Brownian ratchets

Binding and Release Events into Directed Motion 

330 Chapter i8. Physical Kinetics Diffusion, Permeation Flow 

Let s make the model more quantitative. L diffuses along the x-axis for a time Tofi. Plight is the probability that the ligand diffuses to beyond x = a in 

Equation (18.59) can be expressed more compactly in terms of the complementary error function, 

Comparison of the exponents in Equations (18.59) and (18.60) shows that u is a dimensionless quantity given by 

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Peskin C S, Odell G M and Oster G F 1993 Cellular motions and thermal fluctuations the Brownian ratchet Biophys. J. 65 316... 

Figure 4. The Brownian ratchet model of lamellar protrusion (Peskin et al., 1993). According to this hypothesis, the distance between the plasma membrane (PM) and the filament end fluctuates randomly. At a point in time when the PM is most distant from the filament end, a new monomer is able to add on. Consequently, the PM is no longer able to return to its former position since the filament is now longer. The filament cannot be pushed backwards by the returning PM as it is locked into the mass of the cell cortex by actin binding proteins. In this way, the PM is permitted to diffuse only in an outward direction. The maximum force which a single filament can exert (the stalling force) is related to the thermal energy of the actin monomer by kinetic theory according to the following equation ...

FIGURE 9.24 The device consisting of a Brownian ratchet array for DNA separation. The flow angle, 0IMl, is 10.8° with respect to the vertical array axis. //, L, and L were 6, 8, and 10 pm, respectively. The obstacles were 5.6 pm long, 1.4 pm wide, and 3.2 pm tall [686]. Reprinted with permission from the American Chemical Society. 

In the Brownian ratchet model (Simon et al., 1992), Hsp70 molecules act to support unidirectional translocation of preproteins in a somewhat passive way. Brownian motion describes the random thermal motion of a system—in this case, the preprotein. If a preprotein is in transit at the translocation channel, Brownian motion will cause it to oscillate in an unbiased way. However, the binding of Hsp70 to the incoming preprotein at the exit site of the translocation channel prevents its backsliding. Hsp70 bound to preprotein is then released from its anchor (e.g., Sec63p... 

Fig. 3. Models of lumenal Hsp70 action in protein translocation. (I) In the Brownian ratchet model, the preprotein enters the lumen and associates with membrane-bound Hsp70. Hydrolysis of ATP results in the preprotein substrate being more tightly bound...

For mitochondria, the Brownian ratchet model has been supported through a number of different studies. For example, it has been demonstrated that some preproteins can oscillate while in the translocation... 

A mechanism to explain what propels the membrane forward, called the elastic Brownian ratchet model, is based on the elastic mechanical property of an actin filament (Figure... 

Saffarian S et al (2004) Interstitial collagenase is a Brownian ratchet driven by proteolysis of collagen. Science 306(5693) 108-111... 

Peskin et al [1993] have proposed the Brownian ratchet theory to describe the active force production. The main component of that theory was the interaction between a rigid protein and a diffusing object in front of it. If the object undergoes a Brownian motion, and the fiber undergoes polymerization, there are rates at which the polymer can push the object and overcome the external resistance. The problem was formulated in terms of a system of reaction-diffusion equations for the probabilities of the polymer to have certain number of monomers. Two limiting cases, fast diffusion and fast polymerization, were treated analytically that resulted in explicit force/velocity relationships. This theory was subsequently extended to elastic objects and to the transient attachment of the filament to the object. The correspondence of these models to recent experimental data is discussed in the article by Mogilner and Oster [2003]. 

Peskin, C.S., OdeU, G.M., and Oster, G. Cellular motors and thermal fluctuation the Brownian ratchet, Biophys. 65,316,1993. 

Ait-HaddouR, Herzog W (2003) Brownian ratchet models of molecular motors. Cell Biochem Biophys 38 191-213. doi 10.1385/CBB 38 2 191... 

The concept of Brownian ratchets has been applied to construct asymmetric obstacle courses that provide a spatially asymmetric steric potential for biomolecule separation [20, 21], The basic idea is to use such asymmetric obstacles to rectify the Browiuan motion laterally and thereby to deflect diffusing biomolecules based on their sizes. So far, the Brownian ratchet systems have been successfully demonstrated for long DNA and phospholipids [15, 16], even though the separation resolution reported so far was not ideal. 

Matthias S, Muller F (2003) Asymmetric pores in a silicon membrane acting as massively parallel brownian ratchets. Nature 424 53-57... 

Other interesting and recent contributions have shown (i) the utilization of self-complexing molecules as a Brownian ratchet, (ii) the use of reductive electrochemistry to turn on attractive axle-wheel interactions in a rotaxane, (iii) the use of CDs as wheels in redox-switchable rotaxanes,and (iv) redox control on the movements of two... 

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