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

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5.2 Molecular Structure and Elasticity of Model Protein

125

detailed treatment than the brief comments

given here.

5.2.1 The Sequence of Amino Acid

Residues: The Primary Structure

This journey of personal enchantment leading

to the consilient mechanism of protein-based

energy conversion began with the parent model

protein (Gly-Val-Gly-Val-Pro)n.^^ This five

amino acid residue repeat, referred to as a pen-

tamer, recurs 11 times in the elastic fibers of the

pig and cow, that is, the subscript n is

11.^^'^^

our designed model proteins the pentamer gen-

erally repeats some 200 times or more, that is,

the subscript n is often greater than 200. These

protein-based polymers may also be called

polypentapeptides. The general way to indicate

this large repeating pentamer is poly(GVGVP)

or (GVGVP)n, where the value of n is specified

for a given preparation. When made by genetic

engineering, polymers of a precise number of

repeats are obtainable. In Figure 5.1, the data

represent those of a polypentapeptide com-

prised of 251 repeats, that is, (GVGVP)25i.

5.2.2 Secondary, Tertiary, and

Quaternary Structures

5.2.2.1 Hydrogen Bonds Between

Backbone Peptide Groups: The

Secondary Structure

The molecular structure of poly(GVGVP)

is one of a series of P-turns, one in each

pentamer, inserted by the Pro-Gly sequence

as schematically indicated in Figure 5.6A.

Because of the location of the p-turn, which is

a 10-atom hydrogen bonded ring involving

the Val^C-O-HNVal"^, early representations of

the polypentapeptide were written as

poly(VPGVG) or (Val'-Pro'-Gly^-Val'-Gly^n.^^

The detailed p-turn shown in Figure 5.6B was

obtained from the crystal structure of the cyclic

molecule comprised of three pentamers^"^ and

was developed independently by the physical

methods of nuclear magnetic resonance and

circular dichroism and by the computational

methods of molecular mechanics and dynamics.

The p-turn, the 10-atom hydrogen bonded ring

involving the Val^-CO to the Val'^-NH shown in

Figure 5.6B, is the single secondary structural

feature, the only hydrogen bond, in the repeat-

ing pentamer. Studies using Raman scattering

indicate the presence of the j8-turn below Tt,

before the phase transition, and indicate no

change in secondary structure, that is, no

change in hydrogen bonding during the

hydrophobic folding and assembly process

attending the phase change.^^ This means

during the phase transition that the significant

changes within and between the chain mole-

cules are changes in hydrophobic association.

5.2.2.2 Hydrophobic Association

Represents Tertiary and Quaternary

Structure

On raising the temperature above 25° C, the

series of p-turns optimizes hydrophobic con-

tacts within a single chain by wrapping up into

a helical structure, called a ^-spiral, as shown in

detail by stereo pair in Figure 5.6E. The forma-

tion of intramolecular oil-like contacts, for

example, the interaction between the PropCH2*

of pentamer i and the ValyCHs'^^ of pentamer i

-h

3 in the sequence, may be considered changes

in tertiary structure attending the inverse

temperature transition. Finally, hydrophobic

association between chains results in a twisted

filament structure as indicated in Figure 5.6F.

These are quaternary structural changes as

developed from electron micrographs of

negatively stained incipient aggregates formed

on heating, from optical diffraction of the

micrographs,^"^ and from molecular mechanics

and dynamics calculations.^^'^^ In reahty, the

hydrophobic contacts within and between

chains develop simultaneously each assisting

the other, that is, in a cooperative manner.

For simpHcity, we often display a single chain

in the p-spiral structure; in reality, however, we

do not expect such to form readily in isolation,

but rather as part of a twisted filament as in

Figure 5.6F. Accordingly, the schematic repre-

sentations of the P-spiral structure of Figures

5.6C-E are regularly used to simplify but ade-

quately make the intended point.

126

Consilient Mechanisms for Diverse Protein-based Machines

E P^spiral

F twisted filament

of P-spirals

K1.8nm-H

FIGURE 5.6. Description of the molecular structure

of the parent model protein (GVGVP)n, which

should be recognized as equivalent to (VPGVG)n.

(A) A series of P-turns involving residues

VPGV.

(B)

The p-turn obtained from the crystal structure of the

cyclic conformational correlate cyclo(GVGVP)3

shown in Figure 5.4B. (C,D) Schematic helical rep-

resentations without P-turns (in C) and showing

p-turns as spacers between turns of a helix, called

the p-spiral. (E) Cross-eye stereo view of the

poly(GVGVP) P-spiral in side view below and in axis

view above. (F) Cross-eye stereo view of the twisted

filament composed of three P-spirals. Before passing

through the inverse temperature transition to

increased order, as shown in Figure 5.1 and further

characterized in Figures 5.2 through 5.5, this model

protein contains the structural element of the p-turn,

but otherwise is a disordered random chain. In the

process of passing through the ordering transition,

the molecular structure hydrophobically folds and

assembles into a twisted filament composed of

dynamic p-spirals, as represented in parts E and F.

See section 5.2.2 for description and relevant refer-

ences.

(Parts A, B, C, D, E, and F reproduced with

permission from Urry et al.,^^^ Cook et al.,^"^ Urry,^^^

Urry,^^^ and Urry et

al.,"^^

respectively.)

5.2.3 The Nature of the Elasticity of

Cross-Hnked Poly(GVGVP)

5.2.3.1 Ideal, Dominantly

EntropiCy

Elasticity

Stretching an elastic band constitutes an expen-

diture of mechanical energy. For the most

efficient molecular machines, the mechanical

energy expended on stretching the elastic band

should be completely recovered on relaxation

of the stretching force, that is, the force versus

length curve on extension would exactly

overlap with the force versus length curve

obtained on relaxation. Such bands may be said

to exhibit ideal elasticity. Bands of cross-linked

poly(GVGVP), as well as the parent mam-

malian elastic fibers wherein the repeating pen-

tamer sequence was initially observed,^^'^^ have

been found to exhibit such ideal (dominantly

entropic) elasticity.^'^^'^^

Ideal elasticity would not occur when stretch-

ing involves friction-like interactions between

5.2 Molecular Structure and Elasticity of Model Protein

127

the load-bearing chain and surrounding

nonload-bearing chains. In such cases some

of the mechanical energy expended during

stretching is not recovered on removal of the

stretching force. Chains having complex sec-

ondary (hydrogen bonded), tertiary, and qua-

ternary structures provide mechanisms for the

energy expended on extension to be dissipated

away from the load-bearing chain segments.

5.2.3.2 The Decrease of Internal Chain

Motions on Stretching

Stretching of the molecular structure described

in Figure 5.6 does not involve the disruption of

complex secondary, tertiary, and quaternary

structures nor does significant frictional drag

appear to occur between the chain bearing the

load and adjacent nonload-bearing chains. In

the structure most easily seen in stereo in

Figure 5.6E, suspended segments, involving the

VGV sequence, occur between the p-turns

within a single chain. The two peptide groups,

-CONH-, within VGV sequence are quite free

to rotate or rock about the nearly colinear

C-CONH-C bonds in the structure in Figure

5.6E. This motion of the backbone constitutes

chain entropy. On stretching, the amplitude of

these rocking motions decreases, and this

causes the decrease in entropy that provides

the restoring force after stretching. This mech-

anism of elasticity has been called the damping

of internal chain dynamics on extension.^^y^lh^n

the energy of stretching the elastomer primar-

ily decreases internal chain motions, the elas-

tomer becomes an entropic elastomer. This type

of elasticity allows for more efficient energy

conversions.

This mechanism of elasticity provides a

"common groundwork of explanation" for the

elasticity of all chain molecules regardless of

composition and structure as long as there

exists an internal chain motion that becomes

decreased on deformation. For this reason, it

too is a consilient mechanism. To delineate this

consilient mechanism for elasticity from the

consilient mechanism for hydrophobic associa-

tion, as treated extensively in this volume, it

will be referred to as the elastic consilient

mechanism.

5.2.3.3 Importance of the Elastic

Consilient Mechanism to Efficiency of

Energy Conversion

An important element of an ideal elastomer is

that the energy of deformation of an otherwise

kinetically free chain must remain entirely in

the backbone modes where it can be recovered

on relaxation. Should the energy of deforma-

tion find its way into side chain motional

modes, this can be dissipated into the solvent

and into adjacent nonforce sustaining mole-

cules and, therefore, be lost to the recovery

during relaxation. The experimental result of

this dissipation is hysteresis. Cross-linked

poly(GVGVP) exhibits near ideal elasticity;

the extension and relaxation curves overlap

well. Single-chain force-extension curves of

(GVGVP)502 can exhibit extension and

relaxation curves that overlap perfectly

within instrumental limits."^^ On the other hand,

cross-linked poly(GVGIP) always exhibits

hysteresis; the relaxation curve falls well below

the extension curve. Because the work of exten-

sion is the area under the force-extension curve,

when the force-relaxation curve falls below the

force-extension curve, the energy represented

by the difference between extension and

relaxation is lost. Expectedly, therefore, single-

chain force-extension curves of (GVGIP)nx26o

do exhibit marked hysteresis; however, under

conditions of extreme dilution occasional

curves of (GVGIP)nx26o can be obtained

wherein the extension and relaxation curves

superimpose.^^ (GVGIP) nx26o with the greater

tendency for hydrophobic association between

chains, due to the bulkier more hydrophobic

isoleucyl residue in each pentamer resulting

from an added CH2 moiety, provides an

example of energy loss through side chain

motions and interactions.

Hanging a weight on an elastic band of cross-

linked poly(GVGVP), as described in section

5.1.4, constitutes a extending force; the band

increases in length until the area under the

force-extension curve becomes equivalent to

the mechanical energy of the lifted weight.

For elastic-contractile bands operating under

the consilient mechanism, heating the band

through the temperature interval or adding salt

128

Consilient Mechanisms for Diverse Protein-based Machines

to move through the transition zone of Figure

5.5 Ufts a weight a certain distance and results

in the performance of a given amount of

mechanical w^ork. For bands that exhibited

hysteresis, the distance a weight is lifted, on

raising the temperature from below to above

the phase transition for hydrophobic associa-

tion, would be less than for the bands that

exhibited a near ideal elasticity. The former

bands would not be very good molecular

machines for biological energy conversion. All

of the energy conversions of the consilient

mechanism involve changes in hydrophobic

association, whether or not mechanical energy

is the input or output. Because of this, all of the

energy conversions are more efficient when the

protein-based machine is a dominantly entropic

elastomer.

Significantly, for elastin the majority of the

heat and entropy change during chain exten-

sion results from changes in hydrophobic

hydration.^^ Reversibility of an ideal elastomer,

recovery to the same structure on relaxation,

allows that the same change in hydrophobic

hydration occur. To understand energy conver-

sion adequately by the consilient mechanism,

that is, by means of inverse temperature

transitions, solvent entropy changes attending

changes in hydrophobic association require

delineation from changes in chain entropy for

the development of elastic force.

5.2.4 Relationship Between Nature of

Elasticity

and Contractility

Historically, the question of mechanism of

elasticity has been one of evaluating the rela-

tive contributions of three different proposed

mechanisms: (1) the random chain network

(classic rubber elasticity) theory,^^'^^ (2) the

solvent entropy theory,^^"^^ and (3) the damping

of internal chain dynamics on extension.^"^^'^^'^^

The first is due to the Flory school; the second

was initiated by Weis-Fogh and Andersen, and

the third is due to the present author and

coworkers of the last quarter century.

The atomic force microscopy (AFM) single-

chain force-extension studies on the elastic

model proteins^'"^^ demonstrate entropic elastic-

ity for single chains without the presence of

random chain networks with Gaussian distrib-

utions of end-to-end chain lengths as would

have been required for the random chain

network theory.^^ This leaves the proper delin-

eation of solvent entropy and internal chain

dynamics. The solvent entropy theory of elas-

ticity requires consideration in the case of our

elastic model proteins, because changes in

solvent entropy attend changes in hydrophobic

association during stretching and because most

recent adherents of this view base their per-

spective on calculations of (GVGVP)n.^^'^^ In

addition, a clear understanding of energy con-

version by means of the inverse temperature

transitions exhibited by elastic model proteins

requires accurate delineation of the roles of

chain and solvent entropy. Experimental delin-

eation immediately follows.

5.2.4.1 Experiment to Determine Fraction

of Ideal (Entropic) Elasticity

The classic experiment to estimate the amount

of total elastic force,/, derived from the inter-

nal energy component of force,

/E,

and the

entropic component of force,/s, where/=/£; +

fs,

examines the temperature dependence of

force at constant length. On plotting

ln[//T],

with T in Kelvin, as a function of temperature

while maintaining the elastomer element at

fixed length, the slope of the plot multiplied by

(-T K) provides the f^lf ratio. Such data are

given in Figure 5.7A, where the/E//ratio above

40° C is found to be 0.9.^^ Whether in ethylene

glycoliwater (30:70), curve A, or pure water,

curve B, the elastic band of cross-linked

poly(GVGVP) exhibits an elastic force that

is 90% entropic. When the solvent entropy

change through the temperature interval of the

inverse temperature transition is reduced to

near zero, as occurs in ethylene glycol:water

(30:70),^^

the entropic elastic force actually

increases. This is contrary to the solvent

entropy theory of elasticity. As analyzed below,

however, the increase in entropic elastic force

on going from 25° to 40° C eliminates solvent

entropy change as a direct source of the esti-

mated entropic component elastic force.

5.2 Molecular Structure and Elasticity of Model Protein

Temperature Dependence of Force at Constant Length

129

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-1.5

-2.5 r

-3.5

200

160

120

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FIGURE

5.7. Thermoelasticity experiments to esti-

mate the entropic component of elastic force in pure

water (curves B) and in the solvent mixture of 30%

ethylene glycol: 70% water (curves A). On increas-

ing ethylene to 30%, the heat of the transition

approaches zero, which means that the solvent

entropy change approaches zero. The purpose of the

experiment is to see if solvent entropy change con-

tributes to the force developed on raising the tem-

perature. Interestingly, the 90% entropic elastic force

increases rather than decreases on removing solvent

entropy change. The conclusion is that there is no

evidence for the contribution of solvent entropy.

Analysis of the fact of development of force under

the experimental conditions of fixed length excludes

solvent entropy as a contribution to the entropic

elastic force. See section 5.2.4 for more complete

discussion. (Reproduced with permission from Luan

al.^^).

130

Consilient Mechanisms for Diverse Protein-based Machines

5.2.4.2 Implications of Force Changes at

Constant Length

For poly(GVGVP) the temperature interval

for hydrophobic association is 25° to 40° C. It

is over this temperature range that hydropho-

bic hydration becomes higher entropy bulk

water as the hydrophobic groups associate.

For this temperature interval the AS for

solvent is clearly positive. As shown in Figure

5.7, an elastic force develops over this temper-

ature interval that is 90% entropic. Now,

because /s = -T(9S/3L)yT,n, entropy change

for entropic elastic force development is nega-

tive.

This means that the solvent entropy

change is not contributing to the observed

increase in the entropic component of elastic

force.

The same argument applies for isometric

contraction (force development at fixed length)

driven by protonation of carboxylates (see

Figure

1.4).^'^"^

In this case, protonation of car-

boxylates in the cross-linked elastic matrix

drives hydrophobic association with an increase

in entropic elastic force due to a negative

change in elastomer entropy. Under these

conditions, however, hydrophobic hydration

converts to bulk water; the solvent entropy

change is positive, exactly the wrong sign to

contribute to the entropic elastic force. How

this can occur is depicted in Figure 5.8.^^

5.2.5 Consequences of the Nature of

Elasticity to Biocompatibility

5.2.5.1 Low Frequency

Mechanical Resonances

Low frequency mechanical resonances within

elastic protein-based polymers occur near

kHz

(within the frequency range of sound absorp-

tion) and 5MHz (near radio frequencies).^"^^'^^

The physical methods of dielectric relaxation

(loss permittivity), loss shear modulus, and

acoustic absorption have been used to demon-

strate these mechanical resonances in the

kHz

range, and dielectric relaxation and nuclear

magnetic relaxation data provided evidence for

the

MHz resonance. These motions constitute

an entropic contribution to the stability of the

structure in Figure 5.6. By means of statistical

mechanics, the harmonic oscillator partition

function provides a gross sense of the magnitude

of the favorable free energy of stabilization at

these mechanical resonances; the value is about

9kcal/mole-pentamer for the

MHz resonance

and some 14kcal/mole-pentamer for the

acoustic resonance.^'^^

hydrophobic contact hydrophobic surface

hydrophobic contact

force

transducer

FIGURE 5.8. Hydrophobic association to produce

increased elastic force at fixed length, as experimen-

tally shown in Figure 5.7. (Top) A series of clam-

shaped globular proteins, strung together by an

elastic band attached near the mouth, are at equilib-

rium between open and closed states due to

hydrophobic association. As the distribution shifts

toward more closed

states,

the elastic force increases.

(Bottom) A p-spiral with an equilibrium between

hydrophobic association and dissociation between

turns of the

p-spiral.

the equilibrium shifts toward

more hydrophobic association, turns of the P-spiral

not involved in hydrophobic association become

more extended. The decrease in internal chain

motions in the more extended chain segments rep-

resents a decrease in entropy that is the source of an

increase in entropic elastic force. (Reproduced with

permission from Urry.^^)

5.3 Cataloging the Energy Resources Available to the Consilient Mechanism of Energy Conversion 131

5.2.5.2 Interaction, as in Antigen-

Antibody Complexation, Would Increase

Free Energy

For a molecular species to be antigenic, the

antibody must bind to the antigen in the for-

mation of a complex that would identify the

molecular species as foreign. This necessitates

suppression of the motions of the elastomer, of

the mechanical resonances, at a cost of increas-

ing the free energy of the complex. If the com-

plexation free energy increase were less than

one-half of that calculated by the harmonic

oscillator partition function, the probability of

interaction would be decreased by a factor of

10 million, making its formation insignificant.

Because of this, the elastic protein-based poly-

mers are expected, as they have been found

(see Chapter 9) to be remarkably biocompati-

ble.

This property contributes to the usefulness

of these elastic protein-based polymers over a

large range of medical applications.

5.3 Cataloging the Energy

Resources Available to the

Consilient Mechanism of

Energy Conversion

5.3.1 Each Means of Changing Tt

Represents an Energy Source for

Protein-based Machines

5.3.1.1 Point of

View

Greatest

Simplicity

"One of the principal objects of theoretical

research in any department of knowledge is to

find the point of view from which the subject

appears in its greatest simplicity.''^^ This state-

ment was written by J. Willard Gibbs in 1881,

the same Gibbs that gave us the Gibbs free

energy, AG, so central to the above analyses.

The significance of the quotation is com-

pounded here. We propose the Tt-perspective

to be a point of view of greatest simplicity, and

in section

5.1.3.4

we derived approximations to

the change in Gibbs free energy for hydropho-

bic association, AGHA(%)- From this expression,

we recognize the change in Tt from a reference

Tt to a new value of Tt caused by an energy

input represented by x to provide a measure of

the change in Gibbs free energy for hydropho-

bic association of the protein-based polymer.

Therefore, Tt, the onset temperature for the

inverse temperature transition, represents an

intrinsic property of the hydrophobic consilient

mechanism of energy conversion.

5.3.1.2 Simplicity of the Observations

For our model proteins, determination of Tt

is straightforward. The approximate value of

Tt is evident to the unaided eye. A glass tube

containing the parent model protein,

poly(GVGVP), dissolved in water and at a

comfortable room temperature, forms a clear

solution (see the clear tube in Figure 5.1A). On

grasping the test tube in the palm of one's hand

for a few moments, the clear solution becomes

cloudy, as represented in the middle tube in

Figure 5.1A. On standing at palm temperature,

two separate phases appear. Simply warming

the tube from room temperature to body tem-

perature causes the model protein to fold,

assemble, and phase separate due to the asso-

ciation of oil-Uke groups.

Now, cross-linking the elastic model protein

in the phase-separated state results in elastic

bands.

Similarly warming the band, swollen at

room temperature (just below Tt), to body

temperature (some 15 degrees above Tt) causes

the band to contract with the performance of

mechanical work. The band pumps iron on

raising the temperature from below to above

Tt. As scientific accounts go, the Tt perspective

exemplifies simpUcity.

5.3.1.3 Inputs That Move the Trdivide

Represent Energy Resources for the

Consilient Mechanism of Energy

Conversion Without Changing

Temperature

Any change in Tt indicates a change in free

energy for the folded (hydrophobically associ-

ated) state of the polymer. Therefore, in the first

approximation the effectiveness of the energy

input is obvious from the magnitude of the

change in

Tt.

As a particularly relevant example.

132

Consilient Mechanisms for Diverse Protein-based Machines

the most dramatic increase in Tj occurs on phos-

phorylation. Accordingly, phosphate binding

provides the most effective energy input to

drive unfolding (hydrophobic disassociation),

and phosphate removal imparts the greatest

output for contraction by favoring hydrophobic

association. A list of the Trvalues resulting from

the full range of energy inputs to a reference

model protein becomes the catalog of energy

resources available to the consilient mechanism

for protein-based machines. Changes in the

value of Tt, therefore, constitute the nuts and

bolts of energy conversion by the consilient

mechanism. Most significantly^ the following

Tt-based cataloging of energy resources avail-

able to the consilient mechanism coincides with

the catalog of the energy resources that run

biology's machines.

hydration, or by water that has been oriented

for hydration of charged groups, or by no water

as when in an insoluble state, that is, hydropho-

bically associated.

This section develops the foundation with

which to utilize these different states in engi-

neering protein function and in understanding

the function of proteins as molecular machines.

It does so by developing a scale that determines

the relative effectiveness of chemical groups

associated with protein to change the tem-

perature at which the phase transition of

poly(GVGVP) takes place, that is, to move the

Tt-divide in Figure 5.3. That relative effective-

ness in changing the location of the Tt-divide,

as noted above, provides a measure of the

relative effectiveness of the energy input that

caused the ATf

5.3.1.4 Impact of the Relative Oil-like

Character of Functional Groups of

Proteins on the Trdivide

The capacity to exist in two different states

defines a functional group. Here we divide the

two different states into more and less

hydrophobic or, from the opposite perspective,

more and less polar. The clearest examples of

functional groups are those groups that can be

either uncharged or charged, that is, either

neutral or ionized. The most obvious examples

of ionizable functional groups of protein are

the carboxyl/carboxylate, -COOH/-COO", and

the amino/ammonium, -NH2/-NH3"^, chemical

couples. A change in the amount of acid, H^,

present in the solution can change the state of

the chemical couple from one into the other.

Importantly, the interaction between oil-like

side chains and these functional groups changes

the amount of acid required to convert from

one state to the other (see Figures 1.2 and 5.20B

and section 5.7.7). In other words, the extent of

the oil-like character of the domain in which

the functional group occurs can change the

state of a functional group. From this perspec-

tive,

the oil-like residues, normally considered

nonfunctional, exhibit functionality by their

capacity to change the state of a functional

group. Oil-like groups can also be in different

states;

they can be surrounded by hydrophobic

5.3.2 The Tt-based Hydrophobicity

Scale for Amino Acid Residues

5.3.2.1 The Preferred Site of Substitution

For our model protein, poly(GVGVP),^^

replacement of either of the Gly residues or

the Pro residue markedly alters the structure

and properties of the resulting protein-based

polymer. For example, substitution of the Gly

and Pro residues can destroy the favorable elas-

ticity of the polymers. These positions will not

be used for the comparisons of interest here.

Substitution of the Val preceding the Pro is pos-

sible by most amino acid residues, but not all.

Fortunately, any one of the 20 naturally occur-

ring amino acid residues can replace the V of

GVG without significant change to the basic

structure and function.

5.3.2.2 An Expression for Substitution in

Chemically Synthesized Model Proteins

The approach, therefore, is to introduce a guest

residue in place of the V residue in the GVG

sequence by preparing the pentamer GXGVP

where X is any of the naturally occurring amino

acid residues or a chemical modification of bio-

logical interest. (See Table 5.1 for identification

of each of the R-groups of the 20 natural amino

acid residues.) The pentamer with the guest

5.3 Cataloging the Energy Resources Available to the Consilient Mechanism of Energy Conversion 133

residue, X, is mixed in the reaction solution with

the parent pentamer, GVGVP, at different

ratios in different reaction vessels, and each

mixture is polymerized. The result is a series of

model proteins with different amounts of the

guest residue.

The general expression for the composition

of this series of model proteins becomes

poly[f,(GXGVP),fv(GVGVP)], where f, and fv

are called mole fractions wherein fx + fv = 1. By

way of example, if fx were 0.2 and, therefore, fv

were 0.8 (i.e., 1 - 0.2), there would be four

GVGVP pentamers for each GXGVP pen-

tamer, which means that on the average there

would be 1 substitution, that is, one X residue,

for every 25 residues or 4 substituted residues

in every 100 residues.

5.3.2.3 The Experimental Observation

As long as the model proteins are not too oil-

like,

they are soluble at low temperature in a

biological salt solution (physiological saline,

0.15NNaCl), that is, the experiment begins at

low temperature with a clear solution. The solu-

tion is heated; the temperature increases, and,

at a critical temperature unique to the compo-

sition of the model protein, the sample becomes

cloudy. This is shown in Figure 5.IB, where

aggregation of the model protein causes cloudi-

ness.

A graph representing clear solutions of a

number of different model protein composi-

tions that turn cloudy at different temperatures

on increasing the temperature is shown in

Figure 5.9A. The temperature for the onset of

FIGURE

5.9.

Experimental data for devel-

opment of the Tt-based hydrophobicity

scale. The general composition for

the protein-based polymer is poly

[fx(GXGVP),fv(GVGVP)], where X is

the guest amino acid residue to be eval-

uated and fx and fy are mole fractions

wherein fx + fv = 1. Part A contains the

raw data for a number of guest residues

substituted at a mole fraction of 0.2,

which means 4 substituted residues

per 100 residues of poly(GVGVP). The

experimental conditions were 40mg/ml

of polymer of a molecular weight of

about 100,000 Da in 0.15N NaCl and 0.01

M phosphate at pH

7.4.

Experimental Tt-

values were obtained as shown in part A

for

fx =

0.2,

and additional polymers were

characterized with different fx values

such that a plot of fx versus Tj could be

constructed as in part

Extrapolation of

the linear plots in part B to fx = 1 gave

the Tt-values that became the basis for

the Tt-based hydrophobicity scale given

in Table 5.1. (Adapted with permission

from Urry.^)

Composition Dependence of T|.

for poly[f ^(VPGVG),fx(VPGXG)] where f^ = 0.2

, 40 60

Temperature, °C

B Temperature of Inverse Temperature Transition, T|.

: forpoly[f^(VPGVG),fx(VPGXG)] ;

(\ H-,

Kj.y)

0.1"

0.2-

0.3-

0.4-

0.5-

, i V 1

yr":/-,^^ '•:

W .6 * ." o- •^- 85^.0 ^.-

Y •••;•.•. »-••

•6-

• -.v-

0 • • ,©• 0

.• • 0 P::;;;D°,A;.

; • M •••K° V"G-.

• E™H+HyP-r R,Q

H°(pH8) LI • E°,C N,S "

1 1 1 1 1 1 i 1 1

Ser(i>6t) •

E7,Glu(COO')

« . • i .

*. D',Asp(COO')

•••Y-,Tyr(<|)-0-) '

K+,Lys(NH5)'-

•

—1 1 1 1 1 1

0 10 20 30 40 50 60 70 80

Tf (°C)

134

Consilient Mechanisms

for

Diverse Protein-based Machines

aggregation

(of

cloudiness) changes remark-

ably with substitution

only

guest residues

100

residues.

established above

section

5.1.3.4,

increased oil-like character lowers

the temperature

for the

onset

oil-like aggre-

gation,

and an

increased vinegar-like character

raises

the

temperature

for

onset

oil-like

aggregation.

5.3.2.4

Scale

for

Measuring Relative

Oil-like Character

Establishing

scale requires

the

choice

of ref-

erence conditions. We choose

one

guest residue

per pentamer

as the

reference.

Now, for the

most oil-like residues

the

temperature

for

onset

of aggregation

for one

guest residue

per pen-

tamer

below

the

freezing point

water,

and

for the

very vinegar-like residues

the

tem-

perature

for

aggregation

for one

vinegar-like

residue

per

pentamer would

above

the

boiling point

water.

such cases, fewer guest

residues

are

used,

for

example,

one in

five

pen-

tamers

and one in ten

pentamers,

and the

onset

temperatures

for

aggregation

are

plotted.

The

plots give straight lines

shown

Figure

5.9B,

the

fraction

guest residue increases.

The

lines

can be

extended

to the

value expected

for

one guest residue

per

pentamer, that is,

for f^ =

and

this value

of Tt

becomes

the

measure

relative oil-Hke character.

The relative oil-like character

each amino

acid residue

given

terms

of the

Tt-based

hydrophobicity scale

Table

5.1. Tj is

mea-

sured

plotting

indicated

Figure 5.9;

and

the technical term

for

oil-like, hydrophobic

(meaning water fearing),

used.

The

commonly used technical term, hydrophobicity,

replaces

the

equivalent statement

oil-like

character.

5.3.2.5 Effect

Making R-groups More

Oil-like Axiom

Most simply stated, oil

is a

string

CH2 groups.

Adding

CH2 group,

more generally only

hydrocarbons (carbons,

C, and

hydrogens,

H),

the

R-group

of a

protein clearly represents

an increase

oil-like character. Changing

the

R-group from

the -CH3 of

alanine (Ala,

A) to

the -CH(CH3)2

vaUne

(Val, V) and to the

-CH2CH(CH3)2

leucine

(Leu, L)

progres-

sively creates more oil-like model proteins.

Replacing

the X in

poly(GXGVP)

by A,

L progressively lowers

the

temperature

for

onset

aggregation

the model proteins from

45°

C to

24°

C and to

5° C, respectively,

shown

the

data

Figure

5.9 and

listed

Table 5.1.

Accordingly,

stepwise increase

oil-like

character

of the

R-group stepwise lowers

the

temperature

for

aggregation!

Henceforth,

any

R-group substitution cap-

able

lowering

the

temperature

for

aggrega-

tion

recognized

more oil-like than

the

R-group

replaced.

perspective

so self-

evident warrants statement

as an

axiom.

In the

following axiom,

the

transition

defined

by the

temperature interval, where

the

onset tempera-

tures,

noted above, identify

the low

tempera-

ture sides

of the

respective temperature inter-

vals,

shown

Figures

5.1C and 5.5.

Axiom 1:

The

change

temperature interval,

over which occurs

the

oil-like folding

and

assembly transition

of a

host model protein

on introduction

different guest substituents,

becomes

functional measure of relative oil-like

character

the substituents, that

is,

their rel-

ative hydrophobicity,

and it

provides

measure

of the change

free energy

the hydrophobi-

cally associated state.

5.3.2.6 Effect

Changing

the

State

Vinegar-like Side Chains

Above,

the

increase

oil-like character

lowered

the

value

of Tt and, by

Equation

(5.9)

for

AGHA(%), lowered

the

free energy

the hydrophobically associated state.

The

reverse occurs

for a

series

side chains that

increase

the

vinegar-like character. Addition

R-groups containing charged amino groups,

-NHB^, like that

lysine (Lys,

K) or

containing

charged carboxylates, -COO", like that

glutamic acid

(Glu, E)

into poly(GXGVP)

increases

the

temperature

for

aggregation

extrapolated values

120°

C for X = K and

250°

C for X = E

under

the

conditions described

in more detail below. Accordingly,

stepwise

increase

in the

vinegar-like character

of the R-

group stepwise raises

the

temperature

for