A mathematical model to investigate quorum sensing regulation and its heterogeneity in Pseudomonas syringae on leaves

Cooperation in bioluminescence: understanding the role of autoinducers by a stochastic random resistor model

Quorum sensing is a communication mechanism adopted by different bacterial strains for the regulation of gene transcription. It takes place through the exchange of molecules called autoinducers. Bioluminescence is an emergent threshold phenomenon shown by some bacteria strains. Its precise relationship to quorum sensing is a debated topic, particularly regarding the role of the different autoinducers used by bacteria. In this paper, assuming a direct relationship between bioluminescence and quorum sensing, we investigate the role of multiple autoinducers in the bioluminescence response of Vibrio harveyi, considered as a model bioluminescent strain, due to its quorum sensing circuitry involving an array of three different autoinducers. Experiments on mutants of this bacterium, obtained by suppression of one or more autoinducers, reveal their relative non-trivial relevance and cooperative interaction patterns. The proposed analysis is implemented on a regular lattice, whose nodes represent microbial entities equipped with charges, which represent the ability to up/down regulate the gene expression. Quorum sensing results from a Coulomb-type field, produced by the charges. In analogy with random resistor network models, the lattice is permeated by an effective current which accounts for the amount and distribution of the charges. We propose that the presence of different autoinducers correspond to a different up/down regulation of gene expression, i.e., to a different way to account for the charges. Then, by introducing a modulation of the charge dependence into the current flowing within the network, we show that it is able to describe the bioluminescence exhibited by V. harveyi mutants. Furthermore, modulation of the charge dependence allows the interactions between the different autoinducers to be taken into account, providing a prediction regarding the data obtainable under specific growth conditions.

Numerical investigation of microbial quorum sensing under various flow conditions

Microorganisms efficiently coordinate phenotype expressions through a decision-making process known as quorum sensing (QS). We investigated QS amongst distinct, spatially distributed microbial aggregates under various flow conditions using a process-driven numerical model. Model simulations assess the conditions suitable for QS induction and quantify the importance of advective transport of signaling molecules. In addition, advection dilutes signaling molecules so that faster flow conditions require higher microbial densities, faster signal production rates, or higher sensitivities to signaling molecules to induce QS. However, autoinduction of signal production can substantially increase the transport distance of signaling molecules in both upstream and downstream directions. We present empirical approximations to the solutions of the advection–diffusion–reaction equation that describe the concentration profiles of signaling molecules for a wide range of flow and reaction rates. These empirical relationships, which predict the distribution of dissolved solutes along pore channels, allow to quantitatively estimate the effective communication distances amongst multiple microbial aggregates without further numerical simulations.

Drug-Induced Resistance in Micrometastases: Analysis of Spatio-Temporal Cell Lineages

Resistance to anti-cancer drugs is a major cause of treatment failure. While several intracellular mechanisms of resistance have been postulated, the role of extrinsic factors in the development of resistance in individual tumor cells is still not fully understood. Here we used a hybrid agent-based model to investigate how sensitive tumor cells develop drug resistance in the heterogeneous tumor microenvironment. We characterized the spatio-temporal evolution of lineages of the resistant cells and examined how resistance at the single-cell level contributes to the overall tumor resistance. We also developed new methods to track tumor cell adaptation, to trace cell viability trajectories and to examine the three-dimensional spatio-temporal lineage trees. Our findings indicate that drug-induced resistance can result from cells adaptation to the changes in drug distribution. Two modes of cell adaptation were identified that coincide with microenvironmental niches—areas sheltered by cell micro-communities (protectorates) or regions with limited drug penetration (refuga or sanctuaries). We also recognized that certain cells gave rise to lineages of resistant cells (precursors of resistance) and pinpointed three temporal periods and spatial locations at which such cells emerged. This supports the hypothesis that tumor micrometastases do not need to harbor cell populations with pre-existing resistance, but that individual tumor cells can adapt and develop resistance induced by the drug during the treatment.

Comparative genomic analysis of Pseudomonas amygdali pv. lachrymans NM002: Insights into its potential virulence genes and putative invasion determinants

Pseudomonas amygdali pv. lachrymans is currently of important plant pathogenic bacteria that causes cucumber angular leaf spot worldwide. The pathogen has been studied for its roles in pathogenicity and plant inheritance resistance. To further delineate traits critical to virulence, invasion and survival in the phyllosphere, we reported the first complete genome of P. amygdali pv. lachrymans NM002. Analysis of the whole genome in comparison with three closely-related representative pathovars of P. syringae identified the conservation of virulence genes, including flagella and chemotaxis, quorum-sensing systems, two-component systems, and lipopolysaccharide and antiphagocytosis. It also revealed differences of invasion determinants, such as type III effectors, phytotoxin (coronatine, syringomycin and phaseolotoxin) and cell wall-degrading enzyme, which may contribute to infectivity. The aim of this study was to derive genomic information that would reveal the probable molecular mechanisms underlying the virulence, infectivity and provide a better understanding of the pathogenesis of the P. syringae pathovars.

Mapping quorum sensing onto neural networks to understand collective decision making in heterogeneous microbial communities

Microbial communities frequently communicate via quorum sensing (QS), where cells produce, secrete, and respond to a threshold level of an autoinducer (AI) molecule, thereby modulating gene expression. However, the biology of QS remains incompletely understood in heterogeneous communities, where variant bacterial strains possess distinct QS systems that produce chemically unique AIs. AI molecules bind to 'cognate' receptors, but also to 'non-cognate' receptors found in other strains, resulting in inter-strain crosstalk. Understanding these interactions is a prerequisite for deciphering the consequences of crosstalk in real ecosystems, where multiple AIs are regularly present in the same environment. As a step towards this goal, we map crosstalk in a heterogeneous community of variant QS strains onto an artificial neural network model. This formulation allows us to systematically analyze how crosstalk regulates the community's capacity for flexible decision making, as quantified by the Boltzmann entropy of all QS gene expression states of the system. In a mean-field limit of complete cross-inhibition between variant strains, the model is exactly solvable, allowing for an analytical formula for the number of variants that maximize capacity as a function of signal kinetics and activation parameters. An analysis of previous experimental results on the Staphylococcus aureus two-component Agr system indicates that the observed combination of variant numbers, gene expression rates and threshold concentrations lies near this critical regime of parameter space where capacity peaks. The results are suggestive of a potential evolutionary driving force for diversification in certain QS systems.

Three-Dimensional Numerical Simulations of Biofilm Dynamics with Quorum Sensing in a Flow Cell

We develop a multiphasic hydrodynamic theory for biofilms taking into account interactions among various bacterial phenotypes, extracellular polymeric substance (EPS), quorum sensing (QS) molecules, solvent, and antibiotics. In the model, bacteria are classified into down-regulated QS, up-regulated QS, and non-QS cells based on their QS ability. The model is first benchmarked against an experiment yielding an excellent fit to experimental measurements on the concentration of QS molecules and the cell density during biofilm development. It is then applied to study development of heterogeneous structures in biofilms due to interactions of QS regulation, hydrodynamics, and antimicrobial treatment. Our 3D numerical simulations have confirmed that (i). QS is beneficial for biofilm development in a long run by building a robust EPS population to protect the biofilm; (ii). biofilms located upstream can induce QS downstream when the colonies are close enough spatially; (iii). QS induction may not be fully operational and can even be compromised in strong laminar flows; (v). the hydrodynamic stress alters the biofilm morphology. Through further numerical investigations, our model suggests that (i). QS-regulated EPS production contributes to the structural formation of heterogeneous biofilms; (ii) QS down-regulated cells tend to grow at the surface of the biofilm while QS up-regulated ones tend to grow in the bulk; (iii) when nutrient supply is sufficient, QS induction might be more effective upstream than downstream; (iv) QS may be of little benefit in a short timescale in term of fighting against invading strain/species; (v) the material properties of biomass (bacteria and EPS) have strong impact on the dilution of QS molecules under strong shear flow. In addition, with this modeling framework, hydrodynamic details and rheological quantities associated with biofilm formation under QS regulation can be resolved.

An age-dependent model to analyse the evolutionary stability of bacterial quorum sensing

Bacterial communication is enabled through the collective release and sensing of signalling molecules in a process called quorum sensing. Cooperative processes can easily be destabilized by the appearance of cheaters, who contribute little or nothing at all to the production of common goods. This especially applies for planktonic cultures. In this study, we analyse the dynamics of bacterial quorum sensing and its evolutionary stability under two levels of cooperation, namely signal and enzyme production. The model accounts for mutation rates and switches between planktonic and biofilm state of growth. We present a mathematical approach to model these dynamics using age-dependent colony models. We explore the conditions under which cooperation is stable and find that spatial structuring can lead to long-term scenarios such as coexistence or bistability, depending on the non-linear combination of different parameters like death rates and production costs.

Mathematical Modelling of Bacterial Quorum Sensing: A Review

Bacterial quorum sensing (QS) refers to the process of cell-to-cell bacterial communication enabled through the production and sensing of the local concentration of small molecules called autoinducers to regulate the production of gene products (e.g. enzymes or virulence factors). Through autoinducers, bacteria interact with individuals of the same species, other bacterial species, and with their host. Among QS-regulated processes mediated through autoinducers are aggregation, biofilm formation, bioluminescence, and sporulation. Autoinducers are therefore "master" regulators of bacterial lifestyles. For over 10 years, mathematical modelling of QS has sought, in parallel to experimental discoveries, to elucidate the mechanisms regulating this process. In this review, we present the progress in mathematical modelling of QS, highlighting the various theoretical approaches that have been used and discussing some of the insights that have emerged. Modelling of QS has benefited almost from the onset of the involvement of experimentalists, with many of the papers which we review, published in non-mathematical journals. This review therefore attempts to give a broad overview of the topic to the mathematical biology community, as well as the current modelling efforts and future challenges.

Quorum Sensing Desynchronization Leads to Bimodality and Patterned Behaviors

Quorum Sensing (QS) drives coordinated phenotypic outcomes among bacterial populations. Its role in mediating infectious disease has led to the elucidation of numerous autoinducers and their corresponding QS signaling pathways. Among them, the Lsr (LuxS-regulated) QS system is conserved in scores of bacteria, and its signal molecule, autoinducer-2 (AI-2), is synthesized as a product of 1-carbon metabolism. Lsr signal transduction processes, therefore, may help organize population scale activities in numerous bacterial consortia. Conceptions of how Lsr QS organizes population scale behaviors remain limited, however. Using mathematical simulations, we examined how desynchronized Lsr QS activation, arising from cell-to-cell population heterogeneity, could lead to bimodal Lsr signaling and fractional activation. This has been previously observed experimentally. Governing these processes are an asynchronous AI-2 uptake, where positive intracellular feedback in Lsr expression is combined with negative feedback between cells. The resulting activation patterns differ from that of the more widely studied LuxIR system, the topology of which consists of only positive feedback. To elucidate differences, both QS systems were simulated in 2D, where cell populations grow and signal each other via traditional growth and diffusion equations. Our results demonstrate that the LuxIR QS system produces an ‘outward wave’ of autoinduction, and the Lsr QS system yields dispersed autoinduction from spatially-localized secretion and uptake profiles. In both cases, our simulations mirror previously demonstrated experimental results. As a whole, these models inform QS observations and synthetic biology designs.

Bacterial behavior is responsive to a multitude of soluble molecular cues. Among them are self-secreted autoinducers that control quorum sensing (QS) processes. While new quorum sensing systems are constantly being discovered, several systems have been well defined in terms of their molecular and genetic topologies, each influencing a variety of resultant phenotypes. These quorum sensing systems include LuxIR homologs that use an array of species specific autoinducers and Lsr system homologs that share a single autoinducer among numerous species. Here we suggest that the regulatory topology of these two systems mark them as opposites of a sort. Whereas the LuxIR system bears a strong positive intercellular feedback mechanism, the Lsr system bears strong negative intercellular feedback. In our simulations these differences are manifested in distinct patterns of signaling. This was readily visualized in the outward spread of autogenous LuxIR expression in a growing bacterial 2D ‘colony’ whereas a dispersed activity was produced by autogenous Lsr expression in an otherwise identical colony. Here, this dispersed activity is a reflection of bimodal Lsr expression. We show that this bimodality could arise from desynchronized Lsr driven autoinducer import (intercellular negative feedback). This may have consequences on the arrangement of downstream phenotypes.