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This article is from PLoS Genetics , volume 10 . Abstract A multicellular organism is not a monolayer of cells in a flask; it is a complex, spatially structured environment, offering both challenges and opportunities for viruses to thrive. Whereas virus infection dynamics at the host and within-cell levels have been documented, the intermediate between-cell level remains poorly understood. Here, we used flow cytometry to measure the infection status of thousands of individual cells in virus-infected plants. This approach allowed us to determine accurately the number of cells infected by two virus variants in the same host, over space and time as the virus colonizes the host. We found a low overall frequency of cellular infection (

This article is from PLoS ONE , volume 9 . Abstract We studied the dynamics of the proteome of influenza virus A/PR/8/34 (H1N1) infected Madin-Darby canine kidney cells up to 12 hours post infection by mass spectrometry based quantitative proteomics using the approach of stable isotope labeling by amino acids in cell culture (SILAC). We identified 1311 cell proteins and, apart from the proton channel M2, all major virus proteins. Based on their abundance two groups of virus proteins could be distinguished being in line with the function of the proteins in genesis and formation of new virions. Further, the data indicate a correlation between the amount of proteins synthesized and their previously determined copy number inside the viral particle. We employed bioinformatic approaches such as functional clustering, gene ontology, and pathway (KEGG) enrichment tests to uncover co-regulated cellular protein sets, assigned the individual subsets to their biological function, and determined their interrelation within the progression of viral infection. For the first time we are able to describe dynamic changes of the cellular and, of note, the viral proteome in a time dependent manner simultaneously. Through cluster analysis, time dependent patterns of protein abundances revealed highly dynamic up- and/or down-regulation processes. Taken together our study provides strong evidence that virus infection has a major impact on the cell status at the protein level.

This article is from Viruses , volume 6 . Abstract The determinants of Colony Collapse Disorder (CCD), a particular case of collapse of honey bee colonies, are still unresolved. Viruses including the Israeli acute paralysis virus (IAPV) were associated with CCD. We found an apiary with colonies showing typical CCD characteristics that bore high loads of IAPV, recovered some colonies from collapse and tested the hypothesis if IAPV was actively replicating in them and infectious to healthy bees. We found that IAPV was the dominant pathogen and it replicated actively in the colonies: viral titers decreased from April to September and increased from September to December. IAPV extracted from infected bees was highly infectious to healthy pupae: they showed several-fold amplification of the viral genome and synthesis of the virion protein VP3. The health of recovered colonies was seriously compromised. Interestingly, a rise of IAPV genomic copies in two colonies coincided with their subsequent collapse. Our results do not imply IAPV as the cause of CCD but indicate that once acquired and induced to replication it acts as an infectious factor that affects the health of the colonies and may determine their survival. This is the first follow up outside the US of CCD-colonies bearing IAPV under natural conditions.

In this paper, we propose a mathematical model for HIV-1 infection with intracellular delay. The model examines a viral-therapy for controlling infections through recombining HIV-1 virus with a genetically modified virus. For this model, the basic reproduction number $\mathcal{R}_0$ are identified and its threshold properties are discussed. When $\mathcal{R}_0 < 1$, the infection-free equilibrium $E_0$ is globally asymptotically stable. When $\mathcal{R}_0 > 1$, $E_0$ becomes unstable and there occurs the single-infection equilibrium $E_s$, and $E_0$ and $E_s$ exchange their stability at the transcritical point $\mathcal{R}_0 =1$. If $1 < \mathcal{R}_0 < R_1$, where $R_1$ is a positive constant explicitly depending on the model parameters, $E_s$ is globally asymptotically stable, while when $\mathcal{R}_0 > R_1$, $E_s$ loses its stability to the double-infection equilibrium $E_d$. There exist a constant $R_2$ such that $E_d$ is asymptotically stable if $R_1

We describe a stochastic virus evolution model representing genomic diversification and within-host selection during experimental serial passages under cell culture or live-host conditions. The model incorporates realistic descriptions of the virus genotypes in nucleotide and amino acid sequence spaces, as well as their diversification from error-prone replications. It quantitatively considers factors such as target cell number, bottleneck size, passage period, infection and cell death rates, and the replication rate of different genotypes, allowing for systematic examinations of how their changes affect the evolutionary dynamics of viruses during passages. The relative probability for a viral population to achieve adaptation under a new host environment, quantified by the rate with which a target sequence frequency rises above 50%, was found to be most sensitive to factors related to sequence structure (distance from the wild type to the target) and selection strength (host cell number and bottleneck size). For parameter values representative of RNA viruses, the likelihood of observing adaptations during passages became negligible as the required number of mutations rose above two amino acid sites. We modeled the specific adaptation process of influenza A H5N1 viruses in mammalian hosts by simulating the evolutionary dynamics of H5 strains under the fitness landscape inferred from multiple sequence alignments of H3 proteins. In light of comparisons with experimental findings, we observed that the evolutionary dynamics of adaptation is strongly affected not only by the tendency toward increasing fitness values but also by the accessibility of pathways between genotypes constrained by the genetic code.

This article is from F1000Research , volume 2 . Abstract Envelope glycoproteins of Hepatitis C Virus (HCV) play an important role in the virus assembly and initial entry into host cells. Conserved charged residues of the E2 transmembrane (TM) domain were shown to be responsible for the heterodimerization with envelope glycoprotein E1. Despite intensive research on both envelope glycoproteins, the structural information is still not fully understood. Recent findings have revealed that the stem (ST) region of E2 also functions in the initial stage of the viral life cycle. We have previously shown the effect of the conserved charged residues on the TM helix monomer of E2. Here, we extended the model of the TM domain by adding the adjacent ST segment. Explicit molecular dynamics simulations were performed for the E2 amphiphilic segment of the ST region connected to the putative TM domain (residues 683-746). Structural conformation and behavior are studied and compared with the nuclear magnetic resonance (NMR)-derived segment of E2 ( 2KQZ.pdb). We observed that the central helix of the ST region (residues 689 - 703) remained stable as a helix in-plane to the lipid bilayer. Furthermore, the TM domain appeared to provide minimal contribution to the structural stability of the amphipathic region. This study also provides insight into the orientation and positional preferences of the ST segment with respect to the membrane lipid-water interface.

This article is from PLoS ONE , volume 9 . Abstract The success of recombinant virus-like particles (VLPs) for human papillomavirus and hepatitis B demonstrates the potential of VLPs as safe and efficacious vaccines. With new modular designs emerging, the effects of antigen module insertion on the self-assembly and structural integrity of VLPs should be clarified so as to better enabling improved design. Previous work has revealed insights into the molecular energetics of a VLP subunit, capsomere, comparing energetics within various solution conditions known to drive or inhibit self-assembly. In the present study, molecular dynamics (MD) simulations coupled with the molecular mechanics-Poisson-Boltzmann surface area (MM-PBSA) method were performed to examine the molecular interactions and energetics in a modular capsomere of a murine polyomavirus (MPV) VLP designed to protect against influenza. Insertion of an influenza antigenic module is found to lower the binding energy within the capsomere, and a more active state is observed in Assembly Buffer as compared with that in Stabilization Buffer, which has been experimentally validated through measurements using differential scanning calorimetry. Further in-depth analysis based on free-energy decomposition indicates that destabilized binding can be attributed to electrostatic interaction induced by the chosen antigen module. These results provide molecular insights into the conformational stability of capsomeres and their abilities to be exploited for antigen presentation, and are expected to be beneficial for the biomolecular engineering of VLP vaccines.

This article is from Viruses , volume 5 . Abstract Successful infection of herpes simplex virus is dependent upon chromatin modulation by the cellular coactivator host cell factor-1 (HCF-1). This review focuses on the multiple chromatin modulation components associated with HCF-1 and the chromatin-related dynamics mediated by this coactivator that lead to the initiation of herpes simplex virus (HSV) immediate early gene expression.

This article is from Osong Public Health and Research Perspectives , volume 5 . Abstract Objectives: Mathematical models can be helpful to understand the complex dynamics of human immunodeficiency virus infection within a host. Most of work has studied the interactions of host responses and virus in the presence of active cytotoxic immune cells, which decay to zero when there is no virus. However, recent research highlights that cytotoxic immune cells can be inactive but never be depleted. Methods: We propose a mathematical model to investigate the human immunodeficiency virus dynamics in the presence of both active and inactive cytotoxic immune cells within a host. We explore the impact of the immune responses on the dynamics of human immunodeficiency virus infection under different disease stages. Results: Standard mathematical and numerical analyses are presented for this new model. Specifically, the basic reproduction number is computed and local and global stability analyses are discussed. Conclusion: Our results can give helpful insights when designing more effective drug schedules in the presence of active and inactive immune responses.

This article is from Virology Journal , volume 10 . Abstract Abstract: About sixty thousand new cases of Hepatitis C virus (HCV) infection are recorded in Brazil each year. These cases are currently treated with pegylated interferon (PEG-IFN) and ribavirin (RBV) with an overall success rate of 50%. New compounds for anti-HCV therapy targeted to the HCV NS3 protease are being developed and some already form the components of licensed therapies. Mapping NS3 protease resistance mutations to protease inhibitors or anti-viral drug candidates is important to direct anti-HCV drug treatment. Methods: Sequence analysis of the HCV NS3 protease was conducted in a group of 68 chronically infected patients harboring the HCV genotype 1. The patients were sampled before, during and after a course of PEG-IFN-RBV treatment. Results: Resistance mutations to the protease inhibitors, Boceprevir and Telaprevir were identified in HCV isolated from three patients (4.4%); the viral sequences contained at least one of the following mutations: V36L, T54S and V55A. In one sustained virological responder, the T54S mutation appeared during the course of PEG-IFN and RBV therapy. In contrast, V36L and V55A mutations were identified in virus isolated from one relapsing patient before, during, and after treatment, whereas the T54S mutation was identified in virus isolated from one non-responding patient, before and during the treatment course. Conclusions: The incidence and persistence of protease resistance mutations occurring in HCV from chronically infected patients in Brazil should be considered when using protease inhibitors to treat HCV disease. In addition, patients treated with the current therapy (PEG-IFN and RBV) that are relapsing or are non-responders should be considered candidates for protease inhibitor therapy.

The current situation of the ongoing new Corona virus pandemic offers a rare chance to investigate the dynamics of the relation between perceived risks for oneself and one’s social environment, known health-behavior related factors (i.e., self-efficacy, perceived efficacy of different preventive behaviors, perceived social norms), and the self-reported intention and adoption of protective behaviors over time. This project will take this chance and investigate these dynamics in a longitudinal study representative of the Swiss population.

Prey predator population dynamics has been frequently studied in literature to model many robust but contrastive biological populations. In this paper, based on prey predator population dynamics, a nonlinear model to predict the behavior of virus treatment of cancer cells is suggested. Based on the goals of virus curing and consideration of some practical issues, the suggested model has the capability to cover these following cases: both cancer cells and viruses vanish, one is eliminated by the other, or both survive in a robust periodically convergent manner or both become divergent. Relative to the values of some parameters such as the virus intrinsic growth rate, carrying capacity, capturing rate, half saturation constant, maximal tumor cells growth rate, and tumor cells mortality rate, and the initial population values of both tumor cells and viruses, some examples are solved. These examples exhibit logical and feasible behavior for the system. They show under which conditions the virus therapy fails or succeeds; as well when the bifurcation occurs or when the trajectories converge to a limit cycle.

This article is from Scientific Reports , volume 3 . Abstract Here, we used a biologically contained Ebola virus system to characterize the spatio-temporal distribution of Ebola virus proteins and RNA during virus replication. We found that viral nucleoprotein (NP), the polymerase cofactor VP35, the major matrix protein VP40, the transcription activator VP30, and the minor matrix protein VP24 were distributed in cytoplasmic inclusions. These inclusions enlarged near the nucleus, became smaller pieces, and subsequently localized near the plasma membrane. GP was distributed in the cytoplasm and transported to the plasma membrane independent of the other viral proteins. We also found that viral RNA synthesis occurred within the inclusions. Newly synthesized negative-sense RNA was distributed inside the inclusions, whereas positive-sense RNA was distributed both inside and outside. These findings provide useful insights into Ebola virus replication.

A two-patch mathematical model of Dengue virus type 2 (DENV-2) that accounts for vectors' vertical transmission and between patches human dispersal is introduced. Dispersal is modeled via a Lagrangian approach. A host-patch residence-times basic reproduction number is derived and conditions under which the disease dies out or persists are established. Analytical and numerical results highlight the role of hosts' dispersal in mitigating or exacerbating disease dynamics. The framework is used to explore dengue dynamics using, as a starting point, the 2002 outbreak in the state of Colima, Mexico.

This article is from PLoS Pathogens , volume 10 . Abstract Over the past fifty years, annual honeybee (Apis mellifera) colony losses have been steadily increasing worldwide. These losses have occurred in parallel with the global spread of the honeybee parasite Varroa destructor. Indeed, Varroa mite infestations are considered to be a key explanatory factor for the widespread increase in annual honeybee colony mortality. The host-parasite relationship between honeybees and Varroa is complicated by the mite's close association with a range of honeybee viral pathogens. The 10-year history of the expanding front of Varroa infestation in New Zealand offered a rare opportunity to assess the dynamic quantitative and qualitative changes in honeybee viral landscapes in response to the arrival, spread and level of Varroa infestation. We studied the impact of de novo infestation of bee colonies by Varroa on the prevalence and titres of seven well-characterised honeybee viruses in both bees and mites, using a large-scale molecular ecology approach. We also examined the effect of the number of years since Varroa arrival on honeybee and mite viral titres. The dynamic shifts in the viral titres of black queen cell virus and Kashmir bee virus mirrored the patterns of change in Varroa infestation rates along the Varroa expansion front. The deformed wing virus (DWV) titres in bees continued to increase with Varroa infestation history, despite dropping infestation rates, which could be linked to increasing DWV titres in the mites. This suggests that the DWV titres in mites, perhaps boosted by virus replication, may be a major factor in maintaining the DWV epidemic after initial establishment. Both positive and negative associations were identified for several pairs of viruses, in response to the arrival of Varroa. These findings provide important new insights into the role of the parasitic mite Varroa destructor in influencing the viral landscape that affects honeybee colonies.

In this paper we present a delay induced model for hepatitis C virus incorporating the healthy and infected hepatocytes as well as infectious and noninfectious virions. The model is mathematically analyzed and characterized, both for the steady states and the dynamical behavior of the model. It is shown that time delay does not affect the local asymptotic stability of the uninfected steady state. However, it can destabilize the endemic equilibrium, leading to Hopf bifurcation to periodic solutions with realistic data sets. The model is also validated using 12 patient data obtained from the study, conducted at the University of Sao Paulo Hospital das clinicas.

We present a mathematical analysis of the early detection of Ebola virus. The propagation of the virus is analysed by using a Susceptible, Infected, Recovered (SIR) model. In order to provide useful predictions about the potential transmission of the virus, we analyse and simulate the SIR model with vital dynamics, by adding demographic effects and an induced death rate. Then, we compute the equilibria of the model. The numerical simulations confirm the theoretical analysis. Our study describes the 2015 detection of Ebola virus in Guinea, the parameters of the model being identified from the World Health Organization data. Finally, we consider an optimal control problem of the propagation of the Ebola virus, minimizing the number of infected individuals while taking into account the cost of vaccination.

This article is from Retrovirology , volume 10 . Abstract Background: Differently from HIV-1, HIV-2 disease progression usually takes decades without antiretroviral therapy and the majority of HIV-2 infected individuals survive as elite controllers with normal CD4+ T cell counts and low or undetectable plasma viral load. Neutralizing antibodies (Nabs) are thought to play a central role in HIV-2 evolution and pathogenesis. However, the dynamic of the Nab response and resulting HIV-2 escape during acute infection and their impact in HIV-2 evolution and disease progression remain largely unknown. Our objective was to characterize the Nab response and the molecular and phenotypic evolution of HIV-2 in association with Nab escape in the first years of infection in two children infected at birth. Results: CD4+ T cells decreased from about 50% to below 30% in both children in the first five years of infection and the infecting R5 viruses were replaced by X4 viruses within the same period. With antiretroviral therapy, viral load in child 1 decreased to undetectable levels and CD4+ T cells recovered to normal levels, which have been sustained at least until the age of 12. In contrast, viral load increased in child 2 and she progressed to AIDS and death at age 9. Beginning in the first year of life, child 1 raised high titers of antibodies that neutralized primary R5 isolates more effectively than X4 isolates, both autologous and heterologous. Child 2 raised a weak X4-specific Nab response that decreased sharply as disease progressed. Rate of evolution, nucleotide and amino acid diversity, and positive selection, were significantly higher in the envelope of child 1 compared to child 2. Rates of R5-to-X4 tropism switch, of V1 and V3 sequence diversification, and of convergence of V3 to a β-hairpin structure were related with rate of escape from the neutralizing antibodies. Conclusion: Our data suggests that the molecular and phenotypic evolution of the human immunodeficiency virus type 2 envelope are related with the dynamics of the neutralizing antibody response providing further support for a model in which Nabs play an important role in HIV-2 pathogenesis.

This article is from PLoS ONE , volume 9 . Abstract Bluetongue virus (BTV) is the cause of an economically important arboviral disease of domestic and wild ruminants. The occurrence of BTV infection of livestock is distinctly seasonal in temperate regions of the world, thus we determined the dynamics of BTV infection (using BTV-specific real time reverse transcriptase polymerase chain reaction) among sentinel cattle and vector Culicoides sonorensis (C. sonorensis) midges on a dairy farm in northern California throughout both the seasonal and interseasonal (overwintering) periods of BTV activity from August 2012 until March 2014. The data confirmed widespread infection of both sentinel cattle and vector midges during the August – November period of seasonal BTV transmission, however BTV infection of parous female midges captured in traps set during daylight hours also was detected in February of both 2013 and 2014, during the interseasonal period. The finding of BTV-infected vector midges during mid-winter suggests that BTV may overwinter in northern California by infection of long-lived female C. sonorensis midges that were infected during the prior seasonal period of virus transmission, and reemerged sporadically during the overwintering period; however the data do not definitively preclude other potential mechanisms of BTV overwintering that are also discussed.

This article is from Viruses , volume 3 . Abstract The dynamics of viruses are critical to our understanding of disease pathogenesis. Using honey bee Deformed wing virus (DWV) as a model, we conducted field and laboratory studies to investigate the roles of abiotic and biotic stress factors as well as host health conditions in dynamics of virus replication in honey bees. The results showed that temperature decline could lead to not only significant decrease in the rate for pupae to emerge as adult bees, but also an increased severity of the virus infection in emerged bees, partly explaining the high levels of winter losses of managed honey bees, Apis mellifera, around the world. By experimentally exposing adult bees with variable levels of parasitic mite Varroa destructor, we showed that the severity of DWV infection was positively correlated with the density and time period of Varroa mite infestation, confirming the role of Varroa mites in virus transmission and activation in honey bees. Further, we showed that host conditions have a significant impact on the outcome of DWV infection as bees that originate from strong colonies resist DWV infection and replication significantly better than bee originating from weak colonies. The information obtained from this study has important implications for enhancing our understanding of host‑pathogen interactions and can be used to develop effective disease control strategies for honey bees.

This article is from Emerging Microbes & Infections , volume 2 . Abstract Foamy viruses are complex retroviruses that have been shown to be transmitted from nonhuman primates to humans. In Bangladesh, infection with simian foamy virus (SFV) is ubiquitous among rhesus macaques, which come into contact with humans in diverse locations and contexts throughout the country. We analyzed microsatellite DNA from 126 macaques at six sites in Bangladesh in order to characterize geographic patterns of macaque population structure. We also included in this study 38 macaques owned by nomadic people who train them to perform for audiences. PCR was used to analyze a portion of the proviral gag gene from all SFV-positive macaques, and multiple clones were sequenced. Phylogenetic analysis was used to infer long-term patterns of viral transmission. Analyses of SFV gag gene sequences indicated that macaque populations from different areas harbor genetically distinct strains of SFV, suggesting that geographic features such as forest cover play a role in determining the dispersal of macaques and SFV. We also found evidence suggesting that humans traveling the region with performing macaques likely play a role in the translocation of macaques and SFV. Our studies found that individual animals can harbor more than one strain of SFV and that presence of more than one SFV strain is more common among older animals. Some macaques are infected with SFV that appears to be recombinant. These findings paint a more detailed picture of how geographic and sociocultural factors influence the spectrum of simian-borne retroviruses.

In order to replicate within their cellular host, many viruses have developed self-assembly strategies for their capsids which are sufficiently robust as to be reconstituted in vitro. Mathematical models for virus self-assembly usually assume that the bonds leading to cluster formation have constant reactivity over the time course of assembly (direct assembly). In some cases, however, binding sites between the capsomers have been reported to be activated during the self-assembly process (hierarchical assembly). In order to study possible advantages of such hierarchical schemes for icosahedral virus capsid assembly, we use Brownian dynamics simulations of a patchy particle model that allows us to switch binding sites on and off during assembly. For T1 viruses, we implement a hierarchical assembly scheme where inter-capsomer bonds become active only if a complete pentamer has been assembled. We find direct assembly to be favorable for reversible bonds allowing for repeated structural reorganizations, while hierarchical assembly is favorable for strong bonds with small dissociation rate, as this situation is less prone to kinetic trapping. However, at the same time it is more vulnerable to monomer starvation during the final phase. Increasing the number of initial monomers does have only a weak effect on these general features. The differences between the two assembly schemes become more pronounced for more complex virus geometries, as shown here for T3 viruses, which assemble through homogeneous pentamers and heterogeneous hexamers in the hierarchical scheme. In order to complement the simulations for this more complicated case, we introduce a master equation approach that agrees well with the simulation results.

This article is from PLoS ONE , volume 9 . Abstract Wild and domestic ruminants are susceptible to Bluetongue virus (BTV) infection. Three BTV serotypes (BTV-4, BTV-1 and BTV-8) have been detected in Spain in the last decade. Even though control strategies have been applied to livestock, BTV circulation has been frequently detected in wild ruminant populations in Spain. The aim of the present study is to assess the role for wild ruminants in maintaining BTV after the vaccination programs in livestock in mainland Spain. A total of 931 out 1,914 (48.6%) serum samples, collected from eight different wild ruminant species between 2006 and 2011, were BTV positive by ELISA. In order to detect specific antibodies against BTV-1, BTV-4 and BTV-8, positive sera were also tested by serumneutralisation test (SNT). From the ELISA positive samples that could be tested by SNT (687 out of 931), 292 (42.5%) showed neutralising antibodies against one or two BTV serotypes. For each BTV seroptype, the number of outbreaks in livestock (11,857 outbreaks in total) was modelled with pure autoregressive models and the resulting smoothed values, representing the predicted number of BTV outbreaks in livestock at municipality level, were positively correlated with BTV persistence in wild species. The strength of this relationship significantly decreased as red deer (Cervus elaphus) population abundance increased. In addition, BTV RNA was detected by real time RT-PCR in 32 out of 311 (10.3%) spleen samples from seropositive animals. Although BT outbreaks in livestock have decreased substantially after vaccination campaigns, our results indicated that wild ruminants have been exposed to BTV in territories where outbreaks in domestic animals occurred. The detection of BTV RNA and spatial association between BT outbreaks in livestock and BTV rates in red deer are consistent with the hypothesis of virus circulation and BTV maintenance within Iberian wild ruminant populations.

This article is from PLoS ONE , volume 9 . Abstract The protease domain of the Hepatitis C Virus (HCV) nonstructural protein 3 (NS3) has been targeted for inhibition by several direct-acting antiviral drugs. This approach has had marked success to treat infections caused by HCV genotype 1 predominant in the USA, Europe, and Japan. However, genotypes 3 and 4, dominant in developing countries, are resistant to a number of these drugs and little progress has been made towards understanding the structural basis of their drug resistivity. We have previously developed a 4D computational methodology, based on 3D structure modeling and molecular dynamics simulation, to analyze the active sites of the NS3 proteases of HCV-1b and 4a in relation to their catalytic activity and drug susceptibility. Here, we improved the methodology, extended the analysis to include genotype 3a (predominant in South Asia including Pakistan), and compared the results of the three genotypes (1b, 3a and 4a). The 4D analyses of the interactions between the catalytic triad residues (His57, Asp81, and Ser139) indicate conformational instability of the catalytic site in HCV-3a and 4a compared to that of HCV-1b NS3 protease. The divergence is gradual and genotype-dependent, with HCV-1b being the most stable, HCV-4a being the most unstable and HCV-3a representing an intermediate state. These results suggest that the structural dynamics behavior, more than the rigid structure, could be related to the altered catalytic activity and drug susceptibility seen in NS3 proteases of HCV-3a and 4a.

Although foot-and-mouth disease virus (FMDV) incidence has decreased in South America over the last years, the pathogen still circulates in the region and the risk of re-emergence in previously FMDV-free areas is a veterinary public health concern. In this paper we merge environmental, epidemiological and genetic data to reconstruct spatiotemporal patterns and determinants of FMDV serotypes A and O dispersal in South America. Our dating analysis suggests that serotype A emerged in South America around 1930, while serotype O emerged around 1990. The rate of evolution for serotype A was significantly higher compared to serotype O. Phylogeographic inference identified two well-connected sub networks of viral flow, one including Venezuela, Colombia and Ecuador; another including Brazil, Uruguay and Argentina. The spread of serotype A was best described by geographic distances, while trade of live cattle was the predictor that best explained serotype O spread. Our findings show that the two serotypes have different underlying evolutionary and spatial dynamics and may pose different threats to control programmes. Key-words: Phylogeography, foot-and-mouth disease virus, South America, animal trade.

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 Prey predator population dynamics has been frequently studied in literature to model many robust but contrastive biological populations. In this paper, based on prey predator population dynamics, a nonlinear model to predict the behavior of virus treatment of cancer cells is suggested. Based on the goals of virus curing and consideration of some practical issues, the suggested model has the capability to cover these following cases: both cancer cells and viruses vanish, one is eliminated by the other, or both survive in a robust periodically convergent manner or both become divergent. Relative to the values of some parameters such as the virus intrinsic growth rate, carrying capacity, capturing rate, half saturation constant, maximal tumor cells growth rate, and tumor cells mortality rate, and the initial population values of both tumor cells and viruses, some examples are solved. These examples exhibit logical and feasible behavior for the system. They show under which conditions the virus therapy fails or succeeds; as well when the bifurcation occurs or when the trajectories converge to a limit cycle.

This article is from Retrovirology , volume 9 . Abstract Background: Developing a quantitative understanding of viral kinetics is useful for determining the pathogenesis and transmissibility of the virus, predicting the course of disease, and evaluating the effects of antiviral therapy. The availability of data in clinical, animal, and cell culture studies, however, has been quite limited. Many studies of virus infection kinetics have been based solely on measures of total or infectious virus count. Here, we introduce a new mathematical model which tracks both infectious and total viral load, as well as the fraction of infected and uninfected cells within a cell culture, and apply it to analyze time-course data of an SHIV infection in vitro. Results: We infected HSC-F cells with SHIV-KS661 and measured the concentration of Nef-negative (target) and Nef-positive (infected) HSC-F cells, the total viral load, and the infectious viral load daily for nine days. The experiments were repeated at four different MOIs, and the model was fitted to the full dataset simultaneously. Our analysis allowed us to extract an infected cell half-life of 14.1 h, a half-life of SHIV-KS661 infectiousness of 17.9 h, a virus burst size of 22.1 thousand RNA copies or 0.19 TCID50, and a basic reproductive number of 62.8. Furthermore, we calculated that SHIV-KS661 virus-infected cells produce at least 1 infectious virion for every 350 virions produced. Conclusions: Our method, combining in vitro experiments and a mathematical model, provides detailed quantitative insights into the kinetics of the SHIV infection which could be used to significantly improve the understanding of SHIV and HIV-1 pathogenesis. The method could also be applied to other viral infections and used to improve the in vitro determination of the effect and efficacy of antiviral compounds.

In November 2015, El Salvador reported their first case of Zika virus (Zv) leading to an explosive outbreak that in just two months had over 6000 suspected cases. Many communities along with national agencies initiated the process to implement control measures that ranged from vector control and the use of repellents to the suggestion of avoiding pregnancies for two years, the latter one, in response to the growing number of microcephaly cases in Brazil. In our study, we explore the impact of short term mobility between two idealized interconnected communities where disparities and violence contribute to the Zv epidemic. Using a Lagrangian modeling approach in a two-patch setting, it is shown via simulations that short term mobility may be beneficial in the control of a Zv outbreak when risk is relative low and patch disparities are not too extreme. However, when the reproductive number is too high, there seems to be no benefits. This paper is dedicated to the inauguration of the Centro de Modelamiento Matem\'{a}tico Carlos Castillo-Ch\'{a}vez at Universidad Francisco Gavidia in San Salvador, El Salvador.

This article is from PLoS ONE , volume 9 . Abstract The cytoskeleton is a dynamic network composed of filamentous polymers and regulatory proteins that provide a flexible structural scaffold to the cell and plays a fundamental role in developmental processes. Mutations that alter the spatial orientation of the cortical microtubule (MT) array of plants are known to cause important changes in the pattern of cell wall synthesis and developmental phenotypes; however, the consequences of such alterations on other MT-network-associated functions in the cytoplasm are not known. In vivo observations suggested a role of cortical MTs in the formation and movement of Tobacco mosaic virus (TMV) RNA complexes along the endoplasmic reticulum (ER). Thus, to probe the significance of dynamic MT behavior in the coordination of MT-network-associated functions related to TMV infection and, thus, in the formation and transport of RNA complexes in the cytoplasm, we performed an evolution experiment with TMV in Arabidopsis thaliana tor1/spr2 and tor2 mutants with specific defects in MT dynamics and asked whether TMV is sensitive to these changes. We show that the altered cytoskeleton induced genetic changes in TMV that were correlated with efficient spread of infection in the mutant hosts. These observations demonstrate a role of dynamic MT rearrangements and of the MT-associated protein TORTIFOLIA1/SPIRAL2 in cellular functions related to virus spread and indicate that MT dynamics and MT-associated proteins represent constraints for virus evolution and adaptation. The results highlight the importance of the dynamic plasticity of the MT network in directing cytoplasmic functions in macromolecular assembly and trafficking and illustrate the value of experimental virus evolution for addressing the cellular functions of dynamic, long-range order systems in multicellular organisms.

This article is from PLoS ONE , volume 9 . Abstract The B cell response to influenza infection of the respiratory tract contributes to viral clearance and establishes profound resistance to reinfection by related viruses. Numerous studies have measured virus-specific antibody-secreting cell (ASC) frequencies in different anatomical compartments after influenza infection and provided a general picture of the kinetics of ASC formation and dispersion. However, the dynamics of ASC populations are difficult to determine experimentally and have received little attention. Here, we applied mathematical modeling to investigate the dynamics of ASC growth, death, and migration over the 2-week period following primary influenza infection in mice. Experimental data for model fitting came from high frequency measurements of virus-specific IgM, IgG, and IgA ASCs in the mediastinal lymph node (MLN), spleen, and lung. Model construction was based on a set of assumptions about ASC gain and loss from the sampled sites, and also on the directionality of ASC trafficking pathways. Most notably, modeling results suggest that differences in ASC fate and trafficking patterns reflect the site of formation and the expressed antibody class. Essentially all early IgA ASCs in the MLN migrated to spleen or lung, whereas cell death was likely the major reason for IgM and IgG ASC loss from the MLN. In contrast, the spleen contributed most of the IgM and IgG ASCs that migrated to the lung, but essentially none of the IgA ASCs. This finding points to a critical role for regional lymph nodes such as the MLN in the rapid generation of IgA ASCs that seed the lung. Results for the MLN also suggest that ASC death is a significant early feature of the B cell response. Overall, our analysis is consistent with accepted concepts in many regards, but it also indicates novel features of the B cell response to influenza that warrant further investigation.

This article is from Viruses , volume 5 . Abstract West Nile virus (WNV; Flavivirus; Flaviviridae) is the cause of the most widespread arthropod-borne viral disease in the world and the largest outbreak of neuroinvasive disease ever observed. Mosquito-borne outbreaks are influenced by intrinsic (e.g., vector and viral genetics, vector and host competence, vector life-history traits) and extrinsic (e.g., temperature, rainfall, human land use) factors that affect virus activity and mosquito biology in complex ways. The concept of vectorial capacity integrates these factors to address interactions of the virus with the arthropod host, leading to a clearer understanding of their complex interrelationships, how they affect transmission of vector-borne disease, and how they impact human health. Vertebrate factors including host competence, population dynamics, and immune status also affect transmission dynamics. The complexity of these interactions are further exacerbated by the fact that not only can divergent hosts differentially alter the virus, but the virus also can affect both vertebrate and invertebrate hosts in ways that significantly alter patterns of virus transmission. This chapter concentrates on selected components of the virus-vector-vertebrate interrelationship, focusing specifically on how interactions between vector, virus, and environment shape the patterns and intensity of WNV transmission.

http://uf.catalog.fcla.edu/uf.jsp?st=UF001690052&ix=pm&I=0&V=D&pm=1

This article is from BMC Veterinary Research , volume 10 . Abstract Background: Bovine leukemia virus (BLV) is highly endemic in many countries, including Argentina. As prevention of the spread from infected animals is of primary importance in breaking the cycle of BLV transmission, it is important to know the pathophysiology of BLV infection in young animals, as they are the main source of animal movement. In this work, we determined the proviral load and antibody titers of infected newborn calves from birth to first parturition (36 months). Results: All calves under study were born to infected dams with high proviral load (PVL) in blood and high antibody titers and detectable provirus in the colostrum. The PVL for five out of seven calves was low at birth. All animals reached PVLs of more than 1% infected peripheral blood mononuclear cells (PBMCs), three at 3 months, one at 6 months, and one at 12 months. High PVLs persisted until the end of the study, and, in two animals, exceeded one BLV copy per cell. Two other calves maintained a high PVL from birth until the end of the study. Antibody titers were 32 or higher in the first sample from six out of seven calves. These decayed at 3–6 months to 16 or lower, and then increased again after this point. Conclusions: Calves infected during the first week of life could play an active role in early propagation of BLV to susceptible animals, since their PVL raised up during the first 12 months and persist as high for years. Early elimination could help to prevent transmission to young susceptible animals and to their own offspring. To our knowledge, this is the first study of the kinetics of BLV proviral load and antibody titers in newborn infected calves.

This article is from Virology Journal , volume 9 . Abstract Background: Dengue is the most important mosquito-borne viral disease worldwide. Dengue virus comprises four antigenically related viruses named dengue virus type 1 to 4 (DENV1-4). DENV-3 was re-introduced into the Americas in 1994 causing outbreaks in Nicaragua and Panama. DENV-3 was introduced in Brazil in 2000 and then spread to most of the Brazilian States, reaching the neighboring country, Paraguay in 2002. In this study, we have analyzed the phylogenetic relationship of DENV-3 isolated in Brazil and Paraguay with viruses isolated worldwide. We have also analyzed the evolutionary divergence dynamics of DENV-3 viruses. Results: The entire open reading frame (ORF) of thirteen DENV-3 isolated in Brazil (n = 9) and Paraguay (n = 4) were sequenced for phylogenetic analysis. DENV-3 grouped into three main genotypes (I, II and III). Several internal clades were found within each genotype that we called lineage and sub-lineage. Viruses included in this study belong to genotype III and grouped together with viruses isolated in the Americas within the lineage III. The Brazilian viruses were further segregated into two different sub-lineage, A and B, and the Paraguayan into the sub-lineage B. All three genotypes showed internal grouping. The nucleotide divergence was in average 6.7% for genotypes, 2.7% for lineages and 1.5% for sub-lineages. Phylogenetic trees constructed with any of the protein gene sequences showed the same segregation of the DENV-3 in three genotypes. Conclusion: Our results showed that two groups of DENV-3 genotypes III circulated in Brazil during 2002–2009, suggesting different events of introduction of the virus through different regions of the country. In Paraguay, only one group DENV-3 genotype III is circulating that is very closely related to the Brazilian viruses of sub-lineage B. Different degree of grouping can be observed for DENV-3 and each group showed a characteristic evolutionary divergence. Finally, we have observed that any protein gene sequence can be used to identify the virus genotype.

The virus of Venezuelan equine encephalomyelitis is capable of agglutinating goose erythrocytes at a pH of 5.8--6.0. The 'threshold of infectivity' which is necessary for the exposure of VEE hemagglutinins comprises 4.6--5.7 lg TCD50 1,300,000--2,600,000 plaque forming units). The reaction of hemadsorption makes it possible to expose the multiplication of VEE in 6--9 hours following infection of a sensitive culture. The RGA and the reaction of hemadsorption may be used for determining the dynamics of multiplication of VEE and the early diagnosis of this virus. A prolonged liberation of virus particles into the surrounding medium is characteristic for VEE.

This article is from PLoS ONE , volume 9 . Abstract Influenza A virus infections are widespread in swine herds across the world. Influenza negatively affects swine health and production, and represents a significant threat to public health due to the risk of zoonotic infections. Swine herds can act as reservoirs for potentially pandemic influenza strains. In this study, we develop mathematical models based on experimental data, representing typical breeding and wean-to-finish swine farms. These models are used to explore and describe the dynamics of influenza infection at the farm level, which are at present not well understood. In addition, we use the models to assess the effectiveness of vaccination strategies currently employed by swine producers, testing both homologous and heterologous vaccines. An important finding is that following an influenza outbreak in a breeding herd, our model predicts a persistently high level of infectious piglets. Sensitivity analysis indicates that this finding is robust to changes in both transmission rates and farm size. Vaccination does not eliminate influenza throughout the breeding farm population. In the wean-to-finish herd, influenza infection may persist in the population only if recovered individuals become susceptible to infection again. A homologous vaccine administered to the entire wean-to-finish population after the loss of maternal antibodies eliminates influenza, but a vaccine that only induces partial protection (heterologous vaccine) has little effect on influenza infection levels. Our results have important implications for the control of influenza in swine herds, which is crucial in order to reduce both losses for swine producers and the risk to public health.

This article is from Journal of Biomolecular Structure & Dynamics , volume 32 . Abstract Egypt has the highest prevalence of hepatitis C virus (HCV) infection worldwide with a frequency of 15%. More than 90% of these infections are due to genotype 4, and the subtype 4a (HCV-4a) predominates. Moreover, due to the increased mobility of people, HCV-4a has recently spread to several European countries. The protease domain of the HCV nonstructural protein 3 (NS3) has been targeted for inhibition by several drugs. This approach has had marked success in inhibiting genotype 1 (HCV-1), the predominant genotype in the USA, Europe, and Japan. However, HCV-4a was found to resist inhibition by a number of these drugs, and little progress has been made to understand the structural basis of its drug resistivity. As a step forward, we sequenced the NS3 HCV-4a protease gene (strain ED43) and subsequently built a 3D structural model threaded through a template crystal structure of HCV-1b NS3 protease. The model protease, HCV-4a, shares 83% sequence identity with the template protease, HCV-1b, and has nearly identical rigid structural features. Molecular dynamics simulations predict similar overall dynamics of the two proteases. However, local dynamics and 4D analysis of the interactions between the catalytic triad residues (His57, Asp81, and Ser139) indicate conformational instability of the catalytic site in HCV-4a NS3 protease. These results suggest that the divergent dynamics behavior, more than the rigid structure, could be related to the altered catalytic activity and drug resistivity seen in HCV-4a.

This article is from International Journal of Environmental Research and Public Health , volume 10 . Abstract Over the last two decades West Nile Virus (WNV) has been responsible for significant disease outbreaks in humans and animals in many parts of the World. Its extremely rapid global diffusion argues for a better understanding of its geographic extent. The purpose of this inquiry was to explore spatio-temporal patterns of WNV using geospatial technologies to study populations of the reservoir hosts, vectors, and human hosts, in addition to the spatio-temporal interactions among these populations. Review of the recent literature on spatial WNV disease risk modeling led to the conclusion that numerous environmental factors might be critical for its dissemination. New Geographic Information Systems (GIS)-based studies are monitoring occurrence at the macro-level, and helping pinpoint areas of occurrence at the micro-level, where geographically-targeted, species-specific control measures are sometimes taken and more sophisticated methods of surveillance have been used.

In this article, we propose a mathematical approach that connects an innovative spatio-temporal model to the problem of the EG.5 variant of COVID-19 in a human population. We demonstrate the existence and uniqueness of the global positive solution for our suggested system. The implementation and analysis of an applicable optimal control issue are as follows. The methods of optimal control theory are applied in this work to demonstrate the existence of optimal control, and with necessary op-timality conditions, we discover the explicit expression of optimal control that minimizes the negative impacts of this infectious disease on countries. We provide numerical simulations at the conclusion to demonstrate the efficacy of our chosen strategy.

Containing the recent West African outbreak of Ebola virus (EBOV) required the deployment of substantial global resources. Operationally, health workers and surveillance teams treated cases, collected genetic samples, and tracked case contacts. Despite the substantial progress in analyzing and modeling EBOV epidemiological data, a complete characterization of the spatiotemporal spread of Ebola cases remains a challenge. In this work, we offer a novel perspective on the EBOV epidemic that utilizes virus genome sequences to inform population-level, spatial models. Calibrated to phylogenetic linkages, these dynamic spatial models provide unique insight into the disease mobility of EBOV in Sierra Leone. Further, we developed a model selection framework that identifies important epidemiological variables influencing the spatiotemporal propagation of EBOV. Consistent with other investigations, our results show that the spread of EBOV during the beginning and middle portions of the epidemic strongly depended on the size of and distance between populations. Our analysis also revealed a substantial decline in the dependence on population size at the end of the epidemic, coinciding with the large-scale intervention campaign: Operation Western Area Surge. More generally, we believe this framework, pairing molecular diagnostics with dynamic models, has the potential to be a powerful forecasting tool along with offering operationally-relevant guidance for surveillance and sampling strategies during an epidemic.

This paper presents replica-exchange molecular dynamics simulations of the folding and insertion of a 16- residue Ebola virus fusion peptide into a membrane bilayer. We applied a multi-resolution computational approach of modeling the peptide at the all-atom level and the membrane-aqueous bilayer by a generalized Born continuum approximation. We found that interfacial folding of the peptide is not required for membrane insertion and that regardless of the starting conformation (either folded or unfolded) the simulations of 20 ns converged to yield a conformational preference of forming an (i,i+4) backbone ?-helical structure with the central residues embedded approximately 4-6 ? below the surface of the membrane and the two terminal charged residues exposed to the solvent layer. The conformational population distributions of the peptide and a possible folding/insertion pathway are discussed in terms of energy landscape theory.

We consider within-host virus models with more than one strain and allow mutation between the strains. If there is no mutation, a Lyapunov function establishes global stability of the steady state corresponding to the fittest strain. For small perturbations this steady state persists, perhaps with small concentrations of some or all other strains, depending on the connectivity of the graph describing all possible mutations. Moreover, using a perturbation result due to Smith and Waltman, we show that this steady state also preserves global stability.

We propose a honeybee-mite-virus model that incorporates (1) parasitic interactions between honeybees and the Varroa mites; (2) five virus transmission terms between honeybees and mites at different stages of Varroa mites: from honeybees to honeybees, from adult honeybees to phoretic mites, from honeybee brood to reproductive mites, from reproductive mites to honeybee brood, and from honeybees to phoretic mites; and (3) Allee effects in the honeybee population generated by its internal organization such as division of labor. We provide completed local and global analysis for the full system and its subsystems. Our analytical and numerical results allow us have a better understanding of the synergistic effects of parasitism and virus infections on honeybee population dynamics and its persistence. Interesting findings from our work include: (a) Due to Allee effects experienced by the honeybee population, initial conditions are essential for the survival of the colony. (b) Low adult honeybee to brood ratios have destabilizing effects on the system, generate fluctuated dynamics, and potentially lead to a \emph{catastrophic event} where both honeybees and mites suddenly become extinct. This catastrophic event could be potentially linked to Colony Collapse Disorder (CCD) of honeybee colonies. (c) Virus infections may have stabilizing effects on the system, and could make disease more persistent in the presence of parasitic mites. Our model illustrates how the synergy between the parasitic mites and virus infections consequently generates rich dynamics including multiple attractors where all species can coexist or go extinct depending on initial conditions. Our findings may provide important insights on honeybee diseases and parasites and how to best control them.

In this model we study the dynamics and control of hepatitis B virus (HBV) infection which is a major health problem worldwide by considering condom, vaccination and treatment as control measures. Initially we determined the basic reproduction number R_0 for the model and observe that once R_0 http://www.ijtsrd.com/mathemetics/other/18164/a-mathematical-model-of-the-dynamics-of-hepatitis-b-virus-hbv-infection-with-controls/titus-ifeanyi-chinebu

The field of epidemiology has presented fascinating and relevant questions for mathematicians, primarily concerning the spread of viruses in a community. The importance of this research has greatly increased over time as its applications have expanded to also include studies of electronic and social networks and the spread of information and ideas. We study virus propagation on a non-linear hub and spoke graph (which models well many airline networks). We determine the long-term behavior as a function of the cure and infection rates, as well as the number of spokes n. For each n we prove the existence of a critical threshold relating the two rates. Below this threshold, the virus always dies out; above this threshold, all non-trivial initial conditions iterate to a unique non-trivial steady state. We end with some generalizations to other networks.

In this paper, a reaction-diffusion system is proposed to model the spatial spreading of West Nile virus in vector mosquitoes and host birds in North America. Infection dynamics are based on a simplified model for cross infection between mosquitoes and birds, and the free boundary is introduced to model and explore the expanding front of the infective region. The spatial-temporal risk index $R_0^F(t)$, which involves time and characters of the region, is defined for the simplified model with the free boundary to compare with other related threshold values, including the usual basic reproduction number $R_0$. Sufficient conditions for the virus to vanish or spread are given. Our results suggest that the virus will be in a scenario of vanishing if $R_0\leq 1$, and the virus will spread to the whole region if $R_{0}^F(t_0)\geq 1$ for some $t_0\geq 0$, while if $R^F_0(0)

This article is from BMC Bioinformatics , volume 13 . Abstract The RNA polymerase NS5B of Hepatitis C virus (HCV) is a well-characterised drug target with an active site and four allosteric binding sites. This work presents a workflow for virtual screening and its application to Drug Bank screening targeting the Hepatitis C Virus (HCV) RNA polymerase non-nucleoside binding sites. Potential polypharmacological drugs are sought with predicted active inhibition on viral replication, and with proven positive pharmaco-clinical profiles. The approach adopted was receptor-based. Docking screens, guided with contact pharmacophores and neural-network activity prediction models on all allosteric binding sites and MD simulations, constituted our analysis workflow for identification of potential hits. Steps included: 1) using a two-phase docking screen with Surflex and Glide Xp. 2) Ranking based on scores, and important H interactions. 3) a machine-learning target-trained artificial neural network PIC prediction model used for ranking. This provided a better correlation of IC50 values of the training sets for each site with different docking scores and sub-scores. 4) interaction pharmacophores-through retrospective analysis of protein-inhibitor complex X-ray structures for the interaction pharmacophore (common interaction modes) of inhibitors for the five non-nucleoside binding sites were constructed. These were used for filtering the hits according to the critical binding feature of formerly reported inhibitors. This filtration process resulted in identification of potential new inhibitors as well as formerly reported ones for the thumb II and Palm I sites (HCV-81) NS5B binding sites. Eventually molecular dynamics simulations were carried out, confirming the binding hypothesis and resulting in 4 hits.

This article is from Infectious Disease Reports , volume 5 . Abstract The intra-host evolutionary and population dynamics of the human immunodeficiency virus type 1 (HIV-1), the cause of the acquired immunodeficiency syndrome, have been the focus of one of the most extensive study efforts in the field of molecular evolution over the past three decades. As HIV-1 is among the fastest mutating organisms known, viral sequence data sampled over time from infected patients can provide, through phylogenetic analysis, significant insights about the tempo and mode of evolutionary processes shaped by complex interaction with the host milieu. Five main aspects are discussed: the patterns of HIV-1 intra-host diversity and divergence over time in relation to different phases of disease progression; the impact of selection on the temporal structure of HIV-1 intra-host genealogies inferred from longitudinally sampled viral sequences; HIV-1 intra-host sub-population structure; the potential relationship between viral evolutionary rate and disease progression and the central evolutionary role played by recombination occurring in super-infected cells.

This article is from PeerJ , volume 2 . Abstract In many biological applications, we would like to be able to computationally predict mutational effects on affinity in protein–protein interactions. However, many commonly used methods to predict these effects perform poorly in important test cases. In particular, the effects of multiple mutations, non alanine substitutions, and flexible loops are difficult to predict with available tools and protocols. We present here an existing method applied in a novel way to a new test case; we interrogate affinity differences resulting from mutations in a host–virus protein–protein interface. We use steered molecular dynamics (SMD) to computationally pull the machupo virus (MACV) spike glycoprotein (GP1) away from the human transferrin receptor (hTfR1). We then approximate affinity using the maximum applied force of separation and the area under the force-versus-distance curve. We find, even without the rigor and planning required for free energy calculations, that these quantities can provide novel biophysical insight into the GP1/hTfR1 interaction. First, with no prior knowledge of the system we can differentiate among wild type and mutant complexes. Moreover, we show that this simple SMD scheme correlates well with relative free energy differences computed via free energy perturbation. Second, although the static co-crystal structure shows two large hydrogen-bonding networks in the GP1/hTfR1 interface, our simulations indicate that one of them may not be important for tight binding. Third, one viral site known to be critical for infection may mark an important evolutionary suppressor site for infection-resistant hTfR1 mutants. Finally, our approach provides a framework to compare the effects of multiple mutations, individually and jointly, on protein–protein interactions.