Relationship between the inclusion/exclusion criteria and sample size in randomized controlled trials for SARS-CoV-2 entry inhibitors.

The coronavirus disease 2019 (COVID-19) pandemic that has been ongoing since 2019 is still ongoing and how to control it is one of the international issues to be addressed. Antiviral drugs that reduce the viral load in terms of reducing the risk of secondary infection are important. For the general control of emerging infectious diseases, establishing an efficient method to evaluate candidate therapeutic agents will lead to a rapid response. We evaluated clinical trial designs for viral entry inhibitors that have the potential to be effective pre-exposure prophylactic drugs in addition to reducing viral load after infection. We used a previously developed simulation of clinical trials based on a mathematical model of within-host viral infection dynamics to evaluate sample sizes in clinical trials of viral entry inhibitors against COVID-19. We assumed four measures as outcomes, namely change in log10-transformed viral load from symptom onset, PCR positive ratio, log10-transformed viral load, and cumulative viral load, and then sample sizes were calculated for drugs with 99 % and 95 % antiviral efficacy. Consistent with previous results, we found that sample sizes could be dramatically reduced for all outcomes used in an analysis by adopting inclusion/exclusion criteria such that only patients in the early post-infection period would be included in a clinical trial. A comparison of sample sizes across outcomes demonstrated an optimal measurement schedule associated with the nature of the outcome measured for the evaluation of drug efficacy. In particular, the sample sizes calculated from the change in viral load and from viral load tended to be small when measurements were taken at earlier time points after treatment initiation. For the cumulative viral load, the sample size was lower than that from the other outcomes when the stricter inclusion/exclusion criteria to include patients whose time since onset is earlier than 2 days was used. We concluded that the design of efficient clinical trials should consider the inclusion/exclusion criteria and measurement schedules, as well as outcome selection based on sample size, personnel and budget needed to conduct the trial, and the importance of the outcome regarding the medical and societal requirements. This study provides insights into clinical trial design for a variety of situations, especially addressing infectious disease prevalence and feasible trial sizes. This manuscript was submitted as part of a theme issue on "Modelling COVID-19 and Preparedness for Future Pandemics".

SARS-coronavirus-2 infections: biological instabilities characterized by order parameters.

A four-variable virus dynamics TIIV model was considered that involves infected cells in an eclipse phase. The state space description of the model was transferred into an amplitude space description which is the appropriate general, nonlinear physics framework to describe instabilities. In this context, the unstable eigenvector or order parameter of the model was determined. Subsequently, a model-based analysis of viral load data from eight symptomatic COVID-19 patients was conducted. For all patients, it was found that the initial SARS-CoV-2 infection evolved along the respective patient-specific order parameter, as expected by theoretical considerations. The order parameter amplitude that described the initial virus multiplication showed doubling times between 30 min and 3 h. Peak viral loads of patients were linearly related to the amplitudes of the patient order parameters. Finally, it was found that the patient order parameters determined qualitatively and quantitatively the relationships between the increases in virus-producing infected cells and infected cells in the eclipse phase. Overall, the study echoes the 40 years old suggestion by Mackey and Glass to consider diseases as instabilities.

Maternal embryonic leucine zipper kinase (MELK) optimally regulates the HIV-1 uncoating process.

Human immunodeficiency virus type-1 (HIV-1) attaches to target cells and releases the capsid, an essential component of the viral core that contains viral RNA, into the cytoplasm. After invading target cells, the core structure gradually collapses. The timing of the disassembly of the HIV-1 capsid is essential for efficient viral cDNA synthesis and transport into the nucleus. HIV-1 uncoating is controlled by the host factor maternal embryonic leucine zipper kinase (MELK); however, the quantitative and dynamic relationship between the HIV-1 uncoating process and HIV-1 infection remains unresolved. In this study, we quantified the uncoating process on HIV-1 cDNA synthesis and transport into the nucleus by combining a mathematical model with in vitro data. In addition, detailed in silico simulations demonstrated host factors, including MELK, optimize transport efficiency. Our experimental-mathematical approach revealed quantitative dynamics of the HIV-1 uncoating process, indicating that increasing the speed of uncoating always reduces the amount of HIV-1 cDNA in the nucleus.

Virus Dynamics and Decay in Evaporating Human Saliva Droplets on Fomites.

The transmission of most respiratory pathogens, including SARS-CoV-2, occurs via virus-containing respiratory droplets, and thus, factors that affect virus viability in droplet residues on surfaces are of critical medical and public health importance. Relative humidity (RH) is known to play a role in virus survival, with a U-shaped relationship between RH and virus viability. The mechanisms affecting virus viability in droplet residues, however, are unclear. This study examines the structure and evaporation dynamics of virus-containing saliva droplets on fomites and their impact on virus viability using four model viruses: vesicular stomatitis virus, herpes simplex virus 1, Newcastle disease virus, and coronavirus HCoV-OC43. The results support the hypothesis that the direct contact of antiviral proteins and virions within the "coffee ring" region of the droplet residue gives rise to the observed U-shaped relationship between virus viability and RH. Viruses survive much better at low and high RH, and their viability is substantially reduced at intermediate RH. A phenomenological theory explaining this phenomenon and a quantitative model analyzing and correlating the experimentally measured virus survivability are developed on the basis of the observations. The mechanisms by which RH affects virus viability are explored. At intermediate RH, antiviral proteins have optimal influence on virions because of their largest contact time and overlap area, which leads to the lowest level of virus activity.

Multiscaled causality of infections on viral testing volumes: The case of COVID-19 in Tunisia.

OBJECTIVES: Coronavirus disease (COVID-19) is one of the most detrimental pandemics that affected the humanity throughout the ages. The irregular historical progression of the virus over the first year of the pandemic was accompanied with far-reaching health and social damages. To prepare logistically against this worsening disaster, many public authorities around the world had set up screening and forecasting studies. This article aims to analyse the time-frequency co-evolution of the number of confirmed cases (NCC) in Tunisia and the related number of performed polymerase chain reaction (PCR) tests over the COVID-19 first year. Accurately predicting such a relationship allows Tunisian authorities to set up an effective health prevention plan. STUDY DESIGN: In order to keep pace with the speed of evolution of the virus, we used uninterrupted daily time series from the Tunisian Ministry of Public Health (TMPH) recorded over the COVID-19 first year. The objective is to: (1) analyse the time-frequency progress of the NCC in relationship with the number of PCR tests, (2) identify a multi-scale two-factor stochastic model in order to develop a robust bivariate forecasting technique. METHODS: We assume a bivariate stochastic process which is projected onto a set of wavelet sub-spaces to investigate the scale-by-scale co-evolvement the NCC/PCR over the COVID-19 first year. A wavelet-based multiresolutional causality test is then performed. RESULTS: The main results recommend the rejection of the null hypothesis of no instantaneous causality in both directions, while the statistics of the Granger test suggest failing to reject the null hypothesis of non-causality. However, by proceeding scale-by-scale, the Granger causality is proven significant in both directions over varying frequency bands. CONCLUSIONS: It is important to include the NCC and PCR variables in any time series model intended to predict one of these variables. Such a bivariate and multi-scale model is supposed to better predict the needs of the public health sector in screening tests. On this basis, testing campaigns with multiple periodicities can be planned by the Tunisian authorities.

Modeling the dynamics of Usutu virus infection in birds.

Usutu virus is an emerging zoonotic flavivirus causing high avian mortality rates and occasional severe neurological disorders in humans. Several virus strains are co-circulating and the differences in their characteristics and avian pathogenesis levels are still unknown. In this study, we use within-host mathematical models to characterize the mechanisms responsible for virus expansion and clearance in juvenile chickens challenged with four Usutu virus strains. We find heterogeneity between the virus strains, with the time between cell infection and viral production varying between 16 h and 23 h, the infected cell lifespan varying between 48 min and 9.5 h, and the basic reproductive number R0 varying between 12.05 and 19.49. The strains with high basic reproductive number have short infected cell lifespan, indicative of immune responses. The virus strains with low basic reproductive number have lower viral peaks and longer lasting viremia, due to lower infection rates and high infected cell lifespan. We discuss how the host and virus heterogeneities may differently impact the public health threat presented by these virus strains.

Quantifying antiviral effects against simian/human immunodeficiency virus induced by host immune response.

Chimeric simian and human immunodeficiency viruses (SHIVs) are appropriate animal models for the human immunodeficiency virus (HIV) because HIV has quite a narrow host range. Additionally, SHIVs that encode the HIV-1 Env protein and are infectious to macaques have many strains that show different pathogenesis, such as the highly pathogenic SHIV-KS661 and the less pathogenic SHIV-#64. Therefore, we used SHIVs to understand different aspects of AIDS pathogenesis. In a previous study, we established a mathematical model of in vivo early SHIV infection dynamics, which revealed the expected uninfected and infected dynamics in Rhesus macaques. In concrete, the number of uninfected CD4+ T cells in SHIV-KS661-infected Rhesus macaques decreased more significantly and rapidly than that of SHIV-#64 Rhesus macaques, and these Rhesus macaques did not any induce host immune response. In contrast, the number of uninfected CD4+ T cells in SHIV-#64-infected Rhesus macaques is maintained, and host immune response developed. Although we considered that the peak viral load might determine whether systemic CD4+ T cell depletion occurs or host immune responses develop, we could not investigate this because our model quantified only SHIV infection prior to the development of the pathogenicity or host immune responses. Therefore, we developed a new mathematical model to investigate why SHIV-#64 and SHIV-KS661 showed different long-term viral dynamics. We fitted our new model considering antibody responses to our experimental datasets that included antibody titers, CD4+ T cells, and viral load data. We performed a maximum likelihood estimation using a non-linear mixed effect model. From the results, we derived the basic reproduction numbers of SHIV-#64 and SHIV-KS661 from intravenous infection (IV) and SHIV-KS661 from intrarectal infection (IR), as well as the antiviral effects of antibodies against SHIV-#64(IV) and SHIV-KS661(IR). We found significant differences between the basic reproduction number of SHIV-#64(IV) or -KS661(IR) and that of SHIV-KS661(IV). We found no clear difference between the antiviral effects of SHIV-#64(IV) and SHIV-KS661(IR), and revealed that an antiviral effect more than 90% of that of maximum antibody responses was induced from initial antibody responses (i.e., antibody response just after its inducement). In conclusion, we found that the basic reproduction number, rather than SHIV strains determines whether systemic CD4+ T cell depletion develops, and the subsequent antibody responses occurs.

Quantifying the antiviral effect of APOBEC3 on HIV-1 infection in humanized mouse model.

APOBEC3 proteins inhibit human immunodeficiency virus (HIV)-1 infection by independently impairing viral reverse transcription and inducing G-to-A mutations in viral DNA. An HIV-1-encoded protein, viral infectivity factor (Vif), can counteract these antiviral activities of APOBEC3 proteins. Although previous studies using in vitro cell culture systems have revealed the molecular mechanisms of the antiviral action of APOBEC3 proteins and their antagonism by Vif, it remains unclear how APOBEC3 proteins affect the kinetics of HIV-1 replication in vivo. Here we quantified the time-series of viral load datasets from humanized mice infected with HIV-1 variants in the presence of APOBEC3F, APOBEC3G, or both APOBEC3F/G using a simple mathematical model that accounted for inter-individual variability. Through experimental and mathematical investigation, we formulated and calculated the total antiviral activity of APOBEC3F and APOBEC3G based on the estimated initial growth rates of viral loads in vivo. Interestingly, we quantitatively demonstrated that compared with APOBEC3G, the antiviral activity of APOBEC3F was widely distributed but skewed toward lower activity, although their mean values were similar. We concluded that APOBEC3G markedly and robustly restricted the initial stages of viral growth in vivo. This is the first report to quantitatively elucidate how APOBEC3F and APOBEC3G differ in their anti-HIV-1 modes in vivo.

A within-host mathematical model of H9N2 avian influenza infection and type-I interferon response pathways in chickens.

Chickens infected with avian influenza virus (AIV) transmit the virus via respiratory and cloacal shedding. While previous mathematical models have shown that the innate immune response is necessary for the early suppression of virus production in infected respiratory cells, the different pathways by which the innate immune response can affect cloacal viral shedding have not been studied in chickens. The present study aims to evaluate the sensitivity of H9N2 low pathogenic AIV shedding in chicken gastrointestinal cells to different type-I interferon (IFN) response pathways, and to determine the impact of a cellular eclipse phase (latent period) on the time to peak virus shedding using a mathematical model describing within host viral kinetics. Our model results demonstrate that a mechanistic model that incorporates 1) the intracellular antiviral effects of type-I IFN on virus production, 2) destruction of infected cells by type-I IFN activated Natural Killer cells, and 3) an eclipse phase is most consistent with experimental cloacal virus shedding data. These results provide a potential mechanistic explanation for the delay to peak cloacal virus shedding observed in experimental studies conducted in chickens, as well as an improved understanding of the primary type-I IFN pathways involved in the control of cloacal virus shedding, which may lead to the development of more targeted vaccine candidates.

Revealing uninfected and infected target cell dynamics from peripheral blood data in highly and less pathogenic simian/human immunodeficiency virus infected Rhesus macaque.

Since chimeric simian and human immunodeficiency viruses (SHIVs) used here, that is, SHIV-#64 and -KS661 utilize both CCR5 and CXCR4 chemokine receptors, they have broad target cell properties. A highly pathogenic SHIV strain, SHIV-KS661, causes an infection that systemically depletes the CD4+ T cells of Rhesus macaques, while a less pathogenic strain, SHIV-#64, does not cause severe symptoms in the macaques. In our previous studies, we established in vitro quantification system for virus infection dynamics, and concluded that SHIV-KS661 effectively produces infectious virions compared with SHIV-#64 in the HSC-F cell culture. However, in vivo dynamics of SHIV infection have not been well understood. To quantify SHIV-#64 and -KS661 infection dynamics in Rhesus macaques, we developed a novel approach and analyzed total CD4+ T cells and viral load in peripheral blood, and reproduced the expected dynamics for the uninfected and infected CD4+ T cells in silico. Using our previous cell culture experimental datasets, we revealed that an infection rate constant is different between SHIV-#64 and -KS661, but the viral production rate and the death rate are similar for the both strains. Thus, here, we assumed these relations in our in vivo data and carried out the data fitting. We performed Bayesian estimation for the whole dataset using MCMC sampling, and simultaneously fitted our novel model to total CD4+ T cells and viral load of SHIV-#64 and -KS661 infection. Our analyses explained that the Malthusian parameter (i.e., fitness of virus infection) and the basic reproduction number (i.e., potential of virus infection) for SHIV-KS661 are significantly higher than those of SHIV-#64. In addition, we demonstrated that the number of uninfected CD4+ T cells in SHIV-KS661 infected Rhesus macaques decreases to the significantly lower value than that before the inoculation several days earlier compared with SHIV-#64 infection. Taken together, the differences between SHIV-#64 and -KS661 infection before the peak viral load might determine the subsequent destiny, that is, whether the systemic CD4+ T cell depletion occurs or the host immune response develop.

Stochastic Dynamics of the Latently Infected Cell Reservoir During HIV Infection.

The presence of cells latently infected with HIV is currently considered to be a major barrier to viral eradication within a patient. Here, we consider birth-death-immigration models for the latent cell population in a single patient, and present analytical results for the size of this population in the absence of treatment. We provide results both at steady state (viral set point), and during the non-equilibrium setting of early infection. We obtain semi-analytic results showing how latency-reversing drugs might be expected to affect the size of the latent pool over time. We also analyze the probability of rare mutant viral strains joining the latent cell population, allowing for steady-state and dynamic viral populations within the host.

Predators catalyze an increase in chloroviruses by foraging on the symbiotic hosts of zoochlorellae.

Virus population growth depends on contacts between viruses and their hosts. It is often unclear how sufficient contacts are made between viruses and their specific hosts to generate spikes in viral abundance. Here, we show that copepods, acting as predators, can bring aquatic viruses and their algal hosts into contact. Specifically, predation of the protist Paramecium bursaria by copepods resulted in a >100-fold increase in the number of chloroviruses in 1 d. Copepod predation can be seen as an ecological "catalyst" by increasing contacts between chloroviruses and their hosts, zoochlorellae (endosymbiotic algae that live within paramecia), thereby facilitating viral population growth. When feeding, copepods passed P. bursaria through their digestive tract only partially digested, releasing endosymbiotic algae that still supported viral reproduction and resulting in a virus population spike. A simple predator-prey model parameterized for copepods consuming protists generates cycle periods for viruses consistent with those observed in natural ponds. Food webs are replete with similar symbiotic organisms, and we suspect the predator catalyst mechanism is capable of generating blooms for other endosymbiont-targeting viruses.

Zika virus dynamics in body fluids and risk of sexual transmission in a non-endemic area.

OBJECTIVE: To understand Zika virus (ZIKV) dynamics in fluids of infected individuals and the risk of sexual transmission. METHODS: Prospective study at two centres in Spain. Patients with probable or confirmed diagnosis of ZIKV infection were clinically followed up, and fluid samples were collected from saliva, serum, urine and semen or vaginal secretion following the study protocol. Non-traveller-sexual partners were offered to participate. RESULTS: From January 2016 to December 2016, we included a total of 11 traveller patients and six sexual contacts. Six patients were male, with a median age of 38 years (IQR 30-45). We performed 61 RT-PCR determinations, seven of which were positive. Positive results were retrieved from serum, urine, semen and vaginal tract. One of four women tested positive for ZIKV RNA in vaginal swabs collected during the first 45 days after symptoms onset. Clearance occurred between day 37 and day 69 after symptoms onset. One of five men tested positive for ZIKV RNA in semen collected during the first 45 days after symptoms onset. Clearance occurred between day 23 and 107 after symptoms onset. Six patients had sexual relations during the defined period. All tested patients were negative for ZIKV infection by serological testing. CONCLUSION: ZIKV shedding persistence in genital fluids occurs in a significant number of symptomatic patients after visiting an endemic area. We did not find any ZIKV seroconversion among the three male contacts who were investigated. Diagnostic algorithms may be updated to include genital tract fluid specimens in the diagnostic process.

A PDE multiscale model of hepatitis C virus infection can be transformed to a system of ODEs.

Direct-acting antivirals (DAAs) treat hepatitis C virus (HCV) by targeting its intracellular viral replication. DAAs are effective and deliver high clinical performance against HCV infection, but optimization of the DAA treatment regimen is ongoing. Different classes of DAAs are currently under development, and HCV treatments that combine two or three DAAs with different action mechanisms are being improved. To accurately quantify the antiviral effect of these DAA treatments and optimize multi-drug combinations, we must describe the intracellular viral replication processes corresponding to the action mechanisms by multiscale mathematical models. Previous multiscale models of HCV treatment have been formulated by partial differential equations (PDEs). However, estimating the parameters from clinical datasets requires comprehensive numerical PDE computations that are time consuming and often converge poorly. Here, we propose a user-friendly approach that transforms a standard PDE multiscale model of HCV infection (Guedj J et al., Proc. Natl. Acad. Sci. USA 2013; 110(10):3991-6) to mathematically identical ordinary differential equations (ODEs) without any assumptions. We also confirm consistency between the numerical solutions of our transformed ODE model and the original PDE model. This relationship between a detailed structured model and a simple model is called ``model aggregation problem'' and a fundamental important in theoretical biology. In particular, as the parameters of ODEs can be estimated by already established methods, our transformed ODE model and its modified version avoid the time-consuming computations and are broadly available for further data analysis.

Size-dependent Catalysis of Chlorovirus Population Growth by A Messy Feeding Predator.

Many chloroviruses replicate in endosymbiotic zoochlorellae that are protected from infection by their symbiotic host. To reach the high virus concentrations that often occur in natural systems, a mechanism is needed to release zoochlorellae from their hosts. We demonstrate that the ciliate predator Didinium nasutum foraging on zoochlorellae-bearing Paramecium bursaria can release live zoochlorellae from the ruptured prey cell that can then be infected by chloroviruses. The catalysis process is very effective, yielding roughly 95% of the theoretical infectious virus yield as determined by sonication of P. bursaria. Chlorovirus activation is more effective with smaller Didinia, as larger Didinia typically consume entire P. bursaria cells without rupturing them, precluding the release of zoochlorellae. We also show that the timing of Chlorovirus growth is tightly linked to the predator-prey cycle between Didinium and Paramecium, with the most rapid increase in chloroviruses temporally linked to the peak foraging rate of Didinium, supporting the idea that predator-prey cycles can drive cycles of Chlorovirus abundance.

Dynamics of virus and immune response in multi-epitope network.

The host immune response can often efficiently suppress a virus infection, which may lead to selection for immune-resistant viral variants within the host. For example, during HIV infection, an array of CTL immune response populations recognize specific epitopes (viral proteins) presented on the surface of infected cells to effectively mediate their killing. However HIV can rapidly evolve resistance to CTL attack at different epitopes, inducing a dynamic network of interacting viral and immune response variants. We consider models for the network of virus and immune response populations, consisting of Lotka-Volterra-like systems of ordinary differential equations. Stability of feasible equilibria and corresponding uniform persistence of distinct variants are characterized via a Lyapunov function. We specialize the model to a "binary sequence" setting, where for n epitopes there can be [Formula: see text] distinct viral variants mapped on a hypercube graph. The dynamics in several cases are analyzed and sharp polychotomies are derived characterizing persistent variants. In particular, we prove that if the viral fitness costs for gaining resistance to each epitope are equal, then the system of [Formula: see text] virus strains converges to a "perfectly nested network" with less than or equal to [Formula: see text] persistent virus strains. Overall, our results suggest that immunodominance, i.e. relative strength of immune response to an epitope, is the most important factor determining the persistent network structure.

A highly pathogenic simian/human immunodeficiency virus effectively produces infectious virions compared with a less pathogenic virus in cell culture.

BACKGROUND: The host range of human immunodeficiency virus (HIV) is quite narrow. Therefore, analyzing HIV-1 pathogenesis in vivo has been limited owing to lack of appropriate animal model systems. To overcome this, chimeric simian and human immunodeficiency viruses (SHIVs) that encode HIV-1 Env and are infectious to macaques have been developed and used to investigate the pathogenicity of HIV-1 in vivo. So far, we have many SHIV strains that show different pathogenesis in macaque experiments. However, dynamic aspects of SHIV infection have not been well understood. To fully understand the dynamic properties of SHIVs, we focused on two representative strains-the highly pathogenic SHIV, SHIV-KS661, and the less pathogenic SHIV, SHIV-#64-and measured the time-course of experimental data in cell culture. METHODS: We infected HSC-F with SHIV-KS661 and -#64 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 9 days. The experiments were repeated at two different multiplicities of infection, and a previously developed mathematical model incorporating the infectious and non-infectious viruses was fitted to the full dataset of each strain simultaneously to characterize the infection dynamics of these two strains. RESULTS AND CONCLUSIONS: We quantified virological indices including virus burst sizes and basic reproduction number of both SHIV-KS661 and -#64. Comparing the burst size of total and infectious viruses (viral RNA copies and TCID50, respectively), we found that there was a statistically significant difference between the infectious virus burst size of SHIV-KS661 and -#64, while there was no significant difference between the total virus burst size. Furthermore, our analyses showed that the fraction of infectious virus among the produced SHIV-KS661 viruses, which is defined as the infectious viral load (TCID50/ml) divided by the total viral load (RNA copies/ml), is more than 10-fold higher than that of SHIV-#64 during overall infection (i.e., for 9 days). Taken together, we conclude that the highly pathogenic SHIV produces infectious virions more effectively than the less pathogenic SHIV in cell culture.

Global properties of nested network model with application to multi-epitope HIV/CTL dynamics.

Mathematical modeling and analysis can provide insight on the dynamics of ecosystems which maintain biodiversity in the face of competitive and prey-predator interactions. Of primary interests are the underlying structure and features which stabilize diverse ecological networks. Recently Korytowski and Smith (Theor Ecol 8(1):111-120, 2015) proved that a perfectly nested infection network, along with appropriate life history trade-offs, leads to coexistence and persistence of bacteria-phage communities in a chemostat model. In this article, we generalize their model in order to apply it to the within-host dynamics virus and immune response, in particular HIV and CTL (Cytotoxic T Lymphocyte) cells. Our model can describe sequential viral escape from dominant immune responses and rise in subdominant immune responses, consistent with observed patterns of HIV/CTL evolution. We find a Lyapunov function for the system which leads to rigorous characterization of persistent viral and immune variants, along with informing upon equilibria stability and global dynamics. Results are interpreted in the context of within-host HIV/CTL evolution and numerical simulations are provided.

Quantifying the effect of Vpu on the promotion of HIV-1 replication in the humanized mouse model.

BACKGROUND: Tetherin is an intrinsic anti-viral factor impairing the release of nascent HIV-1 particles from infected cells. Vpu, an HIV-1 accessory protein, antagonizes the anti-viral action of tetherin. Although previous studies using in vitro cell culture systems have revealed the molecular mechanisms of the anti-viral action of tetherin and the antagonizing action of Vpu against tetherin, it still remains unclear how Vpu affects the kinetics of HIV-1 replication in vivo. RESULTS: To quantitatively assess the role of Vpu in viral replication in vivo, we analyzed time courses of experimental data with viral load and target cell levels in the peripheral blood of humanized mice infected with wild-type and vpu-deficient HIV-1. Our recently developed mathematical model describes the acute phase of this infection reasonably, and allowed us to estimate several parameters characterizing HIV-1 infection in mice. Using a technique of Bayesian parameter estimation, we estimate distributions of the basic reproduction number of wild-type and vpu-deficient HIV-1. This reveals that Vpu markedly increases the rate of viral replication in vivo. CONCLUSIONS: Combining experiments with mathematical modeling, we provide an estimate for the contribution of Vpu to viral replication in humanized mice.

Contribution of HIV-1 genomes that do not integrate to the basic reproductive ratio of the virus.

Recent experimental data indicate that HIV-1 DNA that fails to integrate (from now on called uDNA) can by itself successfully produce infectious offspring virions in resting T cells that become activated after infection. This scenario is likely important at the initial stages of the infection. We use mathematical models to calculate the relative contribution of unintegrated and integrated viral DNA to the basic reproductive ratio of the virus, R0, and the models are parameterized with preliminary data. This is done in the context of both free virus spread and transmission of the virus through virological synapses. For free virus transmission, we find that under preliminary parameter estimates, uDNA might contribute about 20% to the total R0. This requires that a single copy of uDNA can successfully replicate. If the presence of more than one uDNA copy is required for replication, uDNA does not contribute to R0. For synaptic transmission, uDNA can contribute to R0 regardless of the number of uDNA copies required for replication. The larger the number of viruses that are successfully transmitted per synapse, however, the lower the contribution of uDNA to R0 because this increases the chances that at least one virus integrates. Using available parameter values, uDNA can maximally contribute 20% to R0 in this case. We argue that the contribution of uDNA to virus reproduction might also be important for continued low level replication of HIV-1 in the presence of integrase inhibitor therapy. Assuming a 20% contribution of uDNA to the overall R0, our calculations suggest that R0=1.6 in the absence of virus integration. While these are rough estimates based on preliminary data that are currently available, this analysis provides a framework for future experimental work which should directly measure key parameters.