Self-Concentration and Large-Scale Coherence in Bacterial Dynamics

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Pattern formation outside of equilibrium

M Cross, P Hohenberg (1993)

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Novel type of phase transition in a system of self-driven particles

Andras Czirok, Ofer Sochet, Tamás Vicsek … (2006)

A simple model with a novel type of dynamics is introduced in order to investigate the emergence of self-ordered motion in systems of particles with biologically motivated interaction. In our model particles are driven with a constant absolute velocity and at each time step assume the average direction of motion of the particles in their neighborhood with some random perturbation (\(\eta\)) added. We present numerical evidence that this model results in a kinetic phase transition from no transport (zero average velocity, \(| {\bf v}_a | =0\)) to finite net transport through spontaneous symmetry breaking of the rotational symmetry. The transition is continuous since \(| {\bf v}_a |\) is found to scale as \((\eta_c-\eta)^\beta\) with \(\beta\simeq 0.45\).

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Physics of chemoreception.

H.C. Berg, E.M Purcell (1977)

Statistical fluctuations limit the precision with which a microorganism can, in a given time T, determine the concentration of a chemoattractant in the surrounding medium. The best a cell can do is to monitor continually the state of occupation of receptors distributed over its surface. For nearly optimum performance only a small fraction of the surface need be specifically adsorbing. The probability that a molecule that has collided with the cell will find a receptor is Ns/(Ns + pi a), if N receptors, each with a binding site of radius s, are evenly distributed over a cell of radius a. There is ample room for many indenpendent systems of specific receptors. The adsorption rate for molecules of moderate size cannot be significantly enhanced by motion of the cell or by stirring of the medium by the cell. The least fractional error attainable in the determination of a concentration c is approximately (TcaD) - 1/2, where D is diffusion constant of the attractant. The number of specific receptors needed to attain such precision is about a/s. Data on bacteriophage absorption, bacterial chemotaxis, and chemotaxis in a cellular slime mold are evaluated. The chemotactic sensitivity of Escherichia coli approaches that of the cell of optimum design.