Model proteins contraction with

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... 

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. 

Most cell lines have lost some or many of the functions characteristic of the differentiated cells from which they were derived. Such relatively undifferentiated cells are poor models for investigating the normal functions of specific cell types. Better in this regard are several more-differentiated cell lines that exhibit many properties of normal nontransformed cells. These lines Include the liver tumor (hepatoma) HepG2 line, which synthesizes most of the serum proteins made by normal liver cells (hepatocytes). Another example consists of cells from a certain cultured fibroblast line, which under certain experimental conditions behave as muscle precursor cells, or myoblasts. These cells can be Induced to fuse to form myotubes, which resemble differentiated multlnucleated muscle cells and synthesize many of the specialized proteins associated with contraction. The results of studies with this cell line have provided valuable information about the differentiation of muscle (Chapter 22). Finally, as discussed previously, the MDCK cell line retains many properties of highly differentiated epithelial cells and forms well-defined epithelial sheets in culture (see Figure 6-6). 

Stepwise increases in oil-like character, as when the mildly oil-like Val (V) residue is replaced by the very oil-like Phe (F) residue, cause the add-base titration curves to be shifted to higher pH values and to be steeper. The energy required to drive the model protein from the phase separated, contracted state to the swollen, relaxed state is proportional to the width of the curve, that is, inversely proportional to the steepness of the curve. Accordingly, the model protein with the steepest curve exhibits the most efficient function for performing the work of lifting a weight. 

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-...

Figure 2.9. A set of reactions is shown, each of which causes the model protein to become more oil-like with the result of a contraction due to association of oil-like groups. See text for further discussion. (Reproduced with permission from Urry." )...

As depicted in reaction ( ) of Figure 2.9, the reaction of OH" with -NH3+ groups of a model protein results in formation of H2O and -NH2 to give a more oil-like model protein. The effect is to form so much oil-like hydration, as shown in the central structure of Figure 2.9, that oil-like solubility is lost with the result of contraction. 

As depicted in reaction (/v) of Figure 2.9, either the neutralization of a negative group (e.g., -COO") of the model protein by a positive ion (e.g., Na or Ca ) from solution or the neutralization of a positive group (e.g., -NHs ) of the model protein by a negative ion (e.g., CT) from solution can cause the model protein to become too oil-like with the result of contraction due to too much oil-like hydration. Contraction occurs as the result of insolubilization of the oil-like model protein and is an example of the lowering of the cusp of insolubility as represented in Figure 1.1. 

What can be demonstrated with model proteins functioning as contractile molecular machines is that two of the most effective means of lowering the temperature of an inverse temperatine transition to drive contraction are positively charged calcium ions (Ca ) binding at paired negatively charged carboxylates (COO ) to decrease net charge... 

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. 

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. 

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. 

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