Computational approaches to parameter estimation and model selection in immunology

Baker, Christopher T. H.; Bocharov, Gennady; Ford, Judith M.; Lumb, Patricia M.; Norton, Stewart J.; Paul, Christopher; Junt, Tobias; Krebs, Philippe; Ludewig, Burkhard

doi:10.1016/j.cam.2005.02.003

Cited by 35 publications

(39 citation statements)

References 39 publications

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“…see [2,3] for further details. The problem of maximizing the likelihood function is equivalent to that of minimizing Φ(p), provided that σ 2 is assigned the value…”

Section: Maximum Likelihood Approachmentioning

confidence: 99%

Computational analysis of CFSE proliferation assay

et al. 2006

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CFSE based tracking of the lymphocyte proliferation using flow cytometry is a powerful experimental technique in immunology allowing for the tracing of labelled cell populations over time in terms of the number of divisions cells undergone. Interpretation and understanding of such population data can be greatly improved through the use of mathematical modelling. We apply a heterogeneous linear compartmental model, described by a system of ordinary differential equations similar to those proposed by Kendall. This model allows division number-dependent rates of cell proliferation and death and describes the rate of changes in the numbers of cells having undergone j divisions. The experimental data set that we specifically analyze specifies the following characteristics of the kinetics of PHA-induced human T lymphocyte proliferation assay in vitro: (i) the total number of live cells, (ii) the total number of dead but not disintegrated cells and (iii) the number of cells divided j times. Following the maximum likelihood approach for data fitting, we estimate the model parameters which, in particular, present the CTL birth-and death rate "functions". It is the first study of CFSE labelling data which convincingly shows that the lymphocyte proliferation and death both in vitro and in vivo are division number dependent. For the first time, the confidence in the estimated parameter values is analyzed by comparing three major methods: the technique based on the variance-covariance matrix, the profile-likelihood-based approach and the bootstrap technique. We compare results and performance of these methods with respect to their robustness and computational cost. We show that for evaluating mathematical models of differing complexity the information-theoretic approach, based upon indicators measuring the information loss for a particular model (Kullback-Leibler information), provides a consistent basis. We specifically discuss methodological and computational difficulties in parameter identification with CFSE data, e.g., the loss of confidence in the parameter estimates starting around the 6-th division. Overall, our study suggests that the heterogeneity inherent in cell kinetics should be explicitly incorporated into the structure of mathematical models.

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“…see [2,3] for further details. The problem of maximizing the likelihood function is equivalent to that of minimizing Φ(p), provided that σ 2 is assigned the value…”

Section: Maximum Likelihood Approachmentioning

confidence: 99%

Computational analysis of CFSE proliferation assay

et al. 2006

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“…Contrary to this assumption, the dependence of cell proliferation on virus concentration is considered in three different forms. We begin with the simplest case where the proliferation rate does not depend on virus concentration reflecting the model of LCMV infection identified in [17]. In this case the studied model is similar to the system of competition of species where there are three main types of behavior of solutions:…”

Section: Discussionmentioning

confidence: 99%

“…In the last case (iii), the system converges to the steady-state with an intermediate viral load which can be interpreted as a chronic infection. Next, we consider the case where the proliferation rate of the immune cells is a linear function of the viral load reflecting another mode of immune response regulation as detailed in [17]. The main difference with the previous case is that the coexisting equilibrium can lose its stability because of the delay in the immune response development.…”

Section: Discussionmentioning

confidence: 99%

“…[17]) and ψ(v) = ψ 0 v reflecting the loss of CTLs on elimination of infection, then for c 0 = 0 we obtain the system…”

Section: Constant ϕ Linear ψmentioning

confidence: 99%

“…Therefore if s 0 > 0 and s µ0 < 0 for some µ 0 > 0, then s µ = 0 for some 0 < µ < µ 0 . Hence system (16), (17) does not contain delay. The speed of the wave, since it is unique, becomes s µ = s 0 > 0.…”

Section: Constant ϕ Linear ψmentioning

confidence: 99%

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Modelling the dynamics of virus infection and immune response in space and time

Bocharov

Meyerhans

Bessonov

et al. 2017

International Journal of Parallel, Emergent and Distributed Sys

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International audienceSpreading of viral infection in the tissues such as lymph nodes or spleendepends on virus multiplication in the host cells, their transport andon the immune response. Reaction–diffusion systems of equations withdelays in proliferation and death terms of the immune cells represent anappropriate model to study this process. The properties of the immuneresponse and the initial viral load determine the regimes of infectionspreading. In the proposed model, the proliferation rate of the immunecells is represented by a bell-shaped function of the virus concentrationwhich increases for small concentrations and decreases if the concentrationis sufficiently high. Here we use such a model system to show that aninfection can be completely eliminated or it can remain present togetherwith a decreased concentration of immune cells. Finally, immune cellscan be completely exhausted leading to a high virus concentration in thetissue. In addition, we predicted two novel regimes of infection dynamicsnot observed before. Infection propagation in the tissue can occur asa superposition of two travelling waves: first wave propagates as a lowlevel infection front followed by a high level infection front with a smallerspeed of propagation. Both of the travelling waves can have a positive or anegative speed corresponding to infection advancement or retreat. Theseregimes can be accompanied by instabilities and the emergence of complexspatiotemporal patterns

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Future Outlook for Systems Biology

Young

Michelson

2011

Systems Biology in Drug Discovery and Development

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Computational approaches to parameter estimation and model selection in immunology

Cited by 35 publications

References 39 publications

Computational analysis of CFSE proliferation assay

Computational analysis of CFSE proliferation assay

Modelling the dynamics of virus infection and immune response in space and time

Future Outlook for Systems Biology

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