Contraction elastic-contractile model

Figure 1.7. Shown are the first reported data of the conversion by an elastic-contractile model protein of chemical energy due to an increase in concentration of acid into the mechanical work of contraction. A Length changes at constant force (isotonic contraction) in phosphate-buffered saline. B Force changes at constant length (isometric contraction) in phosphate-buffered saline. (Reproduced from Urry et al. )...

Figure 2.6. In general, the conversion from the extended state to the contracted state shown in Figure 2.5 is graphed here as a systematic family of sigmoid-shaped curves with a common dependence of oil-like character of the elastic-contractile model protein whether the energy input is thermal, chemi-...

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. 

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. 

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. 

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. 

The phenomena that drive muscle contraction—thermal activation, pH activation, calcium ion activation, stretch activation in insect flight muscle, and dephosphorylation itself—have all been shown to drive contraction by hydrophobic association in the elastic-contractile model proteins discussed in Chapter 5. As concerns a pair of hydrophobic domains, all of these processes surmount the T,-divide (the cusp of insolubility in Figure 7.1) to go from a soluble state to an insoluble state either by raising the... 

Hydrophobic association within a protein chain constitutes an element of contraction. From our design and study of elastic-contractile model proteins, a contraction comprises two distinct but interlinked physical processes. They are... 

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... 

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. 

The concept of two distinct but interlinked mechanical processes, expanded here as the coupling of hydrophobic and elastic consilient mechanisms, entered the public domain in the publication of Urry and Parker. Experimental results on elastic-contractile model proteins forged the concept, and the work of Urry and Parker extended the concept to contraction in biology. Unexpected in our examination of the relevance of this perspective to biology was to find the first clear demonstration of the concept in biology in a protein-based machine of the electron transport chain as a transmembrane protein of the inner mitochondrial membrane. Unimaginable was the occurrence of the coupled forces precisely at the nexus at which electron transfer couples to proton pumping. 

V in Table 5.5 with 0,2,3,4, and 5 F residues per 30-mer exhibits a systematic nonlinear increase in steepness, that is, in positive cooperativity, and an associated nonlinear increased pKa shift, as plotted in Figure 5.34. The energy required to convert from the COOH state to the COO" state systematically in a supralinear way becomes less and less, as more Phe residues replace Val residues. The energy required to convert from the hydrophobically dissociated state of COO" to the hydrophobically associated (contracted) state of COOH becomes less, as the model protein becomes more hydro-phobic. The elastic-contractile protein-based machine becomes more efficient as it becomes more hydrophobic. The cooperativity of Model Protein iv with a Hill coefficient of 2.6 is similar... 

To answer the question of optimal matching between the ventricle and arterial load, we developed a framework of analysis which uses simplified models of ventricular contraction and arterial input impedance. The ventricular model consists only of a single volume (or chamber) elastance which increases to an endsystolic value with each heart beat. With this elastance, stroke volume SV is represented as a linearly decreasing function of ventricular endsystolic pressure. Arterial input impedance is represented by a 3-element Windkessel model which is in turn approximated to describe arterial end systolic pressure as a linearly increasing function of stroke volume injected per heart beat. The slope of this relationship is E. Superposition of the ventricular and arterial endsystolic pressure-stroke volume relationships yields stroke volume and stroke work expected when the ventricle and the arterial load are coupled. From theoretical consideration, a maximum energy transfer should occur from the contracting ventricle to the arterial load under the condition E = Experimental data on the external work that a ventricle performed on extensively varied arterial impedance loads supported the validity of this matched condition. The matched condition also dictated that the ventricular ejection fraction should be nearly 50%, a well-known fact under normal condition. We conclude that the ventricular contractile property, as represented by is matched to the arterial impedance property, represented by a three-element windkessel model, under normal conditions. 

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