Model proteins mechanical work performed

Chapter 16 applies thermodynamics to problems of biological interest. The metabolic processes leading to mechanical work performed by a living organism are described first, followed by discussions of the role of thermodynamics as a tool for understanding the stabilities of biopolymers such as proteins, and oligonucleotides as model compounds for DNA. 

Furthermore, yet to be computed by any program is the fundamental thermo-mechanical transduction wherein the cross-linked elastic-contractile model proteins contract and perform mechanical work on raising the temperature through their respective inverse temperature transitions. These results first appeared in the literature in 1986 and have repeatedly appeared since that time with different preparations, compositions, and experimental characterizations. Additionally, the set of energies converted by moving the temperature of the inverse temperature transition (as the result of input energies for which the elastic-contractile model protein has been designed to be responsive) have yet to be described by computations routinely used to explain protein structure and function. 

Key Molecular Players Perform Mechanical Work in Model Proteins... 

D.W. Urry, L.C. Hayes, and D. Channe Gowda, Electromechanical Transduction Reduction-driven Hydrophobic Folding Demonstrated in a Model Protein to Perform Mechanical Work. Biochem. Biophys. Res. Commun., 204,230-237, 1994. 

Now, cross-linking the elastic model protein in the phase-separated state results in elastic bands. Similarly warming the band, swollen at room temperature (just below T,), to body temperature (some 15 degrees above T,) causes the band to contract with the performance of mechanical work. The band pumps iron on raising the temperature from below to above T,. As scientific accounts go, the T, perspective exemplifies simplicity. 

For the performance of mechanical work by model proteins cross-linked to form elastic bands, a weight is attached to the rubber-like... 

Axiom 2 Heating to raise the temperature from below to above the temperature interval for hydrophobic association of cross-linked elastic model protein chains drives contraction with the performance of mechanical work. 

Accordingly, the values for An are likely to differ by significantly less than a factor of two for the two model proteins. Thus, simply by changing the composition from that of Model Protein ii to that of Model Protein I, the contraction with which to perform mechanical work could possibly occur using one-tenth the amount of the chemical energy and certainly with no more than one-fifth the amount of the chemical energy. (See section 5.9.5.1 for further discussion of the relative efficiencies of Model Proteins I and ii in Table 5.5.)... 

Axiom S At constant temperature, an energy input that changes the temperature interval for thermally driven hydrophobic association in a model protein can drive contraction, that is, oillike folding and assembly, with the performance of mechanical work in other words, the energy input moves the system through the transition zone for contraction due to hydrophobic association. 

Another example is the Principle of Le ChStelier, which may be stated as follows For any system at rest (at equilibrium) the introduction of a stress (in our case an input energy) causes the system to react in such a way as to relieve the stress (in our case by an output energy). This principle reasonably describes protein-catalyzed energy conversion, that is, the function of protein-based machines. Under prescribed conditions, properly designed model protein-based machines exhibit a behavior where for each action there is a reaction. In section 5.4, regardless of the action, which was any one of several different input energies, the performance of mechanical work was the reac-... 

As shown in the hexagonal array in Figure 5.22, five different energy inputs can perform mechanical work by the consilient mechanism. The set of elastic-contractile model proteins capable of direct utilization of hydrophobic association for contraction are called protein-based molecular machines of the first kind. These are enumerated below with brief consideration of the reversibility of these machines. 

Polymers III through VI represent a systematic increase in the number of Val (V) residues replaced by more oil-like Phe (F) residues. Each step increase in oil-like character of the model protein, on going from 0 to 2 to 3 to 4 and to 5 Phe residues for every 30 residues, stepwise increases the affinity of Na for -COO . Each step increase in oil-like character means that less of an increase in salt is required to drive contraction. Polymer VI, when cross-linked into elastic sheets, provides the most efficient molecular machine of the set. This molecular machine requires less chemical energy to produce a given amount of motion, that is, to perform a given amount of mechanical work. 

As was discussed in Chapter 5, for Figure 5.17, addition of electrons to a positively charged redox group increases oil-like character and drives model protein folding, which result in contraction and the performance of mechanical work. The increase in affinity for electrons of the vitamin-like molecule that occurs on replacement of Val by Phe (see Figure 5.20C) makes for a more efficient electron-driven contraction. Thus, a genetic code that would allow easy mutational steps to become more oil-like would, here again, provide for evolution of more efficient protein-based machines. 

The stator of rotary Fi motor is composed of six proteins. Three of them catalyze the hydrolysis of ATP, which drives the rotation of a shaft. The shaft of this Fi complex is glued to a proton turbine called Fq, which is located in the internal membrane of mitochondria. The whole FoFi-ATPase synthesizes ATP using the proton flow across the inner membrane. The Fi protein complex can function in reverse and serve as a motor performing mechanical work. These motors are modeled as stochastic systems with random jumps between the chemical states. If the rotation follows discrete steps and substeps, then the shaft has motions between well-defined orientations corresponding to the chemical states of the motor leading to a stochastic system based on discrete states. The result still will be the transition rates of the random jumps between the discrete states. These transition rates depend on the mass action law of chemical kinetics. 

---