  E.coli serves as prototype for the study of peritrichous enteric bacteria
that perform runs and tumbles alternately. Bacteria run forward as a result of
the counterclockwise (CCW) rotation of their flagella bundle and perform
tumbles when at least one of their flagella rotates clockwise (CW), moving away
from the bundle. The flagella are hooked to molecular rotary motors of
nanometric diameter able to make transitions between CCW and CW rotations that
last up to one hundredth of a second. At the same time, flagella move or rotate
the bacteria's body microscopically during lapses that range between a tenth
and ten seconds. We assume that the transitions between CCW and CW rotations
occur solely by fluctuations of CheY-P molarity in the presence of two
threshold values, and that a veto rule selects the run or tumble motions. We
present Langevin eqs for the CheY-P molarity in the vicinity of each molecular
motor. This model allows to obtain the run- or tumble-time distribution as a
linear combination of decreasing exponentials that is a function of the steady
molarity of CheY-P in the neighbourhood of the molecular motor, which fits
experimental data. In turn, if the internal signaling system is unstimulated,
we show that the runtime distributions reach power-law behaviour, a
characteristic of self-organized systems, in some time range and, afterwards,
exponential cutoff. In addition, our model explains without any fitting
parameters the ultrasensitivity of the flagella motors as a function of the
steady state of CheY-P molarity. In addition, we show that the tumble bias for
peritrichous bacterium has a similar sigmoid-shape to the CW bias, although
shifted to lower concentrations when the flagella number increases. Thus, the
increment in the flagella number allows lower operational values for each motor
increasing amplification and robustness of the chemotatic pathway.
