An agent-based model of signal transduction in bacterial chemotaxis

Agent-based modelling of iron cycling bacteria provides a framework for testing alternative environmental conditions and modes of action

Iron-reducing and iron-oxidizing bacteria are of interest in a variety of environmental and industrial applications. Such bacteria often co-occur at oxic-anoxic gradients in aquatic and terrestrial habitats. In this paper, we present the first computational agent-based model of microbial iron cycling, between the anaerobic ferric iron (Fe³⁺)-reducing bacteria Shewanella spp. and the microaerophilic ferrous iron (Fe²⁺)-oxidizing bacteria Sideroxydans spp. By including the key processes of reduction/oxidation, movement, adhesion, Fe²⁺-equilibration and nanoparticle formation, we derive a core model which enables hypothesis testing and prediction for different environmental conditions including temporal cycles of oxic and anoxic conditions. We compared (i) combinations of different Fe³⁺-reducing/Fe²⁺-oxidizing modes of action of the bacteria and (ii) system behaviour for different pH values. We predicted that the beneficial effect of a high number of iron-nanoparticles on the total Fe³⁺ reduction rate of the system is not only due to the faster reduction of these iron-nanoparticles, but also to the nanoparticles' additional capacity to bind Fe²⁺ on their surfaces. Efficient iron-nanoparticle reduction is confined to pH around 6, being twice as high than at pH 7, whereas at pH 5 negligible reduction takes place. Furthermore, in accordance with experimental evidence our model showed that shorter oxic/anoxic periods exhibit a faster increase of total Fe³⁺ reduction rate than longer periods.

Agent-Based Modeling of T Cell Receptor Cooperativity

Immunological synapse (IS) formation is a key event during antigen recognition by T cells. Recent experimental evidence suggests that the affinity between T cell receptors (TCRs) and antigen is actively modulated during the early steps of TCR signaling. In this work, we used an agent-based model to study possible mechanisms for affinity modulation during IS formation. We show that, without any specific active mechanism, the observed affinity between receptors and ligands evolves over time and depends on the density of ligands of the antigen peptide presented by major histocompatibility complexes (pMHC) and TCR molecules. A comparison between the presence or absence of TCR–pMHC centrally directed flow due to F-actin coupling suggests that centripetal transport is a potential mechanism for affinity modulation. The model further suggests that the time point of affinity measurement during immune synapse formation is critical. Finally, a mathematical model of F-actin foci formation incorporated in the agent-based model shows that TCR affinity can potentially be actively modulated by positive/negative feedback of the F-actin foci on the TCR-pMHC association rate k_on.

Modelling bacterial chemotaxis for indirectly binding attractants

In bacterial chemotaxis, chemoattractant molecules may bind either directly or indirectly with receptors within the cell periplasmic space. The indirect binding mechanism, which involves an intermediate periplasmic binding protein, has been reported to increase sensitivity to dilute attractant concentrations as well as range of response. Current mathematical models for bacterial chemotaxis at the population scale do not appear to take the periplasmic binding protein (BP) concentration or the indirect binding mechanics into account. We formulate an indirect binding extension to the existing Rivero equation for chemotactic velocity based on fundamental reversible enzyme kinetics. The formulated indirect binding expression accounts for the periplasmic BP concentration and the dissociation constants for binding between attractant and periplasmic BP, as well as between BP and chemoreceptor. We validate the indirect-binding model using capillary assay simulations of the chemotactic responses of E. coli to the indirectly-binding attractants maltose and AI-2. The predicted response agrees well with experimental data from a number of maltose capillary assay studies conducted in previous literature. The model is also able to achieve good agreement with AI-2 capillary assay data of one study out of two tested. The chemotactic response of E. coli towards AI-2 appears to be of higher complexity due to reports of variable periplasmic BP concentration as well as the low concentration of periplasmic BP relative to the total receptor concentration. Our current model is thus suitable for indirect binding chemotactic response systems with constant periplasmic BP concentration that is significantly larger than the total receptor concentration, such as the response of E. coli towards maltose. Further considerations may be taken into account to model the chemotactic response towards AI-2 with greater accuracy.

Increasing and decreasing the ultrastability of bacterial chemotaxis core signaling complexes by modifying protein-protein contacts

The chemosensory signaling array of bacterial chemotaxis is composed of functional core units containing two receptor trimers of dimers, a homodimeric CheA kinase, and two CheW adaptor proteins. In vitro reconstitutions generate individual, functional core units and larger functional assemblies, including dimers, hexagons, and hexagonal arrays. Such reconstituted complexes have been shown to have both quasi-stable and ultrastable populations that decay with lifetimes of 1–2 days and ∼3 weeks at 22 °C, respectively, where decay results primarily from proteolysis of the bound kinase [Erbse, A. H., and Falke, J. J. (2009) Biochemistry 48, 6975–6987; Slivka, P. F., and Falke, J. J. (2012) Biochemistry 51, 10218–10228]. In this work, we show that the ultrastable population can be destabilized to the quasi-stable level via the introduction of a bulky tryptophan residue at either one of two essential protein–protein interfaces within the core unit: the receptor–kinase contact or kinase–adaptor interface 1. Moreover, we demonstrate that the quasi-stable population can be made ultrastable via the introduction of a disulfide bond that covalently stabilizes the latter interface. The resulting disulfide at least doubles the functional lifetime of the ultrastable population, to ≥5.9 weeks at 22 °C, by protecting the kinase from endogenous and exogenous proteases. Together, these results indicate that the ultrastability of reconstituted core complexes requires well-formed contacts among the receptor, kinase, and adaptor proteins, whereas quasi-stability arises from less perfect contacts that allow slow proteolysis of the bound kinase. Furthermore, the results reveal that ultrastability, and perhaps the size or order of chemosensory complexes and arrays, can be increased by an engineered disulfide bond that covalently cross-links a key interface. Overall, it appears that native ultrastability has evolved to provide an optimal rather than maximal level of kinetic durability, suggesting that altered selective pressure could either increase or decrease the functional lifetime of core complexes.

Agent-based modeling of competence phenotype switching in Bacillus subtilis

Background

It is a fascinating phenomenon that in genetically identical bacteria populations of Bacillus subtilis, a distinct DNA uptake phenotype called the competence phenotype may emerge in 10–20% of the population. Many aspects of the phenomenon are believed to be due to the variable expression of critical genes: a stochastic occurrence termed “noise” which has made the phenomenon difficult to examine directly by lab experimentation.

Methods

To capture and model noise in this system and further understand the emergence of competence both at the intracellular and culture levels in B. subtilis, we developed a novel multi-scale, agent-based model. At the intracellular level, our model recreates the regulatory network involved in the competence phenotype. At the culture level, we simulated growth conditions, with our multi-scale model providing feedback between the two levels.

Results

Our model predicted three potential sources of genetic “noise”. First, the random spatial arrangement of molecules may influence the manifestation of the competence phenotype. In addition, the evidence suggests that there may be a type of epigenetic heritability to the emergence of competence, influenced by the molecular concentrations of key competence molecules inherited through cell division. Finally, the emergence of competence during the stationary phase may in part be due to the dilution effect of cell division upon protein concentrations.

Conclusions

The competence phenotype was easily translated into an agent-based model – one with the ability to illuminate complex cell behavior. Models such as the one described in this paper can simulate cell behavior that is otherwise unobservable in vivo, highlighting their potential usefulness as research tools.

Accounting for diffusion in agent based models of reaction-diffusion systems with application to cytoskeletal diffusion

Diffusion plays a key role in many biochemical reaction systems seen in nature. Scenarios where diffusion behavior is critical can be seen in the cell and subcellular compartments where molecular crowding limits the interaction between particles. We investigate the application of a computational method for modeling the diffusion of molecules and macromolecules in three-dimensional solutions using agent based modeling. This method allows for realistic modeling of a system of particles with different properties such as size, diffusion coefficients, and affinity as well as the environment properties such as viscosity and geometry. Simulations using these movement probabilities yield behavior that mimics natural diffusion. Using this modeling framework, we simulate the effects of molecular crowding on effective diffusion and have validated the results of our model using Langevin dynamics simulations and note that they are in good agreement with previous experimental data. Furthermore, we investigate an extension of this framework where single discrete cells can contain multiple particles of varying size in an effort to highlight errors that can arise from discretization that lead to the unnatural behavior of particles undergoing diffusion. Subsequently, we explore various algorithms that differ in how they handle the movement of multiple particles per cell and suggest an algorithm that properly accommodates multiple particles of various sizes per cell that can replicate the natural behavior of these particles diffusing. Finally, we use the present modeling framework to investigate the effect of structural geometry on the directionality of diffusion in the cell cytoskeleton with the observation that parallel orientation in the structural geometry of actin filaments of filopodia and the branched structure of lamellipodia can give directionality to diffusion at the filopodia-lamellipodia interface.