Elastic force development resulting

S Evidence for Elastic Force Development Resulting from Hydrophobic Association... 

A more complete technical description of the consilient mechanisms of concern to biological energy conversion encompasses two distinct but interlinked physical processes of hydrophobic association and of elastic force development. The latter results from a generally applicable... 

Useful elastic force develops at the fixed ends of a chain segment when the motion within the backbone of the chain segment decreases as the result of a deformation such as an increase in... 

Hypothesis Efficient Production of Motion by Muscle Contraction Derives from the Hydrophobic and Elastic Consilient Mechanisms, Whereby Dephosphorylation Results in Hydrophobic Association Coupled to Near-ideal Elastic Force Development... 

The operative component of the comprehensive hydrophobic effect arises from the competition between charged and oil-like groups. This was shown to result in a previously unknown repulsive force embodied within an interaction energy called an apolar-polar repulsive free energy of hydration, AG,p. During function, AG,p works in conjunction with elastic force development by the restriction of internal chain dynamics. These have been called the hydrophobic and elastic consilient mechanisms. In Chapters 6,7, and 8, these consilient mechanisms were demonstrated to be fundamental to understanding the functions of biology s proteins. 

As noted by Ra5mient and coworkers, a number of flexible loops occur in the crossbridge, and we suggest that these are potential sources for elastic force development that results from hydrophobic association of the powerstroke (see Chapter 8, section 8.5.4.5). 

Here, AGeiastic is the contribution due to the elastic retractive forces developed inside the gel and A6mixi g is the result of the spontaneous mixing of the fluid molecules with the polymer chains. The term AGmjXjng is a measure of the compatibility of the polymer with the molecules of the surrounding fluid. This compatibility is usually expressed by the polymer-solvent interaction parameter, xi (Flory, 1953). 

Applying external forces to an elastic body we change the relative position of its different parts which results in a change in body size and shape, i.e. under stressed conditions an elastic body undergoes deformation. As the particles of a body are shifted with respect to each other, the body develops elastic forces, namely stresses, opposing the deformation. In the course of deformation these forces increase and at a certain instant of time they can even counter-balance the effect of the external stress. At this moment the deformation process comes to an end, and the body is in a state of elastic equilibrium. As the stress is removed gradually, the elastic body returns to its initial state however, the abrupt disappearance of the outside force causes the particles inside the body to oscillate. To describe these oscillations, it is necessary to quantify the relationships between the forces arising at each point of the deformed... 

Both RLC phosphorylation and active stiffness increase more rapidly than isometric force during the initiation of the contraction (Kamm and Stull, 1986). These observations suggest that phosphorylation of myosin RLC allows cross-bridge attachment to actin. The delay in force development may result from cooperative effects of phosphorylation on activation whereby force depends on formation of doubly phos-phorylated myosin (Persechini and Hartshorne, 1981 Sellers et al., 1983) however, other contributions, including a delay in the expression of force through series elastic element in the tissue, cannot be excluded (Aksoyetfl/., 1983). 

Figure 7.50. Effect of enzymatic superoxide generating system on the elastic properties of ligamen-tum nuchae elastin. With time of exposure of purified fibrous elastin to Oa" and H2O2, the elastic modulus decreases, and larger and larger extensions are required before development of an elastic force occurs. This is the result of swelling due to hydrophobic dissociation. Once the fiber is hydrophobically dissociated, it becomes susceptible to proteolytic degradation. (Reproduced with permission from Urry et al. )...

The concept of an apolar (hydrophobic)-polar (e.g., charge) repulsive free energy of hydration, AG,p, contributes to understanding the mechanism whereby ATPases function in three distinguishing respects. First and second, ATP binding, and particularly on hydrolysis with formation of ADP plus Pi, has the potential to effect both push and pull components of force. Third, release of Pi results in development of an elastic pull component of force that is most in evidence during isometric contractions. These three elements of force development are discussed immediately below. 

Similarly, apolar-polar repulsion between a highly charged group and very hydrophobic side chains of a chain or loop of protein would be expected to limit the freedom of rotation about backbone bonds of sufficiently kineti-cally free chain segment or loop. This increase in AG,p would decrease the number of states accessible to the polymer and decrease the entropy of the chain. The resulting development of an elastic force in the chain segment or loop of protein could be used to perform... 

As seen in Figure 9B, at fixed extension of the y-irradiation-cross-linked elastic matrix comprised of poly[0.8(GVGVP), 0.2(GEGVP)], protonation of four carboxylates per 100 residues results in development of elastic force. A thermoelasticity characterization of this matrix at low pH gives the same result of dominantly entropic elasticity as found in curve b of Figure 6B for poly(GVGVP) in the absence of carboxyl moieties. 

The process of protonation allows reconstitution of hydrophobic hydration to such an extent that the temperature range for hydrophobic association drops below that of the operating temperature (Urry, 1993, 1997). The result is a contraction due to hydrophobic association. Again, during an isometric contraction (this time chemically driven), hydrophobic hydration becomes less ordered bulk water. The solvent entropy increases during the development of entropic elastic force due to a decrease in entropy. 

Thermoelasticity results are also used to test some of the assumptions used in the development of the molecular theories. The results [72] indicate that the ratio f /f is essentially independent of the degree of swelling of the network, and this supports the postulate made in Section 1.1.4 that intermolecular interactions do not contribute significantly to the elastic force. The assumption is further supported by results [72] showing that the values of the temperature coefficients of the unperturbed dimensions obtained from thermoelasticity experiments are in good agreement with those obtained from viscosity-temperature measurements on the isolated chains in dilute solution. 

The first finite element schemes for differential viscoelastic models that yielded numerically stable results for non-zero Weissenberg numbers appeared less than two decades ago. These schemes were later improved and shown that for some benchmark viscoelastic problems, such as flow through a two-dimensional section with an abrupt contraction (usually a width reduction of four to one), they can generate simulations that were qualitatively comparable with the experimental evidence. A notable example was the coupled scheme developed by Marchal and Crochet (1987) for the solution of Maxwell and Oldroyd constitutive equations. To achieve stability they used element subdivision for the stress approximations and applied inconsistent streamline upwinding to the stress terms in the discretized equations. In another attempt, Luo and Tanner (1989) developed a typical decoupled scheme that started with the solution of the constitutive equation for a fixed-flow field (e.g. obtained by initially assuming non-elastic fluid behaviour). The extra stress found at this step was subsequently inserted into the equation of motion as a pseudo-body force and the flow field was updated. These authors also used inconsistent streamline upwinding to maintain the stability of the scheme. 

The various elastic and viscoelastic phenomena we discuss in this chapter will be developed in stages. We begin with the simplest the case of a sample that displays a purely elastic response when deformed by simple elongation. On the basis of Hooke s law, we expect that the force of deformation—the stress—and the distortion that results-the strain-will be directly proportional, at least for small deformations. In addition, the energy spent to produce the deformation is recoverable The material snaps back when the force is released. We are interested in the molecular origin of this property for polymeric materials but, before we can get to that, we need to define the variables more quantitatively. 

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