{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,28]],"date-time":"2026-03-28T19:21:54Z","timestamp":1774725714215,"version":"3.50.1"},"reference-count":61,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2017,1,10]],"date-time":"2017-01-10T00:00:00Z","timestamp":1484006400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100006769","name":"Russian Science Foundation","doi-asserted-by":"publisher","award":["15-11-00029"],"award-info":[{"award-number":["15-11-00029"]}],"id":[{"id":"10.13039\/501100006769","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Computation"],"abstract":"<jats:p>Human Immunodeficiency Virus (HIV) infection of humans represents a complex biological system and a great challenge to public health. Novel approaches for the analysis and prediction of the infection dynamics based on a multi-scale integration of virus ontogeny and immune reactions are needed to deal with the systems\u2019 complexity. The aim of our study is: (1) to formulate a multi-scale mathematical model of HIV infection; (2) to implement the model computationally following a hybrid approach; and (3) to calibrate the model by estimating the parameter values enabling one to reproduce the \u201cstandard\u201d observed dynamics of HIV infection in blood during the acute phase of primary infection. The modeling approach integrates the processes of infection spread and immune responses in Lymph Nodes (LN) to that observed in blood. The spatio-temporal population dynamics of T lymphocytes in LN in response to HIV infection is governed by equations linking an intracellular regulation of the lymphocyte fate by intercellular cytokine fields. We describe the balance of proliferation, differentiation and death at a single cell level as a consequence of gene activation via multiple signaling pathways activated by IL-2, IFNa and FasL. Distinct activation thresholds are used in the model to relate different modes of cellular responses to the hierarchy of the relative levels of the cytokines. We specify a reference set of model parameter values for the fundamental processes in lymph nodes that ensures a reasonable agreement with viral load and CD4+ T cell dynamics in blood.<\/jats:p>","DOI":"10.3390\/computation5010006","type":"journal-article","created":{"date-parts":[[2017,1,10]],"date-time":"2017-01-10T10:16:18Z","timestamp":1484043378000},"page":"6","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":21,"title":["Towards a Multiscale Model of Acute HIV Infection"],"prefix":"10.3390","volume":"5","author":[{"given":"Anass","family":"Bouchnita","sequence":"first","affiliation":[{"name":"Institut Camille Jordan, UMR 5208 CNRS, University Lyon, 69622 Lyon, France"},{"name":"Laboratoire de Biom\u00e9trie et Biologie Evolutive, UMR 5558, University Lyon, 69622 Lyon, France"},{"name":"Mohammadia School of Engineering, University Mohamed V, 10106 Rabat, Morocco"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5049-0656","authenticated-orcid":false,"given":"Gennady","family":"Bocharov","sequence":"additional","affiliation":[{"name":"Institute of Numerical Mathematics, Russian Academy of Sciences, 119333 Moscow, Russia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0620-5317","authenticated-orcid":false,"given":"Andreas","family":"Meyerhans","sequence":"additional","affiliation":[{"name":"Institute of Numerical Mathematics, Russian Academy of Sciences, 119333 Moscow, Russia"},{"name":"Infection Biology Laboratory, Universitat Pompeu Fabra and ICREA, Pg. Llu\u00eds Companys 23, 08010 Barcelona, Spain"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Vitaly","family":"Volpert","sequence":"additional","affiliation":[{"name":"Institut Camille Jordan, UMR 5208 CNRS, University Lyon, 69622 Lyon, France"},{"name":"Institute of Numerical Mathematics, Russian Academy of Sciences, 119333 Moscow, Russia"},{"name":"INRIA Team Dracula, INRIA Lyon La Doua, 69603 Villeurbanne, France"},{"name":"Laboratoire Poncelet, UMI 2615 CNRS, 119002 Moscow, Russia"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2017,1,10]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Levy, J.A. (2007). HIV and the Pathogenesis of AIDS, ASN Press. [3rd ed.].","DOI":"10.1128\/9781555815653"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"289","DOI":"10.1038\/nm1380","article-title":"Pathogenesis of HIV infection: What the virus spares is as important as what it destroys","volume":"12","author":"Grossman","year":"2006","journal-title":"Nat. Med."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"319","DOI":"10.1038\/nm0402-319","article-title":"CD4+ T cell depletion in HIV infection: Are we closer to understanding the cause?","volume":"8","author":"Grossman","year":"2002","journal-title":"Nat. Med."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"282","DOI":"10.3109\/08830185.2013.779375","article-title":"Pathogenesis and treatment of HIV infection: The cellular, the immune system and the neuroendocrine systems perspective","volume":"32","author":"Chereshnev","year":"2013","journal-title":"Int. Rev. Immunol."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"614","DOI":"10.1016\/S1473-3099(13)70043-4","article-title":"The search for an HIV cure: Tackling latent infection","volume":"13","author":"Kent","year":"2013","journal-title":"Lancet Infect. Dis."},{"key":"ref_6","doi-asserted-by":"crossref","unstructured":"Melkova, Z., Shankaran, P., Madlenakova, M., and Bodor, J. (2016). Current views on HIV-1 latency, persistence, and cure. Folia Microbiol., 1\u201315.","DOI":"10.1007\/s12223-016-0474-7"},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"118","DOI":"10.1038\/ni.2787","article-title":"Unifying immunology with informatics and multiscale biology","volume":"15","author":"Kidd","year":"2014","journal-title":"Nat. Immunol."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"212","DOI":"10.1016\/j.tim.2014.12.008","article-title":"HIV-1 adaptation to HLA: A window into virus-host immune interactions","volume":"23","author":"Carlson","year":"2015","journal-title":"Trends Microbiol."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"357","DOI":"10.1080\/17513750701813184","article-title":"Modelling HIV immune response and validation with clinical data","volume":"2","author":"Banks","year":"2008","journal-title":"J. Biol. Dyn."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"3116","DOI":"10.1002\/eji.201242508","article-title":"A global \u201cimaging\u201d view on systems approaches in immunology","volume":"42","author":"Ludewig","year":"2012","journal-title":"Eur. J. Immunol."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"78","DOI":"10.1051\/mmnp\/20127507","article-title":"Human Immunodeficiency Virus Infection: From Biological Observations to Mechanistic Mathematical Modelling","volume":"7","author":"Bocharov","year":"2012","journal-title":"Math. Model. Nat. Phenom."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"1984","DOI":"10.3390\/v4101984","article-title":"Modelling the course of an HIV infection: Insights from ecology and evolution","volume":"4","author":"Alizon","year":"2012","journal-title":"Viruses"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"431","DOI":"10.1007\/s10928-014-9363-3","article-title":"Viral kinetic modeling: State of the art","volume":"41","author":"Canini","year":"2014","journal-title":"J. Pharmacokinet. Pharmacodyn."},{"key":"ref_14","unstructured":"Weinan, E. (2011). Principles of Multiscale Modelling, Cambridge University Press."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"3472","DOI":"10.4049\/jimmunol.1003299","article-title":"Multi-scale computational modeling reveals a critical role for TNF receptor 1 dynamics in tuberculosis granuloma formation","volume":"186","author":"Marino","year":"2011","journal-title":"J. Immunol."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"119","DOI":"10.1007\/s12195-014-0363-6","article-title":"Strategies for efficient numerical implementation of hybrid multi-scale agent-based models to describe biological systems","volume":"8","author":"Cilfone","year":"2015","journal-title":"Cell. Mol. Bioeng."},{"key":"ref_17","doi-asserted-by":"crossref","unstructured":"Simeone Marino, S., and Kirschner, D.E. (2016). A multi-compartment hybrid computational model predicts key roles for dendritic cells in tuberculosis infection. Computation, 4.","DOI":"10.3390\/computation4040039"},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"159","DOI":"10.3390\/computation2040159","article-title":"Multiscale Modeling of the Early CD8 T-Cell Immune Response in Lymph Nodes: An Integrative Study","volume":"2","author":"Prokopiou","year":"2014","journal-title":"Computation"},{"key":"ref_19","doi-asserted-by":"crossref","unstructured":"Gao, X., Arpin, C., Marvel, J., Prokopiou, S.A., Gandrillon, O., and Crauste, F. (2016). IL-2 sensitivity and exogenous IL-2 concentration gradient tune the productive contact duration of CD8(+) T cell-APC: A multiscale modeling study. BMC Syst. Biol., 10.","DOI":"10.1186\/s12918-016-0323-y"},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"131","DOI":"10.3390\/computation2040131","article-title":"Computational Models of the NF-\u03baB Signaling Pathway","volume":"2","author":"Williams","year":"2014","journal-title":"Computation"},{"key":"ref_21","doi-asserted-by":"crossref","unstructured":"Baldazzi, V., Paci, P., Bernaschi, M., and Castiglione, F. (2009). Modeling lymphocyte homing and encounters in lymph nodes. BMC Bioinform., 10.","DOI":"10.1186\/1471-2105-10-387"},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"169","DOI":"10.1016\/j.jtbi.2013.06.016","article-title":"Predicting lymph node output efficiency using systems biology","volume":"335","author":"Gong","year":"2013","journal-title":"J. Theor. Biol."},{"key":"ref_23","doi-asserted-by":"crossref","unstructured":"Palsson, S., Hickling, T.P., Bradshaw-Pierce, E.L., Zager, M., Jooss, K., O\u2019Brien, P.J., Spilker, M.E., Palsson, B.O., and Vicini, P. (2013). The development of a fully-integrated immune response model (FIRM) simulator of the immune response through integration of multiple subset models. BMC Syst. Biol., 7.","DOI":"10.1186\/1752-0509-7-95"},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"527","DOI":"10.1146\/annurev-immunol-030409-101317","article-title":"Systems biology in immunology\u2014A computational modeling perspective","volume":"29","author":"Germain","year":"2011","journal-title":"Annu. Rev. Immunol."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"211","DOI":"10.1016\/j.jtbi.2016.01.040","article-title":"T cell and reticular network co-dependence in HIV infection","volume":"395","author":"Donovan","year":"2016","journal-title":"J. Theor. Biol."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"a007005","DOI":"10.1101\/cshperspect.a007005","article-title":"HIV pathogenesis: The host","volume":"2","author":"Lackner","year":"2012","journal-title":"Cold Spring Harb. Perspect. Med."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"321","DOI":"10.1016\/j.mpmed.2009.03.008","article-title":"The immune response to HIV","volume":"37","author":"McMichael","year":"2009","journal-title":"Medicine"},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"a007054","DOI":"10.1101\/cshperspect.a007054","article-title":"The T cell response to HIV","volume":"2","author":"Walker","year":"2012","journal-title":"Cold Spring Harb. Perspect. Med."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"591","DOI":"10.1016\/j.immuni.2015.08.012","article-title":"Magnitude and Kinetics of CD8+ T Cell Activation during Hyperacute HIV Infection Impact Viral Set Point","volume":"43","author":"Ndhlovu","year":"2015","journal-title":"Immunity"},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"859","DOI":"10.1038\/sj.cdd.4401595","article-title":"Apoptosis of HIV-specific CD8+ T cells: An HIV evasion strategy","volume":"12","author":"Petrovas","year":"2005","journal-title":"Cell Death Differ."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"1217","DOI":"10.1016\/j.aml.2012.02.053","article-title":"Mathematical modeling of erythropoiesis in vivo with multiple erythroblastic islands","volume":"25","author":"Bessonov","year":"2012","journal-title":"Appl. Math. Lett."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"92","DOI":"10.1016\/j.jtbi.2012.01.002","article-title":"Modelling erythroblastic islands: Using a hybrid model to assess the function of central macrophage","volume":"298","author":"Fischer","year":"2012","journal-title":"J. Theor. Biol."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"2246","DOI":"10.1137\/100815517","article-title":"Hybrid model of erythropoiesis and leukemia treatment with cytosine arabinoside","volume":"71","author":"Kurbatova","year":"2011","journal-title":"SIAM J. Appl. Math."},{"key":"ref_34","unstructured":"Glade, N., and Stephanou, A. (2013). Le Vivant Discret et Continu, Editions Materiologiques."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"305","DOI":"10.1007\/s10441-013-9188-2","article-title":"Hybrid Model of Erythropoiesis","volume":"61","author":"Kurbatova","year":"2013","journal-title":"Acta Biotheor."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"71","DOI":"10.1007\/s00285-014-0758-y","article-title":"The role of spatial organization of cells in erythropoiesis","volume":"70","author":"Eymard","year":"2015","journal-title":"J. Math. Biol."},{"key":"ref_37","doi-asserted-by":"crossref","unstructured":"Yeghiazarian, L., Cumberland, W.G., and Yang, O.O. (2013). A stochastic multi-scale model of HIV-1 transmission for decision-making: Application to a MSM population. PLoS ONE, 8.","DOI":"10.1371\/journal.pone.0070578"},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"37","DOI":"10.1051\/mmnp\/201611103","article-title":"Hybrid modeling in biology: A classification review","volume":"11","author":"Volpert","year":"2016","journal-title":"Math. Model. Nat. Phenom."},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"378","DOI":"10.1016\/j.cels.2016.04.016","article-title":"Distinct NFkB and MAPK Activation Thresholds Uncouple Steady-State Microbe Sensing from Anti-pathogen Inflammatory Responses","volume":"2","author":"Gottschalk","year":"2016","journal-title":"Cell Syst."},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"909","DOI":"10.1007\/s00285-015-0940-x","article-title":"Dynamics of HIV infection in lymphoid tissue network","volume":"72","author":"Nakaoka","year":"2016","journal-title":"J. Math. Biol."},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"774","DOI":"10.1007\/s11538-013-9834-5","article-title":"Turing patterns from dynamics of early HIV infection","volume":"7","author":"Stancevic","year":"2013","journal-title":"Bull. Math. Biol."},{"key":"ref_42","doi-asserted-by":"crossref","first-page":"1425","DOI":"10.1007\/s00285-012-0593-y","article-title":"Mathematical modeling of viral infection dynamics in spherical organs","volume":"67","author":"Dunia","year":"2013","journal-title":"J. Math. Biol."},{"key":"ref_43","doi-asserted-by":"crossref","first-page":"85","DOI":"10.1006\/jtbi.2002.3055","article-title":"Spatiotemporal dynamics of HIV propagation","volume":"218","author":"Strain","year":"2002","journal-title":"J. Theor. Biol."},{"key":"ref_44","doi-asserted-by":"crossref","unstructured":"Zhang, C., Zhou, S., Groppelli, E., Pellegrino, P., Williams, I., Borrow, P., Chain, B.M., and Jolly, C. (2015). Hybrid spreading mechanisms and T cell activation shape the dynamics of HIV-1 infection. PLoS Comput. Biol., 11.","DOI":"10.1371\/journal.pcbi.1004179"},{"key":"ref_45","doi-asserted-by":"crossref","unstructured":"Bocharov, G., Z\u00fcst, R., Cervantes-Barragan, L., Luzyanina, T., Chiglintsev, E., Chereshnev, V.A., Thiel, V., and Ludewig, B. (2010). A Systems Immunology Approach to Plasmacytoid Dendritic Cell Function in Cytopathic Virus Infections. PLoS Pathog., 6.","DOI":"10.1371\/journal.ppat.1001017"},{"key":"ref_46","doi-asserted-by":"crossref","first-page":"113","DOI":"10.1016\/S0025-5564(02)00120-7","article-title":"Cells behaving badly: A theoretical model for the Fas\/FasL system in tumour immunology","volume":"179","author":"Webb","year":"2002","journal-title":"Math. Biosci."},{"key":"ref_47","doi-asserted-by":"crossref","first-page":"117","DOI":"10.1080\/10273669708833012","article-title":"Mathematical Modelling of the Interleukin-2 T-Cell System: A Comparative Study of Approaches Based on Ordinary and Delay Differential Equation","volume":"1","author":"Baker","year":"1997","journal-title":"J. Theor. Med."},{"key":"ref_48","doi-asserted-by":"crossref","first-page":"115","DOI":"10.1016\/j.ecolmodel.2006.04.023","article-title":"A standard protocol for describing individual-based and agent-based models","volume":"198","author":"Grimm","year":"2006","journal-title":"Ecol. Model."},{"key":"ref_49","doi-asserted-by":"crossref","first-page":"2760","DOI":"10.1016\/j.ecolmodel.2010.08.019","article-title":"The ODD protocol: A review and first update","volume":"221","author":"Grimm","year":"2010","journal-title":"Ecol. Model."},{"key":"ref_50","doi-asserted-by":"crossref","unstructured":"Bouchnita, A., Bocharov, G., Meyerhans, A., and Volpert, V. (2016). Hybrid approach to model the spatial regulation of T cell responses. BMC Immunol., accepted.","DOI":"10.1186\/s12865-017-0205-0"},{"key":"ref_51","doi-asserted-by":"crossref","first-page":"68","DOI":"10.1016\/j.ebiom.2016.07.024","article-title":"HIV DNA Set Point is Rapidly Established in Acute HIV Infection and Dramatically Reduced by Early ART","volume":"11","author":"Ananworanich","year":"2016","journal-title":"EBioMedicine"},{"key":"ref_52","doi-asserted-by":"crossref","first-page":"43","DOI":"10.1016\/S2055-6640(20)30688-9","article-title":"Virological and immunological characteristics of HIV-infected individuals at the earliest stage of infection","volume":"2","author":"Ananworanich","year":"2016","journal-title":"J. Virus Erad."},{"key":"ref_53","doi-asserted-by":"crossref","first-page":"1099","DOI":"10.1038\/13410","article-title":"Ongoing HIV dissemination during HAART","volume":"5","author":"Grossman","year":"1999","journal-title":"Nat. Med."},{"key":"ref_54","doi-asserted-by":"crossref","unstructured":"Likhoshvai, V.A., Khlebodarova, T.M., Bazhan, S.I., Gainova, I.A., Chereshnev, V.A., and Bocharov, G.A. (2014). 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. BMC Genom., 15.","DOI":"10.1186\/1471-2164-15-S12-S1"},{"key":"ref_55","doi-asserted-by":"crossref","first-page":"9836","DOI":"10.1128\/JVI.01001-13","article-title":"High production rates sustain in vivo levels of PD-1high simian immunodeficiency virus-specific CD8 T cells in the face of rapid clearance","volume":"87","author":"Petrovas","year":"2013","journal-title":"J. Virol."},{"key":"ref_56","doi-asserted-by":"crossref","unstructured":"Peligero, C., Argilaguet, J., G\u00fcerri-Fernandez, R., Torres, B., Ligero, C., Colomer, P., Plana, M., Knobel, H., Garc\u00eda, F., and Meyerhans, A. (2015). PD-L1 Blockade Differentially Impacts Regulatory T Cells from HIV-Infected Individuals Depending on Plasma Viremia. PLoS Pathog., 11.","DOI":"10.1371\/journal.ppat.1005270"},{"key":"ref_57","doi-asserted-by":"crossref","first-page":"677","DOI":"10.1146\/annurev-immunol-032712-100027","article-title":"Dynamic tuning of lymphocytes: Physiological basis, mechanisms, and function","volume":"33","author":"Grossman","year":"2015","journal-title":"Annu. Rev. Immunol."},{"key":"ref_58","doi-asserted-by":"crossref","first-page":"503","DOI":"10.1158\/2326-6066.CIR-14-0046","article-title":"Pathogen-sensing and regulatory T cells: Integrated regulators of immune responses","volume":"2","author":"Paul","year":"2014","journal-title":"Cancer Immunol. Res."},{"key":"ref_59","doi-asserted-by":"crossref","first-page":"157","DOI":"10.1515\/rnam-2015-0015","article-title":"Mathematical modeling of the within-host HIV quasispecies dynamics in response to antiviral treatment","volume":"30","author":"Bocharov","year":"2015","journal-title":"Russ. J. Numer. Anal. Math. Model."},{"key":"ref_60","doi-asserted-by":"crossref","first-page":"2171","DOI":"10.1084\/jem.20070567","article-title":"Progressive CD4+ central memory T cell decline results in CD4+ effector memory insufficiency and overt disease in chronic SIV infection","volume":"204","author":"Okoye","year":"2007","journal-title":"J. Exp. Med."},{"key":"ref_61","doi-asserted-by":"crossref","first-page":"265","DOI":"10.1101\/sqb.2013.78.020198","article-title":"Pathogen-sensing, regulatory T cells, and responsiveness-tuning collectively regulate foreign- and self-antigen mediated T cell responses","volume":"78","author":"Paul","year":"2013","journal-title":"Cold Spring Harb. Symp. Quant. Biol."}],"container-title":["Computation"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2079-3197\/5\/1\/6\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T18:25:47Z","timestamp":1760207147000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2079-3197\/5\/1\/6"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2017,1,10]]},"references-count":61,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2017,3]]}},"alternative-id":["computation5010006"],"URL":"https:\/\/doi.org\/10.3390\/computation5010006","relation":{},"ISSN":["2079-3197"],"issn-type":[{"value":"2079-3197","type":"electronic"}],"subject":[],"published":{"date-parts":[[2017,1,10]]}}}