Process Noise: An Explanation for the Fluctuations in the Immune Response during Acute Viral Infection

Milutinović, Dejan; Boer, Rob J. de

doi:10.1529/biophysj.106.094508

Cited by 13 publications

(14 citation statements)

References 17 publications

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“…Furthermore, the mouse age at the time of infection differs between the study by Wherry et al (4) and that by Miller et al (14), which might affect the number of CD8 ϩ T cells in the spleen. Even within a laboratory, data fluctuations are expected due to the intrinsic stochasticity of the immune response, the so-called process noise (33). Alternatively, the estimated kinetic differences could derive from the number of measurements over time.…”

Section: Discussionmentioning

confidence: 99%

Dynamics of CD8+ T Cell Responses during Acute and Chronic Lymphocytic Choriomeningitis Virus Infection

Althaus

Ganusov

Boer

2007

The Journal of Immunology

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Infection of mice with lymphocytic choriomeningitis virus (LCMV) is frequently used to study the underlying principles of viral infections and immune responses. We fit a mathematical model to recently published data characterizing Ag-specific CD8+ T cell responses during acute (Armstrong) and chronic (clone 13) LCMV infection. This allows us to analyze the differences in the dynamics of CD8+ T cell responses against different types of LCMV infections. For the four CD8+ T cell responses studied, we find that, compared with the responses against acute infection, responses against chronic infection are generally characterized by an earlier peak and a faster contraction phase thereafter. Furthermore, the model allows us to give a new interpretation of the effect of thymectomy on the dynamics of CD8+ T cell responses during chronic LCMV infection: a smaller number of naive precursor cells is sufficient to account for the observed differences in the responses in thymectomized mice. Finally, we compare data characterizing LCMV-specific CD8+ T cell responses from different laboratories. Although the data were derived from the same experimental model, we find quantitative differences that can be solved by introducing a scaling factor. Also, we find kinetic differences that are at least partly due to the infrequent measurements of CD8+ T cells in the different laboratories.

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Section: Discussionmentioning

confidence: 99%

Dynamics of CD8+ T Cell Responses during Acute and Chronic Lymphocytic Choriomeningitis Virus Infection

Althaus

Ganusov

Boer

2007

The Journal of Immunology

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“…With one hundred initial cells, the coefficient of variation is one tenth of these numbers and with ten thousand initial cells, it is one hundredth, making the dispersion in the distribution extremely small. The method developed here offers an alternative way to calculate the expected variation attributed to the selection and stochastic variation in cell division and death lifetimes to that used by Milutinović and De Boer [23]. These authors referred to this source of variation as "process variation" to distinguish it from that contributed by experimental error.…”

Section: Discussionmentioning

confidence: 99%

“…Alternatively, if K * has bounded support (sup{k * : P (K * = k * ) > 0} < ∞), this also suffices to ensure the scheme terminates after a finite number of iterations. (21)- (22) for {F l k (s, t)} and finally evaluating the weighted sum in equation (23).…”

Section: Incorporating Division Destinymentioning

confidence: 99%

Determining the expected variability of immune responses using the cyton model

et al. 2007

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During an adaptive immune response, lymphocytes proliferate for five to twenty cell divisions, then stop and die over a period of weeks. The cyton model for regulation of lymphocyte proliferation and survival was introduced by Hawkins et al.[17] to provide a framework for understanding this response and its regulation. The model assumes stochastic values for division and survival times for each cell in a responding population. Experimental evidence indicates that the choice of times is drawn from a skewed distribution such as the lognormal, with the fate of individual cells being potentially highly variable. For this reason we calculate the higher moments of the model so that the expected variability can be determined. To do this we formulate a new analytic framework for the cyton model by introducing a generalization to the Bellman-Harris branching process.We use this framework to introduce two distinct approaches to predicting variability in the immune response to a mitogenic signal. The first method enables explicit calculations for certain distributions and qualitatively exhibits the full range of observed immune responses. The second approach does not facilitate analytic solutions, but allows simple numerical schemes for distributions for which there is little prospect of analytic formulae.We compare the predictions derived from the second method to experimentally observed lymphocyte population sizes from in vivo and in vitro experiments. The model predictions for both data sets are remarkably accurate. The important biological conclusion is that there is limited variation around the expected value of the population size irrespective of whether the response is mediated by small numbers of cells undergoing many divisions or for many cells pursuing a small number of divisions. Therefore, we conclude the immune response is robust and predictable despite the potential for great variability in the experience of each individual cell.

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“…The values of the parameters are shown in Table 1. The stochastic noises of immune systems are mainly due to measurement errors, modeling errors and process noises (Milutinovic & De Boer, 2007). The rate of continuing introduction of exogenous pathogen and environmental disturbances 14 ww are unknown but bounded signals.…”

Section: Remarkmentioning

confidence: 99%