1
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Williams T, McCaw JM, Osborne JM. Spatial information allows inference of the prevalence of direct cell-to-cell viral infection. PLoS Comput Biol 2024; 20:e1012264. [PMID: 39042664 DOI: 10.1371/journal.pcbi.1012264] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/30/2023] [Revised: 08/02/2024] [Accepted: 06/19/2024] [Indexed: 07/25/2024] Open
Abstract
The role of direct cell-to-cell spread in viral infections-where virions spread between host and susceptible cells without needing to be secreted into the extracellular environment-has come to be understood as essential to the dynamics of medically significant viruses like hepatitis C and influenza. Recent work in both the experimental and mathematical modelling literature has attempted to quantify the prevalence of cell-to-cell infection compared to the conventional free virus route using a variety of methods and experimental data. However, estimates are subject to significant uncertainty and moreover rely on data collected by inhibiting one mode of infection by either chemical or physical factors, which may influence the other mode of infection to an extent which is difficult to quantify. In this work, we conduct a simulation-estimation study to probe the practical identifiability of the proportion of cell-to-cell infection, using two standard mathematical models and synthetic data that would likely be realistic to obtain in the laboratory. We show that this quantity cannot be estimated using non-spatial data alone, and that the collection of data which describes the spatial structure of the infection is necessary to infer the proportion of cell-to-cell infection. Our results provide guidance for the design of relevant experiments and mathematical tools for accurately inferring the prevalence of cell-to-cell infection in in vitro and in vivo contexts.
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Affiliation(s)
- Thomas Williams
- School of Mathematics and Statistics, University of Melbourne, Melbourne, Australia
| | - James M McCaw
- School of Mathematics and Statistics, University of Melbourne, Melbourne, Australia
- Centre for Epidemiology and Biostatistics, Melbourne School of Population and Global Health, University of Melbourne, Melbourne, Australia
| | - James M Osborne
- School of Mathematics and Statistics, University of Melbourne, Melbourne, Australia
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2
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Deng Q, Guo T, Qiu Z, Chen Y. A mathematical model for HIV dynamics with multiple infections: implications for immune escape. J Math Biol 2024; 89:6. [PMID: 38762831 DOI: 10.1007/s00285-024-02104-w] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/26/2023] [Revised: 12/15/2023] [Accepted: 04/25/2024] [Indexed: 05/20/2024]
Abstract
Multiple infections enable the recombination of different strains, which may contribute to viral diversity. How multiple infections affect the competition dynamics between the two types of strains, the wild and the immune escape mutant, remains poorly understood. This study develops a novel mathematical model that includes the two strains, two modes of viral infection, and multiple infections. For the representative double-infection case, the reproductive numbers are derived and global stabilities of equilibria are obtained via the Lyapunov direct method and theory of limiting systems. Numerical simulations indicate similar viral dynamics regardless of multiplicities of infections though the competition between the two strains would be the fiercest in the case of quadruple infections. Through sensitivity analysis, we evaluate the effect of parameters on the set-point viral loads in the presence and absence of multiple infections. The model with multiple infections predict that there exists a threshold for cytotoxic T lymphocytes (CTLs) to minimize the overall viral load. Weak or strong CTLs immune response can result in high overall viral load. If the strength of CTLs maintains at an intermediate level, the fitness cost of the mutant is likely to have a significant impact on the evolutionary dynamics of mutant viruses. We further investigate how multiple infections alter the viral dynamics during the combination antiretroviral therapy (cART). The results show that viral loads may be underestimated during cART if multiple-infection is not taken into account.
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Affiliation(s)
- Qi Deng
- School of Mathematics and Statistics, Nanjing University of Science and Technology, Nanjing, 210094, People's Republic of China
- Department of Mathematics, Wilfrid Laurier University, Waterloo, N2L 3C5, Canada
| | - Ting Guo
- Aliyun School of Big Data, Changzhou University, Changzhou, 213164, People's Republic of China
| | - Zhipeng Qiu
- School of Mathematics and Statistics, Nanjing University of Science and Technology, Nanjing, 210094, People's Republic of China
| | - Yuming Chen
- Department of Mathematics, Wilfrid Laurier University, Waterloo, N2L 3C5, Canada.
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3
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Ciupe SM, Conway JM. Incorporating Intracellular Processes in Virus Dynamics Models. Microorganisms 2024; 12:900. [PMID: 38792730 PMCID: PMC11124127 DOI: 10.3390/microorganisms12050900] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/13/2024] [Revised: 04/25/2024] [Accepted: 04/26/2024] [Indexed: 05/26/2024] Open
Abstract
In-host models have been essential for understanding the dynamics of virus infection inside an infected individual. When used together with biological data, they provide insight into viral life cycle, intracellular and cellular virus-host interactions, and the role, efficacy, and mode of action of therapeutics. In this review, we present the standard model of virus dynamics and highlight situations where added model complexity accounting for intracellular processes is needed. We present several examples from acute and chronic viral infections where such inclusion in explicit and implicit manner has led to improvement in parameter estimates, unification of conclusions, guidance for targeted therapeutics, and crossover among model systems. We also discuss trade-offs between model realism and predictive power and highlight the need of increased data collection at finer scale of resolution to better validate complex models.
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Affiliation(s)
- Stanca M. Ciupe
- Department of Mathematics, Virginia Polytechnic Institute and State University, Blacksburg, VA 24060, USA
| | - Jessica M. Conway
- Department of Mathematics and Center for Infectious Disease Dynamics, Penn State University, State College, PA 16802, USA
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4
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Rong SY, Guo T, Smith JT, Wang X. The role of cell-to-cell transmission in HIV infection: insights from a mathematical modeling approach. MATHEMATICAL BIOSCIENCES AND ENGINEERING : MBE 2023; 20:12093-12117. [PMID: 37501434 DOI: 10.3934/mbe.2023538] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 07/29/2023]
Abstract
HIV infection remains a serious global public health problem. Although current drug treatment is effective and can reduce plasma viral loads below the level of detection, it cannot eradicate the virus. The reasons for the low virus persistence despite long-term therapy have not been fully elucidated. In addition, multiple HIV infection, i.e., infection of a cell by multiple viruses, is common and can facilitate viral recombination and mutations, evading the immune system and conferring resistance to drug treatment. The mechanisms for multiple HIV infection formation and their respective contributions remain unclear. To answer these questions, we developed a mathematical modeling framework that encompasses cell-free viral infection and cell-to-cell spread. We fit sub-models that only have one transmission route and the full model containing both to the multi-infection data from HIV-infected patients, and show that the multi-infection data can only be reproduced if these two transmission routes are both considered. Computer simulations with the best-fitting parameter values indicate that cell-to-cell spread leads to the majority of multiple infection and also accounts for the majority of overall infection. Sensitivity analysis shows that cell-to-cell spread has reduced susceptibility to treatment and may explain low HIV persistence. Taken together, this work indicates that cell-to-cell spread plays a crucial role in the development of HIV multi-infection and low HIV persistence despite long-term therapy, and therefore has important implications for understanding HIV pathogenesis and developing more effective treatment strategies to control or even eliminate the disease.
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Affiliation(s)
| | - Ting Guo
- Aliyun School of Big Data, Changzhou University, Changzhou 213164, China
- Department of Mathematics, University of Florida, Gainesville, FL 32611, USA
| | - J Tyler Smith
- Department of Mathematics, University of Florida, Gainesville, FL 32611, USA
| | - Xia Wang
- School of Mathematics and Statistics, Xinyang Normal University, Xinyang 464000, China
- Department of Mathematics, University of Florida, Gainesville, FL 32611, USA
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5
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Superinfection exclusion: A viral strategy with short-term benefits and long-term drawbacks. PLoS Comput Biol 2022; 18:e1010125. [PMID: 35536864 PMCID: PMC9122224 DOI: 10.1371/journal.pcbi.1010125] [Citation(s) in RCA: 13] [Impact Index Per Article: 6.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/10/2021] [Revised: 05/20/2022] [Accepted: 04/20/2022] [Indexed: 12/23/2022] Open
Abstract
Viral superinfection occurs when multiple viral particles subsequently infect the same host. In nature, several viral species are found to have evolved diverse mechanisms to prevent superinfection (superinfection exclusion) but how this strategic choice impacts the fate of mutations in the viral population remains unclear. Using stochastic simulations, we find that genetic drift is suppressed when superinfection occurs, thus facilitating the fixation of beneficial mutations and the removal of deleterious ones. Interestingly, we also find that the competitive (dis)advantage associated with variations in life history parameters is not necessarily captured by the viral growth rate for either infection strategy. Putting these together, we then show that a mutant with superinfection exclusion will easily overtake a superinfecting population even if the latter has a much higher growth rate. Our findings suggest that while superinfection exclusion can negatively impact the long-term adaptation of a viral population, in the short-term it is ultimately a winning strategy. Viral social behaviour has recently been receiving increasing attention in the context of ecological and evolutionary dynamics of viral populations. One fascinating and still relatively poorly understood example is superinfection or co-infection, which occur when multiple viruses infect the same host. Among bacteriophages, a wide range of mechanisms have been discovered that enable phage to prevent superinfection (superinfection exclusion) even at the cost of using precious resources for this purpose. What is the evolutionary impact of this strategic choice and why do so many phages exhibit this behaviour? Here, we conduct an extensive simulation study of a phage population to address this question. In particular, we investigate the fate of viral mutations arising in an environment with a constant supply of bacterial hosts designed to mimic a “turbidostat,” as these are increasingly being used in laboratory evolution experiments. Our results show that allowing superinfection in the long-term yields a population which is more capable of adapting to changes in the environment. However, when in direct competition, mutants capable of preventing superinfection experience a very large advantage over their superinfecting counterparts, even if this ability comes at a significant cost to their growth rate. This indicates that while preventing superinfection can negatively impact the long-term prospects of a viral population, in the short-term it is ultimately a winning strategy.
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6
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Abstract
The HIV Env glycoprotein is the surface glycoprotein responsible for viral entry into CD4+ immune cells. During infection, Env also serves as a primary target for antibody responses, which are robust but unable to control virus replication. Immune evasion by HIV-1 Env appears to employ complex mechanisms to regulate what antigenic states are presented to the immune system. Immunodominant features appear to be distinct from epitopes that interfere with Env functions in mediating infection. Further, cell-cell transmission studies indicate that vulnerable conformational states are additionally hidden from recognition on infected cells, even though the presence of Env at the cell surface is required for viral infection through the virological synapse. Cell-cell infection studies support that Env on infected cells is presented in distinct conformations from that on virus particles. Here we review data regarding the regulation of conformational states of Env and assess how regulated sorting of Env within the infected cell may underlie mechanisms to distinguish Env on the surface of virus particles versus Env on the surface of infected cells. These mechanisms may allow infected cells to avoid opsonization, providing cell-to-cell infection by HIV with a selective advantage during evolution within an infected individual. Understanding how distinct Env conformations are presented on cells versus viruses may be essential to designing effective vaccine approaches and therapeutic strategies to clear infected cell reservoirs.
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Affiliation(s)
- Connie Zhao
- Department of Medicine, Icahn School of Medicine at Mount Sinai, New York, New York, USA
| | - Hongru Li
- Division of Infectious Diseases, Department of Medicine, Icahn School of Medicine at Mount Sinai, New York, New York, USA
| | - Talia H. Swartz
- Division of Infectious Diseases, Department of Medicine, Icahn School of Medicine at Mount Sinai, New York, New York, USA
| | - Benjamin K. Chen
- Division of Infectious Diseases, Department of Medicine, Icahn School of Medicine at Mount Sinai, New York, New York, USA
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7
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Segredo-Otero E, Sanjuán R. The role of spatial structure in the evolution of viral innate immunity evasion: A diffusion-reaction cellular automaton model. PLoS Comput Biol 2020; 16:e1007656. [PMID: 32040504 PMCID: PMC7034925 DOI: 10.1371/journal.pcbi.1007656] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/19/2019] [Revised: 02/21/2020] [Accepted: 01/14/2020] [Indexed: 12/20/2022] Open
Abstract
Most viruses have evolved strategies for preventing interferon (IFN) secretion and evading innate immunity. Recent work has shown that viral shutdown of IFN secretion can be viewed as a social trait, since the ability of a given virus to evade IFN-mediated immunity depends on the phenotype of neighbor viruses. Following this idea, we investigate the role of spatial structure in the evolution of innate immunity evasion. For this, we model IFN signaling and viral spread using a spatially explicit approximation that combines a diffusion-reaction model and cellular automaton. Our results indicate that the benefits of preventing IFN secretion for a virus are strongly determined by spatial structure through paracrine IFN signaling. Therefore, innate immunity evasion can evolve as a cooperative or even altruistic trait based on indirect fitness effects that IFN shutdown exerts on other members of the viral population. We identify key factors determining whether evasion from IFN-mediated immunity should evolve, such as population bottlenecks occurring during viral transmission, the relative speed of cellular infection and IFN secretion, and the diffusion properties of the medium.
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Affiliation(s)
- Ernesto Segredo-Otero
- Institute for Integrative Systems Biology (I2SysBio), Consejo Superior de Investigaciones Científicas-Universitat de València, València, Spain
| | - Rafael Sanjuán
- Institute for Integrative Systems Biology (I2SysBio), Consejo Superior de Investigaciones Científicas-Universitat de València, València, Spain
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8
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Sardanyés J, Piñero J, Solé R. Habitat loss‐induced tipping points in metapopulations with facilitation. POPUL ECOL 2019. [DOI: 10.1002/1438-390x.12020] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/11/2022]
Affiliation(s)
- Josep Sardanyés
- Centre de Recerca Matemàtica Campus de Bellaterra Bellaterra Spain
- Barcelona Graduate School of Mathematics (BGSMath) Campus de Bellaterra Bellaterra Spain
| | - Jordi Piñero
- ICREA‐Complex Systems Lab, Department of Experimental and Health Sciences Universitat Pompeu Fabra Barcelona Spain
- Institut de Biologia Evolutiva (CSIC‐Universitat Pompeu Fabra) Barcelona Spain
| | - Ricard Solé
- ICREA‐Complex Systems Lab, Department of Experimental and Health Sciences Universitat Pompeu Fabra Barcelona Spain
- Institut de Biologia Evolutiva (CSIC‐Universitat Pompeu Fabra) Barcelona Spain
- Santa Fe Institute Santa Fe New Mexico
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9
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Koelle K, Farrell AP, Brooke CB, Ke R. Within-host infectious disease models accommodating cellular coinfection, with an application to influenza. Virus Evol 2019; 5:vez018. [PMID: 31304043 PMCID: PMC6613536 DOI: 10.1093/ve/vez018] [Citation(s) in RCA: 27] [Impact Index Per Article: 5.4] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/25/2023] Open
Abstract
Within-host models are useful tools for understanding the processes regulating viral load dynamics. While existing models have considered a wide range of within-host processes, at their core these models have shown remarkable structural similarity. Specifically, the structure of these models generally consider target cells to be either uninfected or infected, with the possibility of accommodating further resolution (e.g. cells that are in an eclipse phase). Recent findings, however, indicate that cellular coinfection is the norm rather than the exception for many viral infectious diseases, and that cells with high multiplicity of infection are present over at least some duration of an infection. The reality of these cellular coinfection dynamics is not accommodated in current within-host models although it may be critical for understanding within-host dynamics. This is particularly the case if multiplicity of infection impacts infected cell phenotypes such as their death rate and their viral production rates. Here, we present a new class of within-host disease models that allow for cellular coinfection in a scalable manner by retaining the low-dimensionality that is a desirable feature of many current within-host models. The models we propose adopt the general structure of epidemiological ‘macroparasite’ models that allow hosts to be variably infected by parasites such as nematodes and host phenotypes to flexibly depend on parasite burden. Specifically, our within-host models consider target cells as ‘hosts’ and viral particles as ‘macroparasites’, and allow viral output and infected cell lifespans, among other phenotypes, to depend on a cell’s multiplicity of infection. We show with an application to influenza that these models can be statistically fit to viral load and other within-host data, and demonstrate using model selection approaches that they have the ability to outperform traditional within-host viral dynamic models. Important in vivo quantities such as the mean multiplicity of cellular infection and time-evolving reassortant frequencies can also be quantified in a straightforward manner once these macroparasite models have been parameterized. The within-host model structure we develop here provides a mathematical way forward to address questions related to the roles of cellular coinfection, collective viral interactions, and viral complementation in within-host viral dynamics and evolution.
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Affiliation(s)
- Katia Koelle
- Department of Biology, Emory University, 1510 Clifton Rd #2006, Atlanta, GA, USA
| | - Alex P Farrell
- Department of Mathematics, North Carolina State University, 2311 Stinson Dr, Raleigh, NC, USA.,Department of Mathematics, University of Arizona, 617 N Santa Rita Ave, Tucson, AZ, USA
| | - Christopher B Brooke
- Department of Microbiology, University of Illinois at Urbana-Champaign, 601 S. Goodwin Ave, IL, USA.,Carl R. Woese Institute for Genomic Biology, University of Illinois at Urbana-Champaign, 601 S. Goodwin Ave, IL, USA
| | - Ruian Ke
- Department of Mathematics, North Carolina State University, 2311 Stinson Dr, Raleigh, NC, USA.,Comparative Medicine Institute, North Carolina State University, Raleigh, NC, USA
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10
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Wodarz D, Levy DN, Komarova NL. Multiple infection of cells changes the dynamics of basic viral evolutionary processes. Evol Lett 2018; 3:104-115. [PMID: 30788146 PMCID: PMC6369963 DOI: 10.1002/evl3.95] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/12/2018] [Accepted: 11/02/2018] [Indexed: 12/27/2022] Open
Abstract
The infection of cells by multiple copies of a given virus can impact viral evolution in a variety of ways, yet some of the most basic evolutionary dynamics remain underexplored. Using computational models, we investigate how infection multiplicity affects the fixation probability of mutants, the rate of mutant generation, and the timing of mutant invasion. An important insight from these models is that for neutral and disadvantageous phenotypes, rare mutants initially enjoy a fitness advantage in the presence of multiple infection of cells. This arises because multiple infection allows the rare mutant to enter more target cells and to spread faster, while it does not accelerate the spread of the resident wild-type virus. The rare mutant population can increase by entry into both uninfected and wild-type-infected cells, while the established wild-type population can initially only grow through entry into uninfected cells. Following this initial advantageous phase, the dynamics are governed by drift or negative selection, respectively, and a higher multiplicity reduces the chances that mutants fix in the population. Hence, while increased infection multiplicity promotes the presence of neutral and disadvantageous mutants in the short-term, it makes it less likely in the longer term. We show how these theoretical insights can be useful for the interpretation of experimental data on virus evolution at low and high multiplicities. The dynamics explored here provide a basis for the investigation of more complex viral evolutionary processes, including recombination, reassortment, as well as complementary/inhibitory interactions.
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Affiliation(s)
- Dominik Wodarz
- Department of Ecology and Evolutionary Biology, 321 Steinhaus Hall University of California Irvine CA 92697.,Department of Mathematics, Rowland Hall University of California Irvine CA 92697
| | - David N Levy
- Department of Basic Science, 921 Schwartz Building New York University College of Dentistry New York NY 10010
| | - Natalia L Komarova
- Department of Ecology and Evolutionary Biology, 321 Steinhaus Hall University of California Irvine CA 92697.,Department of Mathematics, Rowland Hall University of California Irvine CA 92697
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11
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Number of infection events per cell during HIV-1 cell-free infection. Sci Rep 2017; 7:6559. [PMID: 28747624 PMCID: PMC5529392 DOI: 10.1038/s41598-017-03954-9] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/18/2016] [Accepted: 05/09/2017] [Indexed: 12/15/2022] Open
Abstract
HIV-1 accumulates changes in its genome through both recombination and mutation during the course of infection. For recombination to occur, a single cell must be infected by two HIV strains. These coinfection events were experimentally demonstrated to occur more frequently than would be expected for independent infection events and do not follow a random distribution. Previous mathematical modeling approaches demonstrated that differences in target cell susceptibility can explain the non-randomness, both in the context of direct cell-to-cell transmission, and in the context of free virus transmission (Q. Dang et al., Proc. Natl. Acad. Sci. USA 101:632-7, 2004: K. M. Law et al., Cell reports 15:2711-83, 2016). Here, we build on these notions and provide a more detailed and extensive quantitative framework. We developed a novel mathematical model explicitly considering the heterogeneity of target cells and analysed datasets of cell-free HIV-1 single and double infection experiments in cell culture. Particularly, in contrast to the previous studies, we took into account the different susceptibility of the target cells as a continuous distribution. Interestingly, we showed that the number of infection events per cell during cell-free HIV-1 infection follows a negative-binomial distribution, and our model reproduces these datasets.
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12
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WANG XIYING, LIU XINZHI, XU WEI, XIE WEICHAU, LIU WANPING. THE DYNAMICS OF HIV MODELS WITH SWITCHING PARAMETERS AND PULSE CONTROL. J BIOL SYST 2017. [DOI: 10.1142/s0218339016500200] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022]
Abstract
This paper studies some human immunodeficiency virus (HIV) models with switching parameters and pulse control. The classical virus dynamics model is first modified by incorporating switching parameters which are assumed to be time-varying. Some threshold conditions are derived to guarantee the virus elimination by utilizing a Razumikhin-type approach. The results show that the proper switching conditions chosen can increase the counts of CD4+T-cells while reducing viral load. Pulse control strategies are then applied to the above model. More precisely, the treatment strategy and the vaccination strategy are applied to infected cells and uninfected cells, respectively. Each control strategy is analyzed to gauge its success in achieving viral suppression. Numerical simulations are performed to complement the analytical results and motivate future directions.
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Affiliation(s)
- XIYING WANG
- Department of Mathematics and Statistics, Zhoukou Normal University, Zhoukou, Henan 466001, P. R. China
- Department of Applied Mathematics, University of Waterloo, Waterloo, Ontario Canada, N2L 3G1, Canada
| | - XINZHI LIU
- Department of Applied Mathematics, University of Waterloo, Waterloo, Ontario Canada, N2L 3G1, Canada
| | - WEI XU
- Department of Applied Mathematics, Northwestern Polytechnical University, Xi’an, Shaanxi, 710072, P. R. China
| | - WEI-CHAU XIE
- Department of Civil and Environmental Engineering, University of Waterloo, Waterloo, Ontario Canada, N2L 3G1, Canada
| | - WANPING LIU
- College of Computer Science and Engineering, Chongqing University of Technology, Chongqing 400054, P. R. China
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13
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Law KM, Komarova NL, Yewdall AW, Lee RK, Herrera OL, Wodarz D, Chen BK. In Vivo HIV-1 Cell-to-Cell Transmission Promotes Multicopy Micro-compartmentalized Infection. Cell Rep 2016; 15:2771-83. [PMID: 27292632 DOI: 10.1016/j.celrep.2016.05.059] [Citation(s) in RCA: 61] [Impact Index Per Article: 7.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/17/2016] [Revised: 04/07/2016] [Accepted: 05/15/2016] [Indexed: 02/03/2023] Open
Abstract
HIV-1 infection is enhanced by adhesive structures that form between infected and uninfected T cells called virological synapses (VSs). This mode of transmission results in the frequent co-transmission of multiple copies of HIV-1 across the VS, which can reduce sensitivity to antiretroviral drugs. Studying HIV-1 infection of humanized mice, we measured the frequency of co-transmission and the spatiotemporal organization of infected cells as indicators of cell-to-cell transmission in vivo. When inoculating mice with cells co-infected with two viral genotypes, we observed high levels of co-transmission to target cells. Additionally, micro-anatomical clustering of viral genotypes within lymphoid tissue indicates that viral spread is driven by local processes and not a diffuse viral cloud. Intravital splenic imaging reveals that anchored HIV-infected cells induce arrest of interacting, uninfected CD4(+) T cells to form Env-dependent cell-cell conjugates. These findings suggest that HIV-1 spread between immune cells can be anatomically localized into infectious clusters.
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Affiliation(s)
- Kenneth M Law
- Division of Infectious Disease, Department of Medicine, Icahn School of Medicine at Mount Sinai, New York, NY 10029, USA; Immunology Institute, Icahn School of Medicine at Mount Sinai, New York, NY 10029, USA
| | - Natalia L Komarova
- Department of Ecology and Evolutionary Biology and Department of Mathematics, University of California, Irvine, Irvine, CA 92697, USA
| | - Alice W Yewdall
- Division of Infectious Disease, Department of Medicine, Icahn School of Medicine at Mount Sinai, New York, NY 10029, USA; Immunology Institute, Icahn School of Medicine at Mount Sinai, New York, NY 10029, USA
| | - Rebecca K Lee
- Division of Infectious Disease, Department of Medicine, Icahn School of Medicine at Mount Sinai, New York, NY 10029, USA; Immunology Institute, Icahn School of Medicine at Mount Sinai, New York, NY 10029, USA
| | - Olga L Herrera
- Division of Infectious Disease, Department of Medicine, Icahn School of Medicine at Mount Sinai, New York, NY 10029, USA; Immunology Institute, Icahn School of Medicine at Mount Sinai, New York, NY 10029, USA
| | - Dominik Wodarz
- Department of Ecology and Evolutionary Biology and Department of Mathematics, University of California, Irvine, Irvine, CA 92697, USA
| | - Benjamin K Chen
- Division of Infectious Disease, Department of Medicine, Icahn School of Medicine at Mount Sinai, New York, NY 10029, USA; Immunology Institute, Icahn School of Medicine at Mount Sinai, New York, NY 10029, USA; Department of Microbiology, Icahn School of Medicine at Mount Sinai, New York, NY 10029, USA.
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14
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Graw F, Martin DN, Perelson AS, Uprichard SL, Dahari H. Quantification of Hepatitis C Virus Cell-to-Cell Spread Using a Stochastic Modeling Approach. J Virol 2015; 89:6551-61. [PMID: 25833046 PMCID: PMC4468510 DOI: 10.1128/jvi.00016-15] [Citation(s) in RCA: 24] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/08/2015] [Accepted: 03/24/2015] [Indexed: 12/21/2022] Open
Abstract
UNLABELLED It has been proposed that viral cell-to-cell transmission plays a role in establishing and maintaining chronic infections. Thus, understanding the mechanisms and kinetics of cell-to-cell spread is fundamental to elucidating the dynamics of infection and may provide insight into factors that determine chronicity. Because hepatitis C virus (HCV) spreads from cell to cell and has a chronicity rate of up to 80% in exposed individuals, we examined the dynamics of HCV cell-to-cell spread in vitro and quantified the effect of inhibiting individual host factors. Using a multidisciplinary approach, we performed HCV spread assays and assessed the appropriateness of different stochastic models for describing HCV focus expansion. To evaluate the effect of blocking specific host cell factors on HCV cell-to-cell transmission, assays were performed in the presence of blocking antibodies and/or small-molecule inhibitors targeting different cellular HCV entry factors. In all experiments, HCV-positive cells were identified by immunohistochemical staining and the number of HCV-positive cells per focus was assessed to determine focus size. We found that HCV focus expansion can best be explained by mathematical models assuming focus size-dependent growth. Consistent with previous reports suggesting that some factors impact HCV cell-to-cell spread to different extents, modeling results estimate a hierarchy of efficacies for blocking HCV cell-to-cell spread when targeting different host factors (e.g., CLDN1 > NPC1L1 > TfR1). This approach can be adapted to describe focus expansion dynamics under a variety of experimental conditions as a means to quantify cell-to-cell transmission and assess the impact of cellular factors, viral factors, and antivirals. IMPORTANCE The ability of viruses to efficiently spread by direct cell-to-cell transmission is thought to play an important role in the establishment and maintenance of viral persistence. As such, elucidating the dynamics of cell-to-cell spread and quantifying the effect of blocking the factors involved has important implications for the design of potent antiviral strategies and controlling viral escape. Mathematical modeling has been widely used to understand HCV infection dynamics and treatment response; however, these models typically assume only cell-free virus infection mechanisms. Here, we used stochastic models describing focus expansion as a means to understand and quantify the dynamics of HCV cell-to-cell spread in vitro and determined the degree to which cell-to-cell spread is reduced when individual HCV entry factors are blocked. The results demonstrate the ability of this approach to recapitulate and quantify cell-to-cell transmission, as well as the impact of specific factors and potential antivirals.
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Affiliation(s)
- Frederik Graw
- Center for Modeling and Simulation in the Biosciences, BioQuant Center, Heidelberg University, Heidelberg, Germany
| | - Danyelle N Martin
- Program for Experimental and Theoretical Modeling, Division of Hepatology, Department of Medicine, Loyola University Medical Center, Maywood, Illinois, USA
| | - Alan S Perelson
- Theoretical Biology and Biophysics, Los Alamos National Laboratory, Los Alamos, New Mexico, USA
| | - Susan L Uprichard
- Program for Experimental and Theoretical Modeling, Division of Hepatology, Department of Medicine, Loyola University Medical Center, Maywood, Illinois, USA Department of Microbiology and Immunology, Loyola University Medical Center, Maywood, Illinois, USA
| | - Harel Dahari
- Program for Experimental and Theoretical Modeling, Division of Hepatology, Department of Medicine, Loyola University Medical Center, Maywood, Illinois, USA Theoretical Biology and Biophysics, Los Alamos National Laboratory, Los Alamos, New Mexico, USA
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15
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Phan D, Wodarz D. Modeling multiple infection of cells by viruses: Challenges and insights. Math Biosci 2015; 264:21-8. [PMID: 25770053 DOI: 10.1016/j.mbs.2015.03.001] [Citation(s) in RCA: 16] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/30/2014] [Revised: 02/26/2015] [Accepted: 03/03/2015] [Indexed: 11/17/2022]
Abstract
The multiple infection of cells with several copies of a given virus has been demonstrated in experimental systems, and has been subject to previous mathematical modeling approaches. Such models, especially those based on ordinary differential equations, can be characterized by difficulties and pitfalls. One such difficulty arises from what we refer to as multiple infection cascades. That is, such models subdivide the infected cell population into sub-populations that are carry i viruses, and each sub-population can in principle always be further infected to contain i + 1 viruses. In order to study the model with numerical simulations, the infection cascade needs to be cut artificially, and this can influence the results. This is shown here in the context of the simplest setting that involves a single, homogeneous virus population. If the viral replication rate is sufficiently fast, then most infected cells will accumulate in the last member of the infection cascade, leading to incorrect numerical results. This can be observed even with relatively long infection cascades, and in this case computational costs associated with a sufficiently long infection cascade can render this approach impractical. We subsequently examine a more complex scenario where two virus types/strains with different fitness are allowed to compete. Again, we find that the length of the infection cascade can have a crucial influence on the results. Competitive exclusion can be observed for shorter infection cascades, while coexistence can be observed for longer infection cascades. More subtly, the length of the infection cascade can influence the equilibrium level of the populations in numerical simulations. Studying the model in a parameter regime where an increase in the infection cascade length does not influence the results, we examine the effect of multiple infection on the outcome of competition. We find that multiple infection can promote coexistence of virus types if there is a degree of intracellular niche separation. If this is not the case, the only outcome is competitive exclusion, similar to equivalent models that do not take into account multiple infection of cells. We further find that multiple infection has a reduced ability to allow coexistence if virus spread is spatially restricted compared to a well-mixed system. These results provide important insights when analyzing and interpreting multiple infection models.
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Affiliation(s)
- Dustin Phan
- Department of Ecology and Evolutionary Biology, 321 Steinhaus Hall, University of California, Irvine, CA 92617, United States
| | - Dominik Wodarz
- Department of Ecology and Evolutionary Biology, 321 Steinhaus Hall, University of California, Irvine, CA 92617, United States.
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16
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Abstract
This review outlines how mathematical models have been helpful, and continue to be so, for obtaining insights into the in vivo dynamics of HIV infection. The review starts with a discussion of a basic mathematical model that has been frequently used to study HIV dynamics. Some crucial results are described, including the estimation of key parameters that characterize the infection, and the generation of influential theories which argued that in vivo virus evolution is a key player in HIV pathogenesis. Subsequently, more recent concepts are reviewed that have relevance for disease progression, including the multiple infection of cells and the direct cell-to-cell transmission of the virus through the formation of virological synapses. These are important mechanisms that can influence the rate at which HIV spreads through its target cell population, which is tightly linked to the rate at which the disease progresses towards AIDS.
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Affiliation(s)
- Dominik Wodarz
- Department of Ecology and Evolutionary Biology, University of California, 321 Steinhaus Hall, Irvine, CA, 926967, USA,
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17
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Komarova NL, Levy DN, Wodarz D. Synaptic transmission and the susceptibility of HIV infection to anti-viral drugs. Sci Rep 2013; 3:2103. [PMID: 23811684 PMCID: PMC3696900 DOI: 10.1038/srep02103] [Citation(s) in RCA: 30] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/15/2012] [Accepted: 05/30/2013] [Indexed: 12/24/2022] Open
Abstract
Cell-to-cell viral transmission via virological synapses has been argued to reduce susceptibility of the virus population to anti-viral drugs through multiple infection of cells, contributing to low-level viral persistence during therapy. Using a mathematical framework, we examine the role of synaptic transmission in treatment susceptibility. A key factor is the relative probability of individual virions to infect a cell during free-virus and synaptic transmission, a currently unknown quantity. If this infection probability is higher for free-virus transmission, then treatment susceptibility is lowest if one virus is transferred per synapse, and multiple infection of cells increases susceptibility. In the opposite case, treatment susceptibility is minimized for an intermediate number of virions transferred per synapse. Hence, multiple infection via synapses does not simply lower treatment susceptibility. Without further experimental investigations, one cannot conclude that synaptic transmission provides an additional mechanism for the virus to persist at low levels during anti-viral therapy.
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Affiliation(s)
- Natalia L Komarova
- Department of Mathematics, Rowland Hall, University of California, Irvine, CA 92697, USA
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18
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Komarova NL, Wodarz D. Virus dynamics in the presence of synaptic transmission. Math Biosci 2013; 242:161-71. [PMID: 23357287 PMCID: PMC4122664 DOI: 10.1016/j.mbs.2013.01.003] [Citation(s) in RCA: 52] [Impact Index Per Article: 4.7] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/19/2012] [Revised: 01/03/2013] [Accepted: 01/11/2013] [Indexed: 11/16/2022]
Abstract
Traditionally, virus dynamics models consider populations of infected and target cells, and a population of free virus that can infect susceptible cells. In recent years, however, it has become. clear that direct cell-to-cell transmission can also play an important role for the in vivo spread of viruses, especially retroviruses such as human T lymphotropic virus-1 (HTLV-1) and Human immunodeficiency virus (HIV). Such cell-to-cell transmission is thought to occur through the formation of virological synapses that are formed between an infected source cell and a susceptible target cell. Here we formulate and analyze a class of virus dynamics models that include such cell-cell synaptic transmission. We explore different "strategies" of the virus defined by the number of viruses passed per synapse, and determine how the choice of strategy influences the basic reproductive ratio, R0, of the virus and thus its ability to establish a persistent infection. We show that depending on specific assumptions about the viral kinetics, strategies with low or intermediate numbers of viruses transferred may correspond to the highest values of R0. We also explore the evolutionary competition of viruses of different strains, which differ by their synaptic strategy, and show that viruses characterized by synaptic strategies with the highest R0 win the evolutionary competition and exclude other, inferior, strains.
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Affiliation(s)
- Natalia L Komarova
- Department of Mathematics, University of California Irvine, Irvine, CA 92697, USA
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19
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Dunia R, Bonnecaze R. Mathematical modeling of viral infection dynamics in spherical organs. J Math Biol 2012; 67:1425-55. [DOI: 10.1007/s00285-012-0593-y] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/16/2011] [Revised: 09/06/2012] [Indexed: 01/22/2023]
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20
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Ojosnegros S, Delgado-Eckert E, Beerenwinkel N. Competition-colonization trade-off promotes coexistence of low-virulence viral strains. J R Soc Interface 2012; 9:2244-54. [PMID: 22513722 DOI: 10.1098/rsif.2012.0160] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/12/2022] Open
Abstract
RNA viruses exist as genetically diverse populations displaying a range of virulence degrees. The evolution of virulence in viral populations is, however, poorly understood. On the basis of the experimental observation of an RNA virus clone in cell culture diversifying into two subpopulations of different virulence, we study the dynamics of mutating virus populations with varying virulence. We introduce a competition-colonization trade-off into standard mathematical models of intra-host viral infection. Colonizers are fast-spreading virulent strains, whereas the competitors are less-virulent variants but more successful within co-infected cells. We observe a two-step dynamics of the population. Early in the infection, the population is dominated by colonizers, which later are outcompeted by competitors. Our simulations suggest the existence of steady state in which all virulence classes coexist but are dominated by the most competitive ones. This equilibrium implies collective virulence attenuation in the population, in contrast to previous models predicting evolution of the population towards increased virulence.
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Affiliation(s)
- Samuel Ojosnegros
- Department of Biosystems Science and Engineering, ETH Zurich, Basel, Switzerland.
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21
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Cummings KW, Levy DN, Wodarz D. Increased burst size in multiply infected cells can alter basic virus dynamics. Biol Direct 2012; 7:16. [PMID: 22569346 PMCID: PMC3482397 DOI: 10.1186/1745-6150-7-16] [Citation(s) in RCA: 17] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/07/2011] [Accepted: 03/08/2012] [Indexed: 11/10/2022] Open
Abstract
BACKGROUND The dynamics of viral infections have been studied extensively in a variety of settings, both experimentally and with mathematical models. The majority of mathematical models assumes that only one virus can infect a given cell at a time. It is, however, clear that especially in the context of high viral load, cells can become infected with multiple copies of a virus, a process called coinfection. This has been best demonstrated experimentally for human immunodeficiency virus (HIV), although it is thought to be equally relevant for a number of other viral infections. In a previously explored mathematical model, the viral output from an infected cell does not depend on the number of viruses that reside in the cell, i.e. viral replication is limited by cellular rather than viral factors. In this case, basic virus dynamics properties are not altered by coinfection. RESULTS Here, we explore the alternative assumption that multiply infected cells are characterized by an increased burst size and find that this can fundamentally alter model predictions. Under this scenario, establishment of infection may not be solely determined by the basic reproductive ratio of the virus, but can depend on the initial virus load. Upon infection, the virus population need not follow straight exponential growth. Instead, the exponential rate of growth can increase over time as virus load becomes larger. Moreover, the model suggests that the ability of anti-viral drugs to suppress the virus population can depend on the virus load upon initiation of therapy. This is because more coinfected cells, which produce more virus, are present at higher virus loads. Hence, the degree of drug resistance is not only determined by the viral genotype, but also by the prevalence of coinfected cells. CONCLUSIONS Our work shows how an increased burst size in multiply infected cells can alter basic infection dynamics. This forms the basis for future experimental testing of model assumptions and predictions that can distinguish between the different scenarios.
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Affiliation(s)
- Kara W Cummings
- Department of Ecology and Evolutionary Biology, University of California, 321 Steinhaus Hall, 92617, Irvine, CA, USA
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22
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Althaus CL, De Boer RJ. Impaired immune evasion in HIV through intracellular delays and multiple infection of cells. Proc Biol Sci 2012; 279:3003-10. [PMID: 22492063 DOI: 10.1098/rspb.2012.0328] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/12/2022] Open
Abstract
With its high mutation rate, HIV is capable of escape from recognition, suppression and/or killing by CD8(+) cytotoxic T lymphocytes (CTLs). The rate at which escape variants replace each other can give insights into the selective pressure imposed by single CTL clones. We investigate the effects of specific characteristics of the HIV life cycle on the dynamics of immune escape. First, it has been found that cells in HIV-infected patients can carry multiple copies of proviruses. To investigate how this process affects the emergence of immune escape, we develop a mathematical model of HIV dynamics with multiple infections of cells. Increasing the frequency of multiple-infected cells delays the appearance of immune escape variants, slows down the rate at which they replace the wild-type variant and can even prevent escape variants from taking over the quasi-species. Second, we study the effect of the intracellular eclipse phase on the rate of escape and show that escape rates are expected to be slower than previously anticipated. In summary, slow escape rates do not necessarily imply inefficient CTL-mediated killing of HIV-infected cells, but are at least partly a result of the specific characteristics of the viral life cycle.
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Affiliation(s)
- Christian L Althaus
- Theoretical Biology and Bioinformatics, Utrecht University, 3584 CH Utrecht, The Netherlands.
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23
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Duncan CJA, Sattentau QJ. Viral determinants of HIV-1 macrophage tropism. Viruses 2011; 3:2255-79. [PMID: 22163344 PMCID: PMC3230851 DOI: 10.3390/v3112255] [Citation(s) in RCA: 44] [Impact Index Per Article: 3.4] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/16/2011] [Revised: 11/04/2011] [Accepted: 11/04/2011] [Indexed: 01/23/2023] Open
Abstract
Macrophages are important target cells for HIV-1 infection that play significant roles in the maintenance of viral reservoirs and other aspects of pathogenesis. Understanding the determinants of HIV-1 tropism for macrophages will inform HIV-1 control and eradication strategies. Tropism for macrophages is both qualitative (infection or not) and quantitative (replication capacity). For example many R5 HIV-1 isolates cannot infect macrophages, but for those that can the macrophage replication capacity can vary by up to 1000-fold. Some X4 viruses are also capable of replication in macrophages, indicating that cellular tropism is partially independent of co-receptor preference. Preliminary data obtained with a small number of transmitted/founder viruses indicate inefficient macrophage infection, whereas isolates from later in disease are more frequently tropic for macrophages. Thus tropism may evolve over time, and more macrophage tropic viruses may be implicated in the pathogenesis of advanced HIV-1 infection. Compartmentalization of macrophage-tropic brain-derived envelope glycoproteins (Envs), and non-macrophage tropic non-neural tissue-derived Envs points to adaptation of HIV-1 quasi-species in distinct tissue microenvironments. Mutations within and adjacent to the Env-CD4 binding site have been identified that determine macrophage tropism at the entry level, but post-entry molecular determinants of macrophage replication capacity involving HIV-1 accessory proteins need further definition.
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24
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Sattentau QJ. The direct passage of animal viruses between cells. Curr Opin Virol 2011; 1:396-402. [PMID: 22440841 DOI: 10.1016/j.coviro.2011.09.004] [Citation(s) in RCA: 43] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/31/2011] [Accepted: 09/20/2011] [Indexed: 11/28/2022]
Abstract
The paradigm that viruses can move directly, and in some cases covertly, between contacting target cells is now well established for several virus families. The underlying mechanisms of cell-to-cell spread, however, remain to be fully elucidated and may differ substantially depending on the viral exit/entry route and the cellular tropism. Here, two divergent cell-to-cell spread mechanisms are exemplified: firstly by human retroviruses, which rely upon transient adhesive structures that form between polarized immune cells termed virological synapses, and secondly by herpesviruses that depend predominantly on pre-existing stable cellular contacts, but may also form virological synapses. Plant viruses can also spread directly between contacting cells, but are obliged by the rigid host cell wall to move across pore structures termed plasmodesmata. This review will focus primarily on recent advances in our understanding of animal virus cell-to-cell spread using examples from these two virus families, and will conclude by comparing and contrasting the cell-to-cell spread of animal and plant viruses.
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Affiliation(s)
- Quentin J Sattentau
- The Sir William Dunn School of Pathology, The University of Oxford, Oxford OX13RE, UK.
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25
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Abstract
During cell-to-cell transmission of human immunodeficiency virus type 1 (HIV-1), many viral particles can be simultaneously transferred from infected to uninfected CD4 T cells through structures called virological synapses (VS). Here we directly examine how cell-free and cell-to-cell infections differ from infections initiated with cell-free virus in the number of genetic copies that are transmitted from one generation to the next, i.e., the genetic inheritance. Following exposure to HIV-1-expressing cells, we show that target cells with high viral uptake are much more likely to become infected. Using T cells that coexpress distinct fluorescent HIV-1 variants, we show that multiple copies of HIV-1 can be cotransmitted across a single VS. In contrast to cell-free HIV-1 infection, which titrates with Poisson statistics, the titration of cell-associated HIV-1 to low rates of overall infection generates a constant fraction of the newly infected cells that are cofluorescent. Triple infection was also readily detected when cells expressing three fluorescent viruses were used as donor cells. A computational model and a statistical model are presented to estimate the degree to which cofluorescence underestimates coinfection frequency. Lastly, direct detection of HIV-1 proviruses using fluorescence in situ hybridization confirmed that significantly more HIV-1 DNA copies are found in primary T cells infected with cell-associated virus than in those infected with cell-free virus. Together, the data suggest that multiploid inheritance is common during cell-to-cell HIV-1 infection. From this study, we suggest that cell-to-cell infection may explain the high copy numbers of proviruses found in infected cells in vivo and may provide a mechanism through which HIV preserves sequence heterogeneity in viral quasispecies through genetic complementation.
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