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

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8.1 Thesis 335

8.1.8.1.5

Relative Magnitude of the

Endothermic and Exothermic Components

of the Inverse Temperature Transition

and Relevance to Biology's

Protein-based Machines

Recent work by the Rodriguez-Cabello group

in Valladolid, Spain, using temperature-

modulated differential scanning calorimetry

(TMDSC), provides insight into the magnitude

of the exothermic component of the inverse

temperature transition and how much it

reduces the experimentally measured endo-

thermic heat.^^ As shown in Figure 8.1/^ the

TMDSC data for (GVGVP)25i suggests for this

composition that the oppositely signed exother-

mic component due to the physical association

of chains is about one-third the magnitude of

the endothermic heat that effects loss of

hydrophobic hydration. The results in Figure

8.1 should help to clarify the compre-

hensive hydrophobic effect to those in the com-

munity of physical biochemists and bio-

physicists who yet think that the hydrophobic

effect arises dominantly from the exothermic

component. The endothermic heat of

the inverse temperature transition, in fact,

defines the inverse temperature transition

and is the basis for the "hydrophobic effect" or,

as we have called the more complete under-

standing, the comprehensive hydrophobic

effect.

Thus,

values of

AGHA

should be recognized as

the net result of a transition dominated by the

endothermic conversion of hydrophobic hydra-

tion to bulk water attending hydrophobic asso-

ciation with a lesser contribution due to the

exothermic association of the model protein

molecules, resulting from van der Waals inter-

actions usually calculated using the Lennard-

f^mmnnimn:

|0.2

mWl

^lllllflTlTTTmTmrT^

__^/l11lTlTrTmTTTTT^^

)

"(GVGVP)25i

Period: O.Smin

Heating Rate: IC/mim

Amplitude: O.IC

20 25 30 35 40 45

H-H—I—I—I—t—I

I I I—I I I

5 10

I I I—t—HH—HH—I—+—I—I I I I

11 20 25

2IL

50 55 *c

I I I I I I I I

I—h-»-H

35 40 min

FIGURE

8.1.

Component heats of hydrophobic asso-

ciation of an inverse temperature transition obtained

by means of temperature-modulated differential

scanning calorimetry (TMDSC). (Upper curve) An

exothermic component of the inverse temperature

transition due to the physical (van der Waals) inter-

action between associating molecules. (Middle

curve) The endothermic component (due to disrup-

tion of hydrophobic hydration), which is the funda-

mental feature of an inverse temperature transition

of hydrophobic association. (Lower curve) Net

endothermic heat of an inverse temperature transi-

tion that one measures in the standard differential

scanning

calorimetry.

This

is the value used for deter-

mining the Gibbs free energy for hydrophobic asso-

ciation,

AGHA,

arising out of an inverse temperature

transition. Noting the expanded temperature

scale,

is apparent that the width (the transition zone) of the

curves determined here at a much higher concen-

tration is similar to that of Figure 5.1C (Preliminary

communication from J. Carlos Rodriguez-Cabello •

produced with permission of J. Carlos Rodriguez-

Cabello.^0

336

8. Consilient Mechanisms for Protein-based Machines of Biology

Jones 6-12 potential^^ or the Buckingham

potential functions. ^^ It will be interesting, in

future work, to determine the relative magni-

tude of the endothermic and exothermic com-

ponents for each of the amino acid residues and

for other biologically relevant chemical modifi-

cations, as they contribute as guest residues

to the inverse temperature transition of

(GVGVP)n and of other informative host

model proteins.

8.1.8.1.6 The "Waters of Thales" as a

Requirement of the ConsiUent Mechanisms

As regards biology's protein-based machines,

the comprehensive hydrophobic effect, domi-

nated as it is by changes in hydrophobic

hydration of the inverse temperature transi-

tion, would become less dominant as the pres-

ence of water in the more polar state of a

protein-based machine became more limited,

that is, as the "waters of Thales" decrease.^^'^^

The long-recognized idea of cold denaturation

of proteins (enzymes),^^ that is, the loss of

structure required for function on lowering the

temperature, constitutes the same phenomenon

as the formation of structure on raising the tem-

perature. On observation of the phenomenon

in elastic-contractile model proteins, we devel-

oped the more general term of inverse temper-

ature transition, as it can be observed under

circumstances not relevant to cold denatura-

tion, such as the dissolution of crystals of

hydrophobically associated cyclic model pro-

teins on lowering the temperature.^^ Of course,

the comprehensive hydrophobic effect derives

from the inverse temperature transition. The

fundamental change underlying the inverse

temperature transition, however considered, is

one of changing the amount and nature of

protein hydration.

One of the more challenging locations, there-

fore,

for consideration of the comprehensive

hydrophobic effect in the panoply of biological

energy conversions is the electron transport

chain embedded within the inner mito-

chondrial membrane. Essential parts of these

protein-based machines insert into and func-

tion in very hydrophobic lipid bilayers. Here

the ingress and egress of protons for develop-

ment of the proton concentration gradient

across the inner mitochondrial membrane

becomes the output energy of an electron

transfer process that is so crucial to living

organisms. A central player, the ubiquinone

coenzyme Q,^^ converts from very hydrophobic

lipid diffusible species on the one hand to a pos-

itively charged species on oxidation at one site

and on the other hand to a negatively charged

species on receiving electrons at another site.

Both occur as key elements of the function of

Complex III of the electron transport chain.

By the hydrophobic consilient mechanism

and specifically due to the apolar-polar repul-

sive free energy of hydration, AGap, formations

of these charged coenzyme Q species contain

the thermodynamic key to transforming

"buried water molecules"^"^'^^ observed in the

crystal structure into pathways for proton entry

into and exit from the inner mitochondrial

membrane that results in the development of

the proton concentration gradient. In particu-

lar, formation by oxidation of the positively

charged ubiquinol near one side of the mem-

brane would disrupt hydrophobic association,

allowing release of protons to that side of the

membrane, whereas formation of the nega-

tively charged ubiquinone by reduction near

the other side of the membrane would disrupt

hydrophobic association to open channels for

the uptake of proton from that side of the mem-

brane (see discussion below in section 8.4.4).

8.1.8.1.7

The Coupling of Hydrophobic

Association with Development of

Elastic Force

Complex III is an example of the consiUent

mechanism for elasticity that includes the cou-

pUng of hydrophobic association with develop-

ment of an elastic force. In particular, the

Rieske iron protein (RIP) of Complex III

resides on the cytoplasmic side and contains a

long hydrophobic a-helix that passes through

the lipid bilayer from the cytoplasmic side to

emerge on the matrix side with charged

residues that combine to anchor the iron

protein to the membrane. On the cytoplasmic

side,

a sequence of about 15 residues that is

continuous with the transmembrane anchor

8.1 Thesis

337

tethers the globular component containing the

FeS center.

By the hydrophobic and elastic consilient

mechanisms the physical processes would

proceed as follows: The most favorable

hydrophobic association available to RIP is the

hydrophobic association of the hydrophobic tip

containing the FeS center with the Qo site con-

taining the ubiquinol within cytochrome b. For

this most favorable hydrophobic association to

occur, the tether becomes stretched. On chang-

ing the charge by addition of the negative elec-

tron to the FeS center and passing a second

electron on to the heme of cytochrome bL, the

ubiquinol at the Qo oxidation site takes on two

positive charges that disrupt the hydrophobic

association of this site. Hydrophobic dissocia-

tion of the very hydrophobic tip of the FeS

center allows the stretched entropic elastic

segment of the tether to lift the globular com-

ponent of RIP using an aromatic side chain as

a fulcrum and to flip the tip to hydrophobically

associate at the site for reduction of

cytochrome Ci. This represents an interlinking

of hydrophobic association and elastic force

development as repeatedly demonstrated with

the elastic-contractile model proteins in

Chapter 5. On oxidation of the FeS center at

cytochrome Ci, the hydrophobic tip containing

the FeS center returns to its most favorable

hydrophobic association at the Qo site contain-

ing a new molecule of ubiquinol to be posi-

tioned for the next cycle.

Thus,

the challenge to the consilient mecha-

nisms posed by the electron transport chain

transforms into a showcase example that

includes the two distinct but interlinked physi-

cal processes of the development of entropic

elastic force during hydrophobic association to

bring both consilient mechanisms to bear.

8.1.8.1.8

ATt as a Simple On-Off Switch

Another point to note is the simplicity of

looking at hydrophobic association/dissociation

from the perspective of Tt. Should Tt be just

above the operating temperature, say, the phys-

iological temperature of 37°C, then reducing

the expression of charged species sufficient to

lower Tt the width of the temperature interval

for the transition (see Figure 5.5) drives essen-

tially complete hydrophobic association. Thus,

the change in Tt, the ATt, functions as a simple

sliding on-off switch for driving hydrophobic

association/dissociation. For the slope in Figure

5.10 resulting from charge formation, a ATt ade-

quate to turn on or off hydrophobic association

requires a relatively small

AGHA-

8.1.8.1.9

Coherence Between AGap and

AGHA

Calculated Using Different

Experimental Data Demonstrates Presence

and Dominance of the Consilient Mechanism

in Model Proteins

For Model Protein i in Table 5.5, which is

(GVGVP GVGVP GEGVP GVGVP GVGVP

GVGVP)36(GVGVP), abbreviated as E/OF, we

can write AGHA[E /OF -^

E70F],

where E stands

for the -COOH state and E" for the -COO"

state of the glutamic acid (Glu, E) residue.

From Figure 5.10 and Table 5.3, we have that

AGHA[E/OF -^ E70F] is 5.22kcal/mole-

(GEGVP). Using the data in Figure 5.34, the

pKa of Model Protein i is 4.5. Now the pKa of

a carboxyl group in glutamic acid (Glu, E) or

aspartic acid (Asp, D), absent significant elec-

trostatic interactions and hydrophobic compe-

tition for hydration, is 3.8 to 4.0. Therefore, the

pKa of Model Protein i is shifted by 0.5 to 0.7

pH units due to the presence of the vahne (Val,

V) residues from the situation without such

hydrophobic residues and without significant

proximity of other polymer charges.

From Equation (5.13) in Chapter 5, we

have that AGap = 2.3 RT ApKa, such that,

AGap for Model Protein i becomes 0.7 to

1.0kcal/mole(E); this is for one E in six pen-

tamers. As the value of AGHA[E/OF -^ E70F] is

5.22kcal/mole-(GEGVP) for one E in each

pentamer, 5.22kcal/mole-(GEGVP) should be

divided by six (5.22/6 = 0.87) for proper

comparison. As 0.87kcal/mole obtained from

AGHA[E/OF -^ E70F] is within the range of 0.7

to 1.0kcal/mole(E) obtained from AGap of acid-

base titration data, we have coherence between

the effect of ionization on change in the Gibbs

free energy for hydrophobic association, AGHA,

which is derived from calorimetric data and the

hydrophobic induced pKa shift, AGap, which is

338

8. Consilient Mechanisms for Protein-based Machines of Biology

derived from acid-base titration data. Thus, an

additional reason exists why AGHA[E/OF ->

E70F] should be interpreted as resulting from

an apolar-polar repulsive free energy of

hydration.

Accordingly, the comprehensive hydropho-

bic effect provides an explanation for both pKa

shifts and the control of hydrophobic associa-

tion by changes in the polarity of functional

groups such as quinones, flavins, nicotinamides,

and hemes of cytochromes. Furthermore, the

phosphorylation or dephosphorylation of a

serine (Ser, S), of a threonine (Thr, T), or of a

tyrosine (Tyr, Y) and the change from ADP to

ATP and the most polar state of the localized

presence of both ADP and inorganic phosphate

(Pi) represent the most dramatic changes in

polarity that occur routinely in biology. As dis-

cussed in section 8.1.11.2, a sound basis exists

for the view that the high energy released on

hydrolysis of phosphate compounds derives

from a limitation in the availability of adequate

hydration prior to hydrolysis. Therefore,

controlling the availability of hydration for

phosphate groups by varying the presence of

competing hydrophobic groups provides the

means whereby a protein can either energize a

phosphate or utilize the energy of phosphate

hydrolysis.

8.1.8.1.10 Does There Exist a Competition for

Hydration Between Hydrophobic and Polar

(e.g.. Charged) Groups as a Key Part of the

Functioning of Protein-based Machines

of Biology?

In our view, AGap provides the basis whereby

raising the free energy of ADP and

Pi,

by forced

apposition of the very hydrophobic side of the

y-rotor in ATP synthase, results in synthesis of

ATP.

Also, in myosin II motor AGap provides

the basis whereby this ATPase drives muscle

contraction. In particular, in broad-brush

strokes, ATP binds in a cleft directed in two

directions, (1) toward the hydrophobic associa-

tion of the cross-bridge to actin binding site

and (2) toward the hydrophobic association

between the head of the lever arm and the

amino-terminal domain of the cross-bridge.

Directing the ATP thirst for water in both

directions by means of the cleft causes the

cross-bridge to hydrophobically dissociate from

the actin binding site and the head of the lever

arm to hydrophobically dissociate from the

amino-terminal domain of the globular compo-

nent of the cross-bridge. Conversely, the split-

ting of ATP to form ADP plus Pi and release of

Pi results in a decrease in AGap with the conse-

quence of hydrophobic reattachment of

cross-bridge to actin site and hydrophobic

re-association of head of the lever arm to the

amino-terminal domain to provide the power-

stroke (the contraction) of the myosin II motor.

8.1.8.1.11 Positive Cooperativity Increases as

Charged Species Compete for Water with

Additional More-hydrophobic Residues

As developed in Chapter 5, positive coopera-

tivity arises due to competition for hydration

between apolar (hydrophobic) and polar (e.g.,

charged) residues constrained by location to

coexist along a protein sequence and ultimately

within the folded and assembled structure dic-

tated by the sequence. By way of description of

the molecular process, we begin with associated

hydrophobic domains with a proximal car-

boxyl, -COOH. During occasional fluctuations,

paired hydrophobic domains momentarily

begin to dissociate. As too much hydrophobic

hydration forms, re-association (insolubility of

hydrophobic groups) recurs, because the free

energy becomes unfavorable, that

is,

the (-TAS)

term for solubility of the hydrophobic groups

becomes too positive and overwhelms the

inherently negative AH term.

During the occasional fluctuation of

hydrophobic dissociation, a carboxyl ionizes to

form the charged carboxylate, -COO". To form,

the charged carboxylate, however, must achieve

its hydration by destructuring hydrophobic

hydration. This constitutes an increase in free

energy for the system, and reclosure occurs.

Should the pH be high enough to give the

opportunity for formation of a second car-

boxylate during an opening fluctuation, the

second carboxylate actually forms more readily

than the first, because it has less hydrophobic

hydration to disrupt. Because together the

carboxylates destructure more hydrophobic

8.1 Thesis 339

hydration due to overlapping hydration

spheres, the probability for remaining dissoci-

ated increases. The occurrence of two carboxy-

lates increases the chance for formation of a

third and fourth carboxylate, and so forth. As

with the second carboxylate, the third and

fourth carboxylates have less hydrophobic

hydration to destructure, and therefore they

have a greater probabiHty of formation; they

form with a lower pKa.

In fact, as seen in the Hill plots in Figure 5.31,

ionizations of subsequent carboxyls occur at

lower pKa values. As more valine (Val, V)

residues are stepwise replaced by more

hydrophobic phenylalanine (Phe, F) residues,

this trend continues with an increase in the

initial pKa value and greater decreases in the

pKa values for subsequent ionizations during

the hydrophobic dissociation process. By the

time five Val (V) residues have been replaced

by the more hydrophobic Phe (F) residues, as

in Model Protein v, (GVGVP GVGFP GEGFP

GVGVP GVGFP GFGFP)42(GVGVP) in

Figure 5.31A, the mean pKa has increased to

6.4. Furthermore, analysis of the Hill plot in

Figure 5.31 A shows that formation of the first

carboxylate occurs with a pKa of 7.0 and that

of the last carboxylate of the 42 repeating units

of six pentamers occurs with a much lower

pKa of 5.7.

8.1.8.1.12 Ionization of the Last Carboxyl at a

pKa Greater than 3.8 to 4.0 Requires That a

Residual Apolar-Polar Repulsive Free Energy

of Hydration Exists Even in the Completely

Unfolded, Fully Dissolved, Soluble State

Even when (GVGVP GVGFP GEGFP

GVGVP GVGFP GFGFP)42(GVGVP) is

completely unfolded with F residues spatially

distributed toward near-maximal distances

from E" residues, to the extent permitted by the

sequence, there remains an apolar-polar repul-

sive free energy of hydration. Even when the

carboxylates are as completely surrounded

by water as possible, they still cannot access

water completely undisturbed by hydrophobic

residues. The common explanation that pKa

shifts result from the carboxyl being forced by

some "conformational change" into a pocket of

low dielectric constant within a protein is not

tenable for the completely ionized, unfolded

state of this model protein.

Even if the two Phe (F) residues most prox-

imal in the sequence to the carboxylate are Val

(V) residues, as in (GVGVP GVGVP GEGVP

GVGVP GVGFP GFGFP)39(GVGVP), a

residual pKa shift for the hydrophobically dis-

sociated state remains after all carboxyls are

ionized, as shown in Figure 5.31B. These

find-

ings argue that treatments of the structure and

fiinction of protein-based machines are un-

satisfactory until proper inclusion of the

apolar-polar repulsive free energy of hydration

occurs.

8.1.8.2 The Amount of Hydrophobic

Hydration on Potentially Complementary

Surfaces Determines Whether

Hydrophobic Association or

Dissociation Occurs

Figure 8.2 provides an elementary schematic of

the association of globular proteins with con-

toured surfaces for proper steric association,

but each having different elements whereby

complementarity could be achieved.^^ In part

the following paragraphs demonstrate the rele-

vance to globular proteins in the analyses of

Chapter 5 that utilized model proteins of trans-

lational symmetry undergoing phase transi-

tions.

This section is preliminary to the more

involved but parallel discussion of the

hydrophobic association of myosin cross-bridge

with actin (and of components within the cross-

bridge) in the absence of ATP that dissociate in

the presence of bound ATP, as schematically

shown in Figure 2.16.

8.1.8.2.1

Complementary Surfaces Associate

when They Have the Potential for Too

Much Hydrophobic Hydration at a

Given Temperature

Consider a situation with globular protein sub-

units that are soluble in solution at a sufficiently

low temperature and that have simple com-

plementary hydrophobic surfaces covered with

much hydrophobic hydration, as in Figure

8.2A.^^

Raising the temperature from below to

340

8. Consilient Mechanisms for Protein-based Machines of Biology

hydrophobic hydration

Tt below

operating

temperature

residual hydrophobic hydration

2MC+

Tt below operating

temperature

residual hydrophobic hydration

+ 2X-

Tt below operating

temperature

bulk water

sidual hydrophobic hydration

+ Ca-^2

on calcium ion pairing)

Tt below operating

temperature

bulk water

residual hydrophobic hydration (•Tt)

limited polar hydration

(•

pKa)

on lon-painng,

Tt below operating

temperature

•**

'^JM^

bulk water

indivkkially,

Tt above operating

temperature

FIGURE

8.2. Elementary schematics (A^^)( of the association of globular proteins with different elements to

their complementary surfaces. (Reproduced with permission from Urry.^^)

8.1 Thesis 341

above the temperature for the onset of the

inverse temperature transition for hydrophobic

association initiates dimer formation. Now,

whether or not phase separation occurs

depends simply on whether or not the dimer is

soluble. If the dimer is soluble, there would be

no phase separation. If the dimer were itself

insoluble by means of extended association of

dimers, there could be fiber formation with

gelation and even phase separation. The former

applies to hemoglobin S and to actin filament

formation, where G(globular)-actin is soluble,

but, when ATP binding initiates association,

F(filamentous)-actin forms.

Independent of the question of dimer solu-

bility, the dimerization process is one of

hydrophobic association, and the change in

Gibbs free energy for dimer formation by

hydrophobic association, AGHA(dimerization) =

AHD - TASD, obtains. In the case of hydropho-

bic association, the transition is endothermic;

AHD

is positive. Therefore, as with the inverse

temperature transition, association occurs

because of a large negative (-TASD) term that

results from the large positive change in

ASD

more ordered hydrophobic hydration becomes

less ordered bulk water. Accordingly, dimer-

ization occurs due to a sufficiently large and

negative

AGHA,

wherein changes in solvent

entropy drive dimerization. Furthermore, the

process can be discussed in terms'of equilibria,

where the sign and magnitude of the equilib-

rium constant KD = exp(-AGHA/RT). As

written, the dimerizations in Figure 8.2 are

favorable with negative AGHA values as crudely

represented by the size and direction of the

arrows.

8.1.8.2.2

Surfaces with Too Little

Hydrophobic Hydration Do Not

Hydrophobically Associate

When too few hydrophobic residues or too

many charged species occur on the surface, too

little hydrophobic hydration results. Dimeriza-

tion will not occur, that is, the monomeric sub-

units retain their solubility in water. When the

charged species exhibit hydrophobically shifted

pKa values, then the surfaces are poised for

association, particularly if the charges on

opposing surfaces are of the opposite sign and

are arranged in a complementary way, as in

Figure 8.2E. A number of examples follow in

the next paragraph.

8.1.8.2.3

Charged Species Destructure

Hydrophobic Hydration But Experience

an Increase in Free Energy on Doing So

As shown in Figure 8.2B, C, even when suffi-

ciently hydrophobic surfaces have the same

charge, the oppositely signed ion in solution can

pair with the surface charge, and dimerization

by hydrophobic association can result.^^ This

was observed with elastic-contractile model

proteins in Figure 5.12. The more hydrophobic

poly[0.8(GVGIP),0.2(GEGIP)] associates at

physiological temperature in the presence of

0.3 N or more NaCl, whereas the less hydropho-

bic poly[0.8(GVGVP),0.2(GEGVP)] does not

(see Figure 5.12).

In Figure 8.2D calcium ion triggers

hydrophobic association of negatively charged

surfaces. As shown in Figures 5.15 and 5.27,

calcium ion is particularly effective in lowering

the value of Tj of Model Protein I, (GVGIP

GFGEP GEGFP GVGVP GFGFP GFGIP)4o

(GVGVP); 2E/5F/2I, and Model Protein ii:

(GVGVP GVGFP GEGFP GVGVP GVGVP

GVGVP)4o(GVGVP); E/2F When the model

protein is more hydrophobic and contains two

negative carboxylates in position for bidentate

interaction with the divalent calcium ion, the

decrease in Tt occurs at a much lower ion con-

centration for Model Protein I, which may be

considered a poor man's E-F hand. In particu-

lar. Figure 5.27 shows the decrease in Tt to

mirror the increase in hydrophobic hydration,

which ties directly to Figure 8.2D.

When the globular subunits have oppositely

signed charges on their surface, as in Figure

8.2E, each can exist alone as soluble monomers

in solution, but, when combined in a single solu-

tion, they associate to form dimers. The analogy

for the model proteins is shown in Figure 6.3.

In particular, the two model proteins, Model

Protein x': (GVGVP GVGVP GKGVP

GVGVP GVGVP GVGVP)22(GVGVP);

342

8. Consilient Mechanisms for Protein-based Machines of Biology

K/OF and Model Protein ii: (GVGVP GVGFP

GEGFP GVGVP GVGVP GVGVP)4o

(GVGVP); E/2F are each soluble in water at

physiological temperatures. When the two solu-

tions are combined, however, they hydrophobi-

cally associate as the temperature is raised

above 24°C (see Figure 6.3B).

The consilient mechanism depicted in the

elementary structures of Figure 8.2 are relevant

to protein function arising out of association of

globular components of molecular machines.

The principles arise in almost textbook fashion

in the function of the myosin II motor where

the key charged species are ATP, ADP, and Pi,

but in an important way also include the

charged side chains (see section 8.5.3).

8.1.8.3 ''Oil and Vinegar Don't Mix/' But,

When Oil-like and Vinegar-like Side

Chains of Proteins Are Forced to Coexist

by Virtue of Structure (Primary,

Secondary, Tertiary, and Quaternary), They

Interact in the Most Profound Way to

Achieve Function

Thus,

the old adage that "oil and vinegar don't

mix" remains relevant when the oil-like and

vinegar-like groups are constrained to coexist

along a protein sequence and in proximity to a

pair of hydrophobically associating/dissociating

surfaces. Although structure causes these dis-

parate groups to interact, they nonetheless

attempt to separate as oil from vinegar. In fact,

as substituents along a protein chain, oil-like

and vinegar-like side chains effectively repulse

each other as they each reach out for water

undisturbed by the other. Another important

element to recognize is that the apolar-polar

repulsion can propagate along a water-filled

cleft. Ion pairs, at a distance from the ATP

binding site within the hydrophobically fined

cleft, can be caused to separate by ATP binding,

and then the separated ion pairs, even by small

distances, assist to propagate polar dominance

to a more distant pair of hydrophobic faces.

As briefly considered immediately below, this

driving force provides a more efficient mecha-

nism for energy conversion in an aqueous

medium than the more commonly considered

electrostatic mechanisms.

8.1.9 On Efficiencies of Energy

Conversion in the Aqueous Medium

of Biology

This section considers efficiency of energy con-

version by protein-based machines of biology

by noting two points. The points arise from

studies on elastic-contractile model proteins

and draw from relatively new concepts con-

cerned with control of hydrophobic association

and with the nature of elasticity. The first

point provides direct experimental evidence

for a dramatically greater efficiency of the

apolar-polar repulsion mechanism over the

classic electrostatic charge-charge repulsion

mechanism for chemomechanical transduction

by polymers in water. The first point goes on to

address electrochemical transduction efficiency

with relevance, in principle, to the energy con-

version of the electron transport chain.

The second point addresses the nature of

elastic force development in relation to under-

standing efficient energy conversion. If the

energy required for chain deformation during

elastic force development becomes lost to other

parts of the protein and to the surrounding

water, then so too is efficient energy conversion

lost. In other words, elastomeric force develop-

ment on deformation in a protein-based

machine followed by marked hysteresis on

relaxation necessarily denotes an inefficient

protein-based machine.

8.1.9.1 For Mechanochemical

Transduction in Water Apolar-Polar

Repulsion-based Is More Efficient than

Charge-Charge Repulsion-based

Molecular Machines

8.1.9.1.1

Simple Comparisons of the

Chemomechanical Transductional Efficiencies,

r| = fAl/AjixAn, of the Charge-Charge

Repulsion and the Apolar-Polar Repulsion,

AGap, Mechanisms

The two molecular systems to be compared are

PMA, poly(methacryUc acid), which is

[-CH2-(CH3)C(COOH)-]n, and Model Protein

iv in Table 5.5, namely, (GVGVP GVGFP

GEGFP GVGVP GVGFP GVGFP)^

(GVGVP), abbreviated as E/4F. The two poly-

8.1 Thesis

343

mers were cross-linked to achieve similar elastic

moduli, and both respond to changes in proton

chemical energy, AjiAn = (-2.3RTApH)An. In the

following paragraphs, visual comparisons will be

made with reference to Figures 5.34 (comparing

Hill coefficients) and 5.35 (comparing the area

of acid base titration curves).

The statement of efficiency, r|, for proton-

driven chemomechanical engines can be

written as r| = fAL/A|iiAn = fAL/(-2.3RT

ApH)An. Because the chemical energy, AjLiAn, is

proportional to the change in pH, the slope of

the acid-base titration curve provides an imme-

diate comparison, where an increase in the

magnitude of the Hill coefficient means a

proportionately greater efficiency. The Hill

coefficient for PMA is 0.5, whereas, as seen in

Figure 5.34, that for E/4F is 2.7, suggesting on

this basis an expectation of at least a fivefold

more efficient energy conversion by E/4F.

The chemical energy also contains the

number of moles of proton, Ann, consumed in

the process. To consider both

A|IH

and

AUH,

the

acid-base titration curve can be used. The y-

axis contains the amount of acid consumed on

protonating the carboxylates, and the x-axis

provides the ApH required to do so. Accord-

ingly, the area defined by the acid-base titration

curve gives a measure of the chemical energy.

Because PMA has one carboxyl for every two-

backbone atoms, whereas E/4F has only one

carboxyl for every 90-backbone atoms, many

more protons will be consumed on driving the

PMA chemomechanical engine, as is apparent

from Figure 5.35. Missing in this comparison,

however, is the amount of work performed by

each engine. As discussed below, this is directly

determined and compared in Figure 5.36.

8.1.9.1.2

Experimental Comparison Following

pH Dependence of Length at Fixed Force

Using Acid-Base Titration Curves,

That Is, During Actual Performance of

Mechanical Work

Figure 5.36 shows the change in length for the

constant load of 2 grams, where the changes in

length, despite very different consumptions of

energy, are quite similar. In the comparison in

Figure 5.36, the PMA engine required 6.86 x

10"^

mole of protons, whereas the E/4F engine

requires 6.12x 10"^ mole of protons. If compar-

ison is made for the best AL/ApH slopes for

each engine, as shown in Figure 5.36, the ratio

of efficiencies, r|ap/r|cc is of the order of 40.

Clearly, in the aqueous milieu of biology the

electrostatic mechanism of charge-charge repul-

sion is not a serious contender for the efficient

machines available to biology. As noted in

section 8.1.8.3, ionizable functional amino acids

and other polar prosthetic groups forced,

through the process of biosynthesis (see

Chapter 6), to coexist within a protein chain

with substantial hydrophobic residues provides

the ingredients for efficient protein function.

8.1.9.2 Efficiency of Electro-chemical

Transduction in Water

8.1.9.2.1

Experimental Data on

Electro-chemical Transduction Efficiency

The previous considerations of energy conver-

sion resulted in the performance of mechanical

work, and, for the considered model proteins,

there is the obvious realization that hydro-

phobic association is tantamount to contrac-

tion. The control of hydrophobic association,

however, can interconvert any two energies

that can individually drive hydrophobic as-

sociation. The example here draws from the

demonstration that reduction of a redox couple

can power contraction by driving hydrophobic

association and that protonation of a carboxyl

can do likewise. Both processes, protonation of

a carboxylate and reduction of a redox group,

effect a decrease in AGHA, and both functional

groups are affected by any

AGHA-

shown in

Figures 5.20B, 5.23, 5.25, 5.29, 5.31, 5.32, 5.34,

and 5.35B, Chapter 5 is replete with hydropho-

bic-induced pKa shifts. Equivalent hydropho-

bic-induced shifts in reduction potential for

amino-methyl nicotinamide are shown in

Figure 5.20C. Because pKa values and reduc-

tion potential are both coupled to hydro-

phobicity, it is to be expected that a change in

redox state that changes hydrophobicity would

bring about a change in pKa and vice versa.

Here we demonstrate the efficiency of that con-

version for a modest level of host polymer

hydrophobicity.^^

344

8. Consilient Mechanisms

for

Protein-based Machines

Biology

Reduction-induced

pKa

shift

was

demon-

strated

in the

designed polytricosapeptide

Table

5.5,

that

is,

Polymer

Poly(GDGFP

GVGVP GVGVP GFGVP GVGVP

GVGK{NMeN}P), abbreviated

DK{NMeN}/2K containing both redox

(LysNMeN)

and

carboxyl (Asp,

functional

entities. From Table 5.2, the difference

AGHA

on going from the oxidized state, NMeN^, to

the

relevant reduced state,

6-OH

tetrahydro

NMeN,

is an

approximate -4kcal/mole-NMeN.

On the other hand,

for

the pKa shift, the change

in AGHA

AGap

2.3RTApKa

-2.3(582

cal/mole)(2.5)

-3.35kcal/mole. From

the

pre-

ceding information,

the

efficiency

can be

written

as r| =

(output energy/input energy)

100

{AGap/AGHA[LysNMeN^ (oxidized)

LysNmethyl-6-OH-tetrahydronicotinamide

(reduced)]}100

(3.35/4)100

83%. Thus,

one

estimates

high efficiency when the coupling

functional groups occurs

means

of a

common dependency on

AGHA-

8.1.9.2.2

Increase

Hydrophobicity Directly

Shifts Reduction Potentials

and

Increases

Efficiency, That Is,

the

Hill Coefficient

and

Positive Cooperativity,

for

NMeN

Attaching NMeN

to the

appropriate designed

series

microbially prepared polymers gives

the following polymers from Table

5.5:

Model Protein

ii':

(GVGVP GVGFP

{NMeN}GFP GVGVP GVGVP GVGVP)22

(GVGVP), K{NMeN}/2F

Model Protein

Hi':

(GVGVP GVGVP

{NMeNjGVP GVGVP GVGFP GFGFP)22

(GVGVP), K{NMeN}/3F

Model Protein

iv':

(GVGVP GVGFP

{NMeN}GFP GVGVP GVGFP GVGFP)2i

(GVGVP), K{NMeN}/4F

The indicated increases

hydrophobicity

replacing

Val (V) by Phe (F)

were found

cause systematic shifts

in the

reduction poten-

tial

and

corresponding increases

steepness

(positive cooperativity)

shown

Figure

5.20C.

particular,

the

reduction potentials

are K{NMeN}/OF (-145 mV), K{NMeN}/2F

(-127

mV),

K{NMeN}/3F (-107 mV),

and

K{NMeN}/4F (-90mV).'^ Thus,

for the

redox

couple NMeN/NMeN^

the

reduction potentials

and efficiency depend

hydrophobicity

in a

systematic

way,

analogous

to the

dependence

on hydrophobicity

of pKa and

efficiency

for a

chemical couple such

-COOH/-COO~.

this basis,

the

dependence

reduction poten-

tial

on the

hydrophobicity

surrounding

residues

for

players, such

heme

bn and

heme

bL,

in the

electron transport chain

can be

considered.^^

8.1.9.3 Further Consideration

of the

Relevance

of the

Nature

Elastic Force

to Efficient Mechanisms

for

Energy Conversion

8.1.9.3.1

The

Case

Isometric Contractions

The development

force under conditions

fixed length,

as in an

isometric contraction,

involves

the

elastic deformation

of a

chain

chains within

the

protein-based machine.

relaxation, ideal elastic elements return

the

total energy

deformation

to the

protein-

based machine

for the

performance

mechan-

ical work. Thus,

the

approach toward high

efficiency

for the

function

of a

protein-based

linear motor,

even

for

the RIP domain move-

ment

Complex

III,

depends

on how

nearly

the extension

of an

elastomeric chain segment

approaches ideal elasticity.

important

realize that

the

model

protein (GVGVP)25i

can

exhibit ideal elastic

behavior.^

It is

also significant

recognize that

the source

ideal elastic force resides

in the

internal motions,

the

internal chain dynamics,

the

elastic chain segment. To

the

extent that

the energy

deformation becomes dispersed

into molecules

chain segments

not

integral

the

extended chain segment, energy

lost

and efficiency decreases. Thus, the nature

the

elastomeric force limits

the

possible efficiency

protein-based machine.

For an

effective

protein-based machine, deformations

chains

should occur

such

a way

that

the

energies

involved

recoverable.

8.1.9.3.2

Relevance

Nonideal Elasticity

(Hysteresis)

Efficient Performance

Mechanical Work

As noted above

for an

ideal elastomer,

the

energy expended

deformation,

for

example.