Using systemic modeling and Bayesian calibration to investigate the role of the tumor microenvironment on chemoresistance

Using a novel modeling approach based on the so-called environmental stress level (ESL), we develop a mathematical model to describe systematically the collective influence of oxygen concentration and stiffness of the extracellular matrix on the response of tumor cells to a combined chemotherapeutic treatment. We perform Bayesian calibrations of the resulting model using particle filters, with in vitro experimental data for different hepatocellular carcinoma cell lines. The calibration results support the validity of our mathematical model. Furthermore, they shed light on individual as well as synergistic effects of hypoxia and tissue stiffness on tumor cell dynamics under chemotherapy.Comment: Contains supplementary materia

Spatial Heterogeneity of Autoinducer Regulation Systems

Autoinducer signals enable coordinated behaviour of bacterial populations, a phenomenon originally described as quorum sensing. Autoinducer systems are often controlled by environmental substances as nutrients or secondary metabolites (signals) from neighbouring organisms. In cell aggregates and biofilms gradients of signals and environmental substances emerge. Mathematical modelling is used to analyse the functioning of the system. We find that the autoinducer regulation network generates spatially heterogeneous behaviour, up to a kind of multicellularity-like division of work, especially under nutrient-controlled conditions. A hybrid push/pull concept is proposed to explain the ecological function. The analysis allows to explain hitherto seemingly contradicting experimental findings

A mathematical model of quorum sensing regulated EPS production in biofilm communities

<p>Abstract</p> <p>Background</p> <p>Biofilms are microbial communities encased in a layer of extracellular polymeric substances (EPS). The EPS matrix provides several functional purposes for the biofilm, such as protecting bacteria from environmental stresses, and providing mechanical stability. Quorum sensing is a cell-cell communication mechanism used by several bacterial taxa to coordinate gene expression and behaviour in groups, based on population densities.</p> <p>Model</p> <p>We mathematically model quorum sensing and EPS production in a growing biofilm under various environmental conditions, to study how a developing biofilm impacts quorum sensing, and conversely, how a biofilm is affected by quorum sensing-regulated EPS production. We investigate circumstances when using quorum-sensing regulated EPS production is a beneficial strategy for biofilm cells.</p> <p>Results</p> <p>We find that biofilms that use quorum sensing to induce increased EPS production do not obtain the high cell populations of low-EPS producers, but can rapidly increase their volume to parallel high-EPS producers. Quorum sensing-induced EPS production allows a biofilm to switch behaviours, from a colonization mode (with an optimized growth rate), to a protection mode.</p> <p>Conclusions</p> <p>A biofilm will benefit from using quorum sensing-induced EPS production if bacteria cells have the objective of acquiring a thick, protective layer of EPS, or if they wish to clog their environment with biomass as a means of securing nutrient supply and outcompeting other colonies in the channel, of their own or a different species.</p

Mathematical Modeling of Bacteria Communication in Continuous Cultures

Quorum sensing is a bacterial cell-to-cell communication mechanism and is based on gene regulatory networks, which control and regulate the production of signaling molecules in the environment. In the past years, mathematical modeling of quorum sensing has provided an understanding of key components of such networks, including several feedback loops involved. This paper presents a simple system of delay differential equations (DDEs) for quorum sensing of Pseudomonas putida with one positive feedback plus one (delayed) negative feedback mechanism. Results are shown concerning fundamental properties of solutions, such as existence, uniqueness, and non-negativity; the last feature is crucial for mathematical models in biology and is often violated when working with DDEs. The qualitative behavior of solutions is investigated, especially the stationary states and their stability. It is shown that for a certain choice of parameter values, the system presents stability switches with respect to the delay. On the other hand, when the delay is set to zero, a Hopf bifurcation might occur with respect to one of the negative feedback parameters. Model parameters are fitted to experimental data, indicating that the delay system is sufficient to explain and predict the biological observations

The interplay of two Quorum sensing regulation systems of Vibrio fischeri

Many bacteria developed a possibility to recognise aspects of their environment or to communicate with each other by chemical signals. One important case is the so-called Quorum sensing (QS), a regulatory mechanism for the gene expression, where the bacteria measure their own cell density by means of this signalling pathway. One of the best-studied species using QS is the marine luminescent bacterium Vibrio fischeri which is considered here as a model organism. The two main regulatory pathways (lux and ain) are combined to a regulation system, the dynamics is modelled by an ODE system. This system is analysed thoroughly, considering stationary states, dynamical behaviour and the possible biological meaning of it. The influence of different parameter values on the behaviour is examined, the same basic system is able to reflect the peculiarities of different bacteria strains (respectively their mutants).

Optimal multiplicative control of bacterial quorum sensing under external enzyme impact

The use of external enzymes provides an alternative way of reducing communication in pathogenic bacteria that may lead to the degradation of their signal and the loss of their pathogeneity. The present study considers an optimal control problem for the semilinear reaction-diffusion model of bacterial quorum sensing under the impact of external enzymes. Estimates of the solution of the controlled system are obtained, on the basis of which the solvability of the extremal problem is proved and the necessary optimality conditions of the first-order are derived. A numerical algorithm to find a solution of the optimal control problem is constructed and implemented. The conducted numerical experiments demonstrate an opportunity to build an effective strategy of the enzymes impact for treatment

Running Head: Cell-Cell Communication by Quorum Sensing and Dimension-Reduction

The bioluminescence of the bacterium Vibrio fischeri depends strongly on the density of the cells. This phenomenon can be interpreted as the consequence of a communication system between the bacteria and is called quorum sensing. We introduce a modeling approach for the description of this quorum sensing system, including a detailed discussion of the regulatory network and its bistable behavior. Based on this single-cell model we develop and analyse a spatially structured model for a cell population. Special attention is given to the scaling behavior of the cell size (leading to an approximation theorem for stationary solutions) and its consequences for the interpretation of cell communication (quorum sensing versus diffusion sensing). Concluding, we apply the modeling approach to concrete experimental data which allows estimations of model parameters.

A mathematical model of quorum quenching in biofilm colonies and its potential role as an adjuvant for antibiotic treatment

We extend a previously presented mesoscopic (i.e. colony scale) mathematical model of the reaction of bacterial biofilms to antibiotics. In that earlier model, exposure to antibiotics evokes two responses: inactivation as the antibiotics kill the bacteria, and inducing a quorum sensing based stress response mechanism upon exposure to small sublethal dosages. To this model we add now quorum quenching as an adjuvant to antibiotic therapy. Quorum quenchers are modeled like enzymes that degrade the quorum sensing signal concentration. The resulting model is a quasilinear system of seven reaction-diffusion equations for the dependent variables volume fractions of upregulated (protected), downregulated (unprotected) and inert (inactive) biomass [particulate substances], and for concentrations of a growth promoting nutrient, antibiotics, quorum sensing signal, and quorum quenchers [dissolved substances]. The biomass fractions are subject to two nonlinear diffusion effects: (i) degeneracy, as in the porous medium equation, where biomass vanishes, and (ii) a super-diffusion singularity where as it attains its theoretically possible maximum. We study this model in numerical simulations. Our simulations suggest that for maximum efficacy quorum quenchers should be applied early on before quorum sensing induction in the biofilm can take place, and that an antibiotic strategy that by itself might not be successful can be notably improved upon if paired with quorum quenchers as an adjuvant.