 Research
 Open Access
 Published:
A highly pathogenic simian/human immunodeficiency virus effectively produces infectious virions compared with a less pathogenic virus in cell culture
Theoretical Biology and Medical Modelling volume 14, Article number: 9 (2017)
Abstract
Background
The host range of human immunodeficiency virus (HIV) is quite narrow. Therefore, analyzing HIV1 pathogenesis in vivo has been limited owing to lack of appropriate animal model systems. To overcome this, chimeric simian and human immunodeficiency viruses (SHIVs) that encode HIV1 Env and are infectious to macaques have been developed and used to investigate the pathogenicity of HIV1 in vivo. So far, we have many SHIV strains that show different pathogenesis in macaque experiments. However, dynamic aspects of SHIV infection have not been well understood. To fully understand the dynamic properties of SHIVs, we focused on two representative strains—the highly pathogenic SHIV, SHIVKS661, and the less pathogenic SHIV, SHIV#64—and measured the timecourse of experimental data in cell culture.
Methods
We infected HSCF with SHIVKS661 and #64 and measured the concentration of Nefnegative (target) and Nefpositive (infected) HSCF cells, the total viral load, and the infectious viral load daily for 9 days. The experiments were repeated at two different multiplicities of infection, and a previously developed mathematical model incorporating the infectious and noninfectious viruses was fitted to the full dataset of each strain simultaneously to characterize the infection dynamics of these two strains.
Results and conclusions
We quantified virological indices including virus burst sizes and basic reproduction number of both SHIVKS661 and #64. Comparing the burst size of total and infectious viruses (viral RNA copies and TCID_{50}, respectively), we found that there was a statistically significant difference between the infectious virus burst size of SHIVKS661 and #64, while there was no significant difference between the total virus burst size. Furthermore, our analyses showed that the fraction of infectious virus among the produced SHIVKS661 viruses, which is defined as the infectious viral load (TCID_{50}/ml) divided by the total viral load (RNA copies/ml), is more than 10fold higher than that of SHIV#64 during overall infection (i.e., for 9 days). Taken together, we conclude that the highly pathogenic SHIV produces infectious virions more effectively than the less pathogenic SHIV in cell culture.
Background
Human immunodeficiency virus (HIV) is able to infect only humans and chimpanzees. This narrow host range makes it difficult for us to establish an appropriate “animal experimental system” for HIV research in order to more fully understand the pathogenesis of HIV infection in vivo. To overcome these difficulties, chimeric simian and human immunodeficiency viruses (SHIVs) that encode HIV1 Env and are infectious to macaques have been developed [1–3]. For example, a highly pathogenic SHIV strain, SHIVKS661, which has the env gene of HIV1 89.6 and predominantly uses CXCR4 as the secondary receptor for infection, causes an infection that systemically depletes the CD4^{+} Tcells of rhesus macaques within 4 weeks following infection [4, 5]. On the other hand, a less pathogenic strain, SHIV#64, which also predominantly uses CXCR4 as the secondary receptor, does not cause severe symptoms in rhesus macaques [6]. In particular, SHIV#64 infected macaques do not show systemic depletion of CD4^{+} Tcells after infection because viral replication is suppressed by the host immune response [6]. Unlike SHIVKS661 infection [3, 7], the reduced CD4^{+} Tcell depletion observed in SHIV#64 infection might lead to better Tcell dependent help for both antibody and CD8^{+} Tcell responses to the virus [6, 8]. So far, we have many SHIV strains that show different pathogenesis in macaque experiments [1–7, 9, 10]. In our previous study [11], we quantified only SHIVKS661 infection in vitro. However, dynamic aspects of other SHIV strains are not well understood. Quantifying and comparing viral kinetics will provide us with novel insights into the pathogenesis of SHIV strains (and HIV1) [11–14]. To extend our understanding of the dynamic properties of SHIVs in this study, we focused on two representative strains: SHIVKS661 and SHIV#64, and measured the detailed timecourse of experimental data in HSCF cell culture. Using our previously developed method combining in vitro experiments and a mathematical model published in our previous paper [11], we characterized SHIVKS661 and #64, and showed a difference between strains based on virological indices including the virus burst sizes and basic reproduction number. Our main finding was that the fraction of infectious virus among the SHIVKS661 virus progeny is more than 10fold higher than that of SHIV#64 during the overall infection in our cell culture. This is a valuable complement to the welldeveloped in vivo model and can be used to significantly improve our knowledge of SHIV and HIV pathogenesis in vivo.
Methods
Cell culture experiment
Our experimental procedures have been previously published [13] but are repeated here for completeness. The virus solution of SHIVKS661 [5] (or SHIV#64 [6]) was prepared in a CD4^{+} human T lymphoid cell line, M8166 (a subclone of C8166) [15], and was stored in liquid nitrogen until use. The HSCF cell line [16] was cultured in a culture medium (RPMI1640 supplemented with 10% fetal calf serum) at 37 °C and 5% CO_{2} in humidified conditions. Each experiment was performed using two wells of a 24well plate with a total suspension volume of 2 ml (1 ml per well) and an initial cell concentration of T _{0} = 6.46 × 10^{6} cells/ml in each well. Because the initial cell concentration was close to the carrying capacity of a 24well plate and HSCF cells replicate slowly, in the absence of SHIVKS661 (or SHIV#64) infection the population of target cells changed very little during the timescale of our experiment (data not shown). We therefore neglected the effects of potential regeneration of HSCF cells in our analysis and in constructing the mathematical model. For virus infection, cultures of HSCF cells were inoculated 24 h prior to the first infection sampling (t = −24 h) at two different multiplicities of infection (MOIs) of 2.0 × 10^{−4} or 2.0 × 10^{−5} 50% tissue culture infectious dose (TCID_{50}) per cell of SHIVKS661 (or SHIV#64), and were incubated at 37 °C. Four hours after inoculation (t = −20 h), the cells were washed to remove the remaining viruses and were replaced into fresh culture medium. The culture supernatant was harvested daily for 10 days (t = 0,1,…,9d), and was replaced with fresh medium. On a daily basis, 5.5% of the cells in the culture were harvested to measure the concentration of target and infected cells. Cells were counted by staining with an antiSIV Nef monoclonal antibody (04001, Santa Cruz Biotechnology, Santa Cruz, CA) labeled with Zenon Alexa Fluor 488 (Invitrogen, Carlsbad, CA), as previously described [11, 12]. Each harvested supernatant, including 85.4% of the culture virus was stored at 80 °C, and the amount of viral RNA was quantified by RTPCR, as previously described [11, 12, 17]. The infectious viral load was measured by TCID_{50} assay in HFCS cell cultures using 96well flat bottom plates at cell concentrations of 1.0 × 10^{6} cells/ml. The titer of the virus was determined as described by Reed and Muench [18].
Mathematical model
We employed the following mathematical model considering the infectious and noninfectious viruses, which was developed in our previous paper [11]:
where T(t) and I(t) are the concentration of target (susceptible: Nefnegative HSCF cells) and infected (virusproducing: Nefpositive HSCF cells) cells per ml of medium, respectively, and V _{ I } (t) and V _{ NI } (t) are the concentration of RNA copies of infectious and noninfectious virus per ml of medium, respectively. Parameters d, δ, c _{ RNA } and β represent the death rate of target cells, the death rate of infected cells, the degradation rate of viral RNA and the rate constant for infection of target cells by virus, respectively. We assumed that each infected cell releases p _{ RNA } virus particles per day (i.e., p _{ RNA } is the viral production rate of an infected cell), of which a fraction f are infectious and 1  f are noninfectious. Infectious virions lose infectivity at rate c _{50}, becoming noninfectious. A detailed explanation of Eqs. (1,2,3 and 4) can be found in our previous paper [11].
Mathematical model for data analysis
In the experiments discussed above, the viral load was measured either as the total count of extracellular virions, expressed as RNA copies/ml (two RNA copies equals one virion) and measured via quantitative PCR, or as a relative concentration of extracellular infectious virions, expressed as TCID_{50}/ml (proportional to the concentration of infectious virions) and measured via virus titration in cell cultures. To analyze our cell culture experimental datasets, the timecourse of the concentration of Nefnegative and Nefpositive HSCF cells and the viral loads consisting of RNA copies/ml and TCID_{50}/ml, for SHIVKS661 and #64, we transformed Eqs. (1,2,3 and 4) into the following scaled model [11]:
where V _{ RNA }(t) = V _{ I }(t) + V _{ NI }(t) is the total concentration of viral RNA copies, V _{50}(t) = αV _{ I }(t) is the infectious viral load expressed in TCID_{50}/ml, and α is the conversion factor from infectious viral RNA copies to TCID_{50}. Parameters β _{50} = β/α and p _{50} = αfp _{ RNA } are the converted infection rate constant and production rate of infectious virus, respectively. For each of the daily measurements of the cells and virus concentration, the concentration of Nefnegative and Nefpositive HSCF cells must be reduced in our model by 5.5% and the viral loads (RNA copies and TCID_{50}) by 85.4% to account for the experimental harvesting of cells and virus. These losses were modeled in Eqs. (5,6,7 and 8) by approximating the sampling of cells and virus as a continuous exponential decay, yielding a rate of μ = 0.057 per day for cell harvest (i.e., log(1 − 0.055)) and c = 1.93 per day for virus harvest (i.e., log(1 − 0.854)). The rates at which SHIVKS661 and #64 virions lose infectivity, c _{50} = 0.869 and 0.992, per day and the rate at which their viral RNA degrades, c _{ RNA } = 0.091 and 0.160, per day were each estimated directly in separate experiments [13]. These parameter values are summarized in Table 1.
Parameter estimation
The Bayesian inference model adopted in this paper assumes measurement error to follow normal distribution with mean zero and unknown variance (error variance). A distribution of error variance is also inferred with the Gamma distribution as its prior distribution. Posterior predictive parameter distributions as an output of Markov chain Monte Carlo (MCMC) computation represents parameter variability. In relating our daily experimental measurements at time t = 0,1,…,9 day to our mathematical models, we define t = 0 as the time of our first experimental measurements, i.e. when T(0), I(0), V _{ RNA }(0), and V _{50}(0) are measured. As such, by time t = 0, some cells (T) have become infected (I), and while the inoculum virus has been washed, some new virus (V _{50}) will have been produced by the newly infected cells. The remaining five free model parameters (β _{50}, d, δ, p _{ RNA }, p _{50}) along with eight initial (t = 0) values for the variables (four at each of the two MOI values) were determined. Distributions of the model parameters and the initial values were inferred directly by MCMC computations. On the other hand, distributions of the basic reproduction numbers and the other quantities were calculated from the inferred parameter sets (see Figs. 2 and 3a,b for graphical representation). A set of computations for Eqs. (5,6,7 and 8) with estimated parameter sets gives a distribution of outputs (virus load and cell density) as model predictions. To investigate the variation of model predictions, global sensitivity analyses were performed. The range of possible variation is drawn in Figs. 1 and 3c as 95% credible intervals. Technical details of MCMC computations and repeated bootstrap ttest are summarized in Additional file 1.
Results and Discussion
Data fitting to quantify SHIVKS661 and #64 infection in HSCF cells
Correctly estimated parameter sets with possible variation are required to reproduce model predictions for quantification of SHIV dynamics [19–21]. However, point estimation of the model parameter set by a conventional ordinary least square method does not capture possible variations of kinetic parameters and model predictions (see Additional file 2: Figure S1, Additional file 3: Table S1, and Additional file 4: Table S2). To assess the variability of kinetic parameters and model predictions, we performed Bayesian estimation for the whole dataset using MCMC sampling (see Methods and Additional file 1), and simultaneously fitted Eqs. (5,6,7 and 8) to the concentration of Nefnegative and Nefpositive HSCF cells and the viral loads consisting of RNA copies/ml and TCID_{50}/ml with different MOI values, for SHIVKS661 and #64, respectively, as described in [19–21]. We used the parameters in Additional file 3: Table S1 and Additional file 4: Table S2 as the initial estimate of MCMC sampling.
The remaining five free model parameters (β _{50}, d, δ, p _{ RNA }, p _{50}) along with eight initial values for the variables were determined by fitting the model to the data. Experimental measurements, which were below the detection limit, were excluded in the fitting. The estimated parameters of the model and derived quantities are given in Table 1, and the estimated initial values are summarized in Table 2. The typical behavior of the model using these bestfit parameter estimates is shown together with the data in Fig. 1 for SHIVKS661 and #64, which reveals that Eqs. (5,6,7 and 8) describe these in vitro data very well. The shadowed regions correspond to 95% posterior predictive intervals, the solid lines give the bestfit solution (mean) for Eqs. (5,6,7 and 8), and the dots show the experimental datasets.
Malthusian parameter and basic reproduction number for SHIVKS661 and #64 in HSCF cells
The fitness (or speed) of a SHIV strain in cell culture is described by the Malthusian coefficient, M, defined for Eqs. (5,6,7 and 8) [20–22]. Here, the Malthusian coefficient is
Using estimated parameter distributions, we calculated the distribution of M for SHIVKS661 and #64 in Fig. 2a (see Methods). The mean values of M for SHIVKS661 and #64 are significantly different (Fig. 2a; p = 6 × 10^{−6} by repeated bootstrap ttest, see Additional file 1) at 3.08 (95% confidence interval (CI): 2.82–3.52) and 2.59 (95% CI: 2.37–2.80), respectively (Table 1). This difference in the value of M between SHIVKS661 and #64 might explain the earlier and more rapid viral load expansion (i.e., peak viral load) and the systemic depletion of the CD4^{+} Tcells in infected rhesus macaques within a few weeks of SHIVKS661 infection [3–7], implying a strong relationship between SHIV replication ability and its disease severity.
The other important quantity characterizing virus dynamics is the basic reproduction number, R _{0} ^{*} , which is the average number of newly infected cells produced from any one infected cell, under conditions where most of the target cells are uninfected [11, 12, 20–22]. In Eqs. (5,6,7 and 8), the basic reproduction number is defined as
Similarly, we calculated the distributions of R _{0} ^{*} for SHIVKS661 and #64 (Fig. 2b). The mean value of R _{0} ^{*} for SHIVKS661 is 6.25 (95% CI: 5.29–7.51), which is significantly higher (Fig. 2b; p = 4.2 × 10^{− 5} by the repeated bootstrap ttest) than that of SHIV#64 (4.84; 95% CI: 4.13–5.62) (Table 1). Again, this difference in the value of R _{0} ^{*} between SHIVKS661 and #64 implies that the highly pathogenic SHIV strain more efficiently causes systemic CD4^{+} Tcell depletion. In Additional file 5: Figure S2, we calculated the distribution of the basic reproduction number without the effects of removal, R _{0} = β _{50} p _{50} T(0)/δ(c _{ RNA } + c _{50}), defined in our previous paper [14] and observed the same trend.
Viral burst size for SHIVKS661 and #64 in HSCF cells
Interestingly, we found the viral fitness (or speed), M, and the infection potential, R _{0} ^{*} , of SHIVKS661 were significantly higher than those of SHIV#64 in HSCF cells (Fig. 2). Hereafter, to quantitatively explain a possible mechanism that there are significant differences between SHIV strains, we investigated and compared the total and infectious virus burst sizes (i.e., p _{ RNA }/δ and p _{50}/δ, respectively) [11]. In Fig. 3a and b, we calculated the distributions of burst sizes for SHIVKS661 and #64 using all accepted MCMC estimated parameter values. Surprisingly, we found that there was a statistically significant difference in the infectious burst size, measured in TCID_{50}, between SHIVKS661 and #64 (Fig. 3b; p = 2.5 × 10^{− 5} by the repeated bootstrap ttest), while there was no significant difference in the total burst size, measured in viral RNA copies (Fig. 3a; p = 0.34 by the repeated bootstrap ttest). This implies that the highly pathogenic SHIV produces more infectious virions compared with the less pathogenic strain. In addition, we compared experimental measurement of the infectious viral load as a proportion of the total viral load (i.e., the fraction of the infectious virus among the produced viruses), with the time evolution of the proportion calculated by our mathematical model (i.e., V _{50}(t)/V _{ RNA }(t)) in Fig. 3c. Despite MOI values and time post infection, we confirmed that the experimental proportions were shown to be steady state values, and the model predictions converged with those values for both SHIV strains. Of great interest was the more than 10fold difference in the ratios between SHIVKS661 and #64 during the overall infection. This strongly supports our above hypothesis that the highly pathogenic SHIV effectively produces infectious virions, which leads to earlier and more rapid viral load expansion and the systemic depletion of the CD4^{+} Tcells in SHIVKS661infected rhesus macaques.
Conclusion
We inoculated HSCF cells with SHIVKS661 or #64 at two different MOIs (i.e., 2.0 × 10^{−4} or 2.0 × 10^{−5} TCID_{50} per cell) and measured in detail the timecourse of the experimental data (i.e., the concentration of Nefnegative and Nefpositive HSCF cells and the viral loads consisting of RNA copies/ml and TCID_{50}/ml). Using our previously developed method combining in vitro experiments and a mathematical model in our previous paper [11], we quantified and compared the basic reproduction numbers and the virus burst sizes for the SHIVKS661 and #64. Based on our quantitative analysis, we concluded that SHIVKS661 effectively produces infectious virions compared with SHIV#64 in the HSCF cell culture. SHIVKS661 contains mutations in the pol and env genes, which are considered to lead SHIVKS661 to produce more virus and have higher infectivity than SHIV#64 (data not shown), which is consistent with our conclusion. Although we used the Malthusian parameter, M, and the basic reproduction number, R _{0} ^{*} to compare the differences in viral characteristics here, we need to consider evasion of the acquired immune response in infected rhesus macaques to further understand the differing pathogenesis displayed by these viruses, such as systemic CD4^{+} Tcell depletion in SHIVKS661 infections. Since we cannot observe the effect of the immune response in our cell culture experiments, it will be necessary to analyze the in vivo data from SHIV infected macaques in future work.
Abbreviations
 HIV:

Human immunodeficiency virus
 MCMC:

Markov chain Monte Carlo
 MOI:

Multiplicity of infection
 SHIV:

Simian and human immunodeficiency virus
 TCID_{50} :

50% tissue culture infectious dose
References
 1.
Harouse JM, Gettie A, Tan RC, Blanchard J, ChengMayer C. Distinct pathogenic sequela in rhesus macaques infected with CCR5 or CXCR4 utilizing SHIVs. Science (New York, NY). 1999;284(5415):816–9. Epub 1999/04/30.
 2.
Matsuda K, Inaba K, Fukazawa Y, Matsuyama M, Ibuki K, Horiike M, et al. In vivo analysis of a new R5 tropic SHIV generated from the highly pathogenic SHIVKS661, a derivative of SHIV89.6. Virology. 2010;399(1):134–43. doi:10.1016/j.virol.2010.01.008. Epub 2010/01/28.
 3.
Nishimura Y, Igarashi T, Donau OK, BucklerWhite A, Buckler C, Lafont BA, et al. Highly pathogenic SHIVs and SIVs target different CD4+ T cell subsets in rhesus monkeys, explaining their divergent clinical courses. Proc Natl Acad Sci U S A. 2004;101(33):12324–9. Epub 2004/08/07. doi: 10.1073/pnas.0404620101. PubMed PMID: 15297611; PubMed Central PMCID: PMCPMC514404.
 4.
Reimann KA, Li JT, Veazey R, Halloran M, Park IW, Karlsson GB, et al. A chimeric simian/human immunodeficiency virus expressing a primary patient human immunodeficiency virus type 1 isolate env causes an AIDSlike disease after in vivo passage in rhesus monkeys. J Virol. 1996;70(10):6922–8. Epub 1996/10/01. PubMed PMID: 8794335; PubMed Central PMCID: PMCPMC190741.
 5.
Shinohara K, Sakai K, Ando S, Ami Y, Yoshino N, Takahashi E, et al. A highly pathogenic simian/human immunodeficiency virus with genetic changes in cynomolgus monkey. J Gen Virol. 1999;80(Pt 5):1231–40. doi:10.1099/002213178051231. Epub 1999/06/04.
 6.
Kozyrev IL, Ibuki K, Shimada T, Kuwata T, Takemura T, Hayami M, et al. Characterization of less pathogenic infectious molecular clones derived from acutepathogenic SHIV89.6p stock virus. Virology. 2001;282(1):6–13. doi:10.1006/viro.2000.0839. Epub 2001/03/22.
 7.
Nishimura Y, Brown CR, Mattapallil JJ, Igarashi T, BucklerWhite A, Lafont BA, et al. Resting naive CD4+ T cells are massively infected and eliminated by X4tropic simianhuman immunodeficiency viruses in macaques. Proc Natl Acad Sci U S A. 2005;102(22):8000–5. Epub 2005/05/25. doi: 10.1073/pnas.0503233102. PubMed PMID: 15911767; PubMed Central PMCID: PMCPMC1142395.
 8.
Davenport MP, Ribeiro RM, Zhang L, Wilson DP, Perelson AS. Understanding the mechanisms and limitations of immune control of HIV. Immunol Rev. 2007;216:164–75. doi:10.1111/j.1600065X.2006.00485.x. Epub 2007/03/21.
 9.
Otsuki H, Yoneda M, Igarashi T, Miura T. Generation of a monkeytropic human immunodeficiency virus type 1 carrying env from a CCR5tropic subtype C clinical isolate. Virology. 2014;460461:1–10. Epub 2014/07/11. doi: 10.1016/j.virol.2014.04.037.
 10.
Ishida Y, Yoneda M, Otsuki H, Watanabe Y, Kato F, Matsuura K, et al. Generation of a neutralizationresistant CCR5 tropic simian/human immunodeficiency virus (SHIVMK38) molecular clone, a derivative of SHIV89.6. J Gen Virol. 2016;97(5):1249–60. doi:10.1099/jgv.0.000421. Epub 2016/02/07.
 11.
Iwami S, Holder BP, Beauchemin CA, Morita S, Tada T, Sato K, et al. Quantification system for the viral dynamics of a highly pathogenic simian/human immunodeficiency virus based on an in vitro experiment and a mathematical model. Retrovirology. 2012;9:18. doi:10.1186/17424690918. Epub 2012/03/01. PubMed PMID: 22364292; PubMed Central PMCID: PMCPMC3305505.
 12.
Iwami S, Sato K, De Boer RJ, Aihara K, Miura T, Koyanagi Y. Identifying viral parameters from in vitro cell cultures. Front Microbiol. 2012;3:319. doi:10.3389/fmicb.2012.00319. Epub 2012/09/13. PubMed PMID: 22969758; PubMed Central PMCID: PMCPMC3432869.
 13.
Kakizoe Y, Morita S, Nakaoka S, Takeuchi Y, Sato K, Miura T, et al. A conservation law for virus infection kinetics in vitro. J Theor Biol. 2015;376:39–47. doi:10.1016/j.jtbi.2015.03.034. Epub 2015/04/18.
 14.
Kakizoe Y, Nakaoka S, Beauchemin CA, Morita S, Mori H, Igarashi T, et al. A method to determine the duration of the eclipse phase for in vitro infection with a highly pathogenic SHIV strain. Sci Rep. 2015;5:10371. doi:10.1038/srep10371. Epub 2015/05/23. PubMed PMID: 25996439; PubMed Central PMCID: PMCPMC4440524.
 15.
Clapham PR, Weiss RA, Dalgleish AG, Exley M, Whitby D, Hogg N. Human immunodeficiency virus infection of monocytic and Tlymphocytic cells: receptor modulation and differentiation induced by phorbol ester. Virology. 1987;158(1):44–51. Epub 1987/05/01.
 16.
Akari H, Mori K, Terao K, Otani I, Fukasawa M, Mukai R, et al. In vitro immortalization of Old World monkey T lymphocytes with Herpesvirus saimiri: its susceptibility to infection with simian immunodeficiency viruses. Virology. 1996;218(2):382–8. doi:10.1006/viro.1996.0207. Epub 1996/04/15.
 17.
Motohara M, Ibuki K, Miyake A, Fukazawa Y, Inaba K, Suzuki H, et al. Impaired Tcell differentiation in the thymus at the early stages of acute pathogenic chimeric simianhuman immunodeficiency virus (SHIV) infection in contrast to less pathogenic SHIV infection. Microbes Infect. 2006;8(6):1539–49. doi:10.1016/j.micinf.2006.01.011. Epub 2006/05/17.
 18.
Reed L, Muench H. A simple method of estimating fifty per cent endpoints. Am J Hyg. 1938;27:493–7.
 19.
Ikeda H, Nakaoka S, de Boer RJ, Morita S, Misawa N, Koyanagi Y, et al. Quantifying the effect of Vpu on the promotion of HIV1 replication in the humanized mouse model. Retrovirology. 2016;13:23. doi:10.1186/s1297701602522. Epub 2016/04/19. PubMed PMID: 27086687; PubMed Central PMCID: PMCPMC4834825.
 20.
Iwami S, Takeuchi JS, Nakaoka S, Mammano F, Clavel F, Inaba H, et al. Celltocell infection by HIV contributes over half of virus infection. eLife. 2015;4. Epub 2015/10/07. doi: 10.7554/eLife.08150. PubMed PMID: 26441404; PubMed Central PMCID: PMCPMC4592948.
 21.
Martyushev A, Nakaoka S, Sato K, Noda T, Iwami S. Modelling Ebola virus dynamics: Implications for therapy. Antivir Res. 2016;135:62–73. doi:10.1016/j.antiviral.2016.10.004. Epub 2016/10/28.
 22.
Nowak M, May RM. Virus dynamics: mathematical principles of immunology and virology: mathematical principles of immunology and virology. UK: Oxford University Press; 2000.
Acknowledgments
Not applicable.
Funding
This work was supported in part by the JSPS Research Fellowship for Young Scientists Grant Number 16 J03672 (to Y.K.); the Japan Science and Technology Agency (JST) PRESTO program (to S.N. and S.I.); JST RISTEX program (to S.I.); JST CREST program (to S.I.); the Japan Society for the Promotion of Science (JSPS) KAKENHI Grant Numbers 26400388 (to S.M.); 16H04682 (to T.M.); 15KT0147, 15H05707, and 16 K05265 (to S.N.); 15KT0107, 26287025, 16KT0111, 16H04845, and 16 K13777 (to S.I.); the Japan Agency for Medical Research and Development, AMED, Grant Numbers 16fk0410102h0001, 16fk0410201h0102, 16fk0410208h0002, and 15fk0410014h0001 (to T.M.); 16fk0108316h0003 (to S.I.); Mitsui Life Social Welfare Foundation (to. S.I.); The ShinNihon of Advanced Medical Research (to S.I.); GSK Japan Research Grant 2016 (to S.I.).
Availability of data and materials
The datasets generated during and/or analyzed during the current study are available from the corresponding author on reasonable request.
Authors’ contributions
Conceived and designed the study: TM SI. Analyzed the data: SI YK SM SN SI. Wrote the paper: TM SN SI. Contributed reagents/materials/analysis tools: TM. All authors read and approved the final manuscript.
Competing interests
The authors declare that they have no competing interests.
Consent for publication
Not applicable.
Ethics approval and consent to participate
Not applicable.
Publisher’s Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Author information
Additional files
Additional file 1:
Technical details of MCMC computations. (PDF 49 kb)
Additional file 2: Figure S1.
Dynamics of SHIVKS661 and #64 infection in HSCF cells using nonlinear leastsquares regression. We simultaneously fit Eqs. (5,6,7 and 8) to the concentrations of Nefnegative and Nefpositive HSCF cells and the viral loads consisting of the RNA copies/ml and TCID_{50}/ml for both MOIs of SHIVKS661 and #64, respectively, in A and B using nonlinear leastsquares regression that minimizes the sum of squared residuals (SSR). Experimental measurements below the detection limit were excluded when 2 computing the SSR. The solid curves give the bestfit solution for Eqs.(5,6,7 and 8) and the dots are corresponding to the timecourse dataset (log scale): blue, red, green, and yellow represent Nefnegative and Nefpositive HSCF cells and the viral loads consisting of the RNA copies/ml and TCID_{50}/ml, respectively. The estimated parameters of the model and derived quantities are given in Additional file 3: Table S1, and the estimated initial values are summarized in Additional file 4: Table S2. (PDF 146 kb)
Additional file 3 Table S1.
Parameter values for the in vitro experiment by the nonlinear least squared methods. (PDF 57 kb)
Additional file 4: Table S2.
Fitted initial (t = 0) values for the in vitro experiment by the nonlinear least squared methods. (PDF 64 kb)
Additional file 5: Figure S2
Distribution of basic reproduction numbers without removal for SHIVKS661 and #64 in HSCF cells. The distributions of the basic reproduction numbers without the effect of removal, \( R \) _{0}=\( \beta \) _{50} \( p \) _{50} \( T \)(0)/\( \delta \)(\( c \) _{RNA}+\( c \) _{50}), that were calculated from the estimated parameter distributions are shown for SHIVKS661 (red) and #64 (blue) strains. The basic reproduction number for SHIVKS661 is significantly different from that for SHIV#64, as assessed by the repeated bootstrap ttest. (PDF 117 kb)
Rights and permissions
Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. The Creative Commons Public Domain Dedication waiver (http://creativecommons.org/publicdomain/zero/1.0/) applies to the data made available in this article, unless otherwise stated.
About this article
Cite this article
Iwanami, S., Kakizoe, Y., Morita, S. et al. A highly pathogenic simian/human immunodeficiency virus effectively produces infectious virions compared with a less pathogenic virus in cell culture. Theor Biol Med Model 14, 9 (2017) doi:10.1186/s1297601700558
Received
Accepted
Published
DOI
Keywords
 Population dynamics model
 Parameter estimation
 Virus dynamics
 Simian/human immunodeficiency virus