Robust growth of human immunodeficiency virus type 1 (HIV-1)

Markov Chain-Based Stochastic Modelling of HIV-1 Life Cycle in a CD4 T Cell

Replication of Human Immunodeficiency Virus type 1 (HIV) in infected CD4+ T cells represents a key driver of HIV infection. The HIV life cycle is characterised by the heterogeneity of infected cells with respect to multiplicity of infection and the variability in viral progeny. This heterogeneity can result from the phenotypic diversity of infected cells as well as from random effects and fluctuations in the kinetics of biochemical reactions underlying the virus replication cycle. To quantify the contribution of stochastic effects to the variability of HIV life cycle kinetics, we propose a high-resolution mathematical model formulated as a Markov chain jump process. The model is applied to generate the statistical characteristics of the (i) cell infection multiplicity, (ii) cooperative nature of viral replication, and (iii) variability in virus secretion by phenotypically identical cells. We show that the infection with a fixed number of viruses per CD4+ T cell leads to some heterogeneity of infected cells with respect to the number of integrated proviral genomes. The bottleneck factors in the virus production are identified, including the Gag-Pol proteins. Sensitivity analysis enables ranking of the model parameters with respect to the strength of their impact on the size of viral progeny. The first three globally influential parameters are the transport of genomic mRNA to membrane, the tolerance of transcription activation to Tat-mediated regulation, and the degradation of free and mature virions. These can be considered as potential therapeutical targets.

Patterns of virus growth across the diversity of life

Although viruses in their natural habitats add up to less than 10% of the biomass, they contribute more than 90% of the genome sequences [1]. These viral sequences or 'viromes' encode viruses that populate the Earth's oceans [2, 3] and terrestrial environments [4, 5], where their infections impact life across diverse ecological niches and scales [6, 7], including humans [8-10]. Most viruses have yet to be isolated and cultured [11-13], and surprisingly few efforts have explored what analysis of available data might reveal about their nature. Here, we compiled and analyzed seven decades of one-step growth and other data for viruses from six major families, including their infections of archaeal, bacterial and eukaryotic hosts [14-191]. We found that the use of host cell biomass for virus production was highest for archaea at 10%, followed by bacteria at 1% and eukarya at 0.01%, highlighting the degree to which viruses of archaea and bacteria exploit their host cells. For individual host cells, the yield of virus progeny spanned a relatively narrow range (10-1000 infectious particles per cell) compared with the million-fold difference in size between the smallest and largest cells. Furthermore, healthy and infected host cells were remarkably similar in the time they needed to multiply themselves or their virus progeny. Specifically, the doubling time of healthy cells and the delay time for virus release from infected cells were not only correlated (r = 0.71, p < 10-10, n = 101); they also spanned the same range from tens of minutes to about a week. These results have implications for better understanding the growth, spread and persistence of viruses in complex natural habitats that abound with diverse hosts, including humans and their associated microbes.

Modeling of the HIV-1 Life Cycle in Productively Infected Cells to Predict Novel Therapeutic Targets

There are many studies that model the within-host population dynamics of Human Immunodeficiency Virus Type 1 (HIV-1) infection. However, the within-infected-cell replication of HIV-1 remains to be not comprehensively addressed. There exist rather few quantitative models describing the regulation of the HIV-1 life cycle at the intracellular level. In treatment of HIV-1 infection, there remain issues related to side-effects and drug-resistance that require further search "...for new and better drugs, ideally targeting multiple independent steps in the HIV-1 replication cycle" (as highlighted recently by Teldury et al., The Future of HIV-1 Therapeutics, 2015). High-resolution mathematical models of HIV-1 growth in infected cells provide an additional analytical tool in identifying novel drug targets. We formulate a high-dimensional model describing the biochemical reactions underlying the replication of HIV-1 in target cells. The model considers a nonlinear regulation of the transcription of HIV-1 mediated by Tat and the Rev-dependent transport of fully spliced and singly spliced transcripts from the nucleus to the cytoplasm. The model is calibrated using available information on the kinetics of various stages of HIV-1 replication. The sensitivity analysis of the model is performed to rank the biochemical processes of HIV-1 replication with respect to their impact on the net production of virions by one actively infected cell. The ranking of the sensitivity factors provides a quantitative basis for identifying novel targets for antiviral therapy. Our analysis suggests that HIV-1 assembly depending on Gag and Tat-Rev regulation of transcription and mRNA distribution present two most critical stages in HIV-1 replication that can be targeted to effectively control virus production. These processes are not covered by current antiretroviral treatments.

Probabilistic control of HIV latency and transactivation by the Tat gene circuit

The reservoir of HIV latently infected cells is the major obstacle for eradication of HIV infection. The "shock-and-kill" strategy proposed earlier aims to reduce the reservoir by activating cells out of latency. While the intracellular HIV Tat gene circuit is known to play important roles in controlling latency and its transactivation in HIV-infected cells, the detailed control mechanisms are not well understood. Here we study the mechanism of probabilistic control of the latent and the transactivated cell phenotypes of HIV-infected cells. We reconstructed the probability landscape, which is the probability distribution of the Tat gene circuit states, by directly computing the exact solution of the underlying chemical master equation. Results show that the Tat circuit exhibits a clear bimodal probability landscape (i.e., there are two distinct probability peaks, one associated with the latent cell phenotype and the other with the transactivated cell phenotype). We explore potential modifications to reactions in the Tat gene circuit for more effective transactivation of latent cells (i.e., the shock-and-kill strategy). Our results suggest that enhancing Tat acetylation can dramatically increase Tat and viral production, while increasing the Tat-transactivation response binding affinity can transactivate latent cells more rapidly than other manipulations. Our results further explored the "block and lock" strategy toward a functional cure for HIV. Overall, our study demonstrates a general approach toward discovery of effective therapeutic strategies and druggable targets by examining control mechanisms of cell phenotype switching via exactly computed probability landscapes of reaction networks.

Kinetic Modeling of Virus Growth in Cells

When a virus infects a host cell, it hijacks the biosynthetic capacity of the cell to produce virus progeny, a process that may take less than an hour or more than a week. The overall time required for a virus to reproduce depends collectively on the rates of multiple steps in the infection process, including initial binding of the virus particle to the surface of the cell, virus internalization and release of the viral genome within the cell, decoding of the genome to make viral proteins, replication of the genome, assembly of progeny virus particles, and release of these particles into the extracellular environment. For a large number of virus types, much has been learned about the molecular mechanisms and rates of the various steps. However, in only relatively few cases during the last 50 years has an attempt been made-using mathematical modeling-to account for how the different steps contribute to the overall timing and productivity of the infection cycle in a cell. Here we review the initial case studies, which include studies of the one-step growth behavior of viruses that infect bacteria (Qβ, T7, and M13), human immunodeficiency virus, influenza A virus, poliovirus, vesicular stomatitis virus, baculovirus, hepatitis B and C viruses, and herpes simplex virus. Further, we consider how such models enable one to explore how cellular resources are utilized and how antiviral strategies might be designed to resist escape. Finally, we highlight challenges and opportunities at the frontiers of cell-level modeling of virus infections.

Host genotype and time dependent antigen presentation of viral peptides: predictions from theory

The rate of progression of HIV infected individuals to AIDS is known to vary with the genotype of the host, and is linked to their allele of human leukocyte antigen (HLA) proteins, which present protein degradation products at the cell surface to circulating T-cells. HLA alleles are associated with Gag-specific T-cell responses that are protective against progression of the disease. While Pol is the most conserved HIV sequence, its association with immune control is not as strong. To gain a more thorough quantitative understanding of the factors that contribute to immunodominance, we have constructed a model of the recognition of HIV infection by the MHC class I pathway. Our model predicts surface presentation of HIV peptides over time, demonstrates the importance of viral protein kinetics, and provides evidence of the importance of Gag peptides in the long-term control of HIV infection. Furthermore, short-term dynamics are also predicted, with simulation of virion-derived peptides suggesting that efficient processing of Gag can lead to a 50% probability of presentation within 3 hours post-infection, as observed experimentally. In conjunction with epitope prediction algorithms, this modelling approach could be used to refine experimental targets for potential T-cell vaccines, both for HIV and other viruses.

Multiscale modeling of virus replication and spread

Replication and spread of human viruses is based on the simultaneous exploitation of many different host functions, bridging multiple scales in space and time. Mathematical modeling is essential to obtain a systems-level understanding of how human viruses manage to proceed through their life cycles. Here, we review corresponding advances for viral systems of large medical relevance, such as human immunodeficiency virus-1 (HIV-1) and hepatitis C virus (HCV). We will outline how the combination of mathematical models and experimental data has advanced our quantitative knowledge about various processes of these pathogens, and how novel quantitative approaches promise to fill remaining gaps.

Modeling the Effects of Vorinostat In Vivo Reveals both Transient and Delayed HIV Transcriptional Activation and Minimal Killing of Latently Infected Cells

Recent efforts to cure human immunodeficiency virus type-1 (HIV-1) infection have focused on developing latency reversing agents as a first step to eradicate the latent reservoir. The histone deacetylase inhibitor, vorinostat, has been shown to activate HIV RNA transcription in CD4+ T-cells and alter host cell gene transcription in HIV-infected individuals on antiretroviral therapy. In order to understand how latently infected cells respond dynamically to vorinostat treatment and determine the impact of vorinostat on reservoir size in vivo, we have constructed viral dynamic models of latency that incorporate vorinostat treatment. We fitted these models to data collected from a recent clinical trial in which vorinostat was administered daily for 14 days to HIV-infected individuals on suppressive ART. The results show that HIV transcription is increased transiently during the first few hours or days of treatment and that there is a delay before a sustained increase of HIV transcription, whose duration varies among study participants and may depend on the long term impact of vorinostat on host gene expression. Parameter estimation suggests that in latently infected cells, HIV transcription induced by vorinostat occurs at lower levels than in productively infected cells. Furthermore, the estimated loss rate of transcriptionally induced cells remains close to baseline in most study participants, suggesting vorinostat treatment does not induce latently infected cell killing and thus reduce the latent reservoir in vivo.

Combination antiretroviral therapy (cART) for HIV infection must be taken for life due to the existence of long lived latently infected cells. Recent efforts have focused on developing latency reversing agents to eliminate latently infected cells by activating HIV production. In this work, we assess the impact of a latency reversing agent, vorinostat, by fitting dynamic models to data from a clinical trial. Results show that vorinostat treatment induces HIV transcription transiently and that the sustained induction of HIV transcription may depend on the temporal impact of vorinostat on host gene expression. Our results also suggest that vorinostat treatment is not sufficient to induce killing of latently infected cells in a majority of HIV-infected individuals on cART.

Mathematical model of the Tat-Rev regulation of HIV-1 replication in an activated cell predicts the existence of oscillatory dynamics in the synthesis of viral components

Background

The life cycle of human immunodeficiency virus type-1 (HIV-1) makes possible the realization of regulatory strategies that can lead to complex dynamical behavior of the system. We analyze the strategy which is based on two feedback mechanisms, one mediating a positive regulation of the virus replication by Tat protein via the antitermination of the genomic RNAs transcription on TAR (transactivation responsive) element of the proviral DNA and the second mechanism providing a negative regulation of the splicing of the full-length (9 kb) RNAs and incompletely spliced (4 kb) RNAs via their transport from the nucleus to the cytoplasm. Although the existence of these two regulatory feedback loops has been considered in other mathematical models, none of them examined the conditions for the emergence of complex oscillatory patterns in the intracellular dynamics of viral components.

Results

We developed a mechanistic mathematical model for the Tat-Rev mediated regulation of HIV-1 replication, which considers the activation of proviral DNA transcription, the Tat-specific antitermination of transcription on TAR-element, resulting in the synthesis of the full-length 9 kb RNA, the splicing of the 9 kb RNA down to the 4 kb RNA and the 4 kb RNA to 2 kb RNA, the transport of 2 kb mRNAs from the nucleus to the cytoplasm by the intracellular mechanisms, the multiple binding of the Rev protein to RRE (Rev Response Element) sites on 9 kb and 4 kb RNA resulting in their export to the cytoplasm and the synthesis of Tat and Rev proteins in the cytoplasm followed by their transport into the nucleus. The degradation of all viral proteins and RNAs both in the cytoplasm and the nucleus is described. The model parameters values were derived from the published literature data. The model was used to examine the dynamics of the synthesis of the viral proteins Tat and Rev, the mRNAs under the intracellular conditions specific for activated HIV-1 infected macrophages. In addition, we analyzed alternative hypotheses for the re-cycling of the Rev proteins both in the cytoplasm and the nuclear pore complex.

Conclusions

The quantitative mathematical model of the Tat-Rev regulation of HIV-1 replication predicts the existence of oscillatory dynamics which depends on the efficacy of the Tat and TAR interaction as well as on the Rev-mediated transport processes. The biological relevance of the oscillatory regimes for the HIV-1 life cycle is discussed.

Stochastic population switch may explain the latent reservoir stability and intermittent viral blips in HIV patients on suppressive therapy

Highly active antiretroviral therapy can suppress plasma viral loads of HIV-1 infected individuals to below the detection limit of standard clinical assays. However, low-level viremia still persists. Many patients also have transient viral load measurements above the detection limit (the so-called "viral blips"). The latent reservoir consisting of latently infected CD4+ T cells represents a major obstacle to HIV-1 eradication. These cells can be activated to produce virions but the size of the latent reservoir is relatively stable. The mechanisms underlying low viral load persistence, emergence of intermittent viral blips and stability of the latent reservoir are not well understood. Cellular and viral transcription factors play an important role in the establishment and maintenance of HIV-1 latency. Infected cells with intermediate transcriptional activities may either revert to a latent state or become highly activated and produce virions due to intracellular perturbations. Here we develop a mathematical model that includes such stochastic population switch. We demonstrate that the model can generate a stable latent reservoir, intermittent viral blips, as well as low-level viremia persistence. Latently infected cells with intermediate transcription activities may maintain their size through a high level of homeostatic proliferation, while cells with low transcriptional activities are likely to be maintained through the reversion from cells with intermediate transcription activities. Simulations also suggest that treatment intensification or activation therapy may not help to eradicate the latent reservoir. Blocking the proliferation of latently infected cells might be a good strategy. These results provide more insights into the long-term dynamics of virus and latently infected cells in HIV patients on suppressive therapy and may help to develop novel treatment strategies.

Intracellular transactivation of HIV can account for the decelerating decay of virus load during drug therapy

Linking the intracellular transactivation circuit of HIV into a virus dynamics model can account for activation of infected cells and reversion into latency.

We hypothesize that the activation of latently infected cells is governed by the basal transcription rate of the integrated provirus rather than through extracellular stimuli.

This systems approach to modelling virus dynamics offers a promising framework to infer the extracellular dynamics of cell populations from their intracellular reaction networks.

The viral reservoir of latently infected cells is considered to be one of the major barriers for eradicating the virus from patients infected with HIV. During prolonged antiretroviral therapy, it has been shown that the pool of latently infected cells decays very slowly and at a decreasing rate. The underlying mechanisms causing this decelerating decay are still unclear (Lassen et al, 2004a, 2004b; Han et al, 2007). A recent study has shown that HIV can exhibit a switch-like behavior where infected cells can either be activated or become resting in a latent state (Weinberger et al, 2005). To investigate the effect of this switch-like behavior on the viral infection dynamics, we devise a new model that links the intracellular transactivation of the virus with the extracellular virus dynamics (Box 1). The model can explain the typical decelerating decay of HIV that is observed during antiretroviral therapy. We find that the activation of latently infected cells is governed by the basal transcription rate of the inserted provirus. Therefore, our analysis suggests that increasing the basal transcription rate of the HIV provirus could serve as a new therapeutic intervention for eradicating the pool of latently infected cells. In addition, our systems approach to modeling virus dynamics offers a promising framework for inferring the extracellular dynamics of cell populations from their intracellular reaction networks.

Basic virus dynamics models have been essential in understanding quantitative issues of HIV replication. However, several parts of the viral life cycle remain elusive. One of the most critical steps is the start of viral transcription, which is governed by the regulatory protein trans-activator of transcription (Tat) that induces a positive feedback loop. It has been shown that this feedback loop can alternate between two states leading to a transient activation of viral transcription. Using Monte Carlo simulations, we integrate the transactivation circuit into a new virus dynamics model having an age-dependent transactivation rate and reversion into latency. The cycling of infected cells between an activated and latent state results in the typical decelerating decay of virus load following therapy. Further, we hypothesize that the activation of latently infected cells is governed by the basal transcription rate of the integrated provirus rather than the intra- or extracellular environment. Finally, our systems approach to modeling virus dynamics offers a promising framework to infer the extracellular dynamics of cell populations from their intracellular reaction networks.