In this paper we examine the emergent structures of random networks that have undergone bond percolation an arbitrary, but finite, number of times. We define two types of sequential branching processes: a competitive branching process - in which each iteration performs bond percolation on the residual graph (RG) resulting from previous generations; and, a collaborative branching process - where percolation is performed on the giant connected component (GCC) instead. We investigate the behaviour of these models, including the expected size of the GCC for a given generation, the critical percolation probability and other topological properties of the resulting graph structures using the analytically exact method of generating functions. We explore this model for Erdos-Renyi and scale free random graphs. This model can be interpreted as a seasonal N-strain model of disease spreading.

Accurate prediction of aqueous solubility for organic molecules is of great importance across a range of fields, from the design and manufacturing of energy materials, to assessing the environmental impact of potential pollutants. It is of particular significance to the pharmaceutical industry, in which problems with low aqueous solubility frequently hamper the development of new drugs. Experimental measurements of solubility are used extensively, but are often time-consuming, resource intensive and only applicable to already synthesized molecules. As such, there is a need for the development of computational approaches to predict solubility. In recent years, there have been considerable advances in physics-based methods, with several contrasting techniques able to give accurate predictions of solubility and a wealth of thermodynamic data for structural optimization. Here, we provide the reader with a thorough understanding of the theoretical background and practical applications of these physics-based methods to predict solubility. This includes discussions of the various advantages and disadvantages of each approach, and an indication of areas of continuing research. Experimental and data-driven methods to assess solubility are also discussed to provide context.

The solubility of chemical substances in water is a critical parameter in pharmaceutical development, environmental chemistry, agrochemistry, and other fields; however, accurately predicting it remains a challenge. This study aims to evaluate and compare the effectiveness of some of the most popular machine learning modeling methods and molecular featurization techniques in predicting aqueous solubility. Although these methods were not implemented in a competitive environment, some of their performance surpassed previous benchmarks, offering gradual but significant improvements. Our results show that methods based on graph convolution and graph attention mechanisms demonstrated exceptional predictive abilities with high-quality data sets, albeit with a sensitivity to data noise and errors. In contrast, models leveraging molecular descriptors not only provided better interpretability but also showed more resilience when dealing with inherent noise and errors in data. Our analysis of over 4000 molecular descriptors used in various models identified that approximately 800 of these descriptors make a significant contribution to solubility prediction. These insights offer guidance and direction for future developments in solubility prediction.

Bayesian networks represent a useful tool to explore interactions within biological systems. The aims of this study were to identify a reduced number of genes associated with a stress condition in chickens (Gallus gallus) and to unravel their interactions by implementing a Bayesian network approach. Initially, one publicly available dataset (3 control vs. 3 heat-stressed chickens) was used to identify the stress signal, represented by 25 differentially expressed genes (DEGs). The dataset was augmented by looking for the 25 DEGs in other four publicly available databases. Bayesian network algorithms were used to discover the informative relationships between the DEGs. Only ten out of the 25 DEGs displayed interactions. Four of them were Heat Shock Proteins that could be playing a key role, especially under stress conditions, where maintaining the correct functioning of the cell machinery might be crucial. One of the DEGs is an open reading frame whose function is yet unknown, highlighting the power of Bayesian networks in knowledge discovery. Identifying an initial stress signal, augmenting it by combining other databases, and finally learning the structure of Bayesian networks allowed us to find genes closely related to stress, with the possibility of further exploring the system in future studies.

Heavy-isotope substitution into enzymes slows down bond vibrations and may alter transition-state barrier crossing probability if this is coupled to fast protein motions. ATP phosphoribosyltransferase from Acinetobacter baumannii is a multi-protein complex where the regulatory protein HisZ allosterically enhances catalysis by the catalytic protein HisGS. This is accompanied by a shift in rate-limiting step from chemistry to product release. Here we report that isotope-labelling of HisGS has no effect on the nonactivated reaction, which involves negative activation heat capacity, while HisZ-activated HisGS catalytic rate decreases in a strictly mass-dependent fashion across five different HisGS masses, at low temperatures. Surprisingly, the effect is not linked to the chemical step, but to fast motions governing product release in the activated enzyme. Disruption of a specific enzyme-product interaction abolishes the isotope effects. Results highlight how altered protein mass perturbs allosterically modulated thermal motions relevant to the catalytic cycle beyond the chemical step. ATP phosphoribosyltransferase is a multi-protein complex where the catalytic protein HisGS is allosterically regulated by the regulatory protein HisZ; however, the protein dynamics of HisGS in enzyme catalysis remain underexplored. Here, the authors investigate the catalytic effect of isotope-labeled HisGS, revealing that the catalytic rate of HisZ-activated HisGS decreases in a mass-dependent fashion at low temperatures, which correlates to product release.

The solubility of a chemical in water is a critical parameter in drug development and other fields such as environmental chemistry and agrochemistry, but its in silico prediction presents a formidable challenge. Here, we apply a suite of graph-based machine learning algorithms to the benchmark problems posed over several years in international ``solubility challenges'', and also to our own newly-compiled dataset of over 11,000 compounds. We find that graph convolutional networks (GCNs) and graph attention networks (GATs) both show excellent predictive power against these datasets. Although not executed under competition conditions, these approaches achieve better scores in several instances than the best models available at the time. They offer an incremental, but still significant, improvement when compared against a range of existing cheminformatics approaches.

The first step of histidine biosynthesis in Acinetobacter baumannii, the condensation of ATP and 5-phospho-α-d-ribosyl-1-pyrophosphate to produce N1-(5-phospho-β-d-ribosyl)-ATP (PRATP) and pyrophosphate, is catalyzed by the hetero-octameric enzyme ATP phosphoribosyltransferase, a promising target for antibiotic design. The catalytic subunit, HisGS, is allosterically activated upon binding of the regulatory subunit, HisZ, to form the hetero-octameric holoenzyme (ATPPRT), leading to a large increase in kcat. Here, we present the crystal structure of ATPPRT, along with kinetic investigations of the rate-limiting steps governing catalysis in the nonactivated (HisGS) and activated (ATPPRT) forms of the enzyme. A pH-rate profile showed that maximum catalysis is achieved above pH 8.0. Surprisingly, at 25 °C, kcat is higher when ADP replaces ATP as substrate for ATPPRT but not for HisGS. The HisGS-catalyzed reaction is limited by the chemical step, as suggested by the enhancement of kcat when Mg2+ was replaced by Mn2+, and by the lack of a pre-steady-state burst of product formation. Conversely, the ATPPRT-catalyzed reaction rate is determined by PRATP diffusion from the active site, as gleaned from a substantial solvent viscosity effect. A burst of product formation could be inferred from pre-steady-state kinetics, but the first turnover was too fast to be directly observed. Lowering the temperature to 5 °C allowed observation of the PRATP formation burst by ATPPRT. At this temperature, the single-turnover rate constant was significantly higher than kcat, providing additional evidence for a step after chemistry limiting catalysis by ATPPRT. This demonstrates allosteric activation by HisZ accelerates the chemical step.

Correlations among the degrees of vertices in random graphs often occur when clustering is present. In this paper we define a joint-degree correlation function for vertices in the giant component of clustered configuration model networks which are composed of clique subgraphs. We use this model to investigate, in detail, the organization among nearest-neighbor subgraphs for random graphs as a function of subgraph topology as well as clustering. We find an expression for the average joint degree of a neighbor in the giant component at the critical point for these networks. Finally, we introduce a novel edge-disjoint clique decomposition algorithm and investigate the correlations between the subgraphs of empirical networks.

ATP phosphoribosyltransferase (ATPPRT) catalyzes the first step of histidine biosynthesis in bacteria, namely, the condensation of ATP and 5-phospho-α-d-ribosyl-1-pyrophosphate (PRPP) to generate N1-(5-phospho-β-d-ribosyl)-ATP (PRATP) and pyrophosphate. Catalytic (HisGS) and regulatory (HisZ) subunits assemble in a hetero-octamer where HisZ activates HisGS and mediates allosteric inhibition by histidine. In Acinetobacter baumannnii, HisGS is necessary for the bacterium to persist in the lung during pneumonia. Inhibition of ATPPRT is thus a promising strategy for specific antibiotic development. Here, A. baumannii ATPPRT is shown to follow a rapid equilibrium random kinetic mechanism, unlike any other ATPPRT. Histidine noncompetitively inhibits ATPPRT. Binding kinetics indicates histidine binds to free ATPPRT and to ATPPRT:PRPP and ATPPRT:ATP binary complexes with similar affinity following a two-step binding mechanism, but with distinct kinetic partition of the initial enzyme:inhibitor complex. The dipeptide histidine-proline inhibits ATPPRT competitively and likely uncompetitively, respectively, against PRPP and ATP. Rapid kinetics analysis shows His-Pro binds to the ATPPRT:ATP complex via a two-step binding mechanism. A related HisZ that shares 43% sequence identity with A. baumannii HisZ is a tight-binding allosteric inhibitor of A. baumannii HisGS. These findings lay the foundation for inhibitor design against A. baumannii ATPPRT.

Background Relationships among genetic or epigenetic features can be explored by learning probabilistic networks and unravelling the dependencies among a set of given genetic/epigenetic features. Bayesian networks (BNs) consist of nodes that represent the variables and arcs that represent the probabilistic relationships between the variables. However, practical guidance on how to make choices among the wide array of possibilities in Bayesian network analysis is limited. Our study aimed to apply a BN approach, while clearly laying out our analysis choices as an example for future researchers, in order to provide further insights into the relationships among epigenetic features and a stressful condition in chickens ( Gallus gallus ). Results Chickens raised under control conditions (n = 22) and chickens exposed to a social isolation protocol (n = 24) were used to identify differentially methylated regions (DMRs). A total of 60 DMRs were selected by a threshold, after bioinformatic pre-processing and analysis. The treatment was included as a binary variable (control = 0; stress = 1). Thereafter, a BN approach was applied: initially, a pre-filtering test was used for identifying pairs of features that must not be included in the process of learning the structure of the network; then, the average probability values for each arc of being part of the network were calculated; and finally, the arcs that were part of the consensus network were selected. The structure of the BN consisted of 47 out of 61 features (60 DMRs and the stressful condition), displaying 43 functional relationships. The stress condition was connected to two DMRs, one of them playing a role in tight and adhesive intracellular junctions in organs such as ovary, intestine, and brain. Conclusions We clearly explain our steps in making each analysis choice, from discrete BN models to final generation of a consensus network from multiple model averaging searches. The epigenetic BN unravelled functional relationships among the DMRs, as well as epigenetic features in close association with the stressful condition the chickens were exposed to. The DMRs interacting with the stress condition could be further explored in future studies as possible biomarkers of stress in poultry species.

In this paper we examine the emergent structures of random networks that have undergone bond percolation an arbitrary, but finite, number of times. We define two types of sequential branching processes: a competitive branching process, in which each iteration performs bond percolation on the residual graph (RG) resulting from previous generations, and a collaborative branching process, where percolation is performed on the giant connected component (GCC) instead. We investigate the behavior of these models, including the expected size of the GCC for a given generation, the critical percolation probability, and other topological properties of the resulting graph structures using the analytically exact method of generating functions. We explore this model for Erdős-Renyi and scale-free random graphs. This model can be interpreted as a seasonal N-strain model of disease spreading.

Is-PETase has become an enzyme of significant interest due to its ability to catalyse the degradation of polyethylene terephthalate (PET) at mesophilic temperatures. We performed hybrid quantum mechanics and molecular mechanics (QM/MM) at the DSD-PBEP86-D3/ma-def2-TZVP/CHARMM27//rev-PBE-D3/dev2-SVP/CHARMM level to calculate the energy profile for the degradation of a suitable PET model by this enzyme. Very low overall barriers are computed for serine protease-type hydrolysis steps (as low as 34.1 kJ mol(-1)). Spontaneous deprotonation of the final product, terephthalic acid, with a high computed driving force indicates that product release could be rate limiting.

Additional file 2. Differentially methylated regions and their annotations. List of differentially methylated regions (DMR) with their corresponding genetic annotation terms. The first column (“SYMBOL”) represents the abbreviated gene name of the methylated region; those which say “annotated” plus a number means that the symbol for that particular DMR was not available; the second column (“Gene ID”) represents the ENSEMBL gene ID; the third column (“Description”) represents the description of the DMR (NA for those not available); the fourth column (“Chromosome””) represents the chromosome in which the DMR is located; the fifth column (“Location”) represent the location in the chromosome of each particular DMR (chromosome number repeated); the seventh column.

Differences in the expression patterns of genes have been used to measure the effects of non-stress or stress conditions in poultry species. However, the list of genes identified can be extensive and they might be related to several biological systems. Therefore, the aim of this study was to identify a small set of genes closely associated with stress in a poultry animal model, the chicken ( Gallus gallus ), by reusing and combining data previously published together with bioinformatic analysis and Bayesian networks in a multi-step approach. Two datasets were collected from publicly available repositories and pre-processed. Bioinformatics analyses were performed to identify genes common to both datasets that showed differential expression patterns between non-stress and stress conditions. Bayesian networks were learnt using a Simulated Annealing algorithm implemented in the software Banjo. The structure of the Bayesian network consisted of 16 out of 19 genes together with the stress condition. Network structure showed CARD19 directly connected to the stress condition plus highlighted CYGB, BRAT1, and EPN3 as relevant, suggesting these genes could play a role in stress. The biological functionality of these genes is related to damage, apoptosis, and oxygen provision, and they could potentially be further explored as biomarkers of stress.

Networks provide a mathematically rich framework to represent social contacts sufficient for the transmission of disease. Social networks are often highly clustered and fail to be locally treelike. In this paper, we study the effects of clustering on the spread of sequential strains of a pathogen using the generating function formulation under a complete cross-immunity coupling, deriving conditions for the threshold of coexistence of the second strain. We show that clustering reduces the coexistence threshold of the second strain and its outbreak size in Poisson networks, while exhibiting the opposite effects on uniform-degree models. We conclude that clustering within a population must increase the ability of the second wave of an epidemic to spread over a network. We apply our model to the study of multilayer clustered networks and observe the fracturing of the residual graph at two distinct transmissibilities.

Percolation theory can be used to describe the structural properties of complex networks using the generating function formulation. This mapping assumes that the network is locally treelike and does not contain short-range loops between neighbors. In this paper we use the generating function formulation to examine clustered networks that contain simple cycles and cliques of any order. We use the natural generalization to the Molloy-Reed criterion for these networks to describe their critical properties and derive an approximate analytical description of the size of the giant component, providing solutions for Poisson and power-law networks. We find that networks comprising larger simple cycles behave increasingly more treelike. Conversely, clustering composed of larger cliques increasingly deviate from the treelike solution, although the behavior is strongly dependent on the degree-assortativity.

We demonstrate that physics-based calculations of intrinsic aqueous solubility can rival cheminformatics-based machine learning predictions. A proof-of-concept was developed for a physics-based approach via a sublimation thermodynamic cycle, building upon previous work that relied upon several thermodynamic approximations, notably the 2RT approximation, and limited conformational sampling. Here, we apply improvements to our sublimation free-energy model with the use of crystal phonon mode calculations to capture the contributions of the vibrational modes of the crystal. Including these improvements with lattice energies computed using the model-potential-based Ψmol method leads to accurate estimates of sublimation free energy. Combining these with hydration free energies obtained from either molecular dynamics free-energy perturbation simulations or density functional theory calculations, solubilities comparable to both experiment and informatics predictions are obtained. The application to coronene, succinic acid, and the pharmaceutical desloratadine shows how the methods must be adapted for the adoption of different conformations in different phases. The approach has the flexibility to extend to applications that cannot be covered by informatics methods.

Coinfection is the process by which a host that is infected with a pathogen becomes infected by a second pathogen at a later point in time. An immunosuppressant host response to a primary disease can facilitate spreading of a subsequent emergent pathogen among the population. Social contact patterns within the substrate populace can be modeled using complex networks and it has been shown that contact patterns vastly influence the emergent disease dynamics. In this paper, we consider the effect of contact clustering on the coinfection dynamics of two pathogens spreading over a network. We use the generating function formulation to describe the expected outbreak sizes of each pathogen and numerically study the threshold criteria that permit the coexistence of each strain among the network. We find that the effects of clustering on the levels of coinfection are governed by the details of the contact topology.

We present exact solutions for the size of the giant connected component of complex networks composed of cliques following bond percolation. We use our theoretical result to find the location of the percolation threshold of the model, providing analytical solutions where possible. We expect the results derived here to be useful to a wide variety of applications including graph theory, epidemiology, percolation, and lattice gas models, as well as fragmentation theory. We also examine the Erdős-Gallai theorem as a necessary condition on the graphicality of configuration model networks comprising clique subgraphs.

In this paper we introduce a description of the equilibrium state of a bond percolation process on random graphs using the exact method of generating functions. This allows us to find the expected size of the giant connected component (GCC) of two sequential bond percolation processes in which the bond occupancy probability of the second process is modulated (increased or decreased) by a node being inside or outside of the GCC created by the first process. In the context of epidemic spreading this amounts to both an antagonistic partial immunity and a synergistic partial coinfection interaction between the two sequential diseases. We examine configuration model networks with tunable clustering. We find that the emergent evolutionary behavior of the second strain is highly dependent on the details of the coupling between the strains. Contact clustering generally reduces the outbreak size of the second strain relative to unclustered topologies; however, positive assortativity induced by clustered contacts inverts this conclusion for highly transmissible disease dynamics.