the nanoconfinement of the particular nanoparticles, which shields the hydrophobic interactions encountered inside the pores. We show that cyclohexane molecules remain attached on the concave surface of the nanotube or the nanocone without being disturbed by the water molecules entering the cavity.

The ability to track the changes of the surrounding environment is critical for humans and animals to adapt their behaviors. In high-dimensional environments, the interactions between each dimension need to be estimated for better perception and decision making, for example in volatile or social cognition tasks. We develop a hierarchical Bayesian model for inferring and decision making in multi-dimensional volatile environments. The hierarchical Bayesian model is composed of a hierarchical perceptual model and a response model. Using the variational Bayes method, we derived closed-form update rules. These update rules also constitute a complete predictive coding scheme. To validate the effectiveness of the model in multi-dimensional volatile environments, we defined a probabilistic gambling task modified from a two-armed bandit. Simulation results demonstrated that an agent endowed with the proposed hierarchical Bayesian model is able to infer and to update its internal belief on the tendency and volatility of the sensory inputs. Based on the internal belief of the sensory inputs, the agent yielded near-optimal behavior following its response model. Our results pointed this model a viable framework to explain the temporal dynamics of human decision behavior in complex and high dimensional environments.

In this study, an interactive Ising model having the nearest and prolonged next-nearest neighbors defined on a Cayley tree is considered. Inspired by the results obtained for the one-dimensional Ising model, we will construct the partition function and then calculate the free energy of the Ising model having the prolonged next nearest and nearest neighbor interactions and external field on a two-order Cayley tree using the self-similarity of the semi-infinite Cayley tree. The phase transition problem for the Ising system is investigated under the given conditions.

Appropriate levels of arousal potential induce hedonic responses (i.e., emotional valence). However, the relationship between arousal potential and its factors (e.g., novelty, complexity, and uncertainty) have not been formalized. This paper proposes a mathematical model that explains emotional arousal using minimized free energy to represent information content processed in the brain after sensory stimuli are perceived and recognized (i.e., sensory surprisal). This work mathematically demonstrates that sensory surprisal represents the summation of information from novelty and uncertainty, and that the uncertainty converges to perceived complexity with sufficient sampling from a stimulus source. Novelty, uncertainty, and complexity all act as collative properties that form arousal potential. Analysis using a Gaussian generative model shows that the free energy is formed as a quadratic function of prediction errors based on the difference between prior expectation and peak of likelihood. The model predicts two interaction effects on free energy: that between prediction error and prior uncertainty (i.e., prior variance) and that between prediction error and sensory variance. A discussion on the potential of free energy as a mathematical principle is presented to explain emotion initiators. The model provides a general mathematical framework for understanding and predicting the emotions caused by novelty, uncertainty, and complexity. The mathematical model of arousal can help predict acceptable novelty and complexity based on a target population under different uncertainty levels mitigated by prior knowledge and experience.

Natural gas hydrate is a potential energy source in the future, which widely occurs in nature and industrial activities, and its formation and decomposition are identified by phase equilibrium. The calculation of multicomponent gas phase equilibrium is more complex than that of single component gas, which depends on the accurate model characterized by enthalpy and free energy. Based on the Kvamme-Tanaka statistical thermodynamic model, theoretical and experimental methods were used to predict and verify the phase equilibrium of pure methane hydrate and carbon dioxide hydrate in the temperature range of 273.17–289.05 K. The phase equilibrium curves of methane-containing gases such as CH4+CO2,CH4+C2H6,CH4+H2S and CH4+CO2+H2S under different mole fractions were drawn and analyzed, and the decomposition or formation enthalpy and free energy of hydrate were calculated. The results show that, the phase equilibrium curves of the methane containing systems is mainly related to the guest molecule type and the composition of gas. The evolution law of phase equilibrium pressure of different gases varies with composition and temperature, and the phase splitting of CO2at the quadruple point affects the phase equilibrium conditions. Due to the consideration of the interaction between the motion of guest molecules and the vibration of crystal lattice, the model exhibits a good performance, which is quantified in terms of mean square error (MSE) with respect to the experimental data. The magnitudes of MSE percent are respectively 1.2, 4.8, 15.12 and 9.20 MPa2for CH4+CO2, CH4+C2H6, CH4+H2S and CH4+CO2+H2S systems, and the values are as low as 3.57 and 1.32 MPa2for pure methane and carbon dioxide, respectively. This study provides engineers and researchers who want to consult the diagrams at any time with some new and accurate experimental data, calculated results and phase equilibrium curves. The research results are of great significance to the development and utilization of gas hydrate and the flow safety prediction of gas gathering and transportation.