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

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E.2 The Inverse Temperature Transition: The Foundation of the "Vital Force"

545

associates. Also, as shown in Figure 5.25B,

forming charged carboxylates destroys much of

the hydrophobic hydration, as the carboxylate

recruits water for its own hydration. This is

depicted in the leftmost structure in Figure 2.8.

Thus,

indeed the law of physics, called the

second law of thermodynamics, does apply to

living matter. Obeyance occurs, however, under

a special set of circumstances where the water

solvent becomes a key player. Decrease in order

is greater for the change to ordinary water from

structured water surrounding oil-like groups

than is the increase in order of the protein as it

hydrophobically associates to form a more

ordered structure on raising the temperature. In

fact, the changing structure of the protein com-

ponent of the two-component system, acted on

by additional energy inputs, provides function-

ality essential to sustain the living organism.

E.2.7 Biology's ''Vital Force''Arises Out

of Interlinking Thermodynamics and

Molecular Dynamics

Somewhere near its origins, biology reconciled

thermodynamicists' entropy and dynamicists'

reversibility,^"* as it evolved functional protein-

based machines by interlinking the two pro-

cesses that seemed so disparate during the

debates of the 19th century. Energy driven

hydrophobic association with its increase in the

thermodynamicists' entropy on conversion of

hydrophobic solvation to bulk water commonly

couples with a reversible decrease in internal

chain dynamics in the development of a near-

ideal elastic force wherein the force-relaxation

curve exactly follows the same trajectory as

the force-extension curve. As we now stand,

almost paradoxically from the viewpoint of

the early controversy, the entropic contribution

to the elastic force becomes the primary basis

for reversibility and efficiency of energy

conversion.

In our view, the hydrophobic and elastic con-

silient mechanisms comprise the "vital force" of

living matter The forces arising out of inverse

temperature transitions and elastic deforma-

tion,

for example, apolar-polar repulsion and

damping of backbone mobility on deformation,

couple to create biology's "vital force."

E.2.8 The Hydrophobic ConsiHent

Mechanism Derives from the Inverse

Temperature Transition

The energy conversions that produce motion

in living organisms consist of two distinct but

interlinked physical processes of hydrophobic

association and elastic force development, col-

lectively referred to as consilient mechanisms

in that they each provide "a common ground-

work of explanation."^ The association of

oil-like domains, hydrophobic association, has

been characterized in terms of the comprehen-

sive hydrophobic effect (CHE), and elastic

force development has been described in terms

of the damping of internal chain dynamics on

deformation, whether deformation occurs by

extension, compression or solvent-mediated

repulsion (see section E.4.1.2 and Figures E.3

and E.4, below).

In aqueous systems, CHE controls hydropho-

bic association by means of a Gibbs free energy

of hydrophobic association,

AGHA,

which is

quantifiable as a variable-induced change in the

net heat of the endothermic inverse tempera-

ture transition in Figures 7.1 and

8.1.

The mag-

nitude of

AGHA

depends primarily on the

amount of hydrophobic hydration displaced

on hydrophobic association. Fundamentally,

competition for hydration between apolar

(hydrophobic) and polar (e.g., charged) groups

controls the amount of hydrophobic hydration,

as shown in Figure 5.25B, and the competition

is quantifiable as an apolar-polar repulsive

free energy of hydration, AGap. Thus, the

hydrophobic consilient mechanism applies to

all amphiphilic polymers in aqueous systems

regardless of polymer structure.

E.2.9 The Elastic ConsiHent

Mechanism as the Efficient

Mechanical Coupler Within

the "Vital Force"

E.2.9,1 Dynamic Chains Without Random

Chain Networks

The mechanically linked process of entropic

elasticity also constitutes a "common ground-

work of explanation." It applies to all polymer

structures, of whatever composition, that

546

Epilogue

contain a sufficiently kinetically free chain

segment that can exhibit constrained internal

chain

dynamics,

for example, damped backbone

torsional oscillations, on deformation. In par-

ticular, the polymer structure need not be

describable as a random chain network with a

Gaussian distribution of deformable end-to-

end chain lengths as has been characterized'

by the Flory random chain network theory of

elasticity.^^'^^

Importantly, efficient energy conversion

requires the element of entropic (ideal) elastic-

ity where the energy of deformation is recov-

ered on relaxation. Very often deformation/

relaxation curves exhibit significant hysteresis,

where the input energy required to deform a

chain molecule is substantially greater than the

energy recovered on relaxation of the defor-

mation. In

hysteresis,

the energy of deformation

has been lost to chain components that do

not sustain the deformation. Accordingly, the

occurrence of a hysteresis to the deformation

constitutes a loss of energy. Because of

this,

the

occurrence of hysteresis during the structural

changes of a protein-based machine effecting

an energy conversion results in an inefficient

machine.

If the energy of deformation remains in the

backbone of the chain that sustains the deform-

ing force, then it can be recovered on relax-

ation. This occurs when the energy of

deformation results in the damping of internal

chain dynamics. Random chain networks do

this reasonably well, but they do not represent

the only means of doing so. In fact, certain

elastic-contractile model proteins, comprised as

they are of repeating sequences that assemble

into regular dynamic structures, give near-

perfect overlap of force extension and force

relaxation curves. These elastic-contractile

model proteins exhibit mechanical resonances

that have been observed centered at

MHz

(just below radio frequency) and centered near

kHz (positioned over the acoustic frequency

range).

Such mechanical resonances arise from

a regularly repeating dynamic structure. These

properties are not comprehensible by the con-

cepts of the random chain network school of

entropic elasticity, but, in fact, they provide

exciting new materials for the future.

E.2.9,2 Hydrophobic Associations Stretch

Interconnecting Chain Segments

Elastic forces come into play as hydrophobic

associations stretch interconnecting chain seg-

ments. Only if the elastic deformation is ideal

does all of the energy of deformation become

recovered on relaxation. To the extent that

hysteresis occurs in the elastic deformation/

relaxation, energy is lost and the protein-based

machine loses efficiency. Thus, the elastic con-

silient mechanism, whereby the force-extension

curve can be found to overlay the force-

relaxation curve becomes the efficient mechan-

ical coupler within the "vital force." The

objective now becomes one of understanding

the age-old problem of a reluctance to discard

past idols.

E.2.9J Bursts of Apolar-Polar Repulsive

Free Energy on Hydrolysis of ATP, by

the Hydrophobic Elastic Consilient

Mechanism, Can Convert to Elastic

Deformation for Efficient

Energy Conversion

As is briefly noted below in section E.4.1.2 and

as was presented in Chapter 8, a burst of

apolar-polar repulsive free energy of hydration

occurs on hydrolysis of ATP to ADP (adeno-

sine diphosphate) plus inorganic phosphate.

This repulsive burst within the structure of Fi-

ATPase causes elastic deformations in the

protein subunit holding the catalytic site and in

the protein subunit functioning as a hydropho-

bically asymmetric rotor. On the basis of the

hydrophobic elastic consilient mechanism, this

repulsion drives the rotor in a highly efficient

conversion of chemical energy into mechanical

work. By driving the rotation of the rotor in the

opposite direction with the use of the chemical

energy of a proton concentration (actually elec-

trochemical) gradient, ATP

synthesized in the

protein-based machine called ATP synthase.

An understanding of this process, in the

author's view, requires setting aside past idols

relating to the nature of elasticity and the treat-

ments, or nontreatments, of water structures

surrounding protein subunits of protein-based

machines.

E.3 Bacon's "Idols Which Beset Men's Minds" 547

E,2.9A The Problematic 'Idols Which

Beset Men's Minds'' and Acceptance of

the Consilient Mechanisms

Sir Francis Bacon (1561-1626), known as the

patron saint of the scientific revolution, recog-

nized a set of troublesome idols of the mind

some four centuries ago. Zagorin^^ gave defini-

tion as, "Bacon's ... doctrine of the idols of

the mind [are] those fallacies obstructing the

progress of knowledge...." Then there is the

classic statement of Bacon as conveyed by

Boorstin,^^ " 'Being convinced that the human

intellect makes its own difficulties,' Bacon

offered his vivid catalog of the illusions of

knowledge—'idols which beset men's minds.'"

Considered below is one of Bacon's four idols

of the mind, the idol of the mind of most direct

relevance to advances in understanding the

laws of nature with specific relevance to the

hydrophobic and elastic consilient mechanisms

and the elan vital.

E.3 Bacon's "Idols Which Beset

Men's Minds"

E.3.1 "...The Idols of the

Mind [are] Those Fallacies

Obstructing the Progress of

Knowledge "

Bacon wrote of four "idols of the mind." The

fourth applies to our concerns of the mecha-

nisms or elan vital whereby biology's protein-

based machines function, namely, "idols of

the theater ('idola theatri'): these were the

off-

spring of the false dogmas of philosophers, false

demonstrations in logic, and false principles

and axioms in the sciences, which, like stage

plays,

generated fictions and unreal worlds."^^In

our efforts to understand the forces that domi-

nate function of protein-based machines, two

examples of "the idols of the mind" that con-

stitute "fictions and unreal worlds" spring to

mind. The examples derive from impediments

to the utilization of each of the consilient

mechanisms, to the hydrophobic consilient

mechanism and a most cogent example to the

elastic consilient mechanism.

Each consilient mechanism presents a

"common groundwork of explanation" without

employing "fictions and unreal worlds." In past

practice, fictions were born of limited experi-

mental data and mathematical formaUsm. The

"fictions and unreal worlds" were compelled by

the needs of the time and indeed in their time

represented valuable steps toward utilization.

These once helpful fictions, however, paradoxi-

cally turn into idols that restrain acceptance of

new experimental data and thereby impede

utilization.

E.3.2 Idols That Retard Utilization of

the Elastic Consilient Mechanism in

Understanding and Developing

Protein-based Machines

and Materials

A particularly evident fiction underlies the

classic (random chain network) theory of

rubber elasticity. To perform certain calcula-

tions,

there enters the assumption of phantom

chains. Phantom chains occupy no space, and

one chain or chain segment can pass through

another as though it never existed. Of course,

this is patently fiction, but stunningly it has not

prevented the users of the theory to emerge

from such an "unreal world" and make conclu-

sions about structures in the real world.

The argument that emerges from this partic-

ular fiction is that all good elastic materials

must be completely disordered; they must be

random chain networks. In such an unreal

world there is no acceptance of the possibiUty

of mechanical resonances in elastomers with

dynamic and regularly repeating structural ele-

ments.

Yet experimental data on certain elastic-

contractile model proteins, using different

instrumentation measuring from different

physical bases, show resonances near 5 MHz

and importantly near

kHz in the acoustic fre-

quency range. These mechanical resonances

develop on raising the temperature through the

range of the inverse temperature transition.^'^^

In the realm of the elastic consilient mecha-

nism. Bacon's "idols which beset men's minds"

continue their relevance four centuries follow-

ing enlightenment by this "patron saint of the

scientific revolution."

548

Epilogue

E.3.3 Idols That Retard Utilization

of the Hydrophobic Consilient

Mechanism in Understanding and

Developing Protein-based Machines

and Materials

The fiction that blocks recognition of the

primary basis for the "vital force" derives from

ignoring the presence in the real world of

dif-

ferentiated water structures. Section E.2.6.2

briefly reviews unquestioned evidence for the

existence of special water structure surround-

ing hydrophobic groups. All would agree that

structure and thermodynamics of this water

differs from that of bulk water and from that

surrounding charged

groups.

Even the structure

of water surrounding a negatively charged

group differs from that surrounding a positively

charged group. Yet a common approach to

computing the structure and function of

protein-based machines and materials assumes

water to be homogeneous, to be represented by

a mean dielectric constant.

Furthermore, the assumption of a uniform

dielectric constant for all water structures inter-

acting with protein-based machines and mate-

rials conceals the occurrence of competition for

hydration between hydrophobic groups and

charged groups. In the past there has been the

practice of using a dielectric constant of

(that

for bulk water) up to the surface of the protein

and then decreasing the dielectric constant to 5

or less when within the protein. However, what

Solomonic wisdom suffices for choice of dielec-

tric constant to be used for ion-pair formation

within the tortuous surfaces with clefts of

varying shapes from acute to

obtuse.

As seen in

Chapter 8, these clefts may reside inside the

protein-based machine, as found in ATP syn-

thase, or outside the protein-based machine, as

occurs for the myosin II motor.

In our view, governing free energy changes

result from the competition for hydration

between hydrophobic groups and charged

groups; they have been determined experimen-

tally as hydrophobically shifted pKa values, for

example. It is competition with hydrophobic

groups for limited hydration, experienced by

charged groups of opposite

sign,

that drives ion-

pair formation. As demonstrated in Chapter 5,

values for AGap, determined from pKa shifts

of acid-base titration data, corroborate corre-

sponding changes in AGHA, measured from

changes in the heat of the inverse temperature

transition. From our experimental experience

with designed elastic-contractile model pro-

teins,

AGap is no fiction; this measure of the

energetics of competition for hydration be-

tween oil-like and vinegar-like groups is part of

the real world. From the analyses of the protein

structures in Chapter

AGap

(if it had not been

derived from model protein studies) would

have to have been invented to describe the

function of key protein-based machines of

biology. In effect, the insightful analogy to mag-

netic forces by Kinosita and coworkers^ in

describing the behavior of Fi-ATPase implici-

itly recognized the existence of such a force.

Both realms, those of the hydrophobic con-

silient mechanism and of the elastic consilient

mechanism, provide clear examples of Bacon's

"idols which beset men's minds'' of four cen-

turies ago that enhance our own personal jour-

neys of

enchantment

today.

Perhaps we can summarize with the follow-

ing perspective:

Useful approximations of the past

become "idols" in the present

that stand as barriers to the future.

E.4 Protein-based Machines as

Physical Embodiments of the

"Vital Force" That Sustains Life

The phenomenological experimental founda-

tion for the challenging new perspectives

presented by the hydrophobic and elastic

consiHent mechanisms stands on the successful

design of model proteins capable of the extra-

ordinarily diverse set of energy conversions

noted above. The mechanistic foundation

derives from the need to obtain explanation for

otherwise inexpHcable experimental results,

such as stretch-induced pKa shifts, hydropho-

bic-induced pKa shifts, hydrophobic-induced

reduction potential shifts, and systematic in-

creases in steepness (positive cooperativity) of

the experimental curves that follow the change

E.4 Protein-based Machines as Physical Embodiments of the "Vital

Force"

That Sustains Life

549

of state of functional groups as the model

proteins are made more oil-like (see Chapter

5).

Furthermore, yet to be computed by any

program

the fundamental thermo-mechanical

transduction wherein the cross-linked elastic-

contractile model proteins contract and

perform mechanical work on raising the tem-

perature through their respective inverse

temperature transitions.^^'^^ These results first

appeared in the literature in 1986 and have

repeatedly appeared since that time with

dif-

ferent preparations, compositions, and experi-

mental characterizations. Additionally, the set

of energies converted by moving the tempera-

ture 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.

We consider these repeatedly demonstrated

properties, using designed elastic-contractile

model proteins, to be fundamental to the func-

tion of the protein machines of biology, as most

directly examined in Chapter 8. The function

of Complex III of the electron transport chain,

of the Fi-motor of ATP synthase, and of the

myosin II motor of muscle contraction consti-

tute protein-based machines that appear to

have their functions well-described by the

hydrophobic and elastic consilient mechanisms.

These protein-based machines represent three

major classes of energy conversion of biology,

and the relevance of their function to the con-

silient mechanisms, derived using the designed

elastic-contractile model proteins, comes into

focus in the synopses given immediately below.

E.4.1 Three Primary Classes

of Energy Conversion by

Protein-based Machines

E.4.L1 Production of

Proton

Concentration Gradient, an Example of

Electro-chemical Transduction

The

flow

of electrons (from reduced nucleotides

of intermediary metabolism through Com-

plexes I, II, III, and finally IV of the electron

transport chain within the inner mitochondrial

membrane) pumps protons from the matrix side

to the cytoplasmic side of the membrane. Using

flow

of electrons to pump the chemical, proton

(the acid, H"^), represents electro-chemical

transduction, and the protein-based machine

capable of doing so may be called an electro-

chemical transducer. Of the four complexes, at

this stage, the function of Complex III provides

stunning examples of both hydrophobic and

elastic consilient mechanisms.

E.4.1.1.1 In the Complex III Example

Formation of Negative Charges and of

Positive Charges Individually Open Pathways

to Effect Proton Translocation Across the

Inner Mitochondrial Membrane

On the matrix side of the membrane, two elec-

trons are added to ubiquinone to become neg-

atively charged. By the apolar-polar repulsion

AGap,

the negative charge disrupts hydropho-

bic association to open an aqueous channel

allowing ingress of two protons from the matrix

side of the membrane to result in uncharged

and lipid soluble ubiquinol. On the cytoplasmic

side of the membrane hydrophobic association

holds the FeS center of the Rieske Iron Protein

at the ubiquinol site, where ubiquinol gives up

two electrons to carry a double positive charge.

The two positive charges on ubiquinol, again by

means of

AGap,

disrupt the noted hydrophobic

association on the cytoplasmic side of the mem-

brane, and the two positive charges, released as

two protons to the cytoplasmic side, return

ubiquinol to ubiquinone. This completes the

transit of two protons across the inner mito-

chondrial membrane.

E.4.1.1.2 Mechanical Coupling of

Hydrophobic Dissociation and Elastic

Retraction Achieves Electron Transfer on the

Pathway from Complex III to Complex IV

Formation of the hydrophobic association

between the hydrophobic tip of the Rieske Iron

Protein and the hydrophobic ubiquinol-

containing site stretches an interconnecting

chain segment. This extended chain segment

functions as a free-standing tether originating

from an anchor in the membrane and bridging

550

Epilogue

to the globular component of the Rieske Iron

Protein that contains the electron transferring

FeS center on the cytoplasmic side of the mem-

brane. This is depicted in Figures 8.14 through

8.19 and from a somewhat different represen-

tation in Figure E.l. On oxidation to result in

double positive charge on ubiquinol, the hydra-

tion-based repulsive force between charged

and hydrophobic groups, AGap, disrupts the

hydrophobic association holding the Rieske

Iron Protein at the ubiquinol (Qo) site, and the

stretched tether, making use of an aromatic

side chain as a fulcrum and applying force at

the appropriate angle, lifts the FeS center of

the Rieske Iron Protein from the ubiquinol

site over a hydrophobic rim and places it at

the cytochrome Ci site. From the heme of

cytochrome Ci the electron transfers to the

heme of cytochrome c. Cytochrome c then

dif-

fuses to Complex IV in the transfer of an elec-

tron from Complex III to Complex IV. Within

Complex IV the electron completes its transit

from glucose to reach its ultimate goal of reduc-

ing molecular oxygen.

E.4.1.1.3 An Astounding Example of

Coupled Hydrophobic and Elastic

Consilient Mechanisms

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.

The figurative critical crossroad between

electron transfer and proton translocation

exhibits a Uteral crossing of elastic structures in

Figure E.l.^"^ Electron flow couples to proton

pumping by interlinking the physical processes

of charge disruption of hydrophobic associa-

tion and relaxation of damped internal chain

dynamics. Coupled hydrophobic dissociation of

the hydrophobic consiUent mechanism and

elastic retraction of the elastic consilient mech-

anism simultaneously release proton to the

inner membrane space and move the reduced

FeS center within the Rieske Iron Protein for

electron transfer to the cytochrome Ci site for

further transfer to cytochrome c, followed by

diffusional transit to Complex IV.

Such is our journey of Ionian Enchantment

from de novo design of elastic-contractile model

protein-based machines to enlightenment at a

key juncture of energy conversion within living

matter.

E.4J,2 Use of the Proton Gradient to

Produce ATP, the Energy Coin of Biology,

an Example of Chemo-chemical

Transduction

ATP synthase produces nearly 90% of the ATP

utilized by living organisms. The structure and

phenomenology of ATP synthase gives rise to a

set of predictions that can test the relevance of

the hydrophobic and elastic consilient mecha-

nisms to the function of this central protein-

based motor of biology. ATP, the energy coin of

the biological realm, derives from the coupling

of two rotary motors driven by the chemical

energy of the proton concentration gradient

considered above. The structural coupling

element is a rotor that extends perpendicular

to the inner mitochondrial membrane and is

driven by the membrane-bound Fo-motor.

Return of excess proton from the cytoplasmic

side of the inner mitochondrial membrane

powers the Fo-motor that turns the rotor in a

clockwise direction. The rotor turns within an

extramembranous catalytic motor housing,

collectively called the Fj-motor, to produce

ATP by adding inorganic phosphate. Pi, to

ADP (see Figures 8.26 through 8.41).

By the reverse process of catalyzing the

hydrolysis of ATP to ADP plus Pi, the Fi-motor

can operate in reverse to drive the rotor in a

counterclockwise direction. In this mode the Fi-

motor is called the Fi-ATPase. The predictions

E.4 Protein-based Machines as Physical Embodiments of the "Vital Force" That Sustains Life

551

lipid layer

of inner

mitochond:

membrani

matrix

FIGURE E.l. Stereo view of homodimeric structure

(gray) of yeast Complex

III,

plus cytochrome c (dark

gray at upper right), but with white Reiske Iron

Protein (RIP) in space-filling representation (rising

left to right) and ribbon representation (rising right

to left) whereby the globular components cross

into the opposite monomers by means of free-

standing, elastic tethers that become extended on

hydrophobic association at the Qo site of the very

hydrophobic tip of the globular component of RIP

that contains the FeS center. (A) Nearly complete

structure. (B) Stereo view of redox centers showing

electron transfers with the RIP of both monomers

included to clarify the basis for the relocation of the

FeS center from the Qo site to the heme Ci site. On

reduction of the FeS center and passing a second

oves to

electron to heme

HL,

the ubiquinol at the Qo site

becomes oxidized to form QH2^^. By means of the

Gibbs apolar-polar repulsive free energy of hydra-

tion (AGap), the hydrophobic association of the FeS

center with the Qo site becomes sufficiently weak-

ened by the positive charge of QH2^^ that the

stretched elastic tether contracts to move the FeS

center from the Qo site to the heme Ci site. This

domain movement (characterized in Figures 8.14

through 8.19) achieves transfer of an electron from

the ubiquinol (characterized in Figures 8.14 through

8.19) to cytochrome

Ci,

where it is then passed on to

the heme of cytochrome c. (Prepared using the crys-

tallographic results of Lange and Hunte^"* as

obtained from the Protein Data Bank, Structure File

IKYO.)

552

Epilogue

of the hydrophobic and elastic consiUent

mechanisms address the ATPase function, and

the predictions readily reverse when the rotor

is driven by the Fo-motor to describe the func-

tion of ATP synthase.

On the basis of the hydrophobic consilient

mechanism as presented in Chapter 8, function

results from an aqueous-based repulsion, called

an apolar-polar repulsive free energy of hydra-

tion and represented as AGap. The repulsion

occurs between the most hydrophobic side of

the rotor and the most charged occupancy state

(AD? plus Pi) of a catalytic site in a P-subunit.

The repulsion either drives the rotor in a coun-

terclockwise direction on hydrolysis of ATP to

produce ADP plus Pj, or, when the rotor is

driven in the clockwise direction by the Fo-

motor, the repulsion causes ADP plus Pi to

convert to ATP as a means of lowering the free

energy of repulsion.

We complete this synopsis with a list of

substantive predictions and their realizations

that flow from the hydrophobic and elastic

consilient mechanisms when confronted with

the structure and phenomenology of the

Fi-ATPase:

Prediction 1: The rotor must be hydrophobi-

cally asymmetric. Because the catalytic

housing of the Fi-ATPase is essentially three-

fold symmetric but with different occupan-

cies in the three p-catalytic subunits, three

different faces of the y-rotor are identified

from the crystal structure with different

occupancies of the three catalytic subunits.^^

Indeed, the three faces are calculated to

have very different Gibbs free energies for

hydrophobic association,

AGHA,

namely, -20,

0, and +9kcal/mole in order of decreasing

hydrophobicity. Thus, the prediction of a

rotor with hydrophobic asymmetry is strik-

ingly borne out. The order of hydrophobicity,

when considered in terms of the apolar-polar

repulsion between occupancy and direction

of rotation, makes sense with respect to

mechanism.

Prediction 2: In the static state the most

hydrophobic side of the rotor faces the least

polar side of the motor housing. Examination

of five crystal structures with different

occupancy states demonstrates the most

hydrophobic side to always be oriented

toward the least polar portion of the motor

housing, that is, toward the least polar occu-

pancy state of the P-subunits. Thus, the

hydrophobic asymmetry properly responds

to the occupancy state as required for it to be

central to mechanism.

Prediction 3: The role of ATP in the noncat-

alytic a-ATP subunits is one of triangulation

of repulsive forces to lessen viscoelastic drag

between rotor and housing as required for

efficiency. The structure of the catalytic

housing of the Fi-ATPase can be given as

(aP)3,

where a and p are paired protein sub-

units arranged in approximate threefold sym-

metry. While unchanging and noncatalytic,

the a-subunits contain ATP. By the

hydrophobic consilient mechanism, the a-

ATPs apply a triangular apolar-polar repul-

sive force between housing and rotor. This

repulsive force, AGap, hniits hydrophobic

association of rotor with housing that

would result in a viscoelastic drag or could

even lock up rotation by hydrophobic asso-

ciation. Thus, the hydrophobic consilient

mechanism ascribes an essential role of facil-

itating rotation to the three a-ATP nucleo-

tides within the noncatalytic part of the

housing.

Prediction 4: There is negative cooperativity

for ATP binding. With three very different

hydrophobic faces to the rotor, ATP would

first bind to the P-catalytic site with minimal

apolar-polar repulsion. The p-catalytic site

exhibiting the least apolar-polar repulsion

would be the one facing the least hydropho-

bic face,

AGHA

~ +9kcal/mole, of the y-rotor.

The second ATP to occupy a catalytic P-

subunit would do so facing the apolar-polar

repulsion of an essentially neutral hydro-

phobic face of the rotor, that is, AGHA ~

kcal/mole.

Finally, to achieve complete occu-

pancy of the three catalytic p-subunits, the

third ATP must bind facing the apolar-polar

repulsion of the most hydrophobic face of the

rotor, namely, with AGHA ~ -20 kcal/mole.

Thus,

by the apolar-polar repulsive free

energy of hydration of the hydrophobic con-

siHent mechanism, negative cooperativity of

E.4 Protein-based Machines as Physical Embodiments of the "Vital Force" That Sustains Life

553

ATP binding naturally results from the

hydrophobically asymmetric rotor.

Prediction 5: There is a positive cooperativity

of increased ATP occupancy of catalytic sites

with rate of hydrolysis (rotation). Positive

cooperativity of ATP occupancy with hydro-

lytic rate has the same basis as the role of the

three a-ATPs of Prediction 3. As more sites

become occupied by the very polar ATP mol-

ecule, progressively less viscoelastic drag

occurs between rotor and housing. Less drag

allows a faster rotation of the rotor on which

the rate of hydrolysis depends.

Prediction 6: Increase in distance between rotor

and housing due to AGap repulsion acting

through water between the most hydrophobic

side of the rotor and the ADP-SO4 analogue

of the most polar state. Menz et

al.^^

reported

the particularly interesting crystal structure

with all sites occupied by nucleotide, as

shown in Figure E.2. In the left side of part

Figure E.2B, a distortion in the arrangement

of ligands (nucleotides) is discernible. The pE-

ADP-S04^~ site in chain E is displaced from

the ttTP-ADP site in chain B and at a greater

distance from the y-rotor. By superposition,

Menz et al.^^ in Figure E.3 better represent

the displacement of housing from y-rotor that

occurs on replacing the empty subunit

(PE)

the structure of Figures 8.30 through 8.34

with the ADP-S04^" analogue of the most

polar ADP-PO4 state. The crystal structure

containing the ADP-S04^~ analogue was used

in Figures 8.35,8.36,8.40, and

8.41.

The super-

position of Figure E.3 clearly shows the

double-stranded a-heUcal coiled coil portion

of the y-rotor and the pE-subunit to be

repulsed from each other on occupancy of

the pE-subunit by the very polar ADP-S04^~

analogue. Again, we see AGap in action.

Menz et al.^^ describe their findings: "the

coiled coil region has moved significantly ...

resulting in an overall rmsd of 2.9A in a-

carbon positions for the entire y subunit.

The two conformations of the y-subunit are

related by a rotation that varies in magnitude

along the length of the C-terminal helix,

ranging from less than 1° for the final

residues (y259-272) to a maximum of about

20° for residues y234-244 (which form the

coiled coil with y20-10)." In their figure

legend, Menz et al.^^ state: "Note that inter-

acting residues in the PE-subunit and the y-

subunit move in opposite directions." This is

exactly as expected for the occurrence of

an apolar-polar repulsion, a AGap, acting

through water between the most hydrophobic

side of the rotor and the ADP-SO4 analogue

of the most polar state that constitutes Pre-

diction 6.

There is also the expectation that the polar

sulfate would tip the competition for hydra-

tion between apolar and polar groups toward

polar groups. Charged groups, previously

driven to ion pair and to hydrogen bond due

to lack of hydration, as shown in Figure 8.39,

assisted by the highly charged ADP-S04^"

occupancy state now access more hydration

and no longer require these associations, as

shown in Figure 8.40. Figure E.4 illustrates

with straight Hues the arc of apolar-polar

repulsion emanating from the sulfate mole-

cule to the hydrophobic side of the y-rotor.

The repulsion due to the emergent charged

residues, for example, D315, D352, D349,

K382,

D386, and R337 in chain E and E399

in chain A, supplement the repulsion due to

the

PE-ADP-S04^~

subunit, as indicated by

the finer straight lines. All charged species

compete for hydration with the hydrophobic

side of the y-rotor. The series of straight inter-

connecting lines represents the lines of force

due to AGap causing the

and y subunits to

move in opposite directions in Figure E.4.

Prediction 7: A repulsive force acting through

"waters of Thales" to store energy in elastic

deformation provides the opportunity for

high efficiencies of energy conversion by Fj-

ATPase. The movement in opposite direc-

tions observed in Figure E.4 of the pE-subunit

from the y-rotor on occupancy of the pE-

subunit by ADP-S04^" constitutes an elastic

deformation. The elastic deformation results

from AGap-based repulsive forces acting

through water, that is, through the "waters

of Thales." Under such circumstances as the

ATPase the deforming forces relax efficiently

into rotational motion of the rotor.

If the application of force for rotation were

instead to occur above the aqueous chamber

554

Epilogue

Y-rotor .jX^;^''^

4|l

glycerol

%,^ ^ fe^""*'^^-

6P.-ADP-SO4-2

»'E (E) ^

<*^

FIGURE E.2. Stereo view of the Fi-motor of ATP

synthase showing the y-rotor in ribbon and Ugands

in space-filling representation with a unique set of

Ugands that result in the ADP-SO4 occupancy

opposed to the most hydrophobic side of the y-rotor.

SO4 presents a stable analogue of hydrolyzed y-

phosphate such that it becomes possible to see

spatial changes indicative of a greater

AGgp

repulsion

that occurs due to that occupancy state. Labeling of

Ugands and subunits combines the identifications of

Menz et al.^^ (in Figure E.3) and those used in

Chapter 8. (A) Side view with aUgned Ugands and

the ADP-SO4 ligand at left. (B) Top view with label-

ing on the left and apparent structural displacements

between rotor and the PE-subunit containing ADP-

SO4.

(Prepared using the crystallographic results of

Menz et al.^^ as obtained from the Protein Data

Bank, Structure File 1H8E.)

between the pE-subunit and the y-rotor, then

it would be difficult to imagine that energy of

motion would not be dissipated irreversibly

into the PE-subunit. Additionally, from the

relative positions of these portions of the PE-

subunit and the y-rotor, shown in Figures E.3

and E.4, the PE-subunit appears to be in front

of the second strand of the double-stranded