Mathematical modelling of antibiotic interaction on evolution of antibiotic resistance: an analytical approach.

Background: The emergence and spread of antibiotic-resistant pathogens have led to the exploration of antibiotic combinations to enhance clinical effectiveness and counter resistance development. Synergistic and antagonistic interactions between antibiotics can intensify or diminish the combined therapy's impact. Moreover, these interactions can evolve as bacteria transition from wildtype to mutant (resistant) strains. Experimental studies have shown that the antagonistically interacting antibiotics against wildtype bacteria slow down the evolution of resistance. Interestingly, other studies have shown that antibiotics that interact antagonistically against mutants accelerate resistance. However, it is unclear if the beneficial effect of antagonism in the wildtype bacteria is more critical than the detrimental effect of antagonism in the mutants. This study aims to illuminate the importance of antibiotic interactions against wildtype bacteria and mutants on the deacceleration of antimicrobial resistance. Methods: To address this, we developed and analyzed a mathematical model that explores the population dynamics of wildtype and mutant bacteria under the influence of interacting antibiotics. The model investigates the relationship between synergistic and antagonistic antibiotic interactions with respect to the growth rate of mutant bacteria acquiring resistance. Stability analysis was conducted for equilibrium points representing bacteria-free conditions, all-mutant scenarios, and coexistence of both types. Numerical simulations corroborated the analytical findings, illustrating the temporal dynamics of wildtype and mutant bacteria under different combination therapies. Results: Our analysis provides analytical clarification and numerical validation that antibiotic interactions against wildtype bacteria exert a more significant effect on reducing the rate of resistance development than interactions against mutants. Specifically, our findings highlight the crucial role of antagonistic antibiotic interactions against wildtype bacteria in slowing the growth rate of resistant mutants. In contrast, antagonistic interactions against mutants only marginally affect resistance evolution and may even accelerate it. Conclusion: Our results emphasize the importance of considering the nature of antibiotic interactions against wildtype bacteria rather than mutants when aiming to slow down the acquisition of antibiotic resistance.

Effect of sojourn time distributions on the early dynamics of COVID-19 outbreak.

Compartmental models are commonly used in practice to investigate the dynamical response of infectious diseases such as the COVID-19 outbreak. Such models generally assume exponentially distributed latency and infectiousness periods. However, the exponential distribution assumption fails when the sojourn times are expected to distribute around their means. This study aims to derive a novel S (Susceptible)-E (Exposed)-P (Presymptomatic)-A (Asymptomatic)-D (Symptomatic)-C (Reported) model with arbitrarily distributed latency, presymptomatic infectiousness, asymptomatic infectiousness, and symptomatic infectiousness periods. The SEPADC model is represented by nonlinear Volterra integral equations that generalize ordinary differential equation-based models. Our primary aim is the derivation of a general relation between intrinsic growth rate r and basic reproduction number R0 with the help of the well-known Lotka-Euler equation. The resulting r-R0 equation includes separate roles of various stages of the infection and their sojourn time distributions. We show that R0 estimates are considerably affected by the choice of the sojourn time distributions for relatively higher values of r. The well-known exponential distribution assumption has led to the underestimation of R0 values for most of the countries. Exponential and delta-distributed sojourn times have been shown to yield lower and upper bounds of the R0 values depending on the r values. In quantitative experiments, R0 values of 152 countries around the world were estimated through our novel formulae utilizing the parameter values and sojourn time distributions of the COVID-19 pandemic. The global convergence, R0=4.58, has been estimated through our novel formulation. Additionally, we have shown that increasing the shape parameter of the Erlang distributed sojourn times increases the skewness of the epidemic curves in entire dynamics.

Machine learning aided multiscale modelling of the HIV-1 infection in the presence of NRTI therapy.

Human Immunodeficiency Virus (HIV) is one of the most common chronic infectious diseases in humans. Extending the expected lifetime of patients depends on the use of optimal antiretroviral therapies. Emergence of the drug-resistant strains can reduce the effectiveness of treatments and lead to Acquired Immunodeficiency Syndrome (AIDS), even with antiretroviral therapy. Investigating the genotype-phenotype relationship is a crucial process for optimizing the therapy protocols of the patients. Here, a mathematical modelling framework is proposed to address the impact of existing mutations, timing of initiation, and adherence levels of nucleotide reverse transcriptase inhibitors (NRTIs) on the evolutionary dynamics of the virus strains. For the first time, the existing Stanford HIV drug resistance data have been combined with a multi-strain within-host ordinary differential equation (ODE) model to track the dynamics of the most common NRTI-resistant strains. Overall, the D4T-3TC, D4T-AZT and TDF-D4T drug combinations have been shown to provide higher success rates in preventing treatment failure and further drug resistance. The results are in line with the genotype-phenotype data and pharmacokinetic parameters of the NRTI inhibitors. Moreover, we show that the undetectable mutant strains at the diagnosis have a significant effect on the success/failure rates of the NRTI treatments. Predictions on undetectable strains through our multi-strain within-host model yielded the possible role of viral evolution on the treatment outcomes. It has been recognized that the improvement of multi-scale models can contribute to the understanding of the evolutionary dynamics, and treatment options, and potentially increase the reliability of genotype-phenotype models.

Prediction of HIV-1 protease resistance using genotypic, phenotypic, and molecular information with artificial neural networks.

Drug resistance is a primary barrier to effective treatments of HIV/AIDS. Calculating quantitative relations between genotype and phenotype observations for each inhibitor with cell-based assays requires time and money-consuming experiments. Machine learning models are good options for tackling these problems by generalizing the available data with suitable linear or nonlinear mappings. The main aim of this study is to construct drug isolate fold (DIF) change-based artificial neural network (ANN) models for estimating the resistance potential of molecules inhibiting the HIV-1 protease (PR) enzyme. Throughout the study, seven of eight protease inhibitors (PIs) have been included in the training set and the remaining ones in the test set. We have obtained 11,803 genotype-phenotype data points for eight PIs from Stanford HIV drug resistance database. Using the leave-one-out (LVO) procedure, eight ANN models have been produced to measure the learning capacity of models from the descriptors of the inhibitors. Mean R2 value of eight ANN models for unseen inhibitors is 0.716, and the 95% confidence interval (CI) is [0.592-0.840]. Predicting the fold change resistance for hundreds of isolates allowed a robust comparison of drug pairs. These eight models have predicted the drug resistance tendencies of each inhibitor pair with the mean 2D correlation coefficient of 0.933 and 95% CI [0.930-0.938]. A classification problem has been created to predict the ordered relationship of the PIs, and the mean accuracy, sensitivity, specificity, and Matthews correlation coefficient (MCC) values are calculated as 0.954, 0.791, 0.791, and 0.688, respectively. Furthermore, we have created an external test dataset consisting of 51 unique known HIV-1 PR inhibitors and 87 genotype-phenotype relations. Our developed ANN model has accuracy and area under the curve (AUC) values of 0.749 and 0.818 to predict the ordered relationships of molecules on the same strain for the external dataset. The currently derived ANN models can accurately predict the drug resistance tendencies of PI pairs. This observation could help test new inhibitors with various isolates.

Exploring the binding capacity of lactic acid bacteria derived bacteriocins against RBD of SARS-CoV-2 Omicron variant by molecular simulations.

The changes in the SARS-CoV-2 genome have resulted in the emergence of new variants. Some of the variants have been classified as variants of concern (VOC). These strains have higher transmission rate and improved fitness. One of the prevalent were the Omicron variant. Unlike previous VOCs, the Omicron possesses fifteen mutations on the spike protein's receptor binding domain (RBD). The modifications of spike protein's key amino acid residues facilitate the virus' binding capability against ACE2, resulting in an increase in the infectiousness of Omicron variant. Consequently, investigating the prevention and treatment of the Omicron variant is crucial. In the present study, we aim to explore the binding capacity of twenty-two bacteriocins derived from Lactic Acid Bacteria (LAB) against the Omicron variant by using protein-peptidedocking and molecular dynamics (MD) simulations. The Omicron variant RBD was prepared by introducing fifteen mutations using PyMol. The protein-peptide complexes were obtained using HADDOCK v2.4 docking webserver. Top scoring complexes obtained from HADDOCK webserver were retrieved and submitted to the PRODIGY server for the prediction of binding energies. RBD-bacteriocin complexes were subjected to MD simulations. We discovered promising peptide-based therapeutic candidates for the inhibition of Omicron variant for example Salivaricin B, Pediocin PA 1, Plantaricin W, Lactococcin mmfii and Enterocin A. The lead bacteriocins, except Enterocin A, are biosynthesized by food-grade lactic acid bacteria. Our study puts forth a preliminary information regarding potential utilization of food-grade LAB-derived bacteriocins, particularly Salivaricin B and Pediocin PA 1, for Covid-19 treatment and prophylaxis.Communicated by Ramaswamy H. Sarma.

Investigating the eco-evolutionary tunnels for establishing cooperative communities.

Diversity is abundant among microbial communities. Understanding the assembly of diverse microbial communities is a significant challenge. One of the recent plausible explanations for the assembly involves eco-evolutionary tunnels, where species interact in the same timescale with the mutational rate. Analysis of data generated by agent-based models was used to understand these tunnels. However, modeling the interactions explicitly by dynamic models is lacking. Here, we present the modeling and characterization of eco-evolutionary tunnels that give rise to cooperative evolutionary stable communities (ESC). We find that higher order, but common interactions are sufficient for eco-evolutionary tunnels. We identify three distinct scenarios: evolution of costly cooperation, mutationally inaccessible assembly, and bistability. Biological interpretations of the models are shedding light on the evolution of cooperation. One of the important findings is that if species maximize their benefit by preying on the other strain when dominant and cooperating at intermediate abundances, the assembly process needs eco-evolutionary tunneling. In addition, we characterize the importance of genetic drift with respect to eco-evolutionary tunnels, intermittently stable communities, and the effect of high population limits on the tunnels.

In Silico Analysis of Bacteriocins from Lactic Acid Bacteria Against SARS-CoV-2.

The COVID-19 pandemic caused by a novel coronavirus (SARS-CoV-2) is a serious health concern in the twenty-first century for scientists, health workers, and all humans. The absence of specific biotherapeutics requires new strategies to prevent the spread and prophylaxis of the novel virus and its variants. The SARS-CoV-2 virus shows pathogenesis by entering the host cells via spike protein and Angiotensin-Converting Enzyme 2 receptor protein. Thus, the present study aims to compute the binding energies between a wide range of bacteriocins with receptor-binding domain (RBD) on spike proteins of wild type (WT) and beta variant (lineage B.1.351). Molecular docking analyses were performed to evaluate binding energies. Upon achieving the best bio-peptides with the highest docking scores, further molecular dynamics (MD) simulations were performed to validate the structure and interaction stability. Protein-protein docking of the chosen 22 biopeptides with WT-RBD showed docking scores lower than -7.9 kcal/mol. Pediocin PA-1 and salivaricin P showed the lowest (best) docking scores of - 12 kcal/mol. Pediocin PA-1, salivaricin B, and salivaricin P showed a remarkable increase in the double mutant's predicted binding affinity with -13.8 kcal/mol, -13.0 kcal/mol, and -12.5 kcal/mol, respectively. Also, a better predicted binding affinity of pediocin PA-1 and salivaricin B against triple mutant was observed compared to the WT. Thus, pediocin PA-1 binds stronger to mutants of the RBD, particularly to double and triple mutants. Salivaricin B showed a better predicted binding affinity towards triple mutant compared to WT, showing that it might be another bacteriocin with potential activity against the SARS-CoV-2 beta variant. Overall, pediocin PA-1, salivaricin P, and salivaricin B are the most promising candidates for inhibiting SARS-CoV-2 (including lineage B.1.351) entrance into the human cells. These bacteriocins derived from lactic acid bacteria hold promising potential for paving an alternative way for treatment and prophylaxis of WT and beta variants.

Using a real-world network to model the trade-off between stay-at-home restriction, vaccination, social distancing and working hours on COVID-19 dynamics.

Background: Human behaviour, economic activity, vaccination, and social distancing are inseparably entangled in epidemic management. This study aims to investigate the effects of various parameters such as stay-at-home restrictions, work hours, vaccination, and social distance on the containment of pandemics such as COVID-19. Methods: To achieve this, we have developed an agent based model based on a time-dynamic graph with stochastic transmission events. The graph is constructed from a real-world social network. The edges of graph have been categorized into three categories: home, workplaces, and social environment. The conditions needed to mitigate the spread of wild-type COVID-19 and the delta variant have been analyzed. Our purposeful agent based model has carefully executed tens of thousands of individual-based simulations. We propose simple relationships for the trade-offs between effective reproduction number (R e), transmission rate, working hours, vaccination, and stay-at-home restrictions. Results: We have found that the effect of a 13.6% increase in vaccination for wild-type (WT) COVID-19 is equivalent to reducing four hours of work or a one-day stay-at-home restriction. For the delta, 20.2% vaccination has the same effect. Also, since we can keep track of household and non-household infections, we observed that the change in household transmission rate does not significantly alter the R e. Household infections are not limited by transmission rate due to the high frequency of connections. For the specifications of COVID-19, the R e depends on the non-household transmissions rate. Conclusions: Our findings highlight that decreasing working hours is the least effective among the non-pharmaceutical interventions. Our results suggest that policymakers decrease work-related activities as a last resort and should probably not do so when the effects are minimal, as shown. Furthermore, the enforcement of stay-at-home restrictions is moderately effective and can be used in conjunction with other measures if absolutely necessary.

Rationally designing antisense therapy to keep up with evolving bacterial resistance.

Antisense molecules used as antibiotics offer the potential to keep up with acquired resistance, by redesigning the sequence of an antisense. Once bacteria acquire resistance by mutating the targeted sequence, new antisense can readily be designed by using sequence information of a target gene. However, antisense molecules require additional delivery vehicles to get into bacteria and be protected from degradation. Based on progress in the last few years it appears that, while redesigning or finding new delivery vehicle will be more difficult than redesigning the antisense cargo, it will perhaps be less difficult than finding new conventional small molecule antibiotics. In this study we propose a protocol that maximizes the combined advantages of engineered delivery vehicle and antisense cargo by decreasing the immediate growth advantage to the pathogen of mutating the entry mechanisms and increasing the advantage to the pathogen of antisense target mutations. Using this protocol, we show by computer simulation an appropriately designed antisense therapy can potentially be effective many times longer than conventional antibiotics before succumbing to resistance. While the simulations describe an in-vitro situation, based on comparison with other in-vitro studies on acquired resistance we believe the advantages of the combination antisense strategy have the potential to provide much more sustainability in vivo than conventional antibiotic therapy.

Emergence of evolutionarily stable communities through eco-evolutionary tunnelling.

Ecological and evolutionary dynamics of communities are inexorably intertwined. The ecological state determines the fate of newly arising mutants, and mutations that increase in frequency can reshape the ecological dynamics. Evolutionary game theory and its extensions within adaptive dynamics have been the mathematical frameworks for understanding this interplay, leading to notions such as evolutionarily stable states (ESS) in which no mutations are favoured, and evolutionary branching points near which the population diversifies. A central assumption behind these theoretical treatments has been that mutations are rare so that the ecological dynamics has time to equilibrate after every mutation. A fundamental question is whether qualitatively new phenomena can arise when mutations are frequent. Here, we describe an adaptive diversification process that robustly leads to complex ESS, despite the fact that such communities are unreachable through a step-by-step evolutionary process. Rather, the system as a whole tunnels between collective states over a short timescale. The tunnelling rate is a sharply increasing function of the rate at which mutations arise in the population. This makes the emergence of ESS communities virtually impossible in small populations, but generic in large ones. Moreover, communities emerging through this process can spatially spread as single replication units that outcompete other communities. Overall, this work provides a qualitatively new mechanism for adaptive diversification and shows that complex structures can generically evolve even when no step-by-step evolutionary path exists.