Chemically Driven Motility of Brownian Particles

Abstract

A simple model is devised to show that an enzymatic Brownian particle in a static electric field can undergo directional movement when coupled with a nonequilibrium chemical reaction which the particle catalyzes, if at least one of the intermediate states of the catalytic cycle is charged. The direction of the movement depends not only on the asymmetry of the electric field, but also on the direction of the chemical reaction and the mechanism of the catalytic cycle. The Brownian particle can also move against an external load and thus do mechanical work. This study suggests that enzyme molecules could be separated based on their enzymatic activities. The formalism developed in this paper can be extended and applied to biological motors. [S0031-9007(96) PACS numbers: 87.15.-v, 05.40.+j Recently the directional movement of Brownian particles in a periodic potential has attracted considerable attention [1][2][3][4][5][6][7]. It is known that the long-time movement of a Brownian particle is not directionally biased in the presence of a periodic potential if the potential is static. But, if the potential is asymmetric within a period and is randomly or regularly switched on and off (so that the force acting on the particles fluctuates), then a net directional movement of the particle can be achieved [1][2][3][4][5]. As in other cases of external fluctuation-induced free energy transduction [8][9][10][11][12], energy from a fluctuating force field is thus found to be able to do mechanical work. Experiments using oscillating electric fields have not only confirmed the existence of directional movement but also shown that particles with different charges or electric properties could be separated [3,4]. In this Letter, we demonstrate with a simple model that a Brownian particle can execute directional movement in a static (nonfluctuating) periodic electric field when coupled with a nonequilibrium chemical reaction. In other words, the free energy of a nonequilibrium chemical reaction can be directly transduced by a Brownian particle to do mechanical work. The general principle of the model can be tested experimentally and should prove useful in biomolecular separation. Moreover, the formalism developed here can be generalized and used for analyzing the motility of single biological motors in vitro, where the effect of Brownian motion may be important.As shown in Fig. 1(a), the Brownian particle E is considered as an enzyme that catalyzes the breakdown of AB into A 1 and B 2 . For simplicity, we consider only the reduced scheme in Fig. 1(b). However, the general conclusions discussed below are expected to be applicable to Fig. 1(a) or other more complicated kinetic schemes. The chemical reaction ͑AB ! A 1 1 B 2 ͒ is assumed to be inhibited in the absence of E and the concentrations of AB, A 1 , and B 2 in solution are assumed to be time independent. We want to study the movement of this chemi- 2 which is catalyzed by the enzymatic Brownian particle (symbolized by a circle). (b) The reduced kinetic scheme after neglect...

Thermodynamics and Kinetics of a Brownian Motor

“…Recent work has focused, however, on the possibility of an energy source other than a thermal gradient to power a microscopic motor. If energy is supplied by external fluctuations (5)(6)(7)(8) or a nonequilibrium chemical reaction (9,10), Brownian motion can be biased if the medium is anisotropic, even in an isothermal system. Thus, directed motion is possible without gravitational force, macroscopic electric fields, or long-range spatial gradients of chemicals.…”

“…(C) Average velocity as a function of the ⌬G of the chemical reaction using the rate constants and field amplitude as in (B). This result can be calculated in general by using reaction-diffusion equations to describe the combined physical motion and chemical reaction of a catalytic Brownian particle as described elsewhere (9,10). Here, k 12 and k 23 were taken to be large so that state 2 could be treated as a steady-state intermediate.…”

Spontaneous Oscillations of Collective Molecular Motors

“…In order to indentify possible physical mechanisms which allow such a motor molecule to convert the chemical energy of a fuel to motion and mechanical work, simple physical models have been suggested [9][10][11][12][13][14][15][16]. One idea [10] is to simplify the internal degrees of freedom of the motor to two different states of a particles which moves along a one-dimensional coordinate x.…”

Open Problems on Information and Feedback Controlled Systems

“…These feedback controlled ratchets can improve the performance over its open-loop counterparts thanks to the information the controller gets about the system state. These information-dependent ratchets are relevant in chemical and biological systems [33][34][35], and also in nanotechnology devices [15][16][17][18][19][20][21][22][23]31]. Other ratchets and Brownian motors inspired by Maxwell's demon present a directed motion when there is a temperature difference between two different parts of the motor (one part could be thought as the controller and the other as the controlled system) [36,37].…”