Cusp of insolubility

Biology thrives near a movable cusp of insolubility, and the forces that, in a positively cooperative manner, power the molecular machines of biology drive paired oil-like domains of proteins back and forth between association (insolubility) and dissociation (solubility), and excursions too far in either direction into the realms of insolubility or solubility spell disease and death. 

The plaques of Alzheimer s disease and the fibrous state of the prions of mad cow disease (both with resulting brain destruction), the thrombi of stroke (cerebral thrombosis) and of heart attack (myocardial infarction), and the familiar manifestation of death (rigor mortis) represent excursions too far in the direction of protein insolubility. The favorable actions of antioxidants keep proteins from becoming so soluble (unfolded) that protein function disappears and proteolytic degradation ensues. Of course, the lack of blood clotting, hemophilia (the lack of clotting proteins to become insoluble by association of oil-like domains), results in death. Such devastations result from loss of proper balance between solubility and insolubility. They represent excursions too far from the cusp of insolubility, that is, too far from the boundary between insolubility and solubility. 

A protein-based machine without water as an integral part of its structure could not function by the consilient mechanism. In other words, water is required in at least one of the two states in order to have a movable cusp of insolubility, and in order for competition for hydration to be relevant there must be adequate water present. The first prerequisite, therefore, in addressing the biological relevance of the consilient mechanism is to assess whether or not water exists within or between the changing structural elements of a protein motor during function. 

The movable cusp of insolubility represented in Figure 1.1 provides a means of visualizing the molecular process. Addition of acid (proton,... 

Figure 1.8. Illustration of a movable (rotating) cusp of insolubility representing the cross section of the Fi-motor of ATP synthase and depicting an asymmetrical rotor with one of its three sides being very oil-like. An oil-like association is shown to occurr each time the most oil-like side of the rotor, rotated by the Fi-motor, resides at an empty site. This provides a literal, spatial demonstration of the movable cusp of insolubility. On rotation of the oil-like side of the rotor from the empty site to an ATP-filled or...

The Fi-Motor s Cusp of Insolubility in Both Assembly and Function... 

When Assembled, the Fi-motor Functions as a Rotating Cusp of Insolubility... 

The movable cusp of insolubility of the Fi-motor becomes both literal and metaphorical. The metaphorical representation occurs as the oil-like side of the rotor passes from association with the oil-like empty P-subunit where the cusp of insolubility, represented in Figure 1.1, resides at low temperature (below physiological temperature) to high temperature, that is, above physiological temperature to result in oil-like dissociation of rotor from sleeve. Thus, the metaphorical representation occurs as the oil-like side of the y-rotor is rotated by the Fq-motor from association with an oil-like empty P-subunit to dissociation from a vinegar-like a-subunit that contains ATP. 

The Cusp of Insolubility for the Fi-motor, Alias the Fi-ATPase When Running in Reverse... 

The Fi-motor structure due to the Walker groups functions ideally to demonstrate the steps whereby the rotating cusp of insolubility would result in the synthesis of ATP. The y-rotor may be represented by the relative oil-like character of its three faces that are calculated in Chapter 8, section S.4.4.3, shown in Figures 8.31 to 8.33, and listed in Table 8.2. As represented in Figure 1.8, there is a very oil-like face (marked by -20 and shown directed toward the empty catalytic site), a neutral face (indicated by 0 and directed toward the P-ADP-t-P site), and a relatively vinegar-like face (indicated by -1-9 and directed toward the site indicated in Figure 1.8 as occupied by P-ADP). 

Hemoglobin Mutation of a Single Amino Acid from Vinegar-like to Oil-like Causes Dysfunction by Shifting the Cusp of Insolubility Too Far Toward Insolubility... 

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. 

Relative Efficiencies by Chemical Energy Required to Move the Cusp of Insolubility Across Biology s Transition Zone... 

When concerned with the physiological operating temperature of 37°C, a model protein with its T,(b)-value at 37°C will not have appreciably hydrophobically associated. Any variable that lowers the Tt(b)-value to 25°C, which is the width of the transition zone for (GVGVP)25i, will have essentially completed the transition to the hydrophobically associated state, as depicted in Figure 5.33. The variable will have moved the cusp of insolubility across the transition zone for biology. In particular, the interest is in the variable of the chemical energy per mole required for a AT, just sufficient to traverse the transition zone from hydrophobically dissociated at 37°C to hydrophobically associated at 25°C. 

Biology thrives near a movable cusp of insolubility, yet excursions too far, either direction, into the realms of insolubility or solubility spell disease and death. 

Figure 7.1. The movable cusp of insolubility represented as the calorimetry curve for the inverse temperature transition of (GVGVP)25, due to hydrophobic association. Hydrophobic association occurs either by raising the temperature from below to above the temperature interval of the transition or by introducing an energy that lowers the cusp of insolubility, that is, lowers the temperature at which the transition occurs. Hydrophobic dissociation occurs either by lowering the temperature from above to below physiological temperature or by moving the cusp to higher temperatures by the introduction of an energy that increases the temperature at which the transition occurs from below to above physiological temperature.

Increasing the temperature to result in insolubility is the hallmark of hydrophobic association by inverse temperature transitions. As temperature is a factor in the positive (-TAS) term for formation of hydrophobic hydration, an increase in temperature obviously increases the magnitude of the positive (-TAS). An increase in the magnitude of the positive (-TAS) term means that AG(solubility) = AH -TAS becomes positive, and solubility is lost. The cusp of insolubility, the Tt-(solubility/insolubil-ity) divide, is surmounted by heating. On... 

---