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

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5.4 Visual Observation of Elastic Protein-based Machines at Work

155

Using the simplified representation of a

single chain of model protein in Figure 5.16,^^

reaction (i) depicts the addition of proton to a

carboxylate.This restores so much hydrophobic

hydration in an intermediate for contraction

such that a larger positive (-TAS) term results

in the insolubility of the oil-like groups and the

chain folds in a contraction. In reality, of course,

the fundamental structure is a multistranded

twisted filament, and the result is a more

complex hydrophobic association involving a

concerted hydrophobic folding and assembly.

Also,

the relation between increased hydropho-

bic hydration and contraction (hydrophobic

folding and assembly) is given below in

section 5.7.

5.4.3.3.2 Addition of Base Can Drive

Contraction by Lowering Temperature

Interval for Heat-driven Contraction

Considering reaction (ii) of Figure 5.16, addi-

tion of base (hydroxyl ion, OH") converts

the positively charged vinegar-like R-group

(-CH2-CH2-CH2-CH2-NH3^) of the lysine

residue to -CH2-CH2-CH2-CH2-NH2, that

is,

-CH2-CH2-CH2-CH2-NH3^ + OH" ->

-CH2-CH2-CH2-CH2-NH2 + H2O.

In the model protein, poly[4(GVGVP),

(GKGVP)] with a ratio of four GVGVP pen-

tamers to one GKGVP pentamer, there is one

lysine residue, designated by the letter K, in 25

residues. This model protein remains soluble in

(/)

OH-

(ii)

(///)

©or0

(/V)

Disordered

bulk water

Spontaneously folding

because transition

temperature is now below

body temperature

Carboxylate (/)

NH|(//)

Positively charged nicotinamide (///)

Carboxylate that pairs with a cation or

an amino group that pairs with an anion (/V)

Carboxyl (/)

NH2 (//)

Uncharged nicotinamide

{Hi)

Ion pair (/V)

Q Very hydrophobic

phenylalanine side chain

FIGURE 5.16. Contraction of a p-spiral as the result

of four different types of reactions that cause

the structure to become more hydrophobic. The

fully hydrated intermediate state is only to indicate

restored hydration potential if hydrophobic associa-

tion had not occurred. (Reproduced with permission

from Urry.^^)

156

Consilient Mechanisms for Diverse Protein-based Machines

neutral or acidic water; it will not begin aggre-

gation in physiological saline until the temper-

ature is greater than 45° C, and the rubber-like

band formed by cross-linking this model protein

will not begin to contract unless the tempera-

ture is greater than 45° C. The temperature

interval begins just above 45° C. If hydroxyl

ion is added to the polymer solution sufficient

to convert all side chains to -CH2-CH2-

CH2-CH2-NH2, then aggregation begins at 28°

C and is complete by 45° C, that is, the temper-

ature interval is now from 28° to 45° C. Simi-

larly, for the cross-linked elastomer, contraction

occurs over the temperature interval from 28°

C to 45° C. Removal of the charged proton to

form the -CH2-CH2-CH2-CH2-NH2 results in

a more oil-like R-group so that the separation

of oil-like R-groups from water occurs at a

lower temperature. With this composition of

model protein, the chemical energy of increas-

ing hydroxyl ion concentration transforms into

the mechanical energy of pumping iron.

Again using the simplified representation of

a single chain of model protein in Figure 5.16,

reaction (ii) depicts the removal of a proton

from an ammonium, NHs^. Forming the

uncharged NH2 restores so much hydrophobic

hydration that a more positive (-TAS) term

causes AG(solubility) to become positive,

resulting in insolubility of the oil-like groups,

and the chain folds in a contraction due to

hydrophobic association.

5.4.3.3.3 Ion Pairing Drives Contraction

by Lowering Temperature Interval for

Heat-driven Contraction

Whether using a model protein with a negatively

charged functional group or one with a posi-

tively charged functional group, pairing with an

oppositely charged ion lowers the temperature

interval for heat-driven hydrophobic associa-

tion. Correspondingly, ion pairing in the cross-

linked elastic matrix moves the system through

the transition zone and drives contraction.

Once more using the simplified representa-

tion of a single chain of the model protein in

Figure 5.16, reaction (iv) depicts the addition

of a counter-ion to the oppositely charged

vinegar-like group. Partial neutralization of the

charged functional group provides yet another

means of restoring sufficient hydrophobic

hydration that the (-TAS) term becomes even

more positive. This results in AG(solubility)

becoming positive and the oil-like groups

becoming insolubile, and again the chain

hydrophobically folds in a contraction.

5.4.4 Electrical Energy Produces

Mechanical Work of Lifting Weight

(Increasing the Electrochemical

Potential Through the Transition Zone

to Reduce Oxidized Redox Groups

Drives Contraction)

5,4.4.1 Reduction (Adding Electrons)

Drives Contraction by Lowering

Temperature Interval for

Heat-driven Contraction

Reduction of the oxidized nicotinamide

(N-methyl nicotinamide, NMeN^) in poly[0.73

(GVGVP),0.27(GK{NMeN}GVP)] lowers the

temperature for the onset of the temperature

interval from 49° to 9° C, for a 60% reduction.^^

When forming the cross-Unked elastic matrix,

as shown in Figure 5.17 at room temperature

and as available in video, reduction drives con-

traction and oxidation drives relaxation.^^

Again with the simplified representation of a

single chain of model protein in Figure 5.16,

reaction (iii) depicts the addition of a negative

electron to a positively charged component

of a redox couple. Forming the reduced,

uncharged component of the redox couple,

again, restores so much hydrophobic hydration

that a positive (-TAS) term causes AG(solubil-

ity) to become positive, resulting in insolubility

of the oil-like groups, and the chain folds due

to hydrophobic association with the result of a

contraction.

5.4.5 Pressure-Volume Energy

Produces Mechanical Work (MW)

(Lowering Pressure Through the

Transition Zone Drives Contraction)

When aromatic groups are present, the appH-

cation of pressure increases the value of Tt.

Pressure increases the temperature range over

which the temperature interval occurs. The

order of responsiveness to increases in pressure

5.4 Visual Observation of Elastic Protein-based Machines at Work 157

A Flow Through B X20.poly[0.73(GVGVP),0.27(GK{NMeN}GVP)]

Electro-Mechanical Redox Video Data

Transduction Cell

L reduced

Dithionite

L oxidized

Ferricyanide

50 100

Time (min)

250

FIGURE

5.17.

Reduction-driven contraction of model

protein as an elastic sheet containing a redox couple.

(A) Flow through cell for reductant and oxidant con-

taining elastic band suspending a weight that is lifted

and lowered. (B) Plot from video showing length

changes attending reduction (contraction) and

oxidation (relaxation). (Reproduced with permission

from Urry et al.^^)

is tryptophan

(Trp,

W) > phenylalanine (Phe, F)

> tyrosine (Tyr,

Y).^"^

Thus, the apphcation of

pressure can drive unfolding, and the release of

pressure can be used to drive contraction.^^ This

has also been captured by video using a model

protein containing aromatic phenylalanine

residues where application of pressure lowers

the weight and removal of pressure causes

contraction.

5.4.6 Electromagnetic (Light) Energy

Produces Mechanical Work

(Electromagnetic Radiation That

Moves Tt Through the Transition Zone

Drives Contraction/Relaxation)

Any interaction of light that causes a change in

the oil-like character of the model protein will

change the value of Tt and hence will change

the location of the temperature interval with

the result of a change in the state of folding.

A simple result of the absorption of hght by

a chromophoric group is the trans to cis

geometrical isomer transformation. In two

light-absorbing molecules, one of biological

origin, cinnamide and the other, azobenzene,

the absorption of 300 nm light converts the cin-

namide molecule from a trans to a cis geomet-

rical isomer. In both cases this light-driven

conversion raises the value of Tt and can be

used to drive unfolding of a model protein to

which it is attached.^^'^^ Either a different wave-

length of light or thermal energy can reverse

the isomerization and result in the hydrophobic

association of contraction.

The results of sections 5.4.3, 5.4.4, 5.4.5, and

5.4.6 form the experimental observations that

give rise to Axiom 3.

158

Consilient Mechanisms for Diverse Protein-based Machines

Axiom

At constant

temperaturCy

an energy

input that changes the temperature interval for

thermally driven hydrophobic association in a

model protein can drive contraction^ that

is,

oil-

like folding and assembly, with the performance

of mechanical work; in other words, the energy

input moves the system through the transition

zone for contraction due to hydrophobic

association.

5.4.7 Summary of Consilient

Protein-based Machines (Engines and

Motors) That Pump Iron, That

Is,

That

Produce Motion

The term machine is a general designation for

any device that converts energy from one form

to another. The particular type of machine that

performs mechanical work or produces motion

is commonly called either a motor or an engine.

Here, we summarize the capacity of protein-

based machines to perform mechanical work

(pump iron) by the consilient mechanism of

hydrophobic association by utilizing a number

of different energy inputs.

5.4,7.1 Pumping Iron by Raising and

Lowering the Temperature Through

the Temperature Interval

Figure 5.18A uses the representation of a single

p-spiral in the extended and contracted states.

The sigmoid curve at a represents the folding

of, and defines the temperature interval for, a

more oil-like model protein chain and that at

b represents the folding of, and defines the

temperature interval for, a less oil-Hke model

protein. Any energy input that makes more

oil-like the model protein with the temperature

interval at b lowers the temperature interval of

b toward that of a and defines the transition

zone c for that energy input. Figure 5.18B, 1),

represents the contraction of a band of elastic

model protein when heating through the tem-

perature interval for hydrophobic folding and

assembly of the model protein.

5.4.7.1.1 Pumping Iron by Protonation of a

Carboxylate (COO" -^ COOH) to Make the

Model Protein More Oil-like

Increasing the concentration of acid, H^, con-

stitutes a particular chemical energy input. The

addition of acid (H^), over the concentration

range that protonates the carboxylate, lowers

the temperature interval for the model protein,

drives contraction, and defines the transition

zone for this energy input indicated as c in

Figure 5.ISA. Figure 5.18B, 2a), represents the

contraction and relaxation by reversible proto-

nation and deprotonation of the carboxyl

functional group, i.e., chemo-mechanical

transduction.

5.4.7.1.2 Pumping Iron by Adding Salt to a

Neutral Model Protein or to a Model Protein

with a Charged Functional Group

Simply by the addition of NaCl, for example, to

a model protein with no ionized functional

groups can lower the temperature interval,

define a transition zone, and drive contraction.

The change in salt concentration required to

drive contraction of an uncharged model

protein can be 10 times more than if a charged

functional group is present. Driving contraction

when there is a charged group to which a

counter-ion from the salt can ion pair requires

a much smaller change in concentration of salt,

that is, a smaller chemical energy input. The

energy conversion achieved by ion pairing is

much more efficient. Both uses of salts are rep-

resented in Figure 5.18B, 2b).

5.4.7.2 Pumping Iron by Reduction of an

Oxidized Functional Group Attached to

the Model Protein

Figure 5.17 shows direct experimental results,

which give rise to the generalized representa-

tion in Figure 5.18,3). In the case of Figure 5.17,

for every 100 residues of model protein, there

are 5.4 lysine residues to each of which is

attached an N-methyl nicotinamide (NMeN)

group. When oxidized, the circumstance is as

indicated by temperature interval b of Figure

5.4 Visual Observation of Elastic Protein-based Machines at Work

159

Performance of Mechanical Work by the Consilient l\/lechanism of Hydrophobic Folding and Assembly

contracted!

relaxed

a. Means of driving contraction b Means of effecting relaxation

p raising the temperature 1) lowering the temperature

transition

I zone for i

j non themnal -

energy

j inputs

J--—------

•/*—i—AT,-

tenf>perature —-^^

interval a for » PCj

more oil-like

temperature

•^interval b for

less oil-like

2a) intrinsic chemical change

e.g.

COO' —^ COOH

(adding add)

2b) extrinsic chemical change

e.g.

adding salt

3) reducing prosthetic group

e.g.

reduction of nicotinamide

4) release of pressure

when aromatic residues

present

5) light-effected photochemical

reaction of suitable

2a) intrinsic chemical change

e.g.

COOH —^ COO"

2b) extrinsic chemical change

e.g.

wash out of salt

3) oxidizing prosthetic group

4) application of pressure

when aromatic residues

present

5) reversing effect of

_(*p.rnophore

^fl'!?!!!".

contracted

relaxed

r~i

Isothermal Energy Conversions

When in the Temperature Range c

?T^

«1

.8.

time

FIGURE

5.18. Performance of mechanical work by hydrophobic association. See text for discussion,

designed protein-based engines: Different energy (Reproduced with permission from Urry.^)

inputs "pump iron" by lowering

AGHA(X)

to drive

5.18A.

On reduction by the chemical dithionite,

the temperature interval for thermally driven

contraction lowers to a temperature interval a

and thereby moves the elastic band through the

transition zone c. Contraction results when the

operating temperature is in zone c. Oxidation

by the chemical ferricyanide relaxes the elastic

band and completes the reduction-oxidation

cycle to return the band and the attached

weight to its original state. With the proper

mediator molecules to diffuse between elec-

trode and redox couple in the cross-linked

matrix, the reduction and oxidation can be

carried out electrically; thus this may correctly

be called electro-mechanical transduction.

5.4.7.3

Pumping Iron by Changing the

Pressure Using Model Proteins with

Aromatic (Large Oil-like Ring Structures)

Side Chains

The appUcation of pressure, when there are

aromatic amino acids in the polymer such as

tryptophan (Trp, W), phenylalanine (Phe, F),

and tyrosine (Tyr, Y) as defined in Table 5.1,

raises the temperature interval from a to b of

Figure

5.18A.

Accordingly, as indicated in

Figure 5.18B, 4), the application of pressure can

cause relaxation, and the release of pressure

can result in contraction with the lifting of a

weight.^^ This is baro-mechanical transduction.

160

Consilient Mechanisms for Diverse Protein-based Machines

5.4.7,4 Pumping Iron by Using Light to

Change the Oil-like Character of a

Chromophore Attached to the

Model Protein

To obtain a change in hydrophobic association

in response to Ught, the natural product cin-

namic acid was attached to a lysine (Lys, K)

residue of the polymer to form the cinnamide.

With a protein-based polymer having IK

residue per 30 residues and generally 21

30-mers forming the high molecular weight

protein-based polymer, the structure can be

represented as (H5C6-CH=CH-CO-NH-

Lys)-polymer. The orientation about the

-CH=CH- bond can be either trans or cis. To

begin with, the configuration is 100% trans, and,

when it absorbs 300 nm ultraviolet light, it con-

verts to about 90% cis. Conversion of cis back

to trans occurs with

270

nm ultraviolet

Ught.

The

temperature interval for the cis isomer occurs

at a higher temperature, like interval b of

Figure 5.18A, while that of the trans isomer

occurs over the lower temperature interval, a.

The trans isomer is more oil-like than the cis

isomer. The change in Tt on an fx = 1 basis

is about 60° C.^^ Figure 5.18B, 5) represents

photo-mechanical transduction.

5.4.7.5 The Set of Energies and Intensive

Variables (Bold Faced) Involved in Using

Model Proteins as Molecular Engines

and Motors

Mechanical work = mechanical force x

distance lifted = fAL = mgh

Pressure-volume = pressure x volume =

PxV

Chemical energy = chemical potential x

number of moles used =

A)X

x An

Thermal energy = heat of the transition =

AHt = temperature x entropy = TASt

Electrical energy = electrochemical potential x

number of electrons used = zFAE x An

Electromagnetic radiation = photon energy(hv)

number of photons used = hv N

5.5 Energy Conversions Due to

Coupling of Functional Groups

Here we discuss the coupling of functional

groups as part of the general phenomena of

action and reaction and most specifically as

an integral part of the consilient mechanism

of energy conversion. The argument may be

given using two statements that derive from

experimental observations to be presented

below.

Statement 1: Within the context of the

hydrophobic consilient mechanism, a func-

tional group is a chemical entity that can exist

in one of two or more interconvertible states,

each with a different hydrophobicity, as mea-

sured by the Tt-based and AGnA-based hydro-

phobicity scales (see Tables 5.1, 5.2 and 5.3).

Examples of functional groups, each with a

strong dependence on hydrophobicity, are:

1) lonizable functional groups that are a

function of pH (the change in chemical poten-

tial of proton,

A|XH)

and exhibit hydrophobicity

dependent pKa values.

2) Redox functional groups with hydro-

phobicity dependent reduction potentials for

conversion between oxidized and reduced

states.

3) Groups that change their state on absorp-

tion of light, e.g., convert from trans to cis.

4) A functional group such as a hydroxyl

that can be reversibly, e.g., enzymatically, phos-

phorylated and dephosphorylated).

Statement

Because the uncharged states of

ionizable functional groups and the reduced

states of oxidized functional groups are each

more oil-like or hydrophobic than the charged

and oxidized states, the formation of the more

hydrophobic state of one functional group can

cause the more polar state of a second kind of

attached and responsive functional group to

convert to its more hydrophobic state. This is

the coupling of functions by the consilient

mechanism!

In particular, the reduction of NMeN^

approximates the replacement of several valine

residues by phenylalanine residues. Just as

5.5 Energy Conversions Due to Coupling of Functional Groups

161

increasing the hydrophobicity of a polymer

causes the protonation of a carboxylate to

occur at a lower acid concentration, it is to be

expected, therefore, that the reduction of

NMeN^ would lower the acid concentration

required to protonate a carboxylate attached to

the same hydrophobic domain.

By the consilient mechanism, energy conver-

sions due to coupling of functional groups result

from a common dependence of the different

functional groups on hydrophobicity of the

model protein. This common dependence of

the essential property of different functional

groups (e.g., pKa, reduction potential) on

hydrophobicity makes possible energy conver-

sion by the coupling of functions using the con-

silient mechanism as described in more detail

below.

5.5.1 Action Begets Reaction

5.5.1.1 For Protein-based Machines Input

Energy Constitutes the Action and Output

Energy Constitutes the Reaction

In physics and chemistry a number of laws, rela-

tions,

and principles are statements that some

action (commonly expressible as an energy

input) causes a reaction (commonly expressible

as an energy output). Examples are Guldberg

and Waage's law of mass action for chemical

reactions, Onsager's reciprocal relations for

transport processes, and Newton's third law of

motion where a force acting on an object results

in a matching reaction force.

Another example is the Principle of Le

ChateUer, which may be stated as follows: For

any system at rest (at equilibrium) the intro-

duction of a stress (in our case an input energy)

causes the system to react in such a way as to

relieve the stress (in our case by an output

energy). This principle reasonably describes

protein-catalyzed energy conversion, that

is,

the

function of protein-based machines. Under

prescribed conditions, properly designed model

protein-based machines exhibit a behavior

where for each action there is a reaction. In

section 5.4, regardless of the action, which was

any one of several different input energies, the

performance of mechanical work was the reac-

tion (there was a common output energy). In

this section the energy inputs, which individu-

ally caused contraction, convert one into the

other by their common dependence on the

change in free energy of the hydrophobically

associated (contracted)

state.

This provides

def-

inition of the subset of protein-based machines

that, despite utilizing the hydrophobic con-

silient mechanism of hydrophobic association,

are not characterized as having mechanical

work as their output energy.

5.5.1.2 For Protein-based Machines, the

Input Energy Must Occur Through the

Transition Zone

Energy input must occur through the transition

zone,

which is determined by the design of

polymer composition, to operate under the

conditions in which the machine is to function.

The change in temperature, in concentration of

solute, in availability of electrons, and so forth,

must be such that the change in the indepen-

dent (intensive) variable traverses the transi-

tion zone of the model protein. When the

variable is temperature, that

is,

when heat is the

energy input, the transition zone would be the

temperature interval (see Figures 5.1 and 5.5A)

and the energy output can be contraction.

When the variable is an increase in the amount

of acid, H^, in solution, that is, an increase in

chemical energy per mole of proton, the transi-

tion zone (see Figure 5.5B) defines the range

for the change in concentration of acid (chem-

ical potential) that converts, for example,

-COO"

to -COOH, and contraction again can

be the energy output. When the variable is the

availabihty of electrons, that

is,

electrical energy

is the input, the transition zone defines the

change in electrochemical potential required to

change an oxidized component of a redox

couple to the reduced component, and again

contraction can be the energy output.

5.5.1.3 A Functional Group Can Occur

in Either One of at Least Two

Different States

Recall that a functional group, for example, a

vinegar-like group, can occur in either one of

162

Consilient Mechanisms for Diverse Protein-based Machines

two or more different states. In general, one

state of a functional group is more oil-like,

and another is more vinegar-like. To say one is

less polar and the other is more polar is an eq-

uivalent statement. The carboxyl/carboxylate,

COOH/COO", pair represents one example of a

functional group, where COOH is more oil-like

(less polar) and COO" is less oil-like (more

polar).

The organic phosphate group can occur

in three different states,-OPOs^,-OPO3H-, and

-OPO3H2, in order of decreasing polarity and

increasing oil-like character. In these cases, the

proton, H^, is the chemical entity that is added

or released. Another functional group is the

redox couple, NMeN"^ and NMeN, where the net

addition of two electron, 2e", and a proton con-

verts the more polar NMeN^ to the more oil-like

(less polar) NMeNH.

5.5.1,4 Each State of a Functional Group

Couples to the States of Another

Functional Group by Contributing to and

Being Affected by the Oil-like Character

of the Polymer

Recall also from section 5.3 that the value of Tj

provides one measure of the oil-Uke character

or hydrophobicity of the model protein. A

lower value of Tt means a more oil-like charac-

ter for the model protein. Accordingly, the cou-

pling of one functional group to another, that is,

the conversion of energy represented by one

functional group to the form represented by

another functional group, occurs because each

energy change has the common action of effect-

ing and being affected by the change in free

energy of hydrophobic association,

AGHA-

5.5.2 Hydrophobicity (Degree of

Oil-like Character) Positions

Transition Zone

5.5.2.1 Changing the Oil-like Character by

Progressive Addition of More Oil-like Phe

Groups Moves the Temperature Interval

(Transition Zone) to Lower Temperatures

When the transition zone is specifically the tem-

perature interval, any change in oil-like charac-

ter of the model protein-based machine moves

the temperature range over which the temper-

ature interval occurs. Specifically, the replace-

ment of a less hydrophobic valine (Val, V)

residue by the more hydrophobic phenylala-

nine (Phe, F) residue lowers and narrows the

temperature interval over which hydrophobic

association occurs. This is schematically repre-

sented in Figure S.IQA,"^ which shows what

happens to a curve like that of Figure 5.5A,

when the polymer involved is subjected to a

systematic change in its oil-like character. As

discussed below, any change in oil-like charac-

ter can move the transition zone of any process

that can itself change the temperature interval

(i.e.,

move the Tj-divide; see sections

5.1.3.4

and

5.3).

5.5.2.2 Changing Oil-like Character by

Progressive Addition of More Oil-like Phe

Groups Moves the Transition Zone,

Increases Affinity of the COOH/COO'

Chemical Couple for Protons, and

Decreases the Change in Chemical Energy

Required to Protonate

Figure 5.19B represents the series of curves that

result when the polymer series containing the

COOH/COO" chemical couple is designed

with systematic changes in hydrophobicity.'* In

practice the polymer may be from the family

(GVGVP GVGXP GEGXP GVGVP GVGXP

GXGXP)n, where E is the glutamic acid residue

with its carboxyl function and X may be either

the less hydrophobic V or the more hydropho-

bic F residue. The less oil-like polymer would

have V at all positions indicated by X. Then, as

more positions indicated by X have their V

residue replaced by the more oil-like F residue,

the curves shift to indicate that lower concen-

trations of acid are able to protonate the

carboxyl, and the protonation occurs over a

narrower transition zone. The same family of

curves is obtained for (GVGVP GVGXP

GKGXP GVGVP GVGXP GXGXP)^, where

K is the lysine residue with its amine chemical

couple (-NH2/-NH3^) but where the indepen-

dent variable involves the concentration of

base (the hydroxyl ion, OH"). Both families of

curves take on the same form as found when

the energy input was thermal in Figure 5.19A.

5.5 Energy Conversions Due to Coupling of Functional Groups

163

100—^

P. o

(COOH) 100 J

(COO-)o

less

hydrophobic

—T"

physiological

pH (7.4)

/_.

^ , /* /' ,- ,- ,- yi

less

hydrophobi?/

[/ / / / /

/^droptobic

/ /''

/' /' /' /b

/ ' -' /

f ••* '' I—^ r

8.0 (pH) 4.0

base w acid

availability of protons

(proton chemical potential)

(reduced) 100 H

•Z3

(oxidized) 0

hydrophobic

less

hydrophobic

electrochemical potential

availability of electrons

FIGURE

5.19. Demonstration of the similar form of

the hydrophobic dependence of contractions inde-

pendent of the form of energy used as long as the

model protein is properly designed for the respective

energy input. (A) Thermally driven contraction due

to hydrophobic association. (B) Protonation-driven

contraction due to hydrophobic association when

acting on a protonatable functional group within

the model protein. (C) Reduction-driven contraction

due to hydrophobic association when acting on a

redox functional group within the model protein.

(Adapted with permission from Urry."^)

164

Consilient Mechanisms for Diverse Protein-based Machines

5.5.2.3 Changing the Oil-like Character by

Progressive Addition of More Oil-like Phe

Groups Moves the Transition Zone,

Increases Affinity of the NMeN/NMeN^

Redox Couple for Electrons, and

Decreases the Electrical Energy Required

to Reduce

Figure 5.19C represents the series of curves that

result when the polymer series containing the

NMeN/NMeN^ redox couple is also designed

with systematic changes in hydrophobicity."^ The

same family of polymers can be designed as

used for the lysine residue, but in this case the

lysine residue is utilized for attachment of the

N-methyl nicotinamide (NMeN), that is,

(GVGVP GVGXP GK[NMeN]GXP GVGVP

GVGXP GXGXP)n. Again, as less oil-like Val

(V) residues are systematically replaced by

more oil-like Phe (F) residues, a lower concen-

tration of electrons (a lower electrochemical

potential) reduces the oxidized state of the

redox couple. Again, the family of curves take

on the same form as occurs when chemical

energy was the input energy and when thermal

energy was the input energy, as in Figure

5.19A,B.

5.5.2.4 Changing the Oil-like Character of

a Model Protein by Any Energy Input, %,

That Moves the Transition Zone Can Be

Used to Change the Energy of a

Functional Group That Is Also Capable of

Changing the Oil-like Character of the

Model Protein

Additional input energies can be light energy

interacting with a chromophore to change its

hydrophobicity and pressure-volume energy

acting most effectively on aromatic groups to

change their expression of hydrophobicity.

Many other interaction energies come from

the electromagnetic frequency spectrum. They

can come from outside of the ultraviolet,

visible, and infrared frequency ranges. All that

is required is an element of the model protein

in water that is able to take up the energy. The

dipole moment of the peptide group with its

positive end at the NH and its negative end at

the oxygen of the CO provides one site of inter-

action. The acoustic and radio frequency ranges

of the electromagnetic radiation spectrum rep-

resent two frequency ranges that are funda-

mental to our elastic model proteins capable of

exhibiting inverse temperature transitions.

When subjected to oscillating electric fields

near

kHz (acoustic frequency) and

MHz

(radio frequency), the peptide group of the

protein backbone reorients its dipole moment

and oscillates with the appUed oscillating elec-

tric fields in these frequency ranges. The uptake

of these energies by the elastic model proteins

change the internal chain dynamics and are

expected to alter the force exerted by a slightly

extended polymer. Of more direct concern to a

change in free energy of hydrophobic associa-

tion dependent on the amount or potential

amount of hydrophobic hydration is the 5 GHz

absorption (microwave frequency) exhibited by

hydrophobic hydration itself (see section 5.7).

Energy absorbed directly by hydrophobic

hydration is expected to affect the TAS

controlling solubility (i.e., hydrophobic

association)

The innumerable ways in which the value of

Tt can be changed constitute the number of

energy inputs, x, that can drive protein-based

machines.

5.5.3 Coupling of Functional Groups

by Means of the Consilient

Mechanism and by Means of Their

Common Dependence on the Gibbs

Free Energy of Hydrophobic

Association,

AGHA

The energy input to a first functional group

causes a change in the free energy of the

hydrophobically associated state,

AG^A-

That

AG/M then causes a change in the free energy of

a second functional group. This is the coupling

of functions by the consilient mechanism. It rep-

resents the most explicit expression of the com-

prehensive hydrophobic effect.

Section 5.4.3 and Tables 5.2 to 5.4 list many

calculated estimates of AGHA arising from many

different energy

inputs.

The estimated values of

AGHA

provide a quantitative measure of how a

given energy input changes the energy of the

hydrophobically associated state. This provides