Publications

The dynamic nature of immune responses requires the development of appropriate experimental and theoretical tools to quantitatively estimate the division and death rates which determine the turnover of immune cells. A number of papers have used experimental data from BrdU and D-glucose labels together with a simple random birth-death model to quantify the turnover of immune cells focusing on HIV/SIV infections [Mohri et al. 279 (1998) 1223-1227, Hellerstein et al. 5 (1999) 83-89, Bonhoeffer et al. 164 (2000) 5049-5054, Mohri et al. 87 (2001) 1277-1287]. We show how uncertainties in the assumptions of the random birth-death model may lead to substantial errors in the parameters estimated. We then show how more accurate estimates can be obtained from the more recent CFSE data which allow to track the number of divisions each cell has undergone. Specifically, we: (i) describe a general stage-structured model of cell division where the probabilities of division and death are functions of time since the previous division; (ii) develop a rescaling method to identify invariant parameters (i.e. the ones that are independent of the specific functions describing division and death); (iii) show how these invariant parameters can be estimated, and (iv) illustrate this technique by applying it to CFSE data taken from the literature.

Models of the within-host dynamics of parasites have been used to consider the evolution of microparasites causing acute infections in vertebrate hosts. In this paper, we use these models to examine how the level of virulence to which a parasite evolves, depends on factors such as the relationship between parasite density and its rate of transmission from infected hosts, and the mechanism of parasite-induced pathogenesis. We show that changes in the terms describing transmissibility and pathogenesis may lead to dramatic differences in the level of virulence to which a parasite evolves. This suggests that no single factor is likely to be responsible for the differences in virulence of different parasites, and that understanding of the evolution of virulence of parasites will require a detailed quantitative understanding of the interaction between the parasite and its host.

Although it is clear that HIV can lyse HIV-infected CD4 T cells, it is still controversial whether the depletion of CD4 T cells seen in HIV-infected patients after years of asymptomatic disease is caused by the direct cytopathic effects of the virus or is mediated by the immune response. Assuming the initial decline in viraemia during highly active antiretroviral therapy (HAART) is caused by the death of cells productively infected with HIV, I investigate how the rate of the virus decline is affected by the efficiency of the cytotoxic T-lymphocyte (CTL) response. I find that whether the stronger immune response causes a more rapid virus decline depends critically on how the virus is controlled by the CTL response (lytic versus non-lytic mechanisms). Moreover, variation in the efficiency of the immune response does not always cause variation in the rate of the virus decline (and, therefore, in the death rate of infected cells), implying that the constancy of the virus decline rate measured in different patients does not necessarily indicate that the virus is cytopathic. The potential problems associated with the model and the approach undertaken are also discussed.

Why do parasites harm their hosts? The general understanding is that if the transmission rate and virulence of a parasite are linked, then the parasite must harm its host to maximize its transmission. The exact nature of such trade-offs remains largely unclear, but for vertebrate hosts it probably involves interactions between a microparasite and the host immune system. Previous results have suggested that in a homogeneous host population in the absence of super- or coinfection, within-host dynamics lead to selection of the parasite with an intermediate growth rate that is just being controlled by the immune system before it kills the host (Antia et al. 1994). In this paper, we examine how this result changes when heterogeneity is introduced to the host population. We incorporate the simplest form of heterogeneity–random heterogeneity in the parameters describing the size of the initial parasite inoculum, the immune response of the host, and the lethal density at which the parasite kills the host. We find that the general conclusion of the previous model holds: parasites evolve some intermediate growth rate. However, in contrast with the generally accepted view, we find that virulence (measured by the case mortality or the rate of parasite-induced host mortality) increases with heterogeneity. Finally, we link the within-host and between-host dynamics of parasites. We show how the parameters for epidemiological spread of the disease can be estimated from the within-host dynamics, and in doing so examine the way in which trade-offs between these epidemiological parameters arise as a consequence of the interaction of the parasite and the immune response of the host.

What determines the stability of plasmid-bearing cells in natural and laboratory conditions? In order to answer this question in a quantitative manner, we need tools allowing the estimation of parameters governing plasmid loss in different environments. In the present work, we have developed two methods for the estimation of the instability parameters of plasmid-bearing cells growing in chemostat. These instability parameters are: (i) selection coefficient (or cost of the plasmid)alpha and (ii) the probability of plasmid loss at cell division tau(0). We have found that generally selection coefficient alpha changes during elimination of plasmid-bearing cells due to changes in substrate concentration; hence, methods which assume constancy of alpha are intrinsically imprecise. Instead, one can estimate selection coefficient at the beginning and the end of cultivation when the substrate concentration is approximately constant. Applying developed techniques to two sets of experimental data, we have found that (i) the cost of the plasmid pBR322 depended on the dilution rate in chemostat and was higher at low dilutions; (ii) high levels of plasmid gene expression led to a high cost of the plasmid pPHL-7; (iii) the probability of plasmid loss was lower at high levels of plasmid gene expression and independent of the dilution rate. We have also discussed the application of our results to understanding the basic biology of bacterial plasmids.

The process of biotic turnover in a closed ecological system (CES) with an external energy flow was analyzed by mathematical modeling of the biotic cycle formation. The formation of hierarchical structure in model CESs is governed by energy criteria. Energy flow through the ecosystem increases when a predator is introduced into a "producer-reducer" system at steady state. Analysis of the model shows that under certain conditions the presence of the primary predator with its high mineralization ability accelerates the biotic turnover measured by primary production. We, therefore, conclude that for every system it is possible to find a suitable predator able to provide the system with a higher biotic turnover rate and energy consumption. Grant numbers: 99-04-96017/2000.

A structural approach to studying the regularities of the population dynamics of unstable recombinant bacterial strains in a chemostat was elaborated. The approach is based on the mathematical modeling of cell distribution in a population with different numbers of plasmid copies. The effect of decreased selective preference of plasmidless variants of the recombinant strain in the chemostat, which is related to a decrease in the number of plasmid copies in cells upon long-term incubation was analyzed. It is shown that the time of half-elimination of plasmids from the bacterial population in the steady state in the chemostat T1/2 does not depend on the maximum number of plasmid copies in cells N but is determined only by the mean time of generation g and the probability of the loss of one plasmid copy tau. The dependence of the preference of bacterial plasmidless variants on the efficiency of expression of genes cloned into plasmids in chemostat was analyzed using the recombinant strain E. coli Z905, whose plasmids pPHL-7 contain cloned genes for the luminescence system of marine luminescing bacteria Photobacterium leiognathi.

The possibility of introducing genetically engineered microorganisms (GEM) into simple biotic cycles of laboratory water microcosms was investigated. The survival of the recombinant strain Escherichia coli Z905 (Apr, Lux+) in microcosms depends on the type of model ecosystems. During the absence of algae blooming in the model ecosystem, the part of plasmid-containing cells E. coli decreased fast, and the structure of the plasmid was also modified. In conditions of algae blooming (Ankistrodesmus sp.) an almost total maintenance of plasmid-containing cells was observed in E. coli population. A mathematics model of GEM's behavior in water ecosystems with different level of complexity has been formulated. Mechanisms causing the difference in luminescent exhibition of different species are discussed, and attempts are made to forecast the GEM's behavior in water ecosystems.