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

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5.1 Introduction 115

Generally applicable statements result on

simply subtracting Equation (5.2) from Equa-

tion (5.1) to give^

AGHA

ix) = [Tt (ref) ASt (ref) - T, (;f) AS^ (x)]

(5.10a)

and as more recently derived^

AGHA

(%) - [AH, (ref) - AH, (%)]

(5.10b)

One should realize that Equation (5.10b)

includes the exothermic heat of van der Waals

contacts due to the folding and assembly of the

model protein during the transition. The asso-

ciation of model protein during the phase sep-

aration would be exothermic. The endothermic

heats obtained from the inverse temperature

(phase) transition arise from the conversion of

hydration of oil-like groups to bulk water.

Accordingly, the AGHA(Z) values calculated

directly from the heat of the inverse tempera-

ture transition, as in Equations (5.10a) and

(5.10b),

would be minimal values when consid-

ered as the change in Gibbs free energy for con-

version of hydrophobic hydration to bulk water

(See Figure 8.1 and associated text).

5.1.3.4.4 Moving the Trdivide by Replacing V

by Other Naturally Occurring Amino Acids

Whatever amino acid replaces the valine (Val,

V) residue, there results a change in the value

Tj.

This dependency of T, becomes a measure

of the relative hydrophobicity of the different

naturally occurring amino acid residues (see

Table 5.1), called the Tj-based hydrophobicity

scale."^ Design of protein function by use of the

Tt-based hydrophobicity scale requires knowl-

edge of Tt only. Changing Tt provides a simple

on-off switch for achieving function. Lowering

Tt from above to below the operating temper-

ature drives hydrophobic association, and

raising Tt from below to above the operating

temperature results in hydrophobic

dissociation.

5.1.3.4.5 Moving the Tt-divide Without

Changing the Amino Acid Composition

There are many ways, in addition to changing

the amino acid composition of the model

protein, to change the location of the Tt-divide.

They fall into two main classes. One class is to

have functional groups attached to the protein

that can exist in two different states, for

example, charged or uncharged, oxidized or

reduced, phosphorylated or dephosphorylated,

and so forth. The second class is to change the

composition of the solvent in ways that alter the

solvation of the oil-like groups without acting

by changing the state of a functional side chain.

Each of these means for moving the Tt-divide

constitute energy inputs, and AGHA(X), ^S iden-

tified above, becomes the energy output. Each

energy input resulting in a

AGHA(3C),

depending

on the sign of AGHA(X), drives hydrophobic

association (when negative) or dissociation

(when positive). For cross-linked matrices, this

is equivalent to contraction or relaxation,

respectively, to produce motion. A negative

AGHA(Z)

produces contraction, and a positive

AGHA(Z)

results in relaxation. Examples of

many energy inputs, as evidenced by changing

Tt, are very briefly noted immediately below.

5.1.3.4.6 Moving the Tt-divide by Adding

Protons to Carboxylates

Protonation, adding a proton, to the carboxy-

late group of the glutamic acid residue, or an

aspartic acid residue, lowers the value of Tt and

represents a chemical energy input that is one

of the most effective ways to drive association

of oil-hke groups, that is, to result in the

mechanical energy output resulting from con-

traction. Protonation of a carboxylate, -COO"

-h H^ ^ -COOH, represents an energy input

similar to reduction of a nicotinamide, and

these are exceeded only by removal of a phos-

phate group in their effectiveness in lowering

the value of Tt and consequently in producing

a negative change in AGHA(Z), with which to

drive hydrophobic association and its equiva-

lent of contraction (see sections 5.14 and 5.15).

5.1.3.4.7 Moving the Tt-divide by Adding

Electrons to Bound Oxidized Group

Reduction of an oxidized nicotinamide drives

association of oil-like groups and is similar

in effectiveness to protonation of a carboxy-

late in lowering the value of Tt. In oxidative

116

Consilient Mechanisms for Diverse Protein-based Machines

TABLE

5.1. Tj-based hydrophobicity scale for protein engineering of naturally occurring amino acid residues

(in order of more hydrophobic [low TJ to more polar [high TJ)^.

Residue R-group Abbreviation Letter

AHt

(kcal/mole''

Tt^' ± 0.05)

ASt

(kcal/mole''

± 0.05)

Tryptophan

-c„,-c

Trp

Tyrosine

Phenylalanine

Histidine

Proline(calc.)^'^

Leucine

Isoleucine

Methionine

Valine

Histidine

Glutamic acid

Cysteine

Lysine

Proline(exptl)^

Alanine

Aspartic acid

Threonine

Asparagine

Serine

Glycine

Arginine

Glutamine

Lysine

Tyrosinate

Aspartate

Glutamate

H :^ J_ H

H H

—™2^p^OH

H H

H^NH

—CH2Cri2Crl2—

-CH2CH(CH3)2

—CH(CH3)CH2CH3

—CH2CH2SCH3

-CH(CH3)2

-CH,^=("

HN;^NH

—CH2CH2C00H

—CH2SH

—CH2CH2CH2CH2NH2

—Cri2CH2Cri2—

—CH3

—CH2COOH

—CH(OH)CH3

—CH2CONH2

—CH2OH

—H

—CH2CH2CH2NHC(NH)NH2

—CH2CH2CONH2

—CH2CH2CH2CH2NH^

H H

—CH2COO-

—CH2CH2COO-

Tyr

Phe

His

Pro

Leu

Met

Val

His^

Glu

Cys

Lys°

Pro

Ala

Asp

Thr

Asn

Ser

Gly

Arg

Gin

Lys

Tyr-

Asp'

Glu-

D-

-90° C

-55° C

-30° C

-10°

120° C

250° C

2.10

1.87

1.93

K°

Y-

(-8°C)

5°C

10° C

20° C

24°

30°

35° C

40° C

45° C

45°

50°

50° C

55°

60°

120°

1.51

1.43

1.00

1.20

0.96

0.71

0.92

0.85

0.78

0.82

0.71

0.59

0.70

0.55

0.31

7.37

6.32

6.61

5.03

4.60

3.29

3.90

3.14

2.26

2.98

2.64

2.57

2.60

2.29

1.86

2.25

1.76

0.94

^ Scale uses poly[fv(GVGVP),fx(GXGVP)]. Poly(GVGVP) becomes reference for AT

^ T| is the onset temperature for the hydrophobic folding and assembly transition, that is, inverse temperature transition,

in pbs

(0.15

N NaCl,

0.01

M phosphate) as determined by light scattering. The values are linearly extrapolated to /x = 1

and rounded to a number divisible by 5. AH and AS are the values at fx = 0.2 on the curve for a linear fit of the DSC

derived endothermic heats and entropies of the transitions for the polymers in water.

"^ Per mole of pentamer.

'^ The calculated Tt value for Pro comes from poly(GVGVP) when the experimental values of Val and Gly are used. This

hydrophobicity value of -8° C is unique to the p-spiral structure, where there is hydrophobic contact between the Val)

7CH3 and the adjacent Pro? 5CH2 and the interturn Pro^+3pCH2 moieties.

' The experimental value determined from poly[/v(GVGVP),/p(GVGPP)].

5.1 Introduction 117

phosphorylation of the inner mitochondrial

membrane, the relationship between the

change of state of a redox group and proton

transport is central to the process of develop-

ing the proton gradient used to drive phospho-

rylation. As discussed in Chapter 8, section

8.3.4, during analysis of the structure and func-

tion of Complex III: ubiquinone: cytochrome c

oxidoreductase (the cytochrome bci complex)

of the electron transport chain of the inner

mitochondrial membrane, the oxidation of

ubiquinol to produce a positively charged

species and the reduction of ubiquinone to

produce a negatively charged species both

disrupt hydrophobic association to effect the

release of two protons from the former and the

uptake of two protons to the latter in effecting

proton transport. In this manner and in the

context of Tt, both the formation of positive

charge and the formation of negative charge

raise the value of Tt to disrupt hydrophobic

association and thereby to allow, respectively,

proton egress into the cytosol and ingress from

the matrix for net transport across the mem-

brane. In a different context, irreversible oxi-

dation of protein components represents a

means of inactivating protein function by irre-

versibly driving hydrophobic dissociation.

5.1.3.4.8 Moving the Trdivide by

Phosphorylation/Dephosphorylation

Phosphorylation, the covalent attachment of a

phosphate to an OH group, has been to date the

most effective way to raise the temperature of

the Tt-divide.Thus, dephosphorylation, removal

of phosphate, has been the most effective way

to lower the temperature of the Tt-divide and

thereby the most effective way to drive

hydrophobic association and its equivalent of

contraction. This is similar to a primary event in

muscle contraction (see Chapters 7 and

8).

The

shift in the Tj-divide on binding of ATP can be

as great as or greater than simple phosphoryla-

tion, depending on the interactions of ATP at

the binding site. As discussed in Chapter 8,

section 8.5, ATP binding drives hydrophobic

dissociation, whereas loss of phosphate drives

hydrophobic association both for the attach-

ment to actin and for the power stroke to

produce motion by the myosin II motor of

muscle contraction.

5.1.3.4.9 Moving the Tt-divide by Ion

Pairing with Oppositely Charged Vinegar-like

R-groups

The ion pairing of sodium ion, Na^, with nega-

tive carboxylate, COO", that is, COO"* • •Na^,

and the ion pairing of the ammonium ion func-

tional group of lysine (Lys, K) with the chloride

ion, that is, -NHa^ • • •CI", markedly lower

the Tt-divide. The effectiveness of ion pairing

in lowering the Tt-divide increases as the

hydrophobicity (oil-like character) of the

domain increases with which the charged

group is associated. Interestingly, chloride ion

(CI") bridges between the Val^(a-NH3^) and the

Arg^^^(guanidinium^) in the ion-pairing

network between subunits of deoxyhemoglo-

bin, and the hydrophobic association of the

deoxy state is further stabilized by the replace-

ment of the a-NHs^* • •CI" with the carbamate,

R-NH-COO", resulting from CO2 pick up in the

tissues (see Chapter 7). The most effective ion

pairing involves association, within a hydropho-

bic domain, of calcium ion with a pair of car-

boxylates, that is, -COO"* • •Ca^^* • •OOC-.

Again, this has a familiar ring as the triggering

event for muscle contraction (see Chapters 7

and 8).

5.1.3.4.10 Moving the Tfdivide by Changing

the Solvent, That Is, Adding Salt to

the Solution

Even when there are no vinegar-like (func-

tional) groups in the model protein, as is the

case for poly(GVGVP), adding salt, NaCl,

lowers the Tt-divide. This effect is very anemic,

however, requiring an order of magnitude

(some 10 times) more salt than when there is a

functional group with which to ion pair in order

to drive hydrophobic association.

5.1.3.4.11 Moving the Tt-divide by Changing

the Solvent, That is, Adding Organic Solutes

to the Solution

The most effective organic solute in raising the

Tfdivide is sodium dodecyl sulfate (SDS).

118

Consilient Mechanisms for Diverse Protein-based Machines

Much less effective is guanidinium hydrochlo-

ride,

followed by urea. Glycerol and ethylene

glycol have only a small effect in lowering the

Tfdivide, and trifluoroethanol is somewhat

more effective in lowering the Tfdivide. On this

basis,

the effectiveness of SDS polyacrylamide

(SDS-PAGE) gels in achieving protein separa-

tions based on size becomes apparent.

5.1.3.4.12 Moving the Tfdivide by Increasing

the Pressure

Especially when there are amino acid residues

with aromatic side chains, such as tryptophan

(Trp,

W), phenylalanine (Phe, F), and tyrosine

(Tyr, Y), increasing the pressure raises the tem-

perature of the Tj-divide and favors protein

unfolding (see the structures of the R-groups in

Table 5.1).

5.1.3.4.13 Moving the Tfdivide by a Bound

Chromophore That Changes Its Oil-like

Character on Absorbing Light

Any chromophore attached to the protein

that changes its hydrophobicity on absorbing a

photon of light will change the temperature of

the Tt-divide. The absorption of light is unique

among the energy conversions of the consilient

mechanism in that it is irreversible, for example,

stretching does not generally cause the emis-

sion of

light.

the best of our knowledge, there

is no simple reversal of a consilient process

driven by the absorption of light that can result

in the emission of the same frequency of elec-

tromagnetic energy. The energy of a relevant

photon is some 70kcal/mole, whereas the

energy output, AGHA(X)' will be an order of

magnitude less, that is, the energy changes of

biology are generally within ±8kcal/mole.^^

5.1.3.5 What Causes Loss of Solubility on

Raising the Temperature from Below to

Above the Trdivide?

By definition of the change in Gibbs free

energy, AG, solubiUty occurs when AG(solubil-

ity) is negative, and solubiUty is lost as AG(sol-

ubility) becomes positive. Here we restate that

shown very early by Butler.^^ AH is negative

and -TAS is positive when oil-like groups dis-

solve in water, that

is,

when hydrophobic hydra-

tion forms. Specifically, the addition of the four

CH2 moieties in the soluble alcohol series from

methanol to n-pentanol results in an average

AH/CH2 of -1.4kcal/mole-CH2, that is, forma-

tion of hydrophobic hydration results in a

favorable release of heat. But (-TAS/CH2) is

-hl.7kcal/mole-CH2. This is why solubility in

water is ultimately lost when enough CH2 moi-

eties have been added such that AG has become

positive.

Accordingly, for a fixed amount of hydropho-

bic hydration, simply raising the temperature

linearly increases the magnitude of the positive

(-TAS) term until it becomes greater than the

negative AH term, that is, until AG becomes

positive and solubility is lost. The result is the

association of hydrophobic groups as an inte-

gral part of the inverse temperature transition of

the hydrophobic folding and assembly transi-

tion. Solubility is lost, which is readily seen in

our model proteins as

phase separation, simply

because increasing the temperature increases

the magnitude of the positive

(-TAS)

term until

it becomes greater than the negative AH term.

Contrary to common description, solubility is

not lost because of thermal destructuring,

melting, or disordering of the hydrophobic

hydration.^^ As shown below in section 5.7.6

and Figure 5.27, the Tj-divide occurs at a higher

temperature when the amount of hydrophobic

hydration for a model protein composition

becomes less.

5.1.3.6 An Experimental Method

for Following Changes in

Hydrophobic Hydration

Improved insight into the role of hydrophobic-

ity in protein folding, assembly, and function

requires an experimental means with which to

estimate and follow changes in hydrophobic

hydration as a function of different variables.

Since the work of Butler^^ and of Frank and

Evans,^^ the search has been for an experimen-

tal method with which to characterize changes

in hydrophobic hydration and particularly to

do so during changes in functional state of

the protein. This goal was reached with the

5.1 Introduction

119

model proteins of focus here in part because

conditions are possible where most of the

water in the system can be hydrophobic

hydration.^^

The experimental method is microwave

dielectric relaxation, which uses the same

energy as that of a kitchen microwave oven.

Hydrophobic hydration absorbs energy in the

microwave frequency range at a slightly lower

frequency than liquid water absorbs energy in

microwave ovens to heat foods. It is now possi-

ble to follow the loss of hydrophobic hydration

as insolubility takes place, that is, as hydropho-

bic association occurs, which includes intra-

molecular hydrophobic folding and/or inter-

molecular assembly. Most significantly, in

section 5.7.3 and Figures 5.24 and 5.25, we can

see the loss of hydrophobic hydration as

hydrophobic association occurs and as vinegar-

hke groups ionize and take limited hydration

away from hydrophobic groups in the process

of obtaining their own hydration.

5.1.3.7 In Summary, Hydrophobic

Hydration Disappears for Two

Different Reasons with Opposite

Consequences of Insolubility

and Solubility

5.1.3.7.1 Hydrophobic Hydration Increases

with Increased Number of Oil-Uke Groups

Until Solubility Is Lost and Then

Hydrophobic Hydration Disappears

Hydrophobic hydration increases as the

number of oil-like groups increases, and then

it abruptly disappears when insolubility is

reached. As shown above with the expression

AG(solubility) = AH - TAS, insolubility occurs

as the positive (-TAS) term becomes greater

than the negative AH term. This is one reason

for the disappearance of hydrophobic hydra-

tion. Knowledge of the source of insolubility

due to hydrophobic association provides one of

the two primary keys to understanding changes

in protein folding during function. De novo

design of elastic-contractile model proteins for

diverse energy conversions using the Tt-based

hydrophobicity scale demonstrates the useful-

ness of this view.

5.1.3.7.2 Hydrophobic Hydration is

Destroyed as Proximal Vinegar-like Species

Achieve Hydration on Becoming Charged

Formation of charged species, by the very act

of requiring more hydration when ionized,

destroys proximal hydrophobic hydration in

the process of becoming charged. Consider a

spatially localized association of oil-like

domains in water. As the clusters of oil-like

groups representing each domain begin to dis-

sociate, hydrophobic hydration forms. As too

much hydrophobic hydration forms, the posi-

tive (-TAS) term becomes larger than the neg-

ative AH term, resulting in a positive AG, and

the association reforms. If, however, a proximal

charged species should form concurrently, the

nascent hydrophobic hydration is destroyed as

the ionizing vinegar-like species gains its hydra-

tion. The result is a negative AG and the disso-

ciation stands, that is, solubility occurs. To be

sure,

water molecules can continue to be adja-

cent to the exposed hydrophobic groups, but in

this case the water molecules may no longer

have the structure represented in Figure 2.8. In

our view, this is the second of the two primary

keys to understanding changes in protein

folding in the process of function. Experimen-

tal studies on model proteins, designed to

perform diverse energy conversions, as reviewed

in this chapter, exemplify these explanations.

5.1.4 Heating/Cooling Pumps Iron!

5.1.4.1 Raising the Temperature from

Below to Above the Temperature Interval

of the Phase Transition Produces Folding

and Association with the Result of Motion

The phase separated state of the parent elastic

protein-based polymer, (GVGVP)n/^ at 37° C is

about 50% polymer and 50% water by weight.

This was the composition for the transitions

represented in Figure 5.2. On exposure of this

state to 20 Mrad^^ of y-irradiation, a nearly ideal

elastic band forms^^ with properties similar to

those of the major elastic arteries. On lowering

the temperature to 25° C or below, the elastic

band swells and increases its volume 10-fold.

A return to body temperature, 37° C (98.6° F),

120

Consilient Mechanisms for Diverse Protein-based Machines

causes the band to contract by hydrophobic

association, which is to deswell. The y-

irradiation cross-Unked (GVGVP)n forms an

elastic-contractile band.

We then hang a weight on the elastic band at

25° C

and it stretches until the elastic force due

to deformation matches the attached weight.

We then raise the temperature to

37°

the

band contacts and lifts the weight. Insignificant

contraction occurs below

25°

and insignifi-

cant contraction occurs above

37°

In the tem-

perature interval from 25° to

37°

thermal

energy converts to the mechanical work of

lifting the weight (see Figures 2.4, 2.5, and

2.6A). This is pumping iron, which we all rec-

ognize as work. When thermal energy pumps

iron,

the technical term becomes thermo-

mechanical transduction. Thermal energy, by

way of this model protein-based machine, con-

verts into mechanical work.

5.1.4.2 Graphic Representation of

Transition from One State to Another as

Temperature Is Raised from Below to

Above a Temperature Interval

Figure 5.5A plots the independent variable,

temperature, and the resultant change in the

dependent variable, contraction. As noted

above, Httle change occurs below and little

change occurs above the temperature interval.

Also,

as noted below, adding chemical energy in

the form of increased concentration of salt

lowers the temperature range of the tempera-

ture interval.This

represents in graphic form the

depiction of thermally driven contraction in

Figure 2.4.

5.1.5 Pumping Iron without

Changing Temperature

5.1.5.1 Using Salt with an Uncharged

Polymer to Move the Temperature Interval

Over Which Thermally Driven

Contraction Occurs

The addition of

grams of NaCl, table salt, to

1 liter of water containing the elastic band of

cross-linked (GVGVP)n lowers the

temperature

interval for the phase separation by

15°

(This is approximately equal to dissolving the

entire contents of the common grocery store

container of table salt in 2 gallons of water.)

Now, raising the temperature from 10° to

25°

in this 1N salt solution causes the elastic strip

to contract and lift a weight. Under these

circumstances no significant contraction

occurred below

10°

and no significant con-

traction occurs above

25°

In the temperature

interval

from 10° to

25°

thermal energy again

performs mechanical work. Now the work of

lifting the weight is complete at

25°

C in

IN NaCl rather than at 37°C in salt-free

water.^^

When we again hang the weight on the

swollen elastic band at

25° C

in pure water and

then add the above noted quantity of salt, the

elastic band contracts and lifts the weight

without heating and without a change in tem-

perature. Further addition of salt at

25°

C has

only a limited effect. Addition of salt consti-

tutes an input of chemical energy, and, under

these circumstances, the addition of chemical

energy results in the performance of mechani-

cal work. The technical term is chemo-

mechanical transduction. Chemical energy, by

means of our model protein-based machine,

produces mechanical work without a change in

temperature. In the absence of a significant

vinegar-Uke R-group, an energy other than heat

can be used to produce mechanical work. In

this case, however, performance of a modest

amount of mechanical work required much

chemical energy. With the correct vinegar-like

R-group and chemical energy input, more effi-

cient chemo-mechanical transduction becomes

possible.

As shown in Figure 5.5B, the indepen-

dent variable can be chemical potential, the

change in Gibbs free energy per mole of chem-

ical added.

5.1.5.2 Using a Chemical Couple to

Lower the Temperature Interval from

Above to Below a Given Temperature

Rather Than Raising the Temperature

Living organisms function without the changes

in temperature required for thermomechanical

transduction by the consilient mechanism.

What makes the mechanism consilient or per-

vasive, however, is that many different energy

5.1 Introduction 121

inputs acting on many different vinegar-like R-

groups change the temperature interval over

which contraction occurs, and the resulting

energy conversions can be very efficient. Now,

as noted with the salt-driven contraction above,

it is emphasized that energy conversions occur

without a change in temperature.

In general, a change in polymer composition

provides a particular vinegar-like group with

which to access other energies. In this general

case,

the other energy input changes the

vinegar-like group from a less to a more oil-like

state.

The functional group of the major com-

ponent of vinegar provides a very effective

chemical couple, namely, -COOH/-COO".

The addition of acid,

H^,

to -COO" converts the

very vinegar-like carboxylate, -COO", to the

more oil-like -COOH. This protonation of a

single carboxylate group in the 100 residues of

poly(GVGVP) can lower the temperature

interval by tens of degrees centigrade and can

require far less chemical energy to pump iron

than is required in the NaCl example above for

the uncharged polymer. Protonation/deproto-

nation very efficiently pumps iron.

Alternatively, the amino/ammonium chemi-

cal couple, -NH2/-NH3^, functions similarly,

although the change from -NH2 to -NHs^ is

only about half as effective in changing the

value of Tt as is the -COOH/-COO" chemical

couple (see Table 5.1).

5.1.5.3 Electrons, Added to a Bound

Redox Couple, Lower the Temperature

Interval from Above to Below a Given

Temperature

Certain vitamins like B2 (riboflavin) and B3

(niacin) become chemically dressed up for

attachment to proteins. As such these attached

vitamins become redox couples that can accept

electrons (become reduced) and give up elec-

trons (become

oxidized).

A change in the redox

state changes the temperature interval for the

phase transition, that is, moves the Tt-divide.

Just as protonation of a carboxylate lowers the

temperature interval, so too does adding elec-

trons to the oxidized state of a redox couple.

Lowering the temperature interval from above

to below the operating temperature by reduc-

tion drives contraction and performs mechani-

cal work. The technical term is electro-

mechanical transduction. In short, reduction/

oxidation pumps iron.

5.1.5.4 Graphic Representation of the

Generalized Transition Zone for

Contraction Due to a Generalized

Independent (Intensive) Variable

As mentioned above in reference to Figure

5.5A, as the temperature is raised, contraction

of a band composed of elastic-contractile

model protein occurs. Contraction occurs as the

temperature is raised through a temperature

interval. Crossing over the Tfdivide, defined in

Figure 5.3, is to pass through the temperature

interval over which contraction occurs; it is the

result of the phase separation, specifically of

the inverse temperature transition. Further-

more, the temperature interval for contraction

occurs at a lower temperature when the model

protein is more hydrophobic and at a higher

temperature when the model protein is less

hydrophobic.

As noted above, the temperature interval

shifts on changing the concentration of a chem-

ical, that is, on changing the chemical potential

of a chemical for which the model protein is

responsive, as in protonation of a carboxylate.

Similarly, the temperature interval shifts on

changing the availability of electrons, that

is,

changing the electrochemical potential, such

that an oxidized component of a redox couple

becomes reduced.

Now, instead of plotting temperature, the

chemical potential or electrochemical potential

can be plotted, and contraction occurs as the

concentration of a chemical passes through the

critical range for reaction or as the availability

of electrons passes through a critical range to

achieve reduction. The range over which the

contraction occurs is the transition zone, and

the plot looks the same as in Figure 5.5A for

temperature. Thus, the graphic representation

in Figure 5.5B is common for all of the inde-

pendent variables, such as temperature, pres-

sure,

and chemical potential, that can drive

contraction, in which case contraction becomes

the dependent variable.

122

Consilient Mechanisms for Diverse Protein-based Machines

In this perspective, the independent variables

are the intensive variables of the free energy.

The input energy to drive contraction, for

example, is the product of two quantities, the

intensive variable times the extensive variable.

In the case of protonation of a carboxylate, the

intensive variable of chemical potential is pro-

portional to the change in concentration of the

protons over which the contraction occurs, and

the extensive variable is the number of protons

utilized in driving the contraction. In the case

of the intensive variable of temperature, the

extensive variable is the entropy of the transi-

tion (ASt), that is, the amount of heat (calories)

divided by the temperature, and the input

energy, of course, is simply the heat of the tran-

sition, AHt (= TtASt) at the Tj-divide.

5.1.6 Energy Conversions in Addition

to Pumping Iron

5.1.6.1 Energy Conversions Not Involving

Mechanical Work

There are at least six kinds of free energy that

interconvert by the consilient mechanism. They

are mechanical, thermal, pressure-volume,

chemical, electrical, and electromagnetic

energy, for example, light, and the correspond-

ing intensive variables are mechanical force,

temperature, pressure, chemical potential, elec-

trochemical potential, and electromagnetic

radiation frequency. Above we noted only three

energies (thermal, chemical, and electrical) of

the five that can provide input energy for the

performance of mechanical work. In fact any

pair of the five, leaving mechanical energy

aside, interconvert one into the other by the

consilient mechanism, as treated more fully

below in section 5.5. Immediately below we

note interconversion of the pair of energies,

chemical and electrical. In fact, some 18 classes

of pairwise energy conversions occur by the

consilient mechanism (see section 5.6).

5.1.6.2 Conversion of Electrical Energy

into Chemical Work and Vice Versa

When a properly designed model protein con-

tains both protonation/deprotonation chemical

couples and reduction/oxidation redox couples,

reduction drives contraction and protonation

drives contraction. Most importantly, how-

ever, reduction (electrons) drives proton (acid)

uptake, and protonation drives electron uptake.

The former is electro-chemical transduction,

and the latter is chemo-electrical transduction.

This is the nature of the consilient mechanism

as further described below. Two distinct energy

sources, each of which performs mechanical

work, can interconvert by effecting the changes

in hydrophobic folding and assembly of the

consilient mechanism.

5.1.7 The Consilient Mechanism in

a Nutshell: The Comprehensive

Hydrophobic Effect

5.1.7.1 Hydrophobic Replaces Oil-like

Hydrophobic, meaning water fearing, is the

more technical term for oil-like. Instead of

speaking of water surrounding oil-like group-

ings of atoms, or oil-like hydration, the term

hydrophobic hydration is generally used. Even

in the scientific community, however, those

not directly active in the field find the term

hydrophobic hydration contradictory and

troublesome. Nonetheless, hydration of hydro-

phobic groups does occur, as shown in the

pentagonal arrangements of water molecules in

Figure 2.8 surrounding an oil-like group, and

understanding the energetics of hydrophobic

hydration is central to the consilient mecha-

nism for function of protein-based machines.

Several key aspects of hydrophobic hydration

that constitute the comprehensive hydrophobic

effect are briefly noted in this section and then

expanded upon in section 5.7.

5.1.7.2 The Comprehensive Hydrophobic

Effect Results from the Actual or Potential

Hydrophobic Hydration That Can Occur

for a Pair of Associable Hydrophobic

Surfaces or Domains

If a pair of hydrophobic domains capable of

association and dissociation would have too

much hydrophobic hydration for a given tem-

5.1 Introduction 123

perature when fully exposed to water, the result

is insolubility of the domains, that is, hydropho-

bic association of the domains with loss of the

hydrophobic hydration. In our analysis we use

the change in Gibbs free energy, AG, which

governs solubility under common experimental

conditions of constant temperature and pres-

sure.

To reiterate, AG involves two terms. The

first term is the heat change (AH) that occurs,

for example, as the molecule dissolves in water.

When heat is released on dissolution, AH is neg-

ative. Release of heat on addition to water indi-

cates solubility. The second term is -TAS, where

AS is the entropy change on dissolution. In par-

ticular, AG(solubility) = AH - TAS. For the

result of insolubility of hydrophobic domains,

the (-TAS) term is positive and of greater mag-

nitude than the negative AH term.

5.1.7.3 Competition for Hydration

Between Apolar (Hydrophobic) and Polar

(e.g., Charged) Groups Controls Amount

of Hydrophobic Hydration

If a charged species appears proximal to

the associated pair of hydrophobic domains

(within a few nanometers) as the pair of

domains exhibit an opening fluctuation, the

ionizing species destructures the nascent

hydrophobic hydration in achieving its own

hydration."^'^^ The decrease in hydrophobic

hydration (in the number of pentagonally

arranged water molecules) results in a smaller

positive (-TAS) term, the negative AH term

dominates, and the hydrophobic domains dis-

sociate. Also, of course, association occurs at a

higher temperature when the positive (-TAS)

term becomes larger than the negative AH

term, that is, Tt is at a higher temperature.

5.1.7.4 The Competition for Hydration

Also Is Responsible for Large

Hydrophobic-induced pKa Shifts with

Positive Cooperativity That Results in

Efficient Protein-based Machines

Competition for hydration between polar (e.g.,

charged) and hydrophobic (apolar) groups,^^

called the apolar-polar repulsive free energy of

hydration, AGap, controls the amount

of hydrophobic hydration."^'^^ Competition for

limited hydration can result in large pKa

shifts,

because the vinegar-like group must do

the work of destroying hydrophobic hydration

in the process of obtaining its own adequate

hydration."^^'"^^ In particular, carboxyls occur as

part of hydrophobically associated domains

that undergo opening and closing fluctuations.

During an opening fluctuation, a carboxyl has

the opportunity to ionize, but if the hydropho-

bic hydration is too great it recovers its proton.

This continues until the pH is so high that the

chance of proton recovery is too small, and a

carboxylate forms, destructuring hydrophobic

hydration to do

so.

The first carboxylate to form

reached out a significant distance in gathering

its hydration shell. The next carboxyl that

has the opportunity to form a carboxylate

during an opening fluctuation finds it has less

hydrophobic hydration to destructure, and

as a consequence its probability of remaining

ionized increases. Thus the probability for the

third carboxyl to remain ionized is even

greater, and so on. This is positive cooperativity

described at the molecular level. The positive

cooperativity arises out of competition for

hydration between hydrophobic and charged

groups, and the mechanism requires that the

energetics of hydrophobic-induced pKa shifts

parallel the energetics reflected in the Hill

coefficient that describes cooperativity. As

shown in Figures 1.2 and 1.3 for Model proteins

i, ii, iii, iv, and v and as will be further con-

sidered in section 5.8, nonlinear increases in

pKa resulting from linear increases in hydro-

phobicity parallel nonlinear increases in Hill

coefficients.

5.1.7.5 Competition by Positively and

Negatively Charged Species for Hydration

that Is Too Limited by Strongly Held

Hydrophobic Hydration is Responsible for

Ion Pair Formation in Protein Folding and

Assembly

Consider an ion pair-containing hydrophobic

association induced to open, due to the emer-

gence of a new proximal polar (e.g., charged)

species. These newly emergent charged species

124

Consilient Mechanisms for Diverse Protein-based Machines

(formerly ion paired in the associated hydro-

phobic domains) propagate destruction of

hydrophobic hydration, causing further re-

moved hydrophobic domains to dissociate. In

this manner, hydrophobic disassociation with

emergence of separated positive and negative

groups propagates hydrophobic dissociation

outv^ard many nanometers in a domino-like

effect. As a consequence, hydrophobic dissoci-

ations occur in a positively cooperative manner

with the result of efficient free energy

transduction."^^

Thus,

common in the consilient mechanism is

formation of ion pairs, the association of nega-

tively charged with positively charged vinegar-

like groups, each of which are part of an oil-like

domain. The association of oppositely charged

groups from two separate oil-like domains

occurs as the oil-like property of the domains

gains dominance, but then dissociation occurs

as the pair of oil-like domains lose dominance

on introduction of a new more polar group, for

example, as a charged vinegar-like component

is introduced into the vicinity of ion-pair-

containing hydrophobic domains.

5.1.7.6 Multidimensional Representations

of Protein-based Polymer Function as

Molecular Machines

5.1.7.6.1 Seven-dimensional Phase

Transitional Space for Protein-based Polymer

Function as Molecular Machines

The position of the Tt-divide that separates

soluble from insoluble (hydrophobically associ-

ated) states in the phase diagram depends on

seven variables: on the six intensive variables"^^

of temperature, chemical potential, electro-

chemical potential, mechanical force, pressure,

and electromagnetic radiation, and on polymer

volume fraction or concentration. Therefore,

diverse protein-catalyzed energy conversions

by the consilient mechanism result from

designs that control the location of the Tfdivide

in this seven-dimensional phase transitional

space. Complete mathematical description has

yet to be written for representation of the Tt-

divide in seven-dimensional phase transitional

space, but it may prove to be more relevant to

molecular machines to develop representation

of energy conversion in multidimensional free

energy space.

5.1.7.6.2 Multidimensional Free Energy

Space for Protein-based Polymer Function as

Molecular Machines

On inclusion of the six energies interconverted

by the consilient mechanism (see Figure 5.2,

below) with the concentration dependence

results in a seven-dimensional free energy

space. In this connection a relationship between

the magnitude of the shift of the Tj-divide

and the change in Gibbs free energy of the

protein-based polymer is given in Equation

(5.9).

Knowledge of the relevant ASt(reference)

in Equation (5.9) for a given variable, %,

would allow calculation of the complete %-

dimensional, energy conversion landscape of

relevance to a specific protein-based machine.

More comprehensive yet would be to break

down each of the six energies into their

intensive and extensive variables. In this case,

the general description for energy conver-

sion becomes a 13-dimensional, free energy

landscape for energy conversion by diverse

protein-based machines. In practice, graphic

representations usually plot two dimensions

or at most three dimensions. Nonetheless,

complete description of this multidimensional

dependency is required for the desired level of

understanding of protein function and in order

most effectively to engineer diverse protein-

based machines.

5.2 Molecular Structure and

Elasticity of Model Protein

Early reviews are available on the development

of the molecular conformation of the tetrapep-

tide,

pentapeptide, and hexapeptide repeating

sequences of elastin'^^'*^' and on the mechanism

of elasticity of the basic elastic-contractile

model protein."^^'"^^ These may be sought for

historical background. Recent reviews of

the mechanism of elasticity"^^"^^ and its relation

to contractility^ may be examined for a more