Apparently, bacteria do not care about math and they do not have in their curricula a calculus course. Yet they are able to exhibit a behaviour which is characterized by statistics which can be described by power-law distributions. For example, the intrinsically random time intervals during which a single flagellum of the E.coli bacterium, an appendage that works as a screw-propeller of the cell, rotates in one direction, may be distributed according to a power law. What is so special in the power-law distributions and the ability of bacteria to produce them?
While most of random events in our lives can be described by well-known exponential or Gaussian distributions, some are not. Distribution of wealth, number of contacts in a social network or number of scientific paper citations just a few examples that may be well approximated by power-law distributions. One particular area which links the power-law statistics and bacteria is foraging and random search. It appears that in some cases searching for randomly distributed rare targets such as food or a mating partner may be more efficient if the lengths of the steps made by the searcher are power-law distributed. And indeed, such statistics of steps was experimentally observed in living organisms varying in scales from a single immune cell to sharks and humans. However, the question of how living organisms can generate this behaviour remains largely unanswered.
According to Professor Mikhail Ivanchenko, Head of the Department of Applied Mathematics at the UNN Institute of Information Technologies, Mathematics and Mechanics, a new study published in Journal of Physics A: Mathematical and General suggests that bacteria are able to naturally generate power-law distributions in the rotation intervals of the flagellar molecular motor by utilizing their internal molecular reaction networks.
Interestingly, there is no need for an external 'noise' of any sort; power laws appear naturally, due to the finite number of fluctuations of reacting protein molecules, a condition common to the intracellular chemistry. When all flagellar motors of E.coli rotate in one direction the cell swims almost in a straight line. Switching of the rotation direction of one of the motors reorients the cell in a new random direction and thus, in fact, creates a random searcher. The potential ability of a single motor to operate in a power-law regime may make the cell more capable in solving searching tasks.
«Researchers from the Lobachevsky University of Nizhny Novgorod, Max Planck Institute for Physics of Complex Systems (Dresden) and University of Augsburg, proposed a simple chemical reaction network based on the existing biological data on E.coli signaling pathway, which yields power-law statistics with tunable exponents», - Mikhail Ivanchenko says.
The exponents are controlled by a few parameters of the reaction network, such as equilibrium number of molecules, sensitivities, and the characteristic relaxation time. This might be one of the first examples where our understanding of the origins of the power-law statistics can be linked to concrete biological counterpart and distinct physical mechanisms in the living organism.