Models Brownian ratchet model

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 ...

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... 

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

Besides the remarkable directionality of the motion, the images also demonstrate a periodic variation of the cluster from an elongated to a circular shape (Fig. 39). The diagrams in Fig. 39 depict the time dependence of the displacement and the cluster size. Until the cluster was finally trapped, the speed remained fairly constant as can be seen from the constant slope in Fig. 39 a. The oscillatory variation of the cluster shape is shown in Fig. 39b. Although a coarse model for the motion has been presented in Fig. 39, the actual cause of the motion remains unknown. The ratchet model proposed by J. Frost requires a non-equiUb-rium variation in the energetic potential to bias the Brownian motion of a molecule or particle under anisotropic boundary conditions [177]. Such local perturbations of the molecular structure are believed to be caused by the mechanical contact with the scaiming tip. A detailed and systematic study of this question is still in progress. 

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]. 

To reify this very important point further, let us consider the two ratchet models shown in Fig. 9. At first glance it would seem that the ratchet in Fig. 9a is designed for transport to the right and that in Fig. 9b is designed for transport to the left. Despite appearances, however, both ratchets operate as Brownian information motors [9]. When the rate constants are assigned consistent with microscopic reversibility, the intrinsic directionality of each ratchet is controlled by the parameter... 

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