Urry D.W. (Ed.) What Sustains Life? : Consilient Mechanisms for Protein-Based Machines and Materials

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5.6 Systematic Classification of Energy Conversions by Consilient Protein-based Machines

175

elastic force. Yet another interesting absorption

in the dielectric relaxation spectrum occurs in

the middle of the acoustic frequency range. All

of these absorptions are expected to be rele-

vant to electromagneto-mechanical transduc-

tion, and they would be expected to exhibit

some reversibility. The most popular aspect of

electromagneto-mechanical transduction, pho-

tomechanical transduction, as relevant to the

consilient mechanism of energy conversion

would be irreversible. A mechanical input alone

would not reversibly result in emission of a

photon of light. While stretching an elastic-con-

tractile model protein could conceivably trigger

emission of a photon, the energy recovered on

relaxation could not reconstitute a chro-

mophore capable of photon emission.

5.6.4.5.1 Photo -^ Mechanical Transduction

The examples demonstrated to date using

elastic protein-based polymers have involved

the light-driven trans to cis geometrical iso-

merization that raises the temperature of the

inverse temperature transition. This has been

seen with azobenzene^^ and with the more bio-

logically relevant cinnamide, discussed above.^^

This capacity to effect relaxation can be

reversed by heating or by a different frequency

of Ught to regain the contracted state. Although

a practical reversibility, this should not be con-

fused with the reversibility in the sense that a

mechanical energy input would result in the

emission of a photon of light.

5.6.4.5.2 Mechano

Transduction

Electromagnetic

Stretching is expected to increase the dielectric

absorption near 5 GHz and to decrease the

dielectric absorptions near

kHz and

MHz.

These effects could be used in the design of a

number of transducers. Perhaps these effects

could be referred to as mechano ^ dielectric

transduction. Furthermore, the

kHz dielectric

relaxation exhibits the counterpart of an

acoustic absorption."^^'^^ This means that the

mechanical oscillation of a sound wave could

be detected as a change in the

kHz dielectric

relaxation.

5,6.4.6 Device Reduction of a Linear

Contracting Engine to a Rotary Engine

5.6.4.6.1 Collagen-Driven Rotary Engine

of Katchalsky

The reduction of the elementary elastic strip

that contracts and relaxes to a rotary motor has

been demonstrated by Steinberg et al.^^ In that

case,

a circular elastic band was constructed. In

a continuous manner it was wrapped around a

set of pulleys and through a pair of baths, one

bath providing the correct chemical energy for

contraction and the other for relaxation. In this

way a chemomechanical rotary motor was

constructed.

5.6.4.6.2 Generalization to Input Energies

Other Than Chemical

Similarly with one bath as the reducing system

and the other as an oxidizing system, an electro-

mechanical rotary motor could be constructed.

Other means of driving contraction and relax-

ation represented in Figures 5.18 and 5.22 could

be used in a similar manner to construct rotary

motors.

5.6.5 Protein-(Tt)-Based Molecular

Machines of the Second Kind

(Molecular Machines for the

Performance of Work Other

Than Mechanical)

Discussion of each of the protein-(Tt)-based

molecular machines of the second kind is

beyond the scope of this volume. Above were

discussed the set of five pairwise energy con-

versions that constituted protein-(Tt)-based

molecular machines of the first kind. This leaves

another 13 pairwise energy conversions of the

second kind, which are listed under Axiom 4 in

section 5.6.3. Most of the protein-(Tt)-based

molecular machines of the second kind are of a

more academic interest. Because they contain

all of the coupling-of-functions, however, many

are of central interest to biology. These have

been discussed in section 5.5. Basically, when a

hydrophobic domain contains two different

vinegar-Hke R-groups, changing one to be more

oil-like can induce the other to become more

176

Consilient Mechanisms for Diverse Protein-based Machines

oil-like; this is one statement of the Principle of

Le Chatelier. A favorable Gibbs free energy for

hydrophobic association, AGHA, is used to

perform work other than mechanical work, and

it does so in a way that gives rise to positive

cooperativity.

ITie sort of energy conversions that consti-

tute protein-(Tt)-based molecular machines of

the second kind have been referred to as

pumping protons and pumping electrons. There

are two aspects to chemo ^-^ chemical trans-

duction. An example would be where a partic-

ular chemical energy input caused the

elastic-contractile model protein to become

more oil-like and thereby to energize another

chemical group such as a phosphate. Another

aspect of chemo-chemical transduction could

include the classic consideration of enzyme

catalysis, in which case there occurs a decrease

in the chemical energy of reactants resulting in

an increase in the chemical energy of products.

Our focus now turns to the physical basis

whereby the energy conversions of the

hydrophobic consilient mechanism occur, and,

of course, it becomes an issue of what con-

trols the inverse temperature transition of

hydrophobic association.

5.7 What Is the Physical Basis

for the Consihent Mechanism of

Energy Conversion?

5.7.1 Answer: The Solvent-Mediated

Interaction Between Oil-like and

Vinegar-like Groups Constrained to

Coexist Along and Between Protein

Chain Molecules

Biology's machines are different from man's

machines, primarily because they evolved to

function efficiently in water. Many of man's

machines commonly operate at high tempera-

tures,

above the boiling temperature for water.

Such conditions are incompatible with life.

Other manmade machines, electric motors, and

generators and the many energy conversions of

the electronic world do not function in water.

As shown in Figure 2.16, even the chemically

driven polymeric machines that do function in

water, but that utilize the interactions of

charges in water, are very inefficient compared

with the protein-based machines available to

biology by means of inverse temperature tran-

sition of the hydrophobic consilient mechanism.

As discussed in this section, the interplay

between oil-like groups and vinegar-like groups

in an aqueous medium is the basis of the energy

conversion by the consilient mechanism. If

there were no oil-like components and no

through solvent interaction between oil-like

and vinegar-like groups, energy conversion

would have to rely on inefficient charge-charge

interactions that are shielded by the high

dielectric constant of water. Present arguments

of "conformational energy" forcing vinegar-like

groups into energetically unfavorable circum-

stances would also play a greater role. The

interactions between apolar and polar compo-

nents constrained by positions in the protein

chain molecule make for efficient protein-

based machines in water. To understand this

better, we need to understand the nature and

dynamics of hydrophobic hydration during the

function of such systems.

5.7.2 The Structure of Water

Surrounding Oil-like R-groups

Water molecules arrange in a special way

around oil-Uke groups. Stackelberg and

Miiller^^ showed this with the crystal structure

of hydrates of hydrocarbon gases (see Figure

2.8).

The waters arrange at the apices of pen-

tagons, and 12 pentagons arrange around a

small oil-like molecule. When structural detail

is sufficient, these pentagonal arrangements of

water molecules have been seen at the surface

of oil-Hke groups in protein. Martha Teeter^^

first observed hydrophobic hydration in

protein, positioned adjacent to an oil-like side

chain. Pentagonal arrangements of water mol-

ecules were observed adjacent to the side chain

of a leucine (Leu, L) residue with its oil-like,

-CH2CH(CH3)2, R-group.

More oil-like R-groups in our model protein

studies resulted in lower temperatures for the

onset of the inverse temperature transition of

hydrophobic folding and assembly (see section

5.3.2). We argued that more oil-like R-groups in

5.7 What Is the Physical Basis for the ConsiUent Mechanism of Energy Conversion?

177

polymers on the soluble side of the Tt-divide

means more hydrophobic hydration and that

more hydrophobic hydration means a lower

temperature for the Tfdivide between solubil-

ity and insolubility. In fact, we proposed that the

amount of hydrophobic hydration determines

the temperature at which the Tfdivide

occurred (section 5.3.5). In particular, as the

argument went, any process that increased the

amount of pentagonally arranged water

lowered, and any process that decreased the

amount of pentagonally arranged water neces-

sarily raised, the temperature interval for

hydrophobic association. Subsequently, the

definitive test of this perspective became pos-

sible—the capacity to measure directly the

amount of hydrophobic hydration and to

determine the effect of increasing and decreas-

ing the amount of hydrophobic hydration on

the value of Tj.The most current studies and the

most definitive studies are described immedi-

ately below in section 5.7.3. Then, the earlier

studies are described in section 5.7.9. These

latter studies preceded and, in fact, provided

the impetus to obtain the equipment required

for the definitive studies.

5.7.3 Direct Measurement of

Hydrophobic Hydration

Two decades ago, during studies of the back-

bone motions of these elastic model proteins

for the purpose of understanding the nature of

the elasticity, an associated observation sug-

gested that energy of the type produced by

microwave ovens was increasingly absorbed

as the amount of hydrophobic hydration

increased.^^'^^ The observation made possible a

more complete understanding of the physical

basis for the consiUent mechanism of energy

conversion that we call the comprehensive

hydrophobic effect and that included thermo-

dynamic characterization in terms of a Gibbs

free energy of hydrophobic association, AGHA

(see sections 5.1.3 and 5.1.7.).

5.7.3.1 Identification of

Hydrophobic Hydration

Microwave absorption by pure water as a func-

tion of frequency is shown in Figure 5.24A.^^ A

solution of approximately half water and half

model protein, (poly(GVGIP), by weight

demonstrates the presence of an absorption at

a lower frequency than that of water alone (see

Figure 5.24B). Subtracting out the peak due to

absorption by pure water leaves a peak for a

kind of water that must be interacting with the

model protein. Because the sum of both peaks

represents a reasonable estimate of the total

amount of water, and because we know the

total amount of water present, the amount of

interacting water can be calculated. Watching

the behavior of the interacting water in

response to several experimental variables pro-

vides for its identification.

How is the water interacting with the model

protein? In Figure 5.25A, the number of inter-

acting water molecules is plotted as a function

of temperature for both poly(GVGIP) and

poly(GVGVP). First, the more oil-Uke polymer,

poly(GVGIP) with an added CH2 group per

pentamer, has more of the interacting water

than the less hydrophobic poly(GVGVP), as

would be expected for hydrophobic hydration.

Most significantly, however, increasing the tem-

perature through the transition temperature

interval of hydrophobic folding and assembly,

that is, from one side to the other of the Tt-

divide, for each model protein causes the inter-

acting water to disappear. We therefore

conclude that the interacting water with its

absorption maximum near 5 GHz is hydropho-

bic hydration. Now, we address the question.

Does the previously deduced competition for

hydration between oil-like and vinegar-like

groups really occur?

5.7.3.2 Direct Observation of Competition

for Hydration

We now examine the hydrophobic hydration

of model proteins containing the vinegar-like

glutamic acid residue with the R-group,

-CH2-CH2-COOH. On decreasing the acid, H^,

concentration, the R-group ionizes to form

-CH2-CH2-COO". The common measure for a

decrease in acid (proton) concentration is an

increase in pH. Initially, the model protein has

the composition, poly[5(GVGVP),(GEGVP)],

but with a precise sequence, (GVGVP GVGVP

178

Consilient Mechanisms for Diverse Protein-based Machines

A 45-

Water

0.01

0.1 1.0 IQ.

frequency (GHz)

B 45

Poly(GVGIP)

Experimental Curve

Theoretical Curve

Simple

Debye

Function

Locked Frequency

Theoretical Curve

Two

Debye Function

0.01

1.0

frequency (GHz)

FIGURE 5.24. Microwave dielectric relaxation

spectra utilized for the direct observation of

hydrophobic hydration. (A) For pure water, showing

a single Debye relaxation indicative of a single mol-

ecular species species. (B) For equal mass of model

protein and water, the complex absorption resolves

into two

peaks,

one for pure water and the other des-

ignated as

interacting

water

(Nhh)-

With the reason-

able approximation that the total absorption area

represents essentially all of the water present, the

relative areas of resolved curves allow calculation of

amount of interacting water,

Nhh,

which is identified

in Figure 5.25. (Reproduced with permission from

Urry et al.^0

GEGVP GVGVP GVGVP GVGVP)36. This is

Model Protein i of Table 5.5. As shown in

Figure 5.25B, when protonated at low pH,

this model protein has a similar amount of

hydrophobic hydration as poly(GVGVP) of

Figure 5.25A,This is consistent with the similar

values of Tt in Table 5.1. On increasing the pH

(as plotted in Figure 5.25B), hydrophobic

hydration decreases as -CH2-CH2-COO~

forms.

As expected, the more hydrophobic Model

Protein ii of Table 5.5, with two Val (V) residues

replaced by two more hydrophobic Phe (F)

residues every six pentamers, is shown in Figure

5.25B

to exhibit more hydrophobic hydration.

Again, as -CH2-CH2-COO" forms on increas-

ing the pH, the amount of hydrophobic hydra-

tion decreases. We conclude that the formation

of carboxylate groups destructures hydrophobic

hydration. Furthermore, the pH at which half of

5.7 What Is the Physical Basis for the ConsiHent Mechanism of Energy Conversion?

179

the carboxyls have converted to carboxylate,

that is, the pKa where [-COOH]/[-COO-] = 1,

occurs at a higher pH, that is, at a lower proton

concentration for the more hydrophobic

200-

100-

0 -

••--\(

(GVGIP)26o; 5mg/ml

(GVGVP)25p 5 mg/ml

T,°C

30 40

200

150

100

Poly(GEGFPGVGVPGVGVP

GVGVPGVGVPGVGFP)

- - - (GVGVPGVGVPGEGVP

GVGVPGVGVPGVGVP)3^

both at 30 mg/ml, 1°C

pK = 4.9

4.6

^^^

» 9

FIGURE 5.25. Temperature and pH dependences of

the interacting water,

Nhh-

(A) Plot of interacting

water,

Nhh,

as a function of temperature where the

interacting

water is seen to disappear as the temper-

ature is raised through the

temperature interval

of the

inverse temperature transition for hydrophobic asso-

ciation.

Therefore, one concludes that the

interacting

water, Nhh, is hydrophobic hydration. (B) Plot

of hydrophobic hydration,

Nhh

, as a function of

decrease in pH where the carboxyl functions of the

two model proteins ionize to form the charged car-

boxylate groups. By the time there is less than one

charged carboxylate per 100 residues, approximately

two-thirds of the hydrophobic hydration has been

lost, and the point at which this occurs is at a higher

pH as the model protein becomes more hydropho-

bic.

From these data we conclude that there exists

a competition for hydration between apolar

(hydrophobic) and polar

(e.g.,

charged) groups.Thus,

there exists an apolar-repulsive free energy for

hydration! (Reproduced with permission from Urry

et al.^0

polymer. This is a measure of the extra work

required for carboxylate to form in the pres-

ence of more hydrophobic hydration.

As further amplified below, the data in Figure

5.25B indicate the two-way street of the com-

petition for hydration. Formation of carboxy-

lates destroys hydrophobic hydration, but the

carboxylate thus hydrated is at a higher Gibbs

free energy as reflected by the higher pKa, the

higher pH required when there is more

hydrophobic hydration.

5,1 A Competition for Hydration

Controls the Amount of Pentagonally

Arranged Water

Salts dissolve very readily in water with release

of heat because the positively and negatively

charged groups (ions) of the salt prefer to have

water surrounding them than to be ion paired

in the salt crystal. The water around charged

groups strongly orients with respect to the

charge. We have just seen that the attraction

between a charged (polar) group and water is

so strong that the charged group, limited from

abundant water by the polymer sequence of

which it is a part, can dismantle the hydration

around oil-like (apolar) groups. Figure 5.26

depicts this competition for hydration with

changing proximity of a polar (e.g., charged)

group to an oil-like (apolar) group. Thus, when

both oil-like groups and charged groups are

constrained to coexist along a protein

sequence, they compete for hydration. The

competition is seen as a loss of hydrophobic

hydration, Nhh, with the consequences of an

increase in Tt and an increase in the pKa, that

is,

a ApKa, which is a measure of the repulsion

between apolar and polar groups.

This competition for hydration between

charged and hydrophobic groups constrained

by sequence to coexist occurs even within a side

chain of a single residue composed of charged

groups and hydrophobic groups. Amino acid

residues such as glutamic acid, arginine, and

lysine contain the charged function at the end

of a string of hydrophobic CH2 groups. It is

interesting that protein crystal structure data

tend to show these side chains, when standing

alone, to be fully extended, as, for example, for

180

Consilient Mechanisms for Diverse Protein-based Machines

small apolar aquaoua

aphera of influanca

(hydrophobic hydration)

^•«0.

eh^||gahy^Hitlon)

^ •ifi^Jiw^^fi^

AG,

ApKd Tt

\Nkh

FIGURE

5.26.

The apolar-polar repulsive free energy

of hydration, where competition for limited hydra-

tion results in less hydrophobic hydration,

NHH,

increase in

Tj,

an increase in

AGap,

that

is,

an increase

in the Gibbs free energy of the ion, AG(ion), and an

increase in the magnitude of the ApKa. (Reproduced

with permission from Urry.^^^)

residues E261 and E264 of the y-rotor of ATP

synthase (see Chapter 8, Figures 8.31 and 8.33)

and the R58 residue that marks the ATP

binding site in the chaperonin structures in

Chapter 7, Figures 7.43 through 7.46. To have

the amino group of lysine folded back beside

the string of four CH2 groups would, by the

apolar-polar repulsive free energy of hydra-

tion, limit the accessible hydration for both and

increase the magnitude of AGap.

The forces between water and charged

groups are much stronger than the forces that

5.7 What Is the Physical Basis for the ConsiUent Mechanism of Energy Conversion?

181

structure water adjacent to oil-like groups. A

few charged residues can destructure much of

the pentagonally arranged water. The forma-

tion of just four carboxylates in 100 residues in

poly[4(GVGVP),(GEGVP)] raises the transi-

tion temperature for oil-like separation from

24° C for -COOH to 69° C for -COO" as shown

in the upper part of Figure 5.3.

There are two sides, however, to the coin of

competition for hydration. The carboxylate

must pay a price to wrench hydration away

from hydrophobic groups and in having to do

so it never achieves the level of hydration that

it would as a dilute carboxylate in bulk water.

The price appears in the amount of hydroxyl

ion, OH", necessary in the solution before the

proton, ff, leaves the -COOH to form a car-

boxylate, that is, OH- + -COOH = -COO" +

H2O.

In the absence of the oil-like residues, the

amount of hydroxyl required to remove the

proton and form COO" is much less. When

there are only 2 carboxyls per 100 residues in

poly[9(GVGIP),(GEGIP)], it is so difficult for

the COO" to form that a pH of 6.4 is required,^^

which is a 250-fold increase in the amount of

hydroxyl ion required. WTien nearly half of the

oil-like Val residues are replaced by more oil-

like Phe residues, as in Polymer V of Table 5.5,

a million-fold increase in the amount of

hydroxyl ion was required to form the car-

boxylate ion of the aspartic acid residues."^^

5.7.5 We Now Know What Controls

Insolubility and Solubility of

Hydrophobic Domains

5.7,5,1 Loss of Solubility Due to Too

Much Hydrophobic Hydration

In general, the solubility of a model protein

such as poly(GVGVP) in water comes from the

presence of the polar peptide group, -CONH-.

The hydrogens of water, HOH, hydrogen bond

to the oxygen of the CO, that is, CO • • • HOH,

and the oxygen of water hydrogen bonds to the

NH, that

is,

• • •

OH2.This hydrogen bonding

gives rise to solubility. As oil-like groups are

added to the model protein in water at a par-

ticular temperature, solubility is ultimately lost.

From Butler,^^ but also from the Tt-based

hydrophobicity scale in Table 5.1, we learn the

unique way in which this happens. Formation of

hydration surrounding oil-like groups is a

favorable exothermic reaction; heat is released;

the heat change for the hydration reaction, AH,

is negative.

Despite this and as contradictory as it may

initially sound, however, too much hydration of

oil-like groups results in loss of solubility. This

is due to the entropy change, AS, that accom-

panies hydrophobic hydration. Recall that sol-

ubility is governed by the Gibbs free energy,

AG(solubility) = AH -

TAS,

where T is the tem-

perature in degrees Kelvin, K, where K = C +

273.

The water molecules of hydrophobic

hydration, the pentagonally arranged water in

Figure 2.8, are more structured than the water

molecules in liquid or bulk water. The entropy

change for formation of hydrophobic hydration

has the opposite sign from the entropy changes

for the melting of ice and the vaporization of

liquid water in Figure 5.2. The latter changes

are to states of less order on raising the tem-

perature; so too is the loss of pentagonally

arranged water to form liquid water on raising

the temperature through the transition zone for

the inverse temperature transition. Therefore,

the entropy change, AS, is negative for forma-

tion of hydrophobic hydration on dissolution of

oil-like groups in water, such that the (-TAS)

term is positive. Now as each oil-like group is

added, the positive increment in the (-TAS)

term is greater than the negative increment in

AH. Accordingly, the oil-like additions can

occur with retention of solubility until at a

given temperature AG(solubility) becomes pos-

itive and solubility is lost.

Whether a particular hydrophobic region or

domain of a model protein or of a natural

protein associates with a second hydrophobic

domain in the same molecule or a separate mol-

ecule, the same process of loss of solubility

occurs. If the two hydrophobic domains can

associate and if together they have so much

hydrophobic hydration that their Tt is below

the temperature of the environment, they

associate; they are insoluble; AG(solubility) is

positive.

182

Consilient Mechanisms for Diverse Protein-based Machines

5.7.5.2 Solubility of Oil-like Groups

Occurs Because Polar Groups Destructure

Hydrophobic Hydration

If a charged vinegar-Uke group with inadequate

hydration appears proximal to an opening fluc-

tuation of associating hydrophobic domains, it

will use the nascent hydrophobic hydration of

the opening fluctuation for its own hydration.

With less hydrophobic hydration, the magni-

tude of the positive (-TAS) term becomes less

than the magnitude of the negative AH term;

AG(solubility) is negative, and the two domains

gain solubility.

5.7.6 The Formation of Ion

Pairs Makes Model Proteins

More Hydrophobic

During the operation of many of biology's

protein-based machines, the formation and sep-

aration of ion pairs is central to function. Very

commonly the ion paired state forms as two oil-

like domains associate, one oil-like domain con-

taining the positive charge and the other the

negative charge. Examples of this are seen in

the binding and release of oxygen by hemoglo-

bin in a manner that enables the transport of

oxygen by hemoglobin from the lungs to the

tissues. Alternatively, the ion for pairing may

come from the solution. In this case, ion pair-

ing at one potentially oil-like domain makes

it more hydrophobic such that the more

hydrophobic domain can then associate with

another hydrophobic domain. Often in biology,

calcium ion is released to the solution where it

can ion pair with carboxylates of a potential

hydrophobic domain. Often, such ion pairing

provides the trigger for function, as in muscle

contraction.

Here we report the effect of calcium ion

binding to carboxylates that exhibit

hydrophobic-induced pKa shifts. The pKa shifts

result from the work required to destructure

hydrophobic hydration in the process of ion-

ization to form the carboxylate. In Figure 5.27,

calcium ion interaction with carboxylates

makes two different model proteins more

hydrophobic to different extents, depending on

their initial oil-like composition. Figure 5.27A

considers Model Protein ii of Table 5.5, which

for every 30 residues (six pentamers) has one

carboxylate (-COO~)-containing glutamic acid

residue (Glu, E) and two, very oil-like pheny-

lalanine (Phe, F) residues with the hydrocarbon

R-group of -CH2-C6H5 having replaced two

valine (Val, V) residues with side chain

-CH2-(CH3)2. As calcium ion is added to 10

times equivalence, the Tt-value decreases, ini-

tially rapidly to about equal amounts of calcium

ion and carboxylate, then much more slowly. In

a near mirror image fashion, as calcium ion is

added, the number of waters of hydrophobic

hydration increases. Clearly, calcium ion pairing

with carboxylates increases hydrophobicity, as

indicated by the decrease in the value of Tf

Clearly, the decrease in Tt correlates with an

increase in hydrophobic hydration. For this

composition, however, not until a twofold

excess of calcium has been added does

hydrophobic association begin at body

temperature.

Figure 5.27B shows the same data for Model

Protein I of Table 5.5 with two proximal car-

boxylate (COO")-containing glutamic acid

residues (Glu, E), with five very hydrophobic F

residues and two more hydrophobic I residues

with the side chain -CH2(CH3)CH2-CH3,

having replaced nine of the valine (Val, V)

residues with side chain -CH2-(CH3)2, in every

30 residues. In this more hydrophobic model

protein, before there is one calcium ion per

carboxylate the temperature for hydrophobic

association drops below 0° C. These polymers,

of course, are the Model Proteins ii and I con-

sidered in section

5.5.3.1

and included in the

plots in Figure 5.20B.

5.7.7 The Amount of Hydrophobic

Hydration Determines the Value of Tt

The data in Figure 5.27 experimentally estab-

lish the relationship between the temperature,

Tt, for the onset of the inverse temperature

transition and the number of molecules of

hydrophobic hydration,

A^^/^.

Without going in to

the details of the experiments, it is possible to

appreciate the relationship by visual inspection.

Microwave absorption by hydrophobic

hydration as a function of frequency provides

5.7 What Is the Physical Basis for the Consihent Mechanism of Energy Conversion?

183

Hydrophobic Hydration Number per Pentamer and

Tj as a Function of [CaCl2]/[Glu]

Model protein

ii:

(GVGVP GVGFP GEGFP GVGVP GVGVP

GVGVP) n,

n= 40

E/2F

200 -r- n 80

T* -Polymer ii

Model protein

(GVGIP G FGEP GEGFP GVGVP GFGFP

GFGIP)26(GVGVP) 2E/5F/2I

175

150

125

100

0 +

• r

1 1 1 r

h 10

Nhh-Polymer I

Tj -Polymer I

[CaCl2]/[Glu]

FIGURE 5.27. Development of hydrophobic hydra-

tion,

Nhh,

on ion pairing shows a mirrored decrease

in, or lowering of, Tf (Top) For the less hydrophobic

Model Protein ii, the increase in

Nhh

is somewhat

modest as is the decrease in the value of

Tj.

(Bottom)

For the more hydrophobic Model Protein I, the

increase in

Nhh

is very abrupt and the lowering of the

value of Tt is correspondingly abrupt. Conclusions:

(1) Amount of hydrophobic hydration,

Nhh

positions

the Tfdivide! (2) Ion pairing markedly restores

hydrophobic hydration,

Nhh,

and, once too much

hydrophobic hydration has formed, the result is

hydrophobic association as the

(-TAS)

term of the

Gibbs free energy for solubihty becomes too positive

and dominates the free energy and insolubility of

hydrophobic association results! (C.-H. Luan and

D.W. Urry, unpublished results.)

an estimate of the number of molecules of

hydrophobic hydration,

A^^^,

for the two model

proteins. The model proteins both contain the

vinegar-Hke group in its carboxylate state,

-COO",

and in both the Val residues have been

replaced with more hydrophobic

residues.

Their

dependence of Tt on concentration of calcium

ion, however, differs remarkably.

The same difference in Tt exhibited by the

two different polymer compositions appears in

184

Consilient Mechanisms for Diverse Protein-based Machines

the inversely related number of water mole-

cules of hydrophobic hydration,

NHH-

This strik-

ing mirroring of Nhh and Tt occurs for each

polymer composition, even though the calcium

ion dependence is itself strikingly different

between the less hydrophobic and the more

hydrophobic polymers. Clearly Tt, the temper-

ature at which the onset of hydrophobic asso-

ciation occurs, depends on the number of

waters of hydrophobic hydration. As the

amount of hydrophobic hydration increases, Tt

decreases in an exactly mirrored manner.

Accordingly, the amount of hydrophobic hydra-

tion determines the value of Tt.

5.7.8 Earlier Studies Indicated the

Fundamental Process to be

Competition for Hydration

Above, the special structural organization of

these model proteins provided the unique

opportunity to identify and observe the behav-

ior of hydrophobic hydration. Under relevant

circumstances hydrophobic hydration was

more prevalent than bulk water. Key variables

showed that the amount of hydrophobic hydra-

tion,

Nhh,

determined Tt. Numerous systematic

studies, however, preceded the direct observa-

tion of hydrophobic hydration by microwave

dielectric relaxation. The earUer studies built

the foundation on which direct observation of

Nhh became the capstone. Below, interpreta-

tions,

implications, and/or conclusions follow

brief descriptions that lay bare the power of the

inverse temperature transition and add to the

panoply of data constituting the comprehensive

hydrophobic effect.

5.7.8,1

Dependence of Heat of Transition,

AHt, on Degree of Ionization

With the protein-based polymer poly

[0.8GVGVP),0.2GEGVP)], at low pH when all

4 of the Glu (E) residues/100 residues are as

COOH, the transition temperature is near

25° C and the heat of the transition, AHt =

0.97kcal/mole-pentamer (see Figure 5.28). On

raising the pH to the point of less than two

COO"/100 residues, the heat of the transition

has been reduced, and AHt = 0.27kcal/mole

pentamers.^"^ The preferred interpretation over

a decade ago was (1) that the formation of 2

COO'/lOO residues destructured almost three-

fourths of the thermodynamically measured

waters of hydrophobic hydration, and (2) that

there exists a competition for hydration between

apolar and polar residues, referred to as an

apolar-polar repulsive free energy of hydration.

100

/iwatts

pH2.5

pH3.5

pH3.8

pH4.0

10 20 30 40 50 60

temperature, °C

FIGURE 5.28. Differential scanning

calorimetry of model protein,

plotted (with heat absorption peak

down) as function of increasing

degree of ionization of carboxyl

function. Ionization to form less

than 2 carboxylates per 100 residues

reduces the heat of the transition to

about one-fourth. Charge destroys

hydrophobic hydration, raises Tt,

and gives rise to solubility. (Repro-

duced with permission from Urry

et al.^0