Ratchet models

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 ...

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. 

N. J. Cordova, B. Ermentrout, and G. E Oster, Dynamics of single-motor molecules the thermal ratchet model, Proc. Natl. Acad. Set USA 89, 339-343 (1992). 

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... 

Michaelis-Menten constants, 50 myosin motors, 65 neck-linker, 49 six AAA domains, dynein, 52 thermal ratchet model, 63 unbinding force, 49 Color tuning, energy flow pathways... 

Almost Hyperbolic Relation from an Information Ratchet Model... 

In contrast, the information ratchet model [9], on which (18) and (19) are based, is consistent with microscopic reversibility for both the chemical and the mechanical processes. The shape of the curve described by (18) is governed by both the force dependence ofr and by the term q that parameterizes the relative likelihood of a forward ATP driven step vs a backward ATP-driven step. The force velocity curve is close to hyperbolic with a=l, but with a = 0, the velocity is nearly constant up to a force of slightly more than half the stopping force and then dramatically decreases to zero at the stopping force, and with a = 0.25 (not shown) the velocity is a nearly linearly decreasing function of the applied force up to Fstaii. The thermodynamic properties such as the step ratio, stoichiometry, efficiency, and stall force are independent of t. ... 

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... 

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

Traditionally, efficiency of molecular motors has been studied within ratchet models where the motor undergoes a continuous motion in a periodic potential that depends on the current chemical. Dissipation then involves both the continuous degree of freedom and the discrete switching of the potential. 

The ratchet model can be used to estimate the forces generated by the depolymerizing microtubule [8]. Each disassembly event allows the motor to rotate toward the minus end of the... 

This model predicted that the bacterial velocity should depend on its diffusion coefficient, and thereby on its size. However, experiments showed that the velocity did not depend on the cell size, so the model was modified to allow thermal fluctuations of the actin filament tips [36], This resolved the size independence issue but the model ran afoul of another observation the actin tail appeared to be attached to the surface of the cell [30,37,38]. This problem was resolved by a further generalization of the model. The tethered ratchet model assumed that the filaments are initiated while attached to the bacterial surface, but subsequently detach and become working filaments as in the elastic ratchet model (Figure 3(a), [19]). The attached fibers are in tension and resist the forward progress of the bacterium. At the same time, the dissociated fibers are in compression, and generate the force of propulsion, each filament developing a force of a few pN. 

Mogilner, A. and G. Oster, The polymerization ratchet model explains the force-velocity relation for growing microtubules. Eur. J. Biophys., 1999, 28 235-242. 

It must be mentioned that the model of translocation as a ratchet is a subset of the one-dimensional drift-diffusion process (Peskin et al. 1993). In the ratchet model, every monomer being translocated gets reflected back at every site along the pore in the direction of translocation and undergoes drift-diffusion between successive sites along the pore. The final results of this model are readily derived from the same drift-diffusion equation (Equation 10.39). 

Reply bv the Authors With pearlitic rail steels there is variation within individual grains. The grains are composed of laminae of cementite and ferrite, materials which differ greatly, the cementite being far harder than the ferrite and also very brittle in comparison. The brick model is capable of modelling such a structure, but is a ratchetting model and cementite will not fail by ratchetting - a more sophisticated model is required. 

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