Physica A: Statistical Mechanics and its Applications

Protein-DNA complexes are involved in vital cellular functions like gene regulation, replication, transcription, packaging, rearrangement, and damage repair. In this work, streamlined geometric formalism for computing the absolute binding free energy was used to obtain chemical accurate in silico estimation of binding free energy of three Protein-DNA complexes. Additionally, molecular interactions between Protein and DNA involved hydrogen bonds, electrostatic, van der Waals, and hydrophobic interactions. Using this formalism, researcher can obtain the absolute binding free energy for a Protein-DNA complex with remarkable accuracy and modest computational cost.

We introduce a spectral existence criterion for the evolution of cooperation in the form of the inequality{lambda} maxb > c, where{lambda} max is the leading eigenvalue of an interaction operator encoding population structure, and b and c represent benefit and cost tradeoffs, respectively. Nowaks five rules for the evolution of cooperation correspond to cases in which the cooperation condition reduces to a scalar assortment coefficient. These results follow from the Price equation, which sheds light on a long-standing debate on the role of inclusive fitness and evolutionary dynamics in explaining the evolution of cooperation.

One of the most critical steps in human reproduction is the selection of the dominant follicle when a single follicle is chosen from a large group of follicles to ovulate. Although this process involves complex hormonal regulation, the complete microscopic picture of unique selectivity remains unclear. We propose a novel stochastic mechanism for dominant follicle selection that incorporates the actions of the most relevant hormones, follicle-stimulating hormone (FSH) and estradiol. Our theoretical picture suggests the following sequence of events. As soon as the FSH concentration reaches the critical threshold, one of the available follicles is randomly selected, which immediately stimulates the production of estradiol, which, via a negative feedback mechanism, suppresses further FSH production, lowering its concentration below the critical threshold. This suppression limits the time window for the possible second follicle selection event, allowing only a single follicle to be selected. Based on this picture, a minimal quantitative theoretical model of dominant follicle selection is developed and analyzed using analytical calculations and computer simulations. Theoretical analysis shows how the interplay between different parameters that govern follicle selection leads to high selectivity. Our theoretical approach can explain some key known observations, providing a quantitative tool for analyzing biological reproduction phenomena.

A methodology for computationally unstructuring proteins is described and the results of its application to a variety of proteins analyzed and discussed. Some proteins prove more susceptible than others, and fold topology plays a part in this. Alpha helical structure is found to be generally somewhat robust, and, perhaps unsurprisingly, unstructuring often begins at exposed chain termini. Phosphofructokinase-1 and phosphofructokinase-2, which have similar sizes but different fold topologies, are found to differ markedly in their unstructuring behaviour.

Dynamical processes on complex networks have a long history of study with increasing applications across many fields. While epidemics in heterogeneous networks have received much attention in terms of how connectivity patterns drive epidemic outbreaks, affect critical thresholds, timescales, final outbreak size and immunization efforts, less attention has been devoted to endemic multi-strain scenarios and questions of selection and coexistence dynamics. Here, we provide an SIS framework for multiple co-circulating strains and co-infection, which can be reduced to a replicator dynamics on a host contact network. Using the analytical tractability of the replicator formalism, we study how network heterogeneity affects multi-strain dynamics, and compare its effects relative to the homogeneous contact distribution, identifying key relevant metrics for comparison. In particular, the pairwise invasion fitness matrix comparison reveals that higher network heterogeneity acts to increase the speed of multi-strain dynamics and typically tends to have stabilizing effects that reduce the number of coexisting strains. While many aspects of the replicator dynamics remain complex to study, especially for high number of strains, the advantage of this model representation lies in the dimensional reduction of a huge system, enabling general, more direct and efficient numerical computations. Furthermore the explicit bottom-up constitution of crucial parameters yields biological and epidemiological insight for critical system transitions across macroscopic gradients and can be used to guide interventions.

This study presents a theoretical and mathematical framework for understanding the dynamical behavior of infectious disease spread using a compartmental modeling approach. The proposed model incorporates memory effects to capture temporal dependencies that are not adequately represented by classical formulations. Qualitative analysis is employed to investigate the stability properties of the system and the role of key mechanisms in shaping long term dynamics. Publicly available surveillance information is used only to illustrate the consistency of the model behavior with observed trends. The results highlight the value of memory based modeling structures for describing complex biological processes and provide a general mathematical perspective for studying epidemic dynamics.

Mass-conserved reaction-diffusion systems are used as mathematical models for various phenomena such as cell polarity. Numerical simulations of this system present transient dynamics in which multiple stripe patterns converge to spatially monotonic patterns. Previous studies indicated that the transient dynamics are driven by a mass conservation law and by variations in the amount of substance contained in each pattern, which we refer to as "pattern flux". However, it is challenging to mathematically investigate these pattern dynamics. In this study, we introduce a reaction-diffusion compartment model to investigate the pattern dynamics in view of the conservation law and the pattern flux. This model is defined on multiple intervals (compartments), and diffusive couplings are imposed on each boundary of the compartments. Corresponding to the transient dynamics in the original system, we consider the dynamics around stripe patterns in the compartment model. We derive ordinary differential equations describing the pattern dynamics of the compartment model and analyze the existence and stability of equilibria for the reduced ODE with respect to the boundary parameters. For a specific parameter setting, we obtained results consistent with previous studies. Moreover, we present that the stripe patterns in the compartment model are potentially stabilized by changing the parameter, which is not observed in the original system. We expect that the methodology developed in this paper is extendable to various directions, such as membrane-induced pattern control.

Alzheimers disease (AD) is characterized by the accumulation of amyloid-{beta} (A{beta}), yet the specific link between plaque burden and cognitive decline remains a subject of intense investigation. This paper presents a mathematical model that simulates the coupled dynamics of A{beta} monomers, soluble oligomers, and fibrillar species in the brain tissue. By modifying existing moment equations to include a dedicated conservation equation for A{beta} monomers, the model explores how various microscopic processes, such as primary nucleation, surface-catalyzed secondary nucleation, fibril elongation, and fragmentation, contribute to macroscopic disease progression. Central to this study is the concept of "accumulated neurotoxicity" as a surrogate marker of biological age, defined as the time-integrated concentration of soluble A{beta} oligomers. Unlike plaque burden, accumulated neurotoxicity cannot be reversed, and the harm it causes depends critically on the sequence of events that produced it. Numerical results demonstrate that while plaque burden and neurotoxicity both increase over time, their relationship is non-linear and highly sensitive to the efficiency of protein degradation machinery. Specifically, impaired degradation leads to a rapid advancement of biological age relative to calendar age. The model further identifies oligomer dissociation and fibril fragmentation as potential protective mechanisms that can counterintuitively reduce neurotoxic burden by diverting monomers away from the soluble oligomer pool. These findings provide a quantitative framework for understanding why individuals with similar plaque burdens may experience vastly different cognitive outcomes, underscoring the importance of targeting soluble oligomers early in therapeutic interventions.

Kinase family proteins constitute the second largest protein class targeted in drug development efforts, most prominently to treat cancer, but also several other diseases associated with kinase dysfunction. In this work we focus on type II kinase inhibitors which bind to the "classical" inactive conformation of the protein kinase catalytic domain where the DFG motif has a "DFG-out" orientation and the activation loop is folded. Many Tyrosine kinases (TKs) exhibit strong binding affinity with a wide spectrum of type II inhibitors while serine/threonine kinases (STKs) often bind more weakly. Recent work suggests this difference is largely due to differences in the folded to extended conformational equilibrium of the activation loop between TKs vs. STKs. The binding affinity of a type II inhibitor to its kinase target can be decomposed into a sum of two contributions: (1) the free energy cost to reorganize the protein from the active to inactive state, and (2) the binding affinity of the type II inhibitor to the inactive kinase conformation. In previous work we used a Potts statistical energy potential based on sequence co-variation to thread sequences over ensembles of active and inactive kinase structures. The threading function was used to estimate the free energy cost to reorganize kinases from the active to classical inactive conformation, and we showed that this estimator is consistent with the results of molecular dynamics free energy simulations for a small set of STKs and TKs. In the current study, we analyze the results of a large-scale study of the binding affinities of 50 type II inhibitors to 348 kinases, of which the results for 16 of the 50 type II inhibitors were reported in an earlier study (the "Davis dataset"); the binding data for the remaining 34 type II inhibitors to the panel of 348 kinases were recently obtained (the "Schrodinger dataset"). We use the Potts statistical energy model to investigate the contribution of protein reorganization to the selectivity of the large kinase panel against the set of 50 type II inhibitors, and find that protein reorganization makes a significant contribution to the selectivity. The AUC of the receiver-operator characteristic curve is [~]0.8. We report the results of an internal "blind test", that shows how Potts threading energies can provide more accurate estimates of kinase selectivity than corresponding predictions using experimental results of small sample size. We discuss why two STK phylogenetic kinase families, STE and CMGC, appear to contain many outliers, and how to improve the ability to predict kinase selectivity with a more complete analysis of the kinase conformational landscape. We compare the performance of Potts threading for predicting binding properties of the large set of (50) Type II inhibitors to 348 kinases, with those of a sequence-based purely machine learning model, DeepDTAGen, a publicly available machine learning model that was trained on the complete Davis dataset, including both Type I and Type II kinase inhibitors. We observe that DeepDTAGen performs well on binding predictions for the 16 type II inhibitors in the Davis dataset, but performs poorly on binding predictions for the 34 type II inhibitors against 348 kinases in the Schrodinger dataset.

During embryogenesis, as cells proliferate and assemble into tissues, they undergo a sequence of transitions between distinct molecular states eventually giving rise to a cellular population consisting of an appropriate distribution of specific functional cell types. Recent progress on the dynamics underlying decision-making in developmental landscape makes it feasible to start analysing the amount of information involved in constructing such systems. To explore this we introduce the notion of potency of a developmental landscape and attempt to calculate it for two development systems of current interest, in-vitro differentiation of epiblast-like cells into neural and mesodermal progenitors and the worm vulva patterning system. Our approach integrates concepts from developmental biology, information theory and dynamical systems to estimate both the number and identity of signalling regimes that give rise to distinguishable temporal response patterns.

The spatial structure of populations may promote the emergence and maintenance of cooperation. Cooperation in the prisoners dilemma is favored under specific update rules in evolutionary graph theory models with one individual per node of a graph, but this effect vanishes in models with well-mixed demes connected by migrations under soft selection. In contrast, experiments and models involving cycles of growth, merging and dilution have shown that spatial structure can favor cooperation. Here, we reconcile these findings by studying deme-structured populations under growth-merging-dilution dynamics, corresponding to a clique (fully connected graph) under hard selection. We obtain analytical conditions for the cooperator fraction to increase during deterministic logistic growth, and to increase on average under dilution-growth-merging cycles, in the weak selection regime. Furthermore, we analytically express the fixation probability of cooperators under weak selection, yielding a criterion for cooperative mutants to have a higher fixation probability than neutral ones. Finally, numerical simulations show that stochastic growth further promotes cooperation. Overall, hard selection is essential for cooperation to be promoted in deme-structured populations.

The analysis of large gene and metabolic networks is often hindered by unknown biochemical parameters and the nonlinear nature of classical S-system models. To address this, we introduce a framework based on combinatorial toric geometry computed with tools such as Normaliz, SageMath, it is worth mentioning this technique in not restrictive to integer vectors, there exists a natural extension to real geometries. Unlike traditional approaches, which rely on parameter dependent fixed points, our method constructs a Topological Environment derived from the dual space of kinetic orders, leading to what we call orthogonal enzyme kinetics. Within this topological setting, fixed points are computed on the algebraic torus, enabling the transformation of nonlinear dynamics into linear forms. Importantly, these fixed points are independent of kinetic parameters and depend only on network topology and interaction signs. Applying this methodology to gene circuits involved in circadian rhythms, we reproduce previously reported oscillatory physiologies.

Fraud in the health landscape is an aggravating issue, with far-reaching consequences burdening the financial stability of the health industry and threatening the quality of medical care. It results from vulnerabilities within the current healthcare framework that are exploited by the fraudsters in their favor. In spite of many developed models that aim to detect fraudulent patterns in insurance claims, the accuracy of such models frequently suffers as a result of the imbalance issue of the Medicare dataset and irrelevant features. This study ventures to improve detection performance and accuracy by employing a deep learning model along with data sampling and feature selection techniques. Comparative analysis among different combinations is conducted to determine their efficacy to enhance the accuracy of the fraud detection model. Hence, the suggested model clearly demonstrates that a combination of myriad data sampling and feature selection techniques is helping to improve accuracy and performance. The accuracy was thus 95.4%, with negligible evidence of overfitting detected using both Chi-square and Synthetic Minority Over-sampling (SMOTE) techniques. Ultimately, the study findings underscore the significance of employing combined techniques instead of using only the baseline deep learning model for better performance in detecting Medicare insurance fraud.

The actin cytoskeleton is an inherently disordered active system. the actomyosin cortex and reconstituted actomyosin systems are globally disordered, yet undergo transitions between distinct disordered states as parameters like motor and crosslinker concentration and filament length and rigidity change. In cells these changes are related to genetic mutations or differences in cell state and dictate fundamental biological processes. However, we dont have well established methods to detect and classify differences in disordered polymer networks. Image-based morphology techniques provide a non-invasive, high-throughput method of extracting information about a system. In this work we simulate biopolymer networks under varying conditions and develop and use morphological descriptors to construct trajectories in morphospace. Using statistical analysis we find that morphological descriptors are able to distinguish between different trajectories of the system, including differences not apparent to the eye. However, no single descriptor alone is able to capture all the differences in the simulated trajectories. Nematic order parameters typically perform the worst for our simulations while curvature and texture descriptors can collectively distinguish between dynamic trajectories. This work helps develop quantification of cytoskeleton dynamics for classification and data-driven modeling.

Our recent work on molecular evolution and population genetics postulated that individuals with a specific mutation exhibit a fluctuation in fitness, short for FSI (fluctuating selection among individuals), whereas the fitness effect of wildtype remains a constant. An intriguing phenomenon called selection-duality emerges, that is, a slightly beneficial mutation could be a negative selection (the substitution rate less than the mutation rate). It appears that selection-duality is bounded by two bounds: the generic neutrality where the mutation is neutral by the means of fitness on average, and the substitution neutrality where the substitution rate equals to the mutation rate. In addition, the middle point of generic neutrality and substitution neutrality is called the FSI-neutrality. An important problem is about the age profile of allele frequency, i.e., the arising timing of a mutation whose frequency in the current population is given (the allele-age problem for short). Solving this problem under selection duality would help extend the standard coalescent theory that based on strict neutrality to a more general form under selection duality. In this paper, we studied the allele-age problem under selection-duality by the first arrival time approach and the mean age approach, respectively. Since the general solution of allele-age problem under selection duality is not available, we focused on solving the problem at the substitution neutrality (the up-bound of selection duality), the FSI-neutrality (the middle-point) and the generic neutrality (the low-bound), respectively. Our analysis results in an overall picture that the mean first-arrival age of a mutation at the substitution neutrality is theoretically identical to that at the FSI-neutrality, which is numerically close to that at the generic neutrality. For illustration, we calculated the mean age of nonsynonymous mutations in the human population and demonstrated that the estimated allele-age could be overestimated considerably when the effect of FSI was neglected.

A common assumption in molecular evolution is the fixed selection nature of a mutation, for instance, a neutral mutation is selectively neutral for all individuals who carry the mutation, and so forth a deleterious or beneficial mutation. Our recent work challenged this presumption, postulating that individuals with a specific mutation exhibit a fluctuation in fitness, short for FSI (fluctuating selection among individuals). Moreover, an intriguing phenomenon called selection-duality emerges, that is, a slightly beneficial mutation could be a negative selection (the substitution rate less than the mutation rate). It appears that selection-duality is bounded: the low-bound is the generic neutrality where the mutation is neutral by the means of fitness on average, while the up-bound is the substitution neutrality where the substitution rate equals to the mutation rate. In this paper, we conducted a thorough theoretical analysis to evaluate how many generations needed for a selection-duality mutation to be fixed in a finite population. A striking finding is that the mean fixation time of a selection-duality mutant, including the generic neutrality and the substitution neutrality, is approximately identical, which is considerably shorter than the case of strict neutrality without FSI. One may further envisage that the fast-fixation nature of selection-duality mutations could result in a considerable genetic reduction at linked sites.

Intrinsically disordered proteins (IDP) or proteins with intrinsically disordered regions (IDR) perform a plethora of functions mostly in a cellular environment. As unfolded proteins, IDPs can adopt molten globule or coil ensembles of conformations. Regarding the latter the question arises whether they are describable as a self-avoiding random coil. Locally, this requires that amino acid residues sample the entire sterically allowed region of the Ramachandran plot with very similar probabilities and independent on the conformational dynamics of their neighbours. However, various lines of experimental and bioinformatic evidence suggest a more restricted, side chain and nearest neighbor dependent conformational space for individual residues. Over the last 25 years short peptides and coil libraries were employed to determine conformational propensities of amino acid residues in unfolded states. The question arises whether conformational ensembles obtained from these two sources are comparable. In this paper, a variety of metrics were used to compare Ramachandran plots of a limited number of GXYG peptides (X,Y: guest residues) with XY dimers in the coil library of Ting et al.(PLOS 6, e1000763, 2010). The results reveal major differences between corresponding plots, which might in part due to the fact that solely the influence of one of the two neighbours of a given residue is probed by the above coil library while averages were taken over the respective opposite neighbours. The presented results suggest that coil libraries alone might not be a sufficient tool for determining the characteristics of statistical coils of IDPS and IDRs alike.

A morphospace is an abstract space of theoretically possible biological traits, shapes, or property values. It is interesting to explore which parts of a morphospace life occupies, as compared to those parts which could be occupied, but are not. Comparing random and natural non-coding (nc) RNA secondary structures is an established approach to studying morphospace occupation for RNA structures. Most earlier studies have focused on the minimum free energy (MFE) structure, while relatively few have looked at the Boltzmann distribution, describing the ensemble of energetically suboptimal RNA folds. These suboptimal structures may have important roles and functions, and hence should be examined carefully. Here we compare random and natural ncRNA in terms of their Boltzmann distributions, finding that natural RNA tend to have very similar profiles to random RNA, with the main difference being that natural RNA are slightly more energetically stable, except for very short sequences (20 to 30 nucleotides) which tend to be slightly less stable. We infer that natural ncRNA occupy similar parts of the morphospace that random RNA do, indicating that the biophysics of the genotype-phenotype map largely determines the ensemble properties of ncRNA.

Background/ObjectivesThe unprecedented structural and binding data for antibodies to the SARS-COV2 virus taken together with the mutations for the spike protein allows for a broad simulation study of antibody-spike protein binding. This provides an understanding of the co-evolution of human immunity and viral immunity escape. MethodsWe utilized the YASARA molecular dynamics program to generate initial antibody-spike structures and simulate to equilibration for six SARS-COV2 variants and 10 different antibodies sampling two different binding regions to the receptor binding domain of the spike (especially for the Class I antibodies in the same part of the spike which attaches to the ACE2 receptor protein) and one to the N-terminal of the spike. Starting structures for antibody binding to variant spike proteins are perturbatively achieved through point mutations and insertions/deletions in the YASARA program. We employed YASARA to measure interfacial hydrogen bound counts between antibodies and variant spike proteins, and the HawkDock MMGBSA program to characterize trends in binding energies with mutation for four of the antibodies. We utilized the VMD program to analyze the time course of hydrogen bond populations. ResultsAs seen in previous studies, interfacial hydrogen bond counts serve as an excellent proxy for binding energies without the large systematic error inherent in the latter. We find that there is generally a decline in antibody binding strength, as measured by interfacial hydrogen bond counts, with viral evolution, but that a modest re-entrance of binding strength is present for most antibodies studied. Generically, the antibody heavy chain binds more strongly to the spike protein, through for approximately half the antibodies the light chain binding strength converges to the heavy chain strength with viral evolution. ConclusionsThe key conclusion is that the identified re-entrant immunity, speculatively arising from a balancing of maintenance of ACE2-spike binding while escaping antibodies through mutation, allows for some maintenance and even strengthening of immunity for later viral strains from early infection or vaccination.

Protein condensates that form via phase separation typically become more viscous over time and can harden in a process referred to as "molecular aging". Several mechanisms have been identified for this phenomenon. Of these, the ones involving enhanced {beta}-sheet or -strand interactions are of pathological relevance since they have been associated with neurodegeneration. Although there is much understanding of biopolymer phase behavior, an inclusive thermodynamic framework that unifies phase separation and {beta}-sheet-based aging is lacking. We present a time-dependent, multi-component extension of associating polymer theory that describes phase separation and aging of an intrinsically disordered protein (IDP) capable of associating through local, reversible folding. The model shows how the Second Law of Thermodynamics applies throughout, whether phase separation precedes and encourages aging or, vice versa, whether the increase in "stickiness" during aging drives phase separation. Our calculations show how the time-dependence of the average valency of associating sites determines the aging kinetics and the development of viscoelastic properties of a biocondensate. The agreement between our calculations and the change in dynamics of condensates of perfect repeat analogues of nucleoporin-98 not only validates the theory but also identifies these Nup98 variants as model systems for studying aging.