arXiv subjects

Sergei S. Pilyugin

Publications and source records attributed to Sergei S. Pilyugin.

7 recordsLinked to original sources

arXiv2024

A chemostat model with variable dilution rate due to biofilm growth

In many real life applications, a continuous culture bioreactor may cease to function properly due to bioclogging which is typically caused by the microbial overgrowth. This is a problem that has been largely overlooked in the chemostat modeling literature, despite the fact that a number of models explicitly accounted for biofilm development inside the bioreactor. In a typical chemostat model, the physical volume of the biofilm is considered negligible when compared to the volume of the fluid. In this paper, we investigate the theoretical consequences of removing such assumption. Specifically, we formulate a novel mathematical model of a chemostat where the increase of the biofilm volume occurs at the expense of the fluid volume of the bioreactor, and as a result the corresponding dilution rate increases reciprocally. We show that our model is well-posed and describes the bioreactor that can operate in three distinct types of dynamic regimes: the washout equilibrium, the coexistence equilibrium, or a transient towards the clogged state which is reached in finite time. We analyze the multiplicity and the stability of the corresponding equilibria. In particular, we delineate the parameter combinations for which the chemostat never clogs up and those for which it clogs up in finite time. We also derive criteria for microbial persistence and extinction. Finally, we present a numerical evidence that a multistable coexistence in the chemostat with variable dilution rate is feasible.

q-bio.PE↗

arXiv2022

Using Restart Sequences to Determine Beneficial First Passage Under Restart

First Passage (FP) processes are utilized widely to model phenomena in many areas of mathematical applications, from biology to computer science. Introducing a mechanism to restart the parent process can alter the first passage characteristics, and the properties of the resulting First Passage Under Restart (FPUR) process have been subject to much recent investigation. Here we seek to more fully characterize whether a discrete FP process can have its mean hitting time reduced through the implementation of restart by analyzing a construct we call the restart sequence, which is determined solely by the distribution of the FP process.

math.PR↗

arXiv2021

First Passage with Restart in Discrete Time: with applications to biased random walks on the half-line

In recent years, it has been well-established that adding a restart mechanism can alter the firstpassage statistics of a stochastic processes in useful and interesting ways. Though different mecha-nisms have been investigated, we derive a probability generating function for a discrete-time FirstPassage process Under Restart and use it to examine two examples, including a biased random walkon the non-negative integers.

math.PR↗

arXiv2007

Immune response to a malaria infection: properties of a mathematical model

We establish some properties of a within host mathematical model of malaria proposed by Recker et al which includes the role of the immune system during the infection. The model accounts for the antigenic variation exhibited by the malaria parasite (P. falciparum). We show that the model can exhibit a wide variety of dynamical behaviors. We provide criteria for global stability, competitive exclusion, and persistence. We also demonstrate that the disease equilibrium can be destabilized by non-symmetric cross-reactive responses.

q-bio.CB↗

arXiv2007

Multi-strain virus dynamics with mutations: A global analysis

We consider within-host virus models with more than one strain and allow mutation between the strains. If there is no mutation, a Lyapunov function establishes global stability of the steady state corresponding to the fittest strain. For small perturbations this steady state persists, perhaps with small concentrations of some or all other strains, depending on the connectivity of the graph describing all possible mutations. Moreover, using a perturbation result due to Smith and Waltman, we show that this steady state also preserves global stability.

q-bio.CB↗

arXiv2006

Bacterial gene regulation in diauxic and nondiauxic growth

When bacteria are grown on 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. Here, we construct the bifurcation diagram of the minimal model. The bifurcation diagram explains several general properties of mixed-substrate growth. (1) In almost all 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 optimality of regulatory mechanisms. Here, we show that the minimal model, which contains only induction, 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.(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, 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 size regulation in development, since it suggests that protein dilution is one mechanism for coupling patterning and growth.

q-bio.MN↗

arXiv2005

Pure competition of multiple species during mixed-substrate microbial growth: Extending the resource-based theory

The simultaneous growth of multiple microbial species is a problem of fundamental ecological interest. In media containing more than one growth-limiting substrate, multiple species can coexist. The question then arises: Can single-species data predict the existence and stability of mixed-culture steady states in mixed-substrate environments? This question has been extensively studied with the help of resource-based models. These studies have shown that the single-species data required to predict mixed-culture behavior consists of the growth isoclines and consumption vectors, which in turn are determined from single-substrate data by making specific assumptions about the kinetics of mixed-substrate growth. Here, we show that these assumptions are not valid for microbial growth on mixtures of substitutable substrates. However, the theory can be developed by determining the growth isoclines and consumption vectors directly from the mixed-substrate data, thus obviating the need for specific assumptions about the kinetics of mixed-substrate growth. We show furthermore that in addition to the growth isoclines and consumption vectors, the single-species, mixed-substrate data yields a new family of curves, which we call the consumption curves. Consideration of the growth isoclines and the consumption curves yields deeper insights into the behavior of the mixed cultures. It yields a priori bounds on the substrate concentrations achieved during coexistence, permits the extension of the theory to systems in which the growth isoclines are non-monotonic, and clarifies earlier results obtained by considering only the growth isoclines.

q-bio.PE↗