Abstract
A common approach to understand and analyze complex biological systems is to describe the dynamics in terms of a system of ordinary differential equations (ODE) depending on numerous biologically meaningful and descriptive parameters that are estimated using observed data. The ODE models are often based on the implicit assumption of well-mixed dynamics, i.e., the delay of interaction due to spatial distribution is not included in the model. In this article, we address the question how the heterogeneity of the underlying system affects the estimated parameter values of the ODE model, and on the other hand, what information about the microscopic system can be drawn from these values. The system we are considering is a pairwise growth competition assay used to quantify ex vivo replicative fitness of different HIV-1 isolates. To overcome the lack of ground truth, we generate data using a detailed microscopic spatially distributed hybrid stochastic-deterministic (HSD) infection model in which the dynamics is controlled by parameters directly related to cell level infection, virus production processes, and diffusion of virus particles. The synthetic data sets are then analyzed using an ODE based well-mixed model, in which the corresponding macroscopic parameter distributions are estimated using Markov chain Monte Carlo (MCMC) methods. This approach provides a comprehensive picture of the statistical dependencies of the model parameter across different scales.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Ball, S. C., Abraha, A., Collins, K. R., Marozsan, A. J., Baird, H., Quiñones-Mateu, M. E., Penn-Nicholson, A., Murray, M., Richard, N., Lobritz, M., et al. (2003). Comparing the ex vivo fitness of CCR5-tropic human immunodeficiency virus type 1 isolates of subtypes B and C. J. Virol., 77(2), 1021–1038.
Banks, H. T., Grove, S., Hu, S., & Ma, Y. (2005). A hierarchical Bayesian approach for parameter estimation in HIV models. Inverse Probl., 21(6), 1803.
Beauchemin, C. (2006). Probing the effects of the well-mixed assumption on viral infection dynamics. J. Theor. Biol., 242(2), 464–477.
Blaak, H., Brouwer, M., Ran, L. J., De Wolf, F., & Schuitemaker, H. (1998). In vitro replication kinetics of human immunodeficiency virus type 1 (HIV-1) variants in relation to virus load in long-term survivors of HIV-1 infection. J. Infect. Dis., 177(3), 600–610.
Bonhoeffer, S., Barbour, A. D., & De Boer, R. J. (2002). Procedures for reliable estimation of viral fitness from time-series data. Proc. R. Soc. Lond. B, Biol. Sci., 269(1503), 1887–1893.
Calvetti, D., & Somersalo, E. (2006). Large-scale statistical parameter estimation in complex systems with an application to metabolic models. Multiscale Model. Simul., 5(4), 1333–1366.
Calvetti, D., & Somersalo, E. (2007). Introduction to Bayesian scientific computing: ten lectures on subjective computing (Vol. 2). New York: Springer.
Dixit, N. M., & Perelson, A. S. (2004). Multiplicity of human immunodeficiency virus infections in lymphoid tissue. J. Virol., 78(16), 8942–8945.
Dixit, N. M., & Perelson, A. S. (2005). HIV dynamics with multiple infections of target cells. Proc. Natl. Acad. Sci. USA, 102(23), 8198–8203.
Dykes, C., & Demeter, L. M. (2007). Clinical significance of human immunodeficiency virus type 1 replication fitness. Clin. Microbiol. Rev., 20(4), 550–578.
Dykes, C., Wang, J., Jin, X., Planelles, V., An, D. S., Tallo, A., Huang, Y., Wu, H., & Demeter, L. M. (2006). Evaluation of a multiple-cycle, recombinant virus, growth competition assay that uses flow cytometry to measure replication efficiency of human immunodeficiency virus type 1 in cell culture. J. Clin. Microbiol., 44(6), 1930–1943.
Funk, G. A., Jansen, V. A. A., Bonhoeffer, S., & Killingback, T. (2005). Spatial models of virus-immune dynamics. J. Theor. Biol., 233(2), 221–236.
Goudsmit, J., de Ronde, A., de Rooij, E., & De Boer, R. (1997). Broad spectrum of in vivo fitness of human immunodeficiency virus type 1 subpopulations differing at reverse transcriptase codons 41 and 215. J. Virol., 71(6), 4479–4484.
Haario, H., Saksman, E., & Tamminen, J. (2001). An adaptive Metropolis algorithm. Bernoulli, 223–242.
Immonen, T., Gibson, R., Leitner, T., Miller, M. A., Arts, E. J., Somersalo, E., & Calvetti, D. (2012). A hybrid stochastic-deterministic computational model accurately describes spatial dynamics and virus diffusion in HIV-1 growth competition assay. J. Theor. Biol.
Kouyos, R. D., von Wyl, V., Hinkley, T., Petropoulos, C. J., Haddad, M., Whitcomb, J. M., Böni, J., Yerly, S., Cellerai, C., Klimkait, T., et al. (2011). Assessing predicted HIV-1 replicative capacity in a clinical setting. PLoS Pathog., 7(11), e1002321.
Levin, S. A., & Durrett, R. (1996). From individuals to epidemics. Philos. Trans. R. Soc. Lond. B, Biol. Sci., 351(1347), 1615–1621.
Marée, A. F. M., Keulen, W., Boucher, C. A. B., & De Boer, R. J. (2000). Estimating relative fitness in viral competition experiments. J. Virol., 74(23), 11067–11072.
Miao, H., Dykes, C., Demeter, L. M., Cavenaugh, J., Park, S. Y., Perelson, A. S., & Wu, H. (2008). Modeling and estimation of kinetic parameters and replicative fitness of HIV-1 from flow-cytometry-based growth competition experiments. Bull. Math. Biol., 70(6), 1749–1771.
Navis, M., Schellens, I., van Baarle, D., Borghans, J., van Swieten, P., Miedema, F., Kootstra, N., & Schuitemaker, H. (2007). Viral replication capacity as a correlate of HLA B57/B5801-associated nonprogressive HIV-1 infection. J. Immunol., 179(5), 3133–3143.
Piguet, V., Gu, F., Foti, M., Demaurex, N., Gruenberg, J., Carpentier, J. L., & Trono, D. (1999). Nef-induced CD4 degradation: a diacidic-based motif in nef functions as a lysosomal targeting signal through the binding of β-COP in endosomes. Cell, 97(1), 63–73.
Quiñones-Mateu, M. E., & Arts, E. J. (2001). HIV-1 fitness: implications for drug resistance, disease progression, and global epidemic evolution. HIV Seq. Compend., 2001, 134–170.
Quiñones-Mateu, M. E., Ball, S. C., Marozsan, A. J., Torre, V. S., Albright, J. L., Vanham, G., Van Der Groen, G., Colebunders, R. L., & Arts, E. J. (2000). A dual infection/competition assay shows a correlation between ex vivo human immunodeficiency virus type 1 fitness and disease progression. J. Virol., 74(19), 9222–9233.
Strain, M. C., Richman, D. D., Wong, J. K., & Levine, H. (2002). Spatiotemporal dynamics of HIV propagation. J. Theor. Biol., 218(1), 85–96.
Troyer, R. M., Collins, K. R., Abraha, A., Fraundorf, E., Moore, D. M., Krizan, R. W., Toossi, Z., Colebunders, R. L., Jensen, M. A., Mullins, J. I., et al. (2005). Changes in human immunodeficiency virus type 1 fitness and genetic diversity during disease progression. J. Virol., 79(14), 9006–9018.
Van den Driessche, P., & Watmough, J. (2002). Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission. Math. Biosci., 180(1), 29–48.
Webb, S. D., Keeling, M. J., & Boots, M. (2007). Host–parasite interactions between the local and the mean-field: how and when does spatial population structure matter? J. Theor. Biol., 249(1), 140–152.
Wu, H., Huang, Y., Dykes, C., Liu, D., Ma, J., Perelson, A. S., & Demeter, L. M. (2006). Modeling and estimation of replication fitness of human immunodeficiency virus type 1 in vitro experiments by using a growth competition assay. J. Virol., 80(5), 2380–2389.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Immonen, T., Somersalo, E. & Calvetti, D. Modeling HIV-1 Dynamics and Fitness in Cell Culture Across Scales. Bull Math Biol 76, 486–514 (2014). https://doi.org/10.1007/s11538-013-9926-2
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11538-013-9926-2