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

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6.5 The Mechanist Versus VitaUst Debate

235

protein synthesis of specified sequences by

small 8kcal/mole steps.

6.4.3 Mutations Accessing New, More

Efficient Machines Make Inevitable

the Flow Toward Greater Diversity

and Complexity

For the universe as a whole, viewed in terms

of the second law of thermodynamics, useful

energy continually decreases; the universe is

becoming less organized; time's arrow for the

universe points toward disorder and energy

death. On the other hand, that component of

the universe, occupied by living systems,

behaves inversely. Time's arrow for living

systems points toward greater organization and

diversity and improved function. Not surpris-

ingly, as seen above. Life does so by continually

consuming energy. Life comprises a set of

energy-accessing machines.

In terms of the biological origins of protein-

based machines, we have been addressing

above what Prigogine and Stengers in Order

Out of Chaos consider one of the two basic

questions of our scientific heritage^^:

Our scientific heritage includes two basic questions

to which till now no answer was provided. One is the

relation between disorder and order. The famous law

of increase of entropy describes the world as evolv-

ing from order to disorder; still, biological or social

evolution shows us the complex emerging from the

simple.

How is this possible? How can structure arise

from disorder? Great progress has been realized in

this

question.

know now that nonequilibrium, the

flow of energy and matter, may be a source of order.

Three key properties of living systems

combine to provide the recipe for an inevitable

flow toward greater diversity and complexity:

(1) a means of producing protein whereby any

sequence is equally likely, that is, at its begin-

nings a protein sequence capable of efficient

energy conversion is no more costly to produce

than an inefficient protein-based machine; (2)

a common groundwork of explanation, a con-

silient mechanism, for the efficient energy con-

versions catalyzed by protein, wherein only

small excursions from equilibrium provide

function; and (3) abundant and enduring

energy sources. One of the necessary ingredi-

ents does not appear to be "far from equilib-

rium conditions." Of course, in a universe where

time's arrow points to increasing disorder and

decreasing energy, at some point in time the

energy sources utilizable by biology will be

neither abundant nor enduring.

6.5 The Mechanist Versus

Vitalist Debate

Webster's Third New International Dictionary

defines vitalism as "a doctrine that the functions

of a living organism are due to a vital principle

distinct from physiochemical forces." The rele-

vant definition of mechanism reads "a doctrine

that holds that natural processes, esp. the

processes of Life, are mechanically determined

and capable of complete explanation by the

laws of physics and chemistry." In the pre-

Wohler era (see Chapter 3), the vitalist position

held sway that an understanding of the mole-

cules of Life was beyond man's grasp. This

position began its fall in 1828 when Wohler

accidentally synthesized urea, the primary non-

ionic urinary excretory product of mammals,

which arises from the natural breakdown of

protein.

For much of twentieth century the mecha-

nist vs. vitalist debate centered on the fossil

record and the issue of a "missing link" in the

evolution of man from lower animals. Recently,

the debate has shifted focus. If there ever were

a critical missing link in the fossil record, there

certainly is no missing link in the exquisite

biochemical record. The common genetic code

solidifies man's relationship to other living

organisms and indeed to the common origins

of all Life. The small detailed differences in

sequences of man's proteins to those of other

Life forms provides a detailed map of those

relationships.

The recent developments in the determina-

tion of the human genome and its comparison

to that of lower species allows not only that all

Life has the same genetic code, but in fact that

a large part of the human genome directly

derives from lower animals. The genes of

236

6. On the Evolution of Protein-based Machines

humans come, in substantial part, from small

modifications of the protein domains of lower

organisms that combine to form new associa-

tions of protein domains giving rise to new

structures and functions. Chapter 7 gives the

myoglobin-hemoglobin example for such mod-

ifications of a protein domain to arrive at new

structure and function.

In his book, Darwin's Black Box: The Bio-

chemical Challenge to Evolution, Behe^ seems

to accept the biochemical argument arising

from a common genetic code and the demon-

stration that protein sequences map man's

kinship to all other Life. In its place the vitaUst

stand of Behe notes the complexity and

interdependency of components of the molecu-

lar machines of Life and argues that the gradu-

aUsm of Darwin cannot work, rather that there

must have been a creator responsible for the

intelligent designs of molecular machines. Over-

all the position of Behe represents a useful

step in the mechanist vs. vitaHst debate,

because it gives a tangible position that can be

examined.

This chapter demonstrates that the gradual-

ism of Darwin is demonstrable in the evolution

of de Azovo-designed protein-based machines

toward diverse function. It has attempted to

show how readily the origins of the diverse mol-

ecular machines of Life can derive from details

of protein biosynthesis, including the genetic

code,

and the consiUent mechanism of energy

conversion. Furthermore, ever-increasing com-

plexity is the natural result of the consiUent

mechanism coupled to mutation during protein

synthesis with the results being acted upon

by natural selection for the estabUshment of

improved molecular machines. At the more

advanced level, the gradualism of Darwin

would seem to be evident in the relationship

between the human genome and that of lower

animals.

6.5.1 The Challenge to the

Mechanist—The Challenge to

the VitaUst

The suggestion that the profound interdepen-

dence and intricate detail of complex molecu-

lar machines is such that gradualism, arising

from a stepwise series of mutations, could not

have given rise to such complexity calls to mind

the exceptional Preface of the 1923 text by G.N.

Lewis and M. RandalP:

There are ancient cathedrals which, apart from their

consecrated purpose, inspire solemnity and awe.

Even the curious visitor speaks of serious things,

with hushed voice, and as each whisper reverberates

through the vaulted nave, the returning echo seems

to bear a message of mystery. The labor of genera-

tions of architects and artisans has been forgotten,

the scaffolding erected for their toil has long since

been removed, their mistakes have been erased, or

have become hidden by the dust of centuries. Seeing

only the perfection of the completed whole, we are

impressed as by some superhuman agency. But

sometimes we enter such an edifice that is still partly

under construction; then the sound of hammers, the

reek of tobacco, the trivial jests bandied from

workman to workman, enable us to realize that these

great structures are but the result of giving to ordi-

nary human effort a direction and a purpose.

6.5.2 "Seeing Only the Perfection

of the Completed Whole, We Are

Impressed as by Some

Superhuman Agency"

The mechanist has yet to define the early

simpler self-sufficient Life forms. In evolution

the mechanist has yet to complete an under-

standing of the temporary scaffoldings that

allowed transition from prebiotic to biotic and

from minimally self-sufficient more primitive

Life forms to result in the more complex com-

pleted edifice that we all celebrate. When plau-

sible transitional scaffoldings from prebiotic

to biotic evolution have been reconstructed,

the mechanist will yet be left with a seemingly

unanswerable query. Why are there immutable

laws that man can identify and that are often so

well-described with a mathematics that man

has derived? It is hard to imagine a state of

knowledge when there would not remain an

unknown without which a "vital force" would

be disallowed.

The future of the mechanist holds many

daunting challenges. To date, however, results

References

237

of the scientific method seem to have provided

Umited guidance in maintaining a healthy social

structure. Therefore, going forward, one could

hope for a constructive role for the modern

vitaUst in utilizing scientific advancements to

support a more complex and humane society.

Informed and wisdom-providing guidance from

the vitaUst would seem appropriate to assist in

bringing the benefits of the Biotechnological

Revolution to relieve suffering, to provide

continual improvement in quaUty of Life, and

generally to raise standard of living while

maintaining respect for the remarkable edifice

that each defined being represents.

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Darwin,

Third Edition,

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2001,

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Darwin's

Black

Box:

The Biochemical

Challenge to Evolution. Simon and Schuster,

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W.-H. Li, Z. Gu, H. Wang, and A. Nekutenko,

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Editorial Comments.

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291,1218,

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D.W. Urry, "Molecular Machines: How Motion

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Urry,

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Machines:

Syn-

thetic Chains of Amino Acids, Patterned After

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9. D.W. Urry, "Physical Chemistry of Biological

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Urry

R.D.

Harris, and K.U. Prasad, "Chem-

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11.

D.W.

Urry

Haynes,

Zhang,

R.D.

Harris, and

K.U. Prasad, "Mechanochemical Coupling in

Synthetic Polypeptides by Modulation of an

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Acad.

Sci. U.S.A.,

85,

3407-3411,1988.

12.

S.C. Schuster and S. Khan, "The Bacterial

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P.D.

Boyer,

"The

Binding Change Mechanism for

ATP Synthase—Some probabilities and possibil-

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Biochim. Biophys. Acta, 1140, 215-250,

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14.

IP Abrahams, A.G.W. LesUe, R. Lutter, and

J.E. Walker, "Structure at 2.8 A Resolution of

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Nature,

370, 621-628,1994.

15.

K. Kinosita, Jr., R. Yasuda, H. Noji, and

K. Adachi, "A Rotary Molecular Motor that

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D.W. Urry L.C. Hayes, T.M. Parker, and R.D.

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336-340,1993.

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D.W. Urry L.C. Hayes, and D. C. Gowda,

"Electromechanical Transduction: Reduction-

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Model Protein to Perform Mechanical Work."

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D.W. Urry L.C. Hayes, D.C. Gowda, S.-Q.

Peng, and N. Jing, "Electro-chemical Transduc-

tion in Elastic Protein-based Polymers."

Biochem. Biophys. Res. Commun., 210, 1031-

1039,1995.

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D. Voet and J. Voet, Biochemistry, Second

Edition, John Wiley & Sons, New York, 1995, p.

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D.W. Urry C.-H. Luan, S.Q. Peng, T.M. Parker,

and D.C. Gowda, "Hierarchical and Modulable

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In point of fact, this design capacity to energize

for structure association has been used to

improve polymer ahgnment for cross-linking to

produce stronger materials useful for a number

of applications (see Chapter 9).

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Out of

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Man's New Dialogue with Nature.

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dynamics and the

Free

Energy of

Chemical

Sub-

stances.

McGraw-Hill, New York, 1923.

Biology Thrives Near a Movable Cusp

of Insolubility

7.1 Introduction

Biology thrives near a movable cusp of insolu-

bility , yet excursions too far, either direction^ into

the realms of insolubility or solubility spell

disease and death.

Even to the casual observer, the past decades

have witnessed remarkable and unparalleled

progress in the understanding and utilizing of

biological processes. Because of this, the pro-

posal of a new pervasive theme such as the con-

siUent mechanism for hydrophobic association

introduced here and its representation by the

sweeping statement that "biology thrives

near a movable cusp of insolubiUty" should

not be undertaken casually. This is particularly

the case, for example, for such thoroughly

researched areas as muscle contraction, com-

plexes of the electron transport chain and ATP

synthase of the inner mitochondrial membrane,

oxygen transport by hemoglobin, blood clot-

ting, chaperones, and so forth.

Nonetheless, the extensive experimental

results detailed in Chapter 5 on elastic-

contractile model proteins in our view are com-

pelling. Furthermore, present daring derives

from the emerging acceptance of our proposed

mechanism of protein elasticity of two decades

ago;

limited encouragement and general dis-

paragement have, in the last few years, trans-

formed into more general acceptance.^'^ The

present work, in fact, gains from our new insight

into entropic (ideal) protein elasticity, which

has earned the right to be considered a con-

sihent mechanism of elasticity. This is because

the mechanism applies to all chain molecules

independent of composition and structure as

long as the chain molecule exhibits internal

motions that decrease in magnitude on defor-

mation. The behef that regular, nonrandom,

dynamic structures could exhibit near-ideal

elasticity allowed the design of elastic model

proteins capable of the diverse energy con-

versions of biology with remarkable positive

cooperativity required for efficient energy con-

version. Reviews of the basic model protein

data^'"^ underlying the consiUent mechanism

for hydrophobic association have been well

received. On the other hand, suggestions of

relevance to specific biological systems, such as

those presented in this and the next chapter,

have met with resistance familiar from the elas-

ticity experience and not uncommon in scien-

tific efforts.^

Most compelling in our view, however, is the

de novo design of diverse protein-based

machines that utilize the unifying principle

presented in Chapter 5. Successful design has

simply been too facile and too comprehensive

not to persevere. Furthermore, when one

begins to apply the single underlying principle

to what is known of natural biological systems,

for example. Life's machines, in our view the

phenomenological correlations appear too

coherent to be unsound.

In particular, in this chapter we examine a

number of protein-based biological systems

that can present excesses of insolubility or sol-

ubility. Some of these, for example, muscle con-

traction and hemoglobin transport of oxygen,

239

240

Biology Thrives Near a Movable Cusp of Insolubility

have been extensively studied, as noted above.

The example of blood clotting (thrombus for-

mation) has great medical significance because,

in our view, good health and life itself require

proper balance near the movable cusp of

insolubility. Shifts toward excess insolubiUty

precipitate heart attacks (coronary occlusion,

thrombus in coronary arteries), strokes

(apoplexy, thrombus in arteries of the brain),

and phlebitis (thrombus in veins). On the

other hand, shifts toward excess solubility result

in the life-threatening bleeding disease of

hemophilia and the degradation of elastic tissue

in the lungs with the result of pulmonary

emphysema.

Other examples have emerged more

recently. Prion proteins induce insolubility and

cause the ravages of Alzheimer's and mad

cow diseases. Then there are chaperones that

reverse inappropriate insolubilities. In these

latter cases considered mechanisms are not so

deeply ingrained. In none of these, however, has

the sense of an apolar-polar repulsive free

energy of hydration, AGap, emerged. In none

of these has there been a suggestion of the

competition for hydration between hydro-

phobic and polar species that is the basis for

repeated experimental demonstrations of large

hydrophobic-induced pKa shifts.

In general, mechanisms have often focused

on the energetics arising out of electrostatics

such as charge-charge repulsion and ion-pair

formation under the assumption of a uniform

medium of low dielectric constant. As for the

rationalization of pKa shifts exhibited by car-

boxylates of glutamic acid and aspartic acid and

by the 8-amino group of lysine, the argument

seems to be that the polar species is forced by

a "conformational change" into unfavorable

low dielectric constant environments in order

to account for states of high free energy. Instead

of such a high-energy state resulting from

a "conformational change," in our view

these high-energy states, such as hydrophobic-

induced pKa shifts, result from competition for

hydration. To restate, in our view, a change in

competition for hydration due to a change in

the state of a functional group drives confor-

mational change, not the reverse.

We again note the simple message contained

within the familiar adage that "oil and vinegar

don't mix" and combine it with the effects of

oil-like and vinegar-like groups being con-

strained to coexist along the chain molecules

made possible by the unique process, reviewed

in Chapter 4, of protein biosynthesis.

Experimental examination of our systemati-

cally designed model proteins reveals the force

that exists between oil-like and vinegar-like

groups. Thermodynamic analysis translates that

force between oil-like and vinegar-like groups

into a change in Gibbs free energy for

hydrophobic association,

AGHA

(see Chapter 5),

a key functional component of which we call

the apolar-polar repulsive free energy of

hydration,

AGap.

We believe

AGHA

and its func-

tional component, AGap, to be a dominant free

energy of interaction that underpins protein

function and disfunction.

Electrostatic interactions such as ion-pair

formation are indeed important, but in our view

their role in protein function resides in their

effect on the value of

AGHA-

In particular,

the electrostatic interactions of ion-pairing

and hydrogen-bonding lower

AGHA

(make

hydrophobic association more favorable) by

relieving the apolar-polar repulsive free ener-

gies of hydration,

AGap.

Ion pairs and hydrogen

bonds form in the aqueous environment within

and between protein domains because of a

Umited hydration of the separated polar groups.

The Umited hydration of polar groups, although

seemingly bathed in water, arises from compe-

tition for hydration with hydrophobic groups.

AGap results from spatial, through water, inter-

actions between oil-like (hydrophobic) and

vinegar-like (polar, e.g. charged) residues con-

strained by protein sequence and relieved

by protein folding and assembly. Changes in

AGap,

CIS

the direct result of changes in the polar

state of a functional group, drive function by

means of effecting changes in folding and

assembly.

Particularly in this and the next chapter, we

regret that time does not permit development

of the desired level of expertise in each of the

protein systems to be considered. Nonetheless,

it is thought that the pervasiveness of the con-

7.2 The Movable Cusp of Insolubility

241

silient mechanism becomes persuasive with the

examples as given, and this allows for a more

timely completion of this volume.

7.2 The Movable Cusp

of Insolubility

The differential calorimetry curve in Figure

5.1C graphically represents a "cusp of insolu-

bility." By definition, a cusp is "a fixed point on

a mathematical curve (graph) at which a point

tracing the curve would exactly reverse its

direction, that is, a point at which traversing

in opposite directions has opposite conse-

quencesT^ In particular, from a point located at

the peak of the curve in Figure 5.1C and for any

one of the cusps in Figure

7.1,

tracing the curve

to lower temperature finds solubility whereas

tracing the curve to higher temperature gives

insolubility. Alternatively, as represented in

Figure

7.1,

at a constant temperature an energy

input to which the protein composition is recep-

tive can move the curve, the cusp of insolubil-

ity, to lower temperature to give insolubility or

move the curve to higher temperature to give

solubihty.

Moving the cusp of insolubility occurs by the

energy inputs that give rise to a change in the

Gibbs free energy of hydrophobic association,

AGHA,

as developed in Chapter 5. An effective

energy input either makes the protein more oil-

like and thereby lowers the temperature inter-

val of the cusp of insolubility (lowers AGHA) or

makes the protein more polar and thereby

raises the temperature for the onset of the cusp

of insolubility (raises AGHA)- Tt (determined

from light-scattering measurements) or Tb

(determined from calorimetry measurements

as the leading (low-temperature) edge of the

temperature interval shown in Figure 7.1)

experimentally defines the onset temperature

for the cusp of insolubihty. Both Tt and Tb

become convenient approximations to the

divide between solubihty and insolubility. In

fact, this boundary between solubility and insol-

ubility, as represented in Figure 5.3, we call the

Tfdivide.

Temperature, °C

FIGURE

7.1.

The movable "cusp of insolubility" rep-

resented as the calorimetry curve for the inverse

temperature transition of (GVGVP)25i 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 intro-

duction of an energy that increases the temperature

at which the transition occurs from below to above

physiological temperature.

As demonstrated in this chapter, moving the

cusp of insolubility too far in one direction or

the other is harmful. Thus, excursions too far,

either direction, into the realms of insolubility or

solubility spell disease and death. Also as noted

below and more extensively in Chapter 8, hving

organisms thrive on relatively small energy

excursions, generally less than ±10kcal/mole

(42kJ/mole). Furthermore, as discussed in

broader context in the Epilogue, life thrives

never very far from equilibrium, that is, never

very far from the Tt-divide, never very far from

the cusp of insolubility. The distinct, stepwise

energy changes that sustain Life are very many

and generally small, but in sum they represent

a substantial quantity of energy.

242

Biology Thrives Near a Movable Cusp of Insolubility

7.2.1 Biological Function by

Association/Dissociation of Pairs

of Spatially Assembled

Hydrophobic Domains

7.2.1.1

Hydrophobic Hydration

Disappears for Two Different Reasons

with Diametrically Opposite Consequences

of Either Insolubility or Solubility

7.2.1.1.1 Hydrophobic Hydration Disappears

When a Pair of Hydrophobic Domains

Associate, That Is, When the Pair of Domains

Becomes Insoluble

If the pair of domains has too much hydropho-

bic hydration for a given temperature, w^hen

fully exposed to water, hydrophobic association

with loss of the hydrophobic hydration results.

As discussed extensively in Chapter 5, the

reason Ues in the statement of the Gibbs free

energy governing solubility, which is AG(solu-

bility) = AH - TAS. When there is too much

hydrophobic hydration, the (-TAS) term is pos-

itive and larger than the negative AH term such

that insolubility ensues. This is because systems

move in the direction of minimizing the free

energy, AG, that is, systems move toward

lower values of AG. Accordingly, the pair of

hydrophobic domains proceeds to solubility

when the AG(solubility) is negative, and insol-

ubility occurs when AG(solubility) is positive.

The change in Gibbs free energy for

hydrophobic association, AG(hydrophobic

association) =

AGHA,

arose in Chapter 5 to

describe those interactions of model proteins

that affect the state of hydrophobic association.

AGHA is calculated from the heat of the inverse

temperature transition, that is, from the area of

the cusp of insolubility in Figure 5.1C and Figure

7.1.

AGHA may also be estimated from a shift of

the cusp of insolubiUty along the temperature

axis,

resulting from introduction of the pertur-

bation, times the entropy change for the transi-

tion (heat of the transition divided by the

transition temperature). The change in Tt mea-

sures the movement of the cusp of insolubility

along the temperature

axis.

When the change is

in the solvent and does not represent a change

in the chemical structure of the model protein,

as in the solute effect on a neutral polymer, the

estimate of the entropy change refers to the

(ref-

erence) state before the perturbation (see Equa-

tions [5.8] and [5.9] in Chapter 5). When the

chemical nature of the polymer varies, then the

entropy change for the chemically altered struc-

ture is used, as in Equation (5.10a) of Chapter 5.

Obviously, AGHA bears the opposite sign

from AG(solubility). AGHA refers to hydropho-

bic association, that is, the loss of solubility of

hydrophobic groups, whereas AG(solubility)

refers to the opposite process of dissolution.

When considering polymers such as proteins

with both oil-like and vinegar-like side chains,

an important distinction between the two rec-

ognizes, for example, that a soluble globular

protein contains hydrophobic association

within the folded structure of the single

macromolecule.

7.2.1.1.2 Some Hydrophobic Hydration

Disappears When a Water-exposed

Hydrophobic Domain Occurs Proximal to

an Emergent Polar (e.g., Charged) Species

Consider a pair of hydrophobic domains

exactly at the cusp of insolubility. In this case

the equilibrium constant for association/

dissociation is essentially one; half of the pairs

of hydrophobic domains are dissociated and

covered with hydrophobic hydration, and the

other half are associated and devoid of

hydrophobic hydration. If an ionizable species

becomes proximal to the transiently dissociated

pair of hydrophobic domains, the ionizing

species destructures hydrophobic hydration in

achieving its own hydration. In terms of

AG(solubility), the loss of hydrophobic hydra-

tion for the open state (with its inherently pos-

itive AS)^ causes the (-TAS) term to become

less positive; the negative AH term for solubil-

ity then dominates, and the shift to the dissoci-

ated state occurs. In terms of AGHA, the

introduction of a polar interaction moves the

cusp of insolubility to a higher temperature,

such that AGHA is positive and hydrophobic

association is lost, that is, solubility results. The

cusp of insolubility moved to a higher temper-

ature, placing the pair of hydrophobic domains

on the soluble side of the cusp. Under these

circumstances, the water at the surface of the

7.2 The Movable Cusp of Insolubility

243

hydrophobic domain is not structured

hydrophobic hydration, but instead orients

toward the charged species and contributes to

its hydration shell.

As discussed in Chapter 5, another expres-

sion of the change in Gibbs free energy for

hydrophobic association results from the exper-

imental observation of hydrophobic-induced

pKa shifts. This change in Gibbs free energy,

referred to as an apolar-polar repulsive free

energy of hydration,

AGap,

is calculable as AGap

= 2.3RTApKa (see the derivation of Equation

[5.13] in Chapter 5). The ApKa arises from

competition for hydration between polar and

hydrophobic groups, and the competition

determines the amount of hydrophobic hydra-

tion. As this dictates whether the hydrophobic

domains are associated or not, it should be

equivalent to AGHA as long as the pKa shift

arises solely due to the competition for hydra-

tion between apolar and polar groups and does

not include charge-charge repulsion as part of

the reason for the pKa shift, that is, for increas-

ing the free energy of the ionized state (See

Equation [5.23] of Chapter 5). Because of this,

AGap is also calculable from the heats of the

inverse temperature transition via Equation

(5.10b) of Chapter 5, i.e.,

AGap

= AGHA[E

/OF

E70F] when properly written per E residue of

the same model protein. This increase in the

Gibbs free energy of a negatively charged

(anionic) state favors neutralization either by

protonation or by ion-pair formation. Ion-pair

(salt-bridge) formation, therefore, can allow so

much hydrophobic hydration to reoccur that a

return to the hydrophobically associated state

results. For this reason, ion-pair formation and

even hydrogen binding are often an integral

part of hydrophobic association in protein

folding, assembly, and function. This is very

relevant to the function of hemoglobin as a

machine for oxygen transport.

7.2.1.2

Identification of Hydrophobic

Association with Rigor in Muscle and with

the Tense, T-State, of Allosteric Proteins

Exhibiting Positive Cooperativity

Rigor is a state of being rigid or

stiff.

The term

is commonly used in relation to muscle

stiff-

ness,

but relevance exists, in general, to the taut

or tense (contracted, insoluble) T-state as

opposed to the relaxed (soluble) R-state of

allosteric proteins such as hemoglobin that

exhibit enhanced effectiveness for oxygen

transport due to the property of positive coop-

erativity. From our perspective, this rigid or stiff

state equates to insolubility due to association

of hydrophobic protein domains, and the

relaxed state equates to the removal or partial

removal of hydrophobic association.

The hydrophobically associated state repre-

sents the insolubility side of the Tf

(solubility/insolubility)divide. As discussed in

Chapter 5, contraction of the model elastic-con-

tractile model proteins capable of inverse tem-

perature transitions arises due to hydrophobic

association. Hydrophobic association occurs,

most fundamentally, on raising the tempera-

ture,

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.

Changing the state of functional groups asso-

ciated with hydrophobic domains occurs with

remarkable positive cooperativity.

Also,

as most

emphatically shown in Figure 5.34 of Chapter

more hydrophobic model proteins exhibit

greater positive cooperativity and correspond-

ingly larger pKa shifts. Importantly, a major

part of the free energy change represented by

the shift in pKa is the same as that represented

by the change in positive cooperativity (the

change in Hill coefficient). In our view, this is

because the pKa shift and the extent of positive

cooperativity result from the same physical

process, the competition for hydration between

hydrophobic (oil-like) and polar (vinegar-like,

e.g., charged) groups constrained by sequence

to coexist in proteins.

It is possible, however, to have a residual pKa

shift after the allosteric interchange between

two states has resulted in the state of complete

solubility. As shown in Figure 5.31 A, when ion-

ization is complete and only the unfolded state

244

Biology Thrives Near a Movable Cusp of Insolubility

is left, there remains a residual pKa shift. The

carboxylates and hydrophobic groups continue

to behave as though repulsed, as they try unsuc-

cessfully to access v^ater completely undis-

turbed by the other.

As discussed below, these considerations

are relevant to formation of the rigor state in

muscle, to the tense or taut T-state of proteins

that exhibit positive cooperativity, to the for-

mation of the oxygenated and deoxygenated

states of hemoglobin, to the proper balance of

blood clotting, to the formation of insoluble

protein-based fibers giving rise to Alzheimer's

and mad cow diseases, to the unfolding and

proper refolding of incorrectly folded protein

by chaperonins, and to the unfolding and degra-

dation of oxidized or otherwise solubilized

protein states.

7.2.2 Rigor: Hydrophobic

Association in Muscle at the Gross

Anatomical Level

A satisfying affirmation of the fundamental sig-

nificance and pervasiveness of hydrophobic as-

sociation of the consilient mechanism is found,

even at the anatomical level, in Borland's

Illustrated Medical Dictionary in the following

definitions, given as alphabetically listed, under

the term rigor?

7.2.2.1

Acid Rigor, ''Coagulation of

Protein of Muscle Produced by Acids''

Webster's Third New International Dictionary

defines coagulation as "the process by which

such change of state takes place consisting of

the alteration of a soluble substance, usually

protein, into an insoluble form... ."^ Acids

produce insolubility of muscle protein. At the

physiological pH of 7.4, all but the most pKa-

shifted carboxyl groups of protein occur as

ionized carboxylates. Acids protonate carboxy-

lates to form the uncharged carboxyl, that is,

-COO-

+ H^ = -COOH.

By the consilient mechanism, protonation of

carboxylates restores hydrophobic hydration to

hydrophobic domains competing for hydration.

As discussed in Chapter 5 and noted above,

introduction of too much hydrophobic hydra-

tion causes insolubility. Recall the expression

for the Gibbs free energy for solubility, that is,

AG(solubility) = AH - TAS. When there is too

much hydrophobic hydration, the magnitude of

the positive (-TAS) term is larger than the neg-

ative AH term. Accordingly, addition of acid to

muscle protein results in an unfavorable posi-

tive AG(solubility) with the result of hydropho-

bic association. In other words, by removal of

charged groups, acids move the cusp of insolu-

bility below physiological temperature to cause

the stiffness called rigor.

7.2.2.2

Calcium Rigor, ''Systolic Cardiac

Arrest Caused by an Excess of Calcium"

From the definitions of systole and systolic in

Borland's Illustrated Medical Dictionary, sys-

tolic cardiac arrest is recognized as the heart

muscle having become fixed in the contracted

state.

We know in the process of muscle con-

traction that release of calcium ion triggers con-

traction by binding at carboxylates, and we

have seen in Figures 5.15 and 5.27 that, with

the appropriate protein composition, a small

increase in calcium ion can drive the hydropho-

bic association of contraction by ion pairing

with pKa-shifted carboxylates. Thus, even on a

macroscopic anatomical scale, it is possible to

see the consequences of the consiUent mecha-

nism of hydrophobic association whereby

calcium ion pairing with carboxylates lowers

the Tt-(solubility/insolubility) divide with the

consequence of hydrophobic association fixing

muscle protein in the contracted state.

7.2.2.3

Heat Rigor "Rigidity of Muscles

Induced by Heat''

Increasing the temperature to result in insolu-

bility is the hallmark of hydrophobic associa-

tion 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