Biomixing by chemotaxis and efficiency of biological reactions: the critical reaction case

Many phenomena in biology involve both reactions and chemotaxis. These processes can clearly influence each other, and chemotaxis can play an important role in sustaining and speeding up the reaction. In continuation of our earlier work, we consider a model with a single density function involving diffusion, advection, chemotaxis, and absorbing reaction. The model is motivated, in particular, by the studies of coral broadcast spawning, where experimental observations of the efficiency of fertilization rates significantly exceed the data obtained from numerical models that do not take chemotaxis (attraction of sperm gametes by a chemical secreted by egg gametes) into account. We consider the case of the weakly coupled quadratic reaction term, which is the most natural from the biological point of view and was left open. The result is that similarly to higher power coupling, the chemotaxis plays a crucial role in ensuring efficiency of reaction. However, mathematically, the picture is quite different in the quadratic reaction case and is more subtle. The reaction is now complete even in the absence of chemotaxis, but the timescales are very different. Without chemotaxis, the reaction is very slow, especially for the weak reaction coupling coefficient. With chemotaxis, the timescale and efficiency of reaction are independent of the coupling parameter.Comment: 10 pages. arXiv admin note: text overlap with arXiv:1101.244

A Minimal Model of Metabolism Based Chemotaxis

Since the pioneering work by Julius Adler in the 1960's, bacterial chemotaxis has been predominantly studied as metabolism-independent. All available simulation models of bacterial chemotaxis endorse this assumption. Recent studies have shown, however, that many metabolism-dependent chemotactic patterns occur in bacteria. We hereby present the simplest artificial protocell model capable of performing metabolism-based chemotaxis. The model serves as a proof of concept to show how even the simplest metabolism can sustain chemotactic patterns of varying sophistication. It also reproduces a set of phenomena that have recently attracted attention on bacterial chemotaxis and provides insights about alternative mechanisms that could instantiate them. We conclude that relaxing the metabolism-independent assumption provides important theoretical advances, forces us to rethink some established pre-conceptions and may help us better understand unexplored and poorly understood aspects of bacterial chemotaxis

Global existence results for complex hyperbolic models of bacterial chemotaxis

Bacteria are able to respond to environmental signals by changing their rules of movement. When we take into account chemical signals in the environment, this behaviour is often called chemotaxis. At the individual-level, chemotaxis consists of several steps. First, the cell detects the extracellular signal using receptors on its membrane. Then, the cell processes the signal information through the intracellular signal transduction network, and finally it responds by altering its motile behaviour accordingly. At the population level, chemotaxis can lead to aggregation of bacteria, travelling waves or pattern formation, and the important task is to explain the population-level behaviour in terms of individual-based models. It has been previously shown that the transport equation framework is suitable for connecting different levels of modelling of bacterial chemotaxis. In this paper, we couple the transport equation for bacteria with the (parabolic/elliptic) equation for the extracellular signals. We prove global existence of solutions for the general hyperbolic chemotaxis models of cells which process the information about the extracellular signal through the intracellular biochemical network and interact by altering the extracellular signal as well. The conditions for global existence in terms of the properties of the signal transduction model are given.Comment: 22 pages, submitted to Discrete and Continuous Dynamical Systems Series

Chemotaxis When Bacteria Remember: Drift versus Diffusion

{\sl Escherichia coli} ({\sl E. coli}) bacteria govern their trajectories by switching between running and tumbling modes as a function of the nutrient concentration they experienced in the past. At short time one observes a drift of the bacterial population, while at long time one observes accumulation in high-nutrient regions. Recent work has viewed chemotaxis as a compromise between drift toward favorable regions and accumulation in favorable regions. A number of earlier studies assume that a bacterium resets its memory at tumbles -- a fact not borne out by experiment -- and make use of approximate coarse-grained descriptions. Here, we revisit the problem of chemotaxis without resorting to any memory resets. We find that when bacteria respond to the environment in a non-adaptive manner, chemotaxis is generally dominated by diffusion, whereas when bacteria respond in an adaptive manner, chemotaxis is dominated by a bias in the motion. In the adaptive case, favorable drift occurs together with favorable accumulation. We derive our results from detailed simulations and a variety of analytical arguments. In particular, we introduce a new coarse-grained description of chemotaxis as biased diffusion, and we discuss the way it departs from older coarse-grained descriptions.Comment: Revised version, journal reference adde

Inhibition of Escherichia coli chemotaxis by omega-conotoxin, a calcium ion channel blocker

Escherichia coli chemotaxis was inhibited by omega-conotoxin, a calcium ion channel blocker. With Tris-EDTA-permeabilized cells, nanomolar levels of omega-conotoxin inhibited chemotaxis without loss of motility. Cells treated with omega-conotoxin swam with a smooth bias, i.e., tumbling was inhibited

PIP3-dependent macropinocytosis is incompatible with chemotaxis

In eukaryotic chemotaxis, the mechanisms connecting external signals to the motile apparatus remain unclear. The role of the lipid phosphatidylinositol 3,4,5-trisphosphate (PIP3) has been particularly controversial. PIP3 has many cellular roles, notably in growth control and macropinocytosis as well as cell motility. Here we show that PIP3 is not only unnecessary for Dictyostelium discoideum to migrate toward folate, but actively inhibits chemotaxis. We find that macropinosomes, but not pseudopods, in growing cells are dependent on PIP3. PIP3 patches in these cells show no directional bias, and overall only PIP3-free pseudopods orient up-gradient. The pseudopod driver suppressor of cAR mutations (SCAR)/WASP and verprolin homologue (WAVE) is not recruited to the center of PIP3 patches, just the edges, where it causes macropinosome formation. Wild-type cells, unlike the widely used axenic mutants, show little macropinocytosis and few large PIP3 patches, but migrate more efficiently toward folate. Tellingly, folate chemotaxis in axenic cells is rescued by knocking out phosphatidylinositide 3-kinases (PI 3-kinases). Thus PIP3 promotes macropinocytosis and interferes with pseudopod orientation during chemotaxis of growing cells