Volume exclusion and elasticity driven directional transport: an alternative model for bacterium motility

On the basis of a model we capture the role of strong attractive interaction in suppressing the rotational degrees of freedom of the system and volume exclusion in keeping microscopic symmetrybreaking intact to result in super-diffusive transport of small systems in a thermal atmosphere over a large time scale. Our results, characterize such systems on the basis of having a super-diffusive intermediate regime in between a very small and large time scales of diffusive regimes. Although, the Brownian ratchet model fails to account for the origin of motility in actin polymerization propelled directional motion of bacterium like Listeria Monocytogene (LM) and similar bio-mimetic systems due to the presence of strong attractive forces, our model can account for the origin of directional transport in such systems on the basis of the same interactions. ∗Electronic address: [email protected] 1 ar X iv :0 90 5. 22 94 v1 [ qbi o. C B ] 1 4 M ay 2 00 9 It is widely believed that the basis of driven directional motion of various motor proteins, bacterium etc., as observed in living systems or in similar environments, is the Brownian Ratchet (BR) mechanism [1, 2, 3]. The BR mechanism essentially requires the assistance of noise, a drive which can be periodic in time and directionless over space and a potential which must have broken reflection symmetry (polar) at a small (microscopic) scale [1]. All of these ingredients are pretty much available in the biological world. The biological systems normally perform at standard room temperatures so, thermal noise is present. Often the tubular tracks on which the motors move are made up of polar units and actin monomers are also polar in nature by polymerizing which some bacteria move. The motion of motor proteins and other bio-systems are invariably driven i.e. are associated with intermittent energy supply to drive them out of equilibrium as a prerequisite of having directional motion in any system. There have been attempts to model the motion of the bacterium Listeria Monocytogene [4] and similar biomimetic systems [5, 6], which moves by polymerizing an actin tail behind it, following BR paradigm [7, 8, 9]. But, subsequently found experimental facts go very much against the basic requirements of the BR theory of such systems. It has been found that the bacterium remains bound to its tail with a strong elastic force (40 pN approx.) during the course of its motion. The bacterium practically undergoes 20 times less Brownian motion than similar objects in the same environment because of this strong binding [10]. These observations practically rule out the scope of BR mechanism to explain the origin of directional transport in such actin polymerization based motile systems like LM. In the present paper we put forward a model based on a structured object unlike the BR models where the moving entity is a point particle. We show that the strong force of attraction between the parts of the system plays an important role in making the motion directional over a considerable time scale by the suppression of rotational degrees of freedom. The other most important observation, on the basis of the present model, is the role of volume exclusion. Volume exclusion helps the system retain the locally broken symmetry. This phenomenon we illustrate by an exactly solvable model in one dimension (1D). Then we extend the analysis to 2D and numerically show that the importance of the volume exclusion remains unaltered in keeping the locally broken symmetry being manifested globally. In experiments it has been revealed that the width of the actin tail, the bacterium polymerizes, is most important to keep the directionality of the motion. The reason for that clearly