Temperature elastic-contractile model

The sigmoid-shaped curves of Figure 2.6A represent the shortening of contraction that occurs on raising the temperature through the relevant temperature interval for the particular extent of oil-like character of the model protein. Elastic-contractile model proteins of more oillike composition contract at lower temperatures and over narrower temperature intervals. 

In general, the key chemicals for changing the folding temperature in our elastic-contractile model proteins are prevalent triggers of function in biology. 

Figure 2.18. Energies are shown that can be inter-converted by means of elastic-contractile model proteins capable of exhibiting inverse temperature transitions functioning by means of the competition for hydration between oil-like and charged groups called an apolar-polar repulsive free energy of hydration. See Chapter 5 for a more complete development of the phenomenology and physical basis and Chapter 8 for details of the molecular process.

D-amino acid residue on the right (an optical isomer that does occur in biology, but in those peptides not encoded for by the genetic code). C The effect of insertion of a D-amino acid residue in an otherwise L-amino acid residue protein in the P-spiral structure of the elastic-contractile model protein of our focus would be to disrupt the regular structure. This is difficult to avoid completely in chemical synthesis, and it increases the temperature at which occurs the inverse temperature transition and decreases the heat of the transition due to less optimal association of oil-like groupings. 

As demonstrated in Figure 5.3 for several model proteins, essentially unlimited solubility occurs at low temperature, and phase separation (insolubility) occurs as the temperature is raised. Also, for our model protein composi-tions, - the curvature of the coexistence line is inverted, having the shape of a valley instead of a smooth mountain peak. Because of this we call the phase transition, exhibited by elastic-contractile model proteins, an inverse temperature transition. Even more compelling reasons exist for the inverse temperature transition label. 

Figure 5.3. Phase diagram for several elastic-contractile model proteins, showing an inverted curvature to the binodal or coexistence line (when compared with petroleum-based polymers) that is equivalent to the T,-divide, with the value of T, determined as noted in Figure 5.IB. Solubility is also inverted with insolubility above and solubility below the binodal line, that is, solubility is lost on raising the temperature whereas solubility is achieved by raising the temperature of most petroleum-based polymers in their solvents. Note that addition of a CHj group lowers the T,-divide and removal of the CH2 group raises the T,-divide. For these and the additional reason of increased ordering on increasing the temperature, the phase transitions of elastic-contractile model proteins are called inverse temperature transitions. (The curve for poly[GVGVP] is adapted with permission from Manno et al. and Sciortino et al. ).

Figure 5.5. Transitions, plotted as independent variable versus dependent variable, showing a response limited to a partieular range of independent variable. (A) Representation of the thermally driven contraction for an elastic-contractile model protein, such as the cross-linked poly(GVGVP), plotted as the percent contraction (dependent variable) versus temperature (independent variable). The plot shows a poorly responsive range below the onset of the transition, the temperature interval of the inverse temperature transition for hydrophobic association, and another poorly responsive region above the tem-...

As mentioned above in reference to Figure 5.5A, as the temperature is raised, contraction of a band composed of elastic-contractile model protein occurs. Contraction occurs as the temperature is raised through a temperature interval. Crossing over the T,-divide, defined in Figure 5.3, is to pass through the temperature interval over which contraction occurs it is the result of the phase separation, specifically of the inverse temperature transition. Furthermore, the temperature interval for contraction occurs at a lower temperature when the model protein is more hydrophobic and at a higher temperature when the model protein is less hydrophobic. 

Several points require consideration on identification of AH,(CH2) - T,(GVGIP)AS,(CH2) as -AGha(CH2). The points include the separability assumption of Equations (5.3) and (5.4), the relevance of the model protein to such identification, and the choice of reference state in order that the nonlinearity of hydrophobic-induced pKa shifts be included. From the data of Butler, the separability is reasonable for a simple CH group, but examination of the calculated result is required to be satisfied whether or not extension to more complex substituents is warranted. As the inverse temperature transition of (GVGVP) has been experimentally shown to involve no Raman detectable changes in secondary structure, the elastic-contractile model proteins of focus here reasonably represent the best known model available for such an effort. It should be noted, however, that NMR studies on the temperature and solvent dependence of peptide NH and... 

Figure 6.2. Differential scanning calorimetry data of elastic-contractile model proteins. (A) Phase separation transition for Polymers I and XII, alone in solution (curves a and c) and when mixed in the same solution (curve b). Even when mixed, the individual polymers separate from each other they demix due to the input of thermal energy during a slow increase in temperature. Also a polymer was syn esized that contained equal amounts of the two pentamers, and its phase transition is found at an intermediate temperature (curve d). (B) With a composition having a carboxylate function, the input of chemical energy of protons (addition of acid to lower the pH) drives the phase separation to lower temperatures. See text for discussion. (Reproduced with permission from Urry et al. )...

The hydrophobically associated state represents the insolubility side of the T,-(solubility/insolubility)divide. As discussed in Chapter 5, contraction of the model elastic-contractile model proteins capable of inverse temperature transitions arises due to hydrophobic association. Hydrophobic association occurs, most fundamentally, on raising the temperature, on adding acid (H" ) to protonate and neutralize carboxylates (-COO ), and on adding calcium ion to bind to and neutralize carboxylates. Most dramatically, hydrophobic association occurs on dephosphorylation of (i.e., phosphate release from) protein, and it commonly occurs with formation of ion pairs or salt bridges between associated hydrophobic domains. 

On the basis of the physical processes identified from the studies on free energy transduction by elastic-contractile model proteins functioning by inverse temperature transitions, the operative interaction energy that alters the orientation of the hydrogen bonds and changes the pKa s of the amino acid residues ... 

As reviewed in Chapter 7 with a focus on the issue of insolubility, extensive phenomenological correlations exist between muscle contraction and contraction by model proteins capable of inverse temperature transitions of hydrophobic association. As we proceed to examination of muscle contraction at the molecular level, a brief restatement of those correlations follows with observations of rigor at the gross anatomical level and with related physiological phenomena at the myofibril level. Each of the phenomena, seen in the elastic-contractile model proteins as an integral part of the comprehensive hydrophobic effect, reappear in the properties and behavior of muscle. More complete descriptions with references are given in Chapter 7, sections 7.2.2, and 7.2.3. 

Raising the temperature to drive contraction by hydrophobic association is the fundamental property of the consilient mechanism as demonstrated in Chapter 5 by means of designed elastic-contractile model proteins. Thermal activation of muscle contraction also correlates with contraction by hydrophobic association, but assisted in this case by the thermal instability of phosphoanhydride bonds associated with ATP, which on breakdown most dramatically drive hydrophobic association. In particular, both muscle and cross-linked elastic protein-based polymer, (GVGVP) contract on raising... 

By T,-type, we mean polymers that exhibit inverse temperature transitions in which the protein-based polymers hydrophobically associate on raising the temperature. T, represents the onset temperature for the transition. For the elastic-contractile model proteins of interest here, the inverse temperature transition is seen as a phase separation resulting from both intermolecular and intramolecular hydrophobic association. On raising the temperature... 

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. 

For our model elastic-contractile proteins in water, a plot of heat absorbed on increasing temperature exhibits an abrupt rise and then a more gradual decline as the temperature reaches the start of and passes through the tran-... 

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