A "trimer of dimers"-based model for the chemotactic signal transduction network in bacterial chemotaxis

A Mathematical Description of Bacterial Chemotaxis in Response to Two Stimuli

Bacteria are often exposed to multiple stimuli in complex environments, and their efficient chemotactic decisions are critical to survive and grow in their native environments. Bacterial responses to the environmental stimuli depend on the ratio of their corresponding chemoreceptors. By incorporating the signaling machinery of individual cells, we analyze the collective motion of a population of Escherichia coli bacteria in response to two stimuli, mainly serine and methyl-aspartate (MeAsp), in a one-dimensional and a two-dimensional environment, which is inspired by experimental results in Y. Kalinin et al., J. Bacteriol. 192(7):1796-1800, 2010. Under suitable conditions, we show that if the ratio of the main chemoreceptors of individual cells, namely Tar/Tsr, is less than a specific threshold, the bacteria move to the gradient of serine, and if the ratio is greater than the threshold, the group of bacteria moves toward the gradient of MeAsp. Finally, we examine the theory with Monte Carlo agent-based simulations and verify that our results qualitatively agree well with the experimental results in Y. Kalinin et al. (2010).

Individual based models exhibiting Lévy-flight type movement induced by intracellular noise

We use an individual-based model and its associated kinetic equation to study the generation of long jumps in the motion of E. coli. These models relate the run-and-tumble process to the intracellular reaction where the intrinsic noise plays a central role. Compared with previous work in Perthame et al. (Z Angew Math Phys 69(3):1-15, 2018), in which the parametric assumptions are mainly targeted for mathematical convenience but not well-suited for numerical simulations or comparison with experimental results, our current paper makes use of biologically meaningful pathways and tumbling kernels. The main contribution of this current work is bridging the gap between the theoretical results and experimentally available data. Some particular forms of how the tumbling frequency depends on the internal variable are proposed. Moreover, we propose two individual-based models, one for the tumbling frequency and the other for the receptor activity, and perform numerical simulations. Power-law decay of the run length distribution, which corresponds to Lévy-type motions, is observed in our numerical results. The particular decay rate agrees quantitatively with the analytical result.

Comparative Genomic Analysis of Three Pseudomonas Species Isolated from the Eastern Oyster (Crassostrea virginica) Tissues, Mantle Fluid, and the Overlying Estuarine Water Column

The eastern oysters serve as important keystone species in the United States, especially in the Gulf of Mexico estuarine waters, and at the same time, provide unparalleled economic, ecological, environmental, and cultural services. One ecosystem service that has garnered recent attention is the ability of oysters to sequester impurities and nutrients, such as nitrogen (N), from the estuarine water that feeds them, via their exceptional filtration mechanism coupled with microbially-mediated denitrification processes. It is the oyster-associated microbiomes that essentially provide these myriads of ecological functions, yet not much is known on these microbiota at the genomic scale, especially from warm temperate and tropical water habitats. Among the suite of bacterial genera that appear to interplay with the oyster host species, pseudomonads deserve further assessment because of their immense metabolic and ecological potential. To obtain a comprehensive understanding on this aspect, we previously reported on the isolation and preliminary genomic characterization of three Pseudomonas species isolated from minced oyster tissue (P. alcaligenes strain OT69); oyster mantle fluid (P. stutzeri strain MF28) and the water collected from top of the oyster reef (P. aeruginosa strain WC55), respectively. In this comparative genomic analysis study conducted on these three targeted pseudomonads, native to the eastern oyster and its surrounding environment, provided further insights into their unique functional traits, conserved gene pools between the selected pseudomonads, as well as genes that render unique characteristics in context to metabolic traits recruited during their evolutionary history via horizontal gene transfer events as well as phage-mediated incorporation of genes. Moreover, the strains also supported extensively developed resistomes, which suggests that environmental microorganisms native to relatively pristine environments, such as Apalachicola Bay, Florida, have also recruited an arsenal of antibiotic resistant gene determinants, thus posing an emerging public health concern.

Bacterial chemotaxis: a way forward to aromatic compounds biodegradation

Worldwide industrial development has released hazardous polycyclic aromatic compounds into the environment. These pollutants need to be removed to improve the quality of the environment. Chemotaxis mechanism has increased the bioavailability of these hydrophobic compounds to microorganisms. The mechanism, however, is poorly understood at the ligand and chemoreceptor interface. Literature is unable to furnish a compiled review of already published data on up-to-date research on molecular aspects of chemotaxis mechanism, ligand and receptor-binding mechanism, and downstream signaling machinery. Moreover, chemotaxis-linked biodegradation of aromatic compounds is required to understand the chemotaxis role in biodegradation better. To fill this knowledge gap, the current review is an attempt to cover PAHs occurrence, chemical composition, and potential posed risks to humankind. The review will cover the aspects of microbial signaling mechanism, the structural diversity of methyl-accepting chemotaxis proteins at the molecular level, discuss chemotaxis mechanism role in biodegradation of aromatic compounds in model bacterial genera, and finally conclude with the potential of bacterial chemotaxis for aromatics biodegradation.

The Roles of Signaling in Cytoskeletal Changes, Random Movement, Direction-Sensing and Polarization of Eukaryotic Cells

Movement of cells and tissues is essential at various stages during the lifetime of an organism, including morphogenesis in early development, in the immune response to pathogens, and during wound-healing and tissue regeneration. Individual cells are able to move in a variety of microenvironments (MEs) (A glossary of the acronyms used herein is given at the end) by suitably adapting both their shape and how they transmit force to the ME, but how cells translate environmental signals into the forces that shape them and enable them to move is poorly understood. While many of the networks involved in signal detection, transduction and movement have been characterized, how intracellular signals control re-building of the cyctoskeleton to enable movement is not understood. In this review we discuss recent advances in our understanding of signal transduction networks related to direction-sensing and movement, and some of the problems that remain to be solved.

The role of intracellular signaling in the stripe formation in engineered Escherichia coli populations

Recent experiments showed that engineered Escherichia coli colonies grow and self-organize into periodic stripes with high and low cell densities in semi-solid agar. The stripes develop sequentially behind a radially propagating colony front, similar to the formation of many other periodic patterns in nature. These bacteria were created by genetically coupling the intracellular chemotaxis pathway of wild-type cells with a quorum sensing module through the protein CheZ. In this paper, we develop multiscale models to investigate how this intracellular pathway affects stripe formation. We first develop a detailed hybrid model that treats each cell as an individual particle and incorporates intracellular signaling via an internal ODE system. To overcome the computational cost of the hybrid model caused by the large number of cells involved, we next derive a mean-field PDE model from the hybrid model using asymptotic analysis. We show that this analysis is justified by the tight agreement between the PDE model and the hybrid model in 1D simulations. Numerical simulations of the PDE model in 2D with radial symmetry agree with experimental data semi-quantitatively. Finally, we use the PDE model to make a number of testable predictions on how the stripe patterns depend on cell-level parameters, including cell speed, cell doubling time and the turnover rate of intracellular CheZ.

Mathematical Analysis of the Escherichia coli Chemotaxis Signalling Pathway

We undertake a detailed mathematical analysis of a recent nonlinear ordinary differential equation (ODE) model describing the chemotactic signalling cascade within an Escherichia coli cell. The model includes a detailed description of the cell signalling cascade and an average approximation of the receptor activity. A steady-state stability analysis reveals the system exhibits one positive real steady state which is shown to be asymptotically stable. Given the occurrence of a negative feedback between phosphorylated CheB (CheB-P) and the receptor state, we ask under what conditions the system may exhibit oscillatory-type behaviour. A detailed analysis of parameter space reveals that whilst variation in kinetic rate parameters within known biological limits is unlikely to lead to such behaviour, changes in the total concentration of the signalling proteins do. We postulate that experimentally observed overshoot behaviour can actually be described by damped oscillatory dynamics and consider the relationship between overshoot amplitude, total cell protein concentration and the magnitude of the external ligand stimulus. Model reductions in the full ODE model allow us to understand the link between phosphorylation events and the negative feedback between CheB-P and receptor methylation, as well as elucidate why some mathematical models exhibit overshoot and others do not. Our paper closes by discussing intercell variability of total protein concentration as a means of ensuring the overall survival of a population as cells are subjected to different environments.

Predicting Escherichia coli's chemotactic drift under exponential gradient

Bacterial species are known to show chemotaxis, i.e., the directed motions in the presence of certain chemicals, whereas the motion is random in the absence of those chemicals. The bacteria modulate their run time to induce chemotactic drift towards the attractant chemicals and away from the repellent chemicals. However, the existing theoretical knowledge does not exhibit a proper match with experimental validation, and hence there is a need for developing alternate models and validating experimentally. In this paper a more robust theoretical model is proposed to investigate chemotactic drift of peritrichous Escherichia coli under an exponential nutrient gradient. An exponential gradient is used to understand the steady state behavior of drift because of the logarithmic functionality of the chemosensory receptors. Our theoretical estimations are validated through the experimentation and simulation results. Thus, the developed model successfully delineates the run time, run trajectory, and drift velocity as measured from the experiments.

Progress and perspectives in signal transduction, actin dynamics, and movement at the cell and tissue level: lessons from Dictyostelium

Movement of cells and tissues is a basic biological process that is used in development, wound repair, the immune response to bacterial invasion, tumour formation and metastasis, and the search for food and mates. While some cell movement is random, directed movement stimulated by extracellular signals is our focus here. This involves a sequence of steps in which cells first detect extracellular chemical and/or mechanical signals via membrane receptors that activate signal transduction cascades and produce intracellular signals. These intracellular signals control the motile machinery of the cell and thereby determine the spatial localization of the sites of force generation needed to produce directed motion. Understanding how force generation within cells and mechanical interactions with their surroundings, including other cells, are controlled in space and time to produce cell-level movement is a major challenge, and involves many issues that are amenable to mathematical modelling.

Derivation of the bacterial run-and-tumble kinetic equation from a model with biochemical pathway

Kinetic-transport equations are, by now, standard models to describe the dynamics of populations of bacteria moving by run-and-tumble. Experimental observations show that bacteria increase their run duration when encountering an increasing gradient of chemotactic molecules. This led to a first class of models which heuristically include tumbling frequencies depending on the path-wise gradient of chemotactic signal. More recently, the biochemical pathways regulating the flagellar motors were uncovered. This knowledge gave rise to a second class of kinetic-transport equations, that takes into account an intra-cellular molecular content and which relates the tumbling frequency to this information. It turns out that the tumbling frequency depends on the chemotactic signal, and not on its gradient. For these two classes of models, macroscopic equations of Keller-Segel type, have been derived using diffusion or hyperbolic rescaling. We complete this program by showing how the first class of equations can be derived from the second class with molecular content after appropriate rescaling. The main difficulty is to explain why the path-wise gradient of chemotactic signal can arise in this asymptotic process. Randomness of receptor methylation events can be included, and our approach can be used to compute the tumbling frequency in presence of such a noise.

Macroscopic equations for bacterial chemotaxis: integration of detailed biochemistry of cell signaling

Chemotaxis of single cells has been extensively studied and a great deal on intracellular signaling and cell movement is known. However, systematic methods to embed such information into continuum PDE models for cell population dynamics are still in their infancy. In this paper, we consider chemotaxis of run-and-tumble bacteria and derive continuum models that take into account of the detailed biochemistry of intracellular signaling. We analytically show that the macroscopic bacterial density can be approximated by the Patlak-Keller-Segel equation in response to signals that change slowly in space and time. We derive, for the first time, general formulas that represent the chemotactic sensitivity in terms of detailed descriptions of single-cell signaling dynamics in arbitrary space dimensions. These general formulas are useful in explaining relations of single cell behavior and population dynamics. As an example, we apply the theory to chemotaxis of bacterium Escherichia coli and show how the structure and kinetics of the intracellular signaling network determine the sensing properties of E. coli populations. Numerical comparison of the derived PDEs and the underlying cell-based models show quantitative agreements for signals that change slowly, and qualitative agreements for signals that change extremely fast. The general theory we develop here is readily applicable to chemotaxis of other run-and-tumble bacteria, or collective behavior of other individuals that move using a similar strategy.

Excitation and adaptation in bacteria-a model signal transduction system that controls taxis and spatial pattern formation

The machinery for transduction of chemotactic stimuli in the bacterium E. coli is one of the most completely characterized signal transduction systems, and because of its relative simplicity, quantitative analysis of this system is possible. Here we discuss models which reproduce many of the important behaviors of the system. The important characteristics of the signal transduction system are excitation and adaptation, and the latter implies that the transduction system can function as a "derivative sensor" with respect to the ligand concentration in that the DC component of a signal is ultimately ignored if it is not too large. This temporal sensing mechanism provides the bacterium with a memory of its passage through spatially- or temporally-varying signal fields, and adaptation is essential for successful chemotaxis. We also discuss some of the spatial patterns observed in populations and indicate how cell-level behavior can be embedded in population-level descriptions.