Biomedical subjects

Sergei S Pilyugin

Publications and source records attributed to Sergei S Pilyugin.

12 recordsLinked to original sources

PubMed2006

Subthreshold and superthreshold coexistence of pathogen variants: the impact of host age-structure.

It is well known that in the most general epidemic models with multiple pathogen variants a competitive exclusion principle is valid, such that the variant with the highest reproduction number eliminates the rest. Mechanisms such as super-infection, coinfection, and cross-immunity can lead to pathogen polymorphism where multiple strains coexist. It is also known that variability of infectivity with host age can destabilize the endemic equilibrium and cause oscillations. In this article we show that the hosts' chronological age can itself lead to coexistence of microparasites in the most basic model where competitive exclusion will occur without the age structure. Moreover, the host age-structure leads to multiple subthreshold dominance equilibria, and both weakly and strongly subthreshold coexistence. We find that the two pathogens cannot cooperate to persist subthreshold if neither one of them can persist subthreshold by itself. If, however, one of them can persist subthreshold by itself, it can cause the two pathogens to coexist in a strongly subthreshold equilibrium. The second strain that persists subthreshold through the mediation of the first always has a lower virulence. Our results show that age structure in infectivity can permit the coexistence of competing pathogens when the incidence is of proportionate mixing type (frequency-dependent transmission) and at least one of the strains is virulent.

Age Factors↗

PubMed2006

Bacterial gene regulation in diauxic and non-diauxic growth.

When bacteria are grown in a batch culture containing a mixture of two growth-limiting substrates, they exhibit a rich spectrum of substrate consumption patterns including diauxic growth, simultaneous consumption, and bistable growth. In previous work, we showed that a minimal model accounting only for enzyme induction and dilution captures all the substrate consumption patterns [Narang, A., 1998a. The dynamical analogy between microbial growth on mixtures of substrates and population growth of competing species. Biotechnol. Bioeng. 59, 116-121, Narang, A., 2006. Comparitive analysis of some models of gene regulation in mixed-substrate microbial growth, J. Theor. Biol. 242, 489-501]. In this work, we construct the bifurcation diagram of the minimal model, which shows the substrate consumption pattern at any given set of parameter values. The bifurcation diagram explains several general properties of mixed-substrate growth. (1) In almost all the cases of diauxic growth, the "preferred" substrate is the one that, by itself, supports a higher specific growth rate. In the literature, this property is often attributed to the optimality of regulatory mechanisms. Here, we show that the minimal model, which accounts for induction and growth only, displays the property under fairly general conditions. This suggests that the higher growth rate of the preferred substrate is an intrinsic property of the induction and dilution kinetics. It can be explained mechanistically without appealing to optimality principles. (2) The model explains the phenotypes of various mutants containing lesions in the regions encoding for the operator, repressor, and peripheral enzymes. A particularly striking phenotype is the "reversal of the diauxie" in which the wild-type and mutant strains consume the very same two substrates in opposite order. This phenotype is difficult to explain in terms of molecular mechanisms, such as inducer exclusion or CAP activation, but it turns out to be a natural consequence of the model. We show furthermore that the model is robust. The key property of the model, namely, the competitive dynamics of the enzymes, is preserved even if the model is modified to account for various regulatory mechanisms. Finally, the model has important implications for the problem of size regulation in development. It suggests that protein dilution may be the mechanism coupling patterning and growth.

Bacteria↗

PubMed2006

How does cross-reactive stimulation affect the longevity of CD8+ T cell memory?

Immunological memory--the ability to "remember" previously encountered pathogens and respond faster upon re-exposure is a central feature of the immune response in vertebrates. The cross-reactive stimulation hypothesis for the maintenance of memory proposes that memory cells specific for a given pathogen are maintained by cross-reactive stimulation following infections with other (unrelated) pathogens. We use mathematical models to examine the cross-reactive stimulation hypothesis. We find that: (i) the direct boosting of cross-reactive lineages only provides a very small increase in the average longevity of immunological memory; (ii) the expansion of cross-reactive lineages can indirectly increase the longevity of memory by reducing the magnitude of expansion of new naive lineages which occupy space in the memory compartment and are responsible for the decline in memory; (iii) cross-reactive stimulation results in variation in the rates of decline of different lineages of memory cells and enrichment of memory cell population for cells that are cross-reactive for the pathogens to which the individual has been exposed.

Animals↗

PubMed2005

Quantifying cell turnover using CFSE data.

The CFSE dye dilution assay is widely used to determine the number of divisions a given CFSE labelled cell has undergone in vitro and in vivo. In this paper, we consider how the data obtained with the use of CFSE (CFSE data) can be used to estimate the parameters determining cell division and death. For a homogeneous cell population (i.e., a population with the parameters for cell division and death being independent of time and the number of divisions cells have undergone), we consider a specific biologically based "Smith-Martin" model of cell turnover and analyze three different techniques for estimation of its parameters: direct fitting, indirect fitting and rescaling method. We find that using only CFSE data, the duration of the division phase (i.e., approximately the S+G2+M phase of the cell cycle) can be estimated with the use of either technique. In some cases, the average division or cell cycle time can be estimated using the direct fitting of the model solution to the data or by using the Gett-Hodgkin method [Gett A. and Hodgkin, P. 2000. A cellular calculus for signal integration by T cells. Nat. Immunol. 1:239-244]. Estimation of the death rates during commitment to division (i.e., approximately the G1 phase of the cell cycle) and during the division phase may not be feasible with the use of only CFSE data. We propose that measuring an additional parameter, the fraction of cells in division, may allow estimation of all model parameters including the death rates during different stages of the cell cycle.

Algorithms↗

PubMed2004

Predicting stability of mixed microbial cultures from single species experiments: 2. Physiological model.

In this paper, we study the equilibria of a physiological model describing the continuous culture in which two microbial populations compete for two substitutable resources. This work is an extension of the stability analysis of the phenomenological model of mixed microbial growth [M.M. Ballyk, G.S.K. Wolkowicz, Exploitative competition in the chemostat for two perfectly substitutable resources, Math. Biosci. 118 (1993) 127-180; S.S. Pilyugin, G.T. Reeves, A. Narang, Predicting stability of mixed microbial cultures from single species experiments: 2. Phenomenological model]. Here, we investigate the influence of the peripheral enzymes that catabolize the substrate uptake on the stability of the mixed culture. We show that, under steady state conditions, an increase in the concentration of one substrate inhibits the uptake of the other substrate(s). We present the criteria for existence, uniqueness, and stability of various types of equilibria. We formulate these criteria in terms of growth isoclines and consumption curves for each of the competing species. Since both types of curves can be obtained from a single species experiment, our approach provides a direct connection between theory and experiment and allows one to infer the dynamics of mixed cultures from the dynamics of single species cultures. By expressing the stability criteria in terms of intracellular properties, the model establishes a link between ecology and molecular biology.

Culture Media↗

PubMed2004

Predicting stability of mixed microbial cultures from single species experiments: 1. Phenomenological model.

The growth of mixed microbial cultures on mixtures of substrates is a fundamental problem of both theoretical and practical interest. On the one hand, the literature is abundant with experimental studies of mixed-substrate phenomena [T. Egli, The ecological and physiological significance of the growth of heterotrophic microorganisms with mixtures of substrates, Adv. Microbiol. Ecol. 14 (1995) 305-386]. On the other hand, a number of mathematical models of mixed-substrate growth have been analyzed in the last three decades. These models typically assume specific kinetic expressions for substrate uptake and biomass growth rates and their predictions are formulated in terms of parameters of the model. In this work, we formulate and analyze a general mathematical model of mixed microbial growth on mixtures of substitutable substrates. Using this model, we study the effect of mutual inhibition of substrate uptake rates on the stability of the equilibria of the model. Specifically, we address the following question: How much of the dynamics exhibited by two competing species can be inferred from single species data? We provide geometric criteria for stability of various types of equilibria corresponding to non-competitive exclusion, competitive exclusion, and coexistence of two competing species in terms of growth isoclines and consumption curves. A growth isocline is a curve in the plane of substrate concentrations corresponding to the zero net growth of a given species. In [G.T. Reeves, A. Narang, S.S. Pilyugin, Growth of mixed cultures on mixtures of substitutable substrates: The operating diagram for a structured model, J. Theor. Biol. 226 (2004) 143-157], we introduced consumption curves as sets of all possible combinations of substrate concentrations corresponding to balanced growth of a single microbial species. Both types of curves can be obtained in single species experiments.

Culture Media↗

PubMed2004

Growth of mixed cultures on mixtures of substitutable substrates: the operating diagram for a structured model.

The growth of mixed microbial cultures on mixtures of substrates is a problem of fundamental biological interest. In the last two decades, several unstructured models of mixed-substrate growth have been studied. It is well known, however, that the growth patterns in mixed-substrate environments are dictated by the enzymes that catalyse the transport of substrates into the cell. We have shown previously that a model taking due account of transport enzymes captures and explains all the observed patterns of growth of a single species on two substitutable substrates (J. Theor. Biol. 190 (1998) 241). Here, we extend the model to study the steady states of growth of two species on two substitutable substrates. The model is analysed to determine the conditions for existence and stability of the various steady states. Simulations are performed to determine the flow rates and feed concentrations at which both species coexist. We show that if the interaction between the two species is purely competitive, then at any given flow rate, coexistence is possible only if the ratio of the two feed concentrations lies within a certain interval; excessive supply of either one of the two substrates leads to annihilation of one of the species. This result simplifies the construction of the operating diagram for purely competing species. This is because the two-dimensional surface that bounds the flow rates and feed concentrations at which both species coexist has a particularly simple geometry: It is completely determined by only two coordinates, the flow rate and the ratio of the two feed concentrations. We also study commensalistic interactions between the two species by assuming that one of the species excretes a product that can support the growth of the other species. We show that such interactions enhance the coexistence region.

Bacteria↗

PubMed2003

The rescaling method for quantifying the turnover of cell populations.

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.

Adoptive Transfer↗

PubMed2003

The dynamics of single-substrate continuous cultures: the role of transport enzymes.

A chemostat limited by a single growth-limiting substrate displays a rich spectrum of dynamics. Depending on the flow rate and feed concentration, the chemostat settles into a steady state or executes sustained oscillations. The transients in response to abrupt increases in the flow rate or the feed concentration are also quite complex. For example, if the increase in the flow rate is small, there is no perceptible change in the substrate concentration. If the increase in the flow rate is large, there is a large increase in the substrate concentration lasting several hours or days before the culture adjusts to a new steady state. In the latter case, the substrate concentration and cell density frequently undergo damped oscillations during their approach to the steady state. In this work, we formulate a simple structured model containing the inducible transport enzyme as the key intracellular variable. The model displays the foregoing dynamics under conditions similar to those employed in the experiments. The model suggests that long recovery times (on the order of several hours to several days) can occur because the initial transport enzyme level is too small to cope with the increased substrate supply. The substrate concentration, therefore, increases until the enzyme level is built up to a sufficiently high level by the slow process of enzyme induction. Damped and sustained oscillations can occur because transport enzyme synthesis is autocatalytic, and hence, destabilizing. At low dilution rates, the response of stabilizing processes, such as enzyme dilution and substrate consumption, becomes very slow, leading to damped and sustained oscillations.

Bacteria↗

PubMed2003

Models of CD8+ responses: 1. What is the antigen-independent proliferation program.

Recent experimental results show that even brief stimulation with antigen can cause antigen-specific CD8 T-cells to undergo sustained proliferation followed by differentiation into memory cells. These results show that the dynamics of these immune responses are not governed by constant monitoring of antigen levels, but rather that following stimulation immune cells commit to a "program". At present relatively little is known about the program which governs CD8 cell proliferation and differentiation. For example, we do not know whether the program is completely specified by the initial encounter of a T cell with antigen, or whether it subsequently can be modified by the amount of antigen present. Nor do we know whether the entire program for T cell proliferation and differentiation resides within the T cell itself, or whether some component(s) of the program are determined by cells or molecules external to the CD8 cell. In this paper we construct simple mathematical models which incorporate antigen-independent proliferation and differentiation of CD8 cells during acute infections. We use these models to determine what characteristics the program must have in order to be consistent with the existing data on the dynamics of CD8 responses, and in particular to answer the questions posed above. Our results suggest that the program is not completely defined by the initial encounter of T cell with antigen but may be augmented by exposure to antigen in a brief window shortly after infection; furthermore, parts of the program may reside external to the T-cells. Finally we examine some of the consequences of the "program" for pathogen-host coevolution.

Animals↗

PubMed2003

Multiple limit cycles in the chemostat with variable yield.

The global asymptotic behavior of solutions of the variable yield model is determined. The model generalizes the classical Monod model and it assumes that the yield is an increasing function of the nutrient concentration. In contrast to the Monod model, it is demonstrated that the variable yield model exhibits sustained oscillations. Moreover, it is shown that the variable yield model may undergo a subcritical Hopf bifurcation and feature at least two distinct limit cycles. Implications for the coexistence of competing populations are discussed.

Bacteria↗

PubMed2003

Global asymptotic stability of a class of dynamical neural networks.

The dynamics of cortical cognitive maps developed by self-organization must include the aspects of long and short-term memory. The behavior of the network is such characterized by an equation of neural activity as a fast phenomenon and an equation of synaptic modification as a slow part of the neural biologically relevant system. We present new stability conditions for analyzing the dynamics of a biological relevant system with different time scales based on the theory of flow invariance. We prove the existence and uniqueness of the equilibrium, and give a quadratic-type Lyapunov function for the flow of a competitive neural system with fast and slow dynamic variables and thus prove the global stability of the equilibrium point.

Algorithms↗