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

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5.3 Cataloging

the

Energy Resources Available

to the

ConsiHent Mechanism

Energy Conversion

145

TABLE

5.4.

AGHA(X)

for

hydrophobic association

of a

given composition

model protein

per

mole

for the

steepest slope

ATt

per

change

salt concentration.

A. Model protein

and

salt

Poly(GVGVP)

NaBr

Poly(GVGVP)

CaCl2

Poly(GVGVP)

NaCl

Poly(GVGVP)

NazCOs

(pH

> 8)

Poly(GVGVP)

(NH4)2S04

Poly(GVGVP)

Na3P04

(pH

Poly[0.8(GVGVP),0.2(GE-GVP)]

NaCl

Poly[0.76(GVGVP),0.24(GK^GVP)]

NaCl

Poly[0.8(GVGVP),0.2(GE-GVP)]

CaCl2

AGHA(salt) (kcal/mol/N)

-0.14

-0.27

-0.57

-1.10

-2.8

-5.7

-9.4

-9.6

-15

*Utilizes solpes defined

Figure 5.10.

See

text

for

discussion.

Model protein

and

organic solute

solvent

Poly(GVGVP)

sodium dodecyl sulfate

Poly(GVGVP)

dimethyl urea

Poly(GVGVP)

methanol

Poly(GVGVP)

ethanol

Poly(GVGVP)

ethylene glycol

Poly(GVGVP)

dioxane

Poly(GVGVP)

dimethyl sulfoxide

Poly(GVGVP)

acetone

Poly(GVGVP)

glycerol

Poly(GVGVP)

guanidine-HCl

Poly(GVGVP)

urea

Poly(GVGVP)

trifluoroethanol

Poly(GVGVP)

guanidine2-H2S04

Poly(GVGVP)

deuterium oxide (D2O)

AGHA(solute) (kcal/mol/M)

+18^

+0.93"

+0.93^*

+0.79^^

+0.7r

+ojr

+0.63^

+0.57'^

+0.41"

+0.23"

-0.37^

-0.43"

-0.26^

Steepest slope

and

concentration range

-3.5°C/N&0N^1N

-6.6°C/N&0N^1N

-14°C/N&0N-»1N

-28°C/N&0N^1N

-69°C/N&0N-^1N

-140°C/N&0N^1N

-395°

C/N

0.15 N

0.25 N*

-177° C/N

0.05 N

0.20

-618° C/N

0.125 N

0.05

Steepest slope

and

concentration range

+360°C/M&0M-^.25M

+12.2°C/M&0M^1M

+^-biphasic

-^ IM

+^-biphasic

-0.6°C/M&0M^1M

+4.9°C/M&0M^1M

+3.3°C/M&0M-^1M

+5.3°C/M&0M^1M

-1.8°C/M&0M->1M

+10.3°C/M&0M^1M

+5.3°C/M&0M-»1M

-8.7°C/M&0M^1M

-11.4°C/M&0M^1M

Calculated using guanidine-HCl AT/M data

calibrate slope

for

estimating

AGHA-

Calculated using Eqn (10b)

and

calorimetry (6AQt) data within Table

3f of

Luan

and

Urry.^^

Calculated using Eqn (10b)

and

calorimetry (AHt) data within Table

3g of

Luan

and

Urry.^^

Calculated using Eqn (10b)

and

calorimetry (AHt) data within Table

3k of

Luan

and

Urry.^^

Calculated using Eqn (10b)

and

calorimetry (AHt) data within Table 3j

Luan

and

Urry^^

but if we assume that SDS has the same slope,

ATt/AGHA, as guanidine-HCl, one obtains an

estimate of

AGHA(0

-^ 0.1 M SDS) - ISkcal/

mole-pentamer/mole-solute. Reasonably, SDS

is the most effective agent identified to date in

causing the polymer to hydrophobically unfold.

This is to be compared with the commonly used

denaturants of guanidineHCl of +0.43 kcal/

mole and of urea of +23 kcal/mole (See

Table 5.4B).

The correlation between ATt and

AGHA,

well demonstrated by the results in Tables 5.3

and 5.4 and in Figure 5.10, breaks down when

it comes to consideration of the effects of

certain organic solvents. This is apparent with

ethanol and methanol where the AT/M is ini-

tially positive and then shifts negative, whereas

the experimental AHt from which

AGHA

obtained by means of Equation (5.10b) simply

decreases as M increases. Two possible expla-

nations for this discrepancy would be the direct

interaction of organic solute or solvent with the

polymer and mixed effects on the structure

of hydrophobic hydration. Elements of the

latter are seen with amino acid side chains

in Figure 5.10, where the -OH in Tyr (Y) and

Thr (T), the -COOH of Glu (E°) and Asp (D°),

the -NH2 of Lys (K°), and so on are displaced

from the diagonal line for the strict correlation.

These functional groups are expected to

interact with the hydrophobic hydration in

ways that could either destabilize or stabilize it,

that is, to modify the thermodynamics of

hydrophobic hydration such that the con-

146

Consilient Mechanisms for Diverse Protein-based Machines

100

Poly[0,8(VPGVG), 0.2(VPGEG)]

100

I- 50-^ t

0.2 0.4 0.6 0.8

Salt Molar Concentration

Poly[0.8(IPGVG),0.2(IPGEG)]

•g 25

0.04

Ca^**----*

-T 1 1 1 1 T-

O 0.2 0.4 0.6 0.8 1

Salt Molar Concentration

FIGURE 5.12. Dependences of Tfvalues

for poly[0.2(GE-GVP),0.8(GVGVP)] on

sodium ion and calcium ion concentra-

tion. (A) At low ion concentrations the

slopes are very steep, being close to

30 times steeper for Na^ than for

poly(GVGVP) and more than 90 times

steeper for Ca^^. This emphasizes the

importance of ion pairing in lowering the

free energy for hydrophobic association,

that is, in inducing hydrophobic associa-

tion. (B) Where there is one additional

CH2 group per pentamer, the steepness

increases by almost a factor of two for

Na^ (some 50 times greater than for

poly[GVGVP]) and a factor of 10 for

Ca^^ (close to 1,000 times greater than for

poly[GVGVP].

Thus,

ion

pairing provides

a powerful force for inducing hydropho-

bic association that becomes greater as

the hydrophobic character of the model

protein increases. (A is plotted from

Tables 3d and 3e of Luan and Urry,^^ and

part B is from C.-H. Luan and D.W. Urry,

unpublished results.)

tributions to AHt are no longer dominated by a

change in the amount of hydrophobic hydra-

tion. After all, the special thermodynamic prop-

erties of hydrophobic hydration determine

AGHA-

Despite these thermodynamic complica-

tions,

there remains the practical utilization

of ATt as a simple sliding on-off switch for

controlling association and dissociation of our

model proteins.

5.3.5 What the Trbased

Hydrophobicity Scale ImpHes About

Physical Basis

If lowering Tt is the result of increased

hydrophobic hydration, as we derived from the

data of Butler^^ and of Frank and Evans,^^ then

the increase in the value of Tt due to the pres-

ence of 1 carboxylate per 100 residues of

5.4 Visual Observation of Elastic Protein-based Machines at Work

147

poly(GVGVP) would seem to arise from the

loss of hydrophobic hydration; this suggests

that the negatively charged ion destructures

hydrophobic hydration in the process of achiev-

ing its own hydration shell. Such insight,

supported by a series of less direct arguments,

became confirmed by the direct observation of

hydrophobic hydration (see in section 5.7).

Before definitively addressing the physical

basis,

however, demonstrations are given of

many of the diverse energy conversion possible

by the consilient mechanism.

5.4 Visual Observation of

Elastic Protein-based Machines

at Work

5.4.1 Straightforward Development of

Elastic Protein-based Machines for

Pumping Iron

Development of our understanding of energy

conversion by the consilient mechanism of

hydrophobic association began with the

expected thermally driven contraction of cross-

linked bands composed of model protein^^'^^

Next, it was anticipated and found that proto-

nation of a carboxylate within the model

protein lowered the temperature of the transi-

tion and that protonation of the carboxylate

within the cross-linked elastic band drove con-

traction.^"^ This was immediately followed by

the predicted demonstration that addition of

salt could drive contraction by lowering the

temperature of the transition of the simple

cross-linked model protein, poly(GVGVP)7^

Subsequently and expectedly came pressure-

driven relaxation with aromatic residues^^ and

reduction-driven contraction using a chemi-

cally attached redox couple.^^ These energy

conversions with the energy output being

the mechanical work of lifting a weight were

visually demonstrated. Elastic bands, with the

appropriate model protein composition and a

suspended weight, contract and lift weights, that

is,

pump iron, when designed to be responsive

to different energy inputs. Despite many differ-

ent energy inputs, all of the contractions utilize

the common mechanism of hydrophobic

association to lift the weights. A video provides

visual recordings of these reversible contrac-

tions and relaxations.

5.4.1.1 Simplicity of the Fundamental

Observations

5.4.1.1.1 Onset of Aggregation on Raising the

Temperature of Model Proteins in Solution

Again, the initial experimental observations are

very simple. For the model proteins in solution,

a clear solution becomes cloudy as the temper-

ature is raised. The onset of cloudiness signals

aggregation, or association, of the model pro-

teins,

as shown in Figure 5.1. During this asso-

ciation, oil-Uke R-groups of the model protein

chains separate from water and become insol-

uble.

Specifically, the differential calorimetry

curve of Figure 5.1C provides graphic repre-

sentation of the "cusp of insolubility." Moving

the cusp to lower temperatures than the

working temperature gives insolubility, and

moving the "cusp" to higher temperatures than

the operating temperature gives solubility. The

temperature range over which aggregation

(insolubilization) occurs is called the tempera-

ture interval. How each of 20 different R-groups

changes the temperature interval for aggrega-

tion becomes the primary experimental data-

base (see Figures 5.5 and 5.10 and associated

discussion). The database, called a Tj-based

hydrophobicity scale, in a most practical form

reports the relative oil-like character of the 20

naturally occurring R-groups (see Table 5.1 and

associated discussions). Figure 5.10 provides

the relationship between Tt and the fundamen-

tal Gibbs free energy of hydrophobic associa-

tion, AGHA, required for a more complete

analysis of energy conversion by protein-based

machines, and relevant values are given in

Tables

5.2,5.3

and 5.4.

5.4.1.1.2 Temperature Dependence of

Solubility of Oil-like Groups and Formation

of Insoluble Structures

In relation to the above discussion of the

Butler^^ alcohol series, which considered solu-

bility of oil-like groups in terms of the equation

AG = AH - TAS, raising the temperature

148

Consilient Mechanisms for Diverse Protein-based Machines

increases the magnitude of the (-TAS) term

until it dominates over the AH term and solu-

bility is lost. In the basic model protein of inter-

est here, poly(GVGVP), the aggregated state

still contains 60% water by weight.^^ Because

of this, the separated oil-like groups become

spatially localized hydrophobic patches on the

surface of helically folded and coiled model

protein. This may be thought of in two steps:

(1),

on folding of the helices (P-spirals) the

localized hydrophobic patches tend to form

helical ribbons of oil-like groups on the surface

of the P-spirals; and (2), the heUcally folded

structures associate by means of the oil-like

heUcal ribbons on the surface to form twisted

filaments (see Figure 5.6E,F). In reality the

hydrophobic folding of a single chain and the

association (coiling) of chains to form twisted

filaments are cooperative and generally

inseparable.

5,4.1.2 Constructing Macroscopic Elastic

Protein-based Machines

The simple process of constructing the contrac-

tile elastic bands follows. It involves forming

the phase-separated state comprised of inter-

penetrating twisted filaments as represented in

Figure 5.6F, shaping the phase-separated state

into thin sheets and cross-linking the sheets

into elastic matrices, most simply, by exposure

to y-irradiation.

5.4.1.2.1 Formation and Shaping of a

Glue-like Substance

As shown in Figure 5.13 with the parent model

protein, poly(GVGVP), the polymer is soluble

in water below 25° C. On heating to 37° C,

hydrophobic association of the model protein

occurs, and, on standing, separation occurs to

form a glue-like phase. The overlying solution

is removed, a pestle is inserted, and the glue-

Uke phase fills the space between the pestle and

tube.

5.4.1.2.2 Cross-linking of the Glue-like

Substance to Form Contractile Elastic

Protein-based Sheets and Bands

The glue-like phase between the concentric

cylinders of pestle and tube are maintained in

the phase-separated state and exposed to 20

Mrad of y-irradiation from a cobalt-60 source.

(Alternatively, chemical cross-linking can occur

with a suitable reactive chemical either without

or with functional side chains, or cross-linking

can occur enzymatically with introduction of

appropriate sequences.) One of the advantages

of y-irradiation is sterilization and biocompati-

bility for medical applications.

heat

above

25°C

let

stand

for

few

hours

at 37°C

remove

overlaying

solution,

re-

insert

pestle

20°C

cross-link

by gamma

radiation,

remove,

cut strip,

equilibrate

at 20°C

in water

raise

temperature

37°C,

strip contracts

37°C

contracted

elastic

strip

clear

solution

cloudy

solution

glue-like

phase

separates

out

glue-like

material

flows into

space

between

pestle

and tube

swollen

elastic

strip

FIGURE

5.13. A procedure for the formation of elastic model proteins into y-irradiation cross-linked sheets

for characterization as elastic-contractile systems for performance of mechanical work of lifting a weight.

5.4 Visual Observation of Elastic Protein-based Machines at Work 149

Informative anecdotes relate to effective

y-irradiation cross-linking. Adequate cross-

linking does not occur unless the temperature

has been raised through the temperature inter-

val to drive the hydrophobic folding and assem-

bly. Solutions of polymer at concentrations

lower than that of the usual phase-separated

state,

obtainable only by being at temperatures

lower than the temperature interval, do not

cross-link. Irreversible denaturation of poly

(GVGVP), as represented by the denaturation

peak of Figure 5.2, results in a phase-separated

state that is twice as concentrated, 70%

polymer and 30% water.^^ Even though at twice

the concentration, the denatured polymer does

not effectively cross-link by y-irradiation. In

each case the absence of the state of inter-

penetrating folded and regularly associated

chains interferes with formation of cross-links

between chains.

The elastic strip or sheet is removed from the

tubes,

and it is found to swell on lowering the

temperature and to contract on raising the tem-

perature through the temperature interval from

20° to 37° C, as depicted at the right in Figure

5.13.

A sheet of y-irradiation cross-linked

(GVGVP)25i is shown in Figure 5.14.

5.4,1.3 Hydrophobic Association in

Solution Becomes Contraction in the

Elastic Matrix

The same process of hydrophobic association,

observed in solution and characterized by the

phase diagram in Figure 5.3, occurs in the

elastic matrix where hydrophobic association

displays as a visible contraction. The parallel

process of cloudy formation of polymers in

solution transforms in the elastic matrix into a

contraction capable of performing mechanical

work.

Contraction of elastic matrices occurs as the

temperature is raised through the temperature

interval of Figure 5.5A; this constitutes the

input of thermal energy (TE), measurable as

the heat of the transition seen in Figure 5.1C.

Visible contraction also occurs as any of the

independent variables move through the tran-

sition zone in Figure 5.5B. Depending on the

composition of the model protein that consti-

FiGURE 5.14. Sheet of elastic model protein of y-

irradiation cross-linked (GVGVP)25i as demon-

strated in Figure 5.13 directly usable in thermally

driven contraction and in chemically driven

contraction.

tutes the elastic matrix, the independent vari-

able can be one of a number of energy inputs

such as chemical energy (CE), electrochemical

energy (ECE), pressure-volume energy (PVE),

and electromagnetic radiation energy (EMRE)

such as

Ught.

Thus, one can design elastic matri-

ces capable of contracting and performing the

mechanical work of lifting weights, and with

the unaided eye all can see that the design is

successful.

As discussed below, some designs of model

proteins require less of a given energy input to

perform a given amount of mechanical work.

The effectiveness of the given energy input in

performing mechanical work depends on the

change in the Gibbs free energy for hydropho-

bic association, AGHA, resulting from the energy

input acting on the particular model protein

composition.

150

Consilient Mechanisms for Diverse Protein-based Machines

5.4,1.4 Solvent Entropy Changes in Elastic

Protein Band on Loading (Stretching)

5.4.1.4.1 Below Tt, Solvent Entropy Changes

due to Stretching of a Fully Swollen

Elastic Band

Carefully hanging a weight on the fully swollen

elastic band causes elastic extension sufficient

to support a light load. The elastic force, /,

within the band that supports the load is com-

prised of two components, an internal energy

component,

Z^,

and an entropy component,/s,

that is.

fE+fs

(5.12)

Stretching at a temperature below Tj of the

fully swollen elastic band results in no change

in hydrophobic hydration. Therefore, any elastic

force developed below Tt is not expected to arise

due to solvent entropy changes The entropy

component,/s, of the elastomeric force arises

from the decrease in the internal chain motion

such as rotation about bonds, while the internal

energy component,/^;, results from straining of

bond lengths and deforming bond angles that

could lead to chain rupture.

5.4.1.4.2 Above Tt, Solvent Entropy

Changes Due to Stretching of a Contracted

Elastic Band

The fully contracted elastic band is in a state of

maximized hydrophobic association. Because

of this, stretching of the contracted band

exposes hydrophobic groups to water. Recall

that when an oil-like group dissolves in water,

formation of hydrophobic hydration occurs

with the release of heat. Thus, hanging a weight

on the contracted band exposes hydrophobic

groups to water and releases heat as hydropho-

bic hydration forms. Associated with the exoth-

ermic hydrophobic hydration is a decrease in

entropy of the water that goes from bulk water

to hydrophobic hydration, such that the change

in the (-TAS) term of the Gibbs free energy is

positive. For elastic bands composed of

poly(GVGVP), 90% of the force developed on

stretching the hydrophobically associated state

is due to/5 (see Figure 5.7).^^

5.4.1.4.3 Effects on Solvent Entropy of

Raising the Temperature of Loaded Elastic

Band Through the Temperature Interval

for Contraction

Obviously, the effect of raising the temperature

of a loaded, cross-linked elastic band composed

of elastic protein-based polymers of the

poly(GVGVP) family is to drive hydrophobic

association with the consequence of lifting of

the attached weight. How does this combine

with the above understanding of elasticity to

perform mechanical work?

Hydrophobic association has the corollary

of a positive change in entropy of water as

hydrophobic hydration becomes bulk water.

This occurs whether the experiment is the

change in length at constant force (load) of

pumping iron and the work done is fAL or

whether the experiment is the increase in force

at constant length and the energy output is LAf.

In the latter case there is an increase in force

as thermally driven hydrophobic association

occurs, and the increase in force occurs when

the solvent entropy change is positive.

Thus, for the LAf case the increase in force

cannot arise from a decrease in solvent entropy,

because, in fact, the process is accompanied by

an increase in solvent entropy. This brings us to

the following perspective. In both cases, the

entropic elastic force is maintained or increased

by greater extension resulting in an increased

damping of internal chain dynamics within a

chain segment of fewer repeats as the chains

within a substantial part of the elastic band

undergo hydrophobic association, as repre-

sented in Figure

5.8.^^

5.4.2 Thermal Energy Produces

Mechanical Work of Lifting a Weight

(Heating Through the Temperature

Interval Drives Contraction)

5.4.2.1 Using Cross-linked Model Proteins

as Thermally Driven Contractile

Elastic Bands

For the performance of mechanical work by

model proteins cross-linked to form elastic

bands,

a weight is attached to the rubber-Uke

5.4 Visual Observation of Elastic Protein-based Machines at Work 151

band and the temperature raised. Over a par-

ticular temperature interval, the band contracts

and lifts the w^eight. Relatively little contraction

occurs below the temperature interval, and rel-

atively little contraction occurs above the tem-

perature interval for the particular composition

(see Figure 5.5

A).

The presence of more oil-like

R-groups low^ers the temperature interval over

which contraction occurs, and the presence of

less oil-like or more polar groups R-groups

raises the temperature interval over which con-

traction occurs. Thus, the temperature depen-

dence of contraction of the cross-Unked elastic

matrix follows the dependence of the Tt-divide

on hydrophobicity of the protein-based poly-

mers in solution. The relative hydrophobicity is

reconfirmed in this simplistic and visual obser-

vation of the conversion of thermal energy

(heat) into mechanical work (see Figures 2.4

and 2.5). An obvious elementary statement of

the experimental findings is given as Axiom 2.

Axiom 2: Heating to raise the temperature

from below to above the temperature interval for

hydrophobic association of cross-linked elastic

model protein chains drives contraction with the

performance of mechanical work.

5.4.2.2 Thermal Energy (TE), Measurable

as the Heat of the Transition of the Band

Under

Load,

AHi, Produces Mechanical

Work (MW) of Lifting a Weight, That Is,

TE^MW

At any temperature within the temperature

interval for the thermally driven transition,

there exists an equilibrium between hydropho-

bic association and dissociation. Obviously, at

the low temperature side of the temperature

interval, Umited hydrophobic association

occurs. At the high temperature side of the

temperature interval, hydrophobic association

is limited only by the extending load. The rela-

tionship is such that hydrophobic association is

inversely proportional to the load.

If we knew the heat of the transition for the

elastic band under load, AHi, we could calculate

the ratio of the mechanical work performed

to the heat input expended in lifting the load.

that is, the efficiency of the energy conversion.

Stretching of these hydrophobically associated

elastomers, however, is exothermic due to the

forced exposure and hydration of hydrophobic

groups. Accordingly, AHi is less than AHt,

but the experimental determination of AHi is

difficult due to the nature of the differential

scanning calorimeter required to determine the

heats of the transitions. Fortunately, the chem-

ical energy expended in moving the loaded

elastomer through the transition zone for the

performance of mechanical work can be deter-

mined, as discussed below.

5.4.3 Chemical Energy Produces

Mechanical Work of Lifting Weight

(Changing Concentration of Chemical

Through the Transition Zone

Drives Contraction)

5.4.3.1 Equivalence of Moving the

Temperature

Interval and Moving

Through the

Transition

Zone

5.4.3.1.1 Moving the Temperature Interval

The temperature interval for aggregation of

poly(GVGVP) begins just above room temper-

ature in water, that is, above 25° C, and ends at

about 37° C (see Figure 5.1C and Figure 5.5A).

Addition of salt (NaCl) at 25° C lowers the

temperature for aggregation and causes the

solution to go cloudy. As discussed below, salt

drives contraction by lowering the temperature

interval for heat-driven contraction.

5.4.3.1.2 Relationship Between Temperature

Interval and Transition Zone for Salt-driven

Contraction in the Absence of Functional

Side Chains

The decrease in temperature for the onset of

the transition due to the addition of salt is 14°

C for the addition of 58 grams in 1 liter, that is,

1 N NaCl.^^ Accordingly, the addition of 1 N

NaCl moves the temperature interval originally

25° to 37° C approximately one interval width

to 11° to 23° C and drives contraction of the

elastic matrix. Increasing the concentration of

salt from 1 N to 2 N, however, does little to

further the contraction. Thus the transition

152

Consilient Mechanisms for Diverse Protein-based Machines

zone for the NaCl-cross-linked-poly(GVGVP)

system is 0 to 1 N NaCl (see Figure 5.5). When

observing the cross-Unked elastic band

attached to a w^eight, added salt causes the

rubber-like band to contract and perform the

work of lifting a weight. The cross-linked

elastic-contractile model protein transforms

chemical energy of increasing salt concentra-

tion into mechanical work of pumping iron.

5.4.3.1.3 Relationship Between Changing the

Temperature Interval and Moving Through

Transition Zone for Contraction by Changing

the State of Functional Side Chains

When the polymer contains vinegar-like func-

tional groups, the appropriate counter-ion of

the salt ion pairs with the functional group. Ion

pairing markedly lowers the temperature inter-

val for contraction. Ion pairing places the tran-

sition zone at a much lower salt concentration,

for example, between 0.01 and 0.15 N NaCl.

In particular, when the counter-ion for a car-

boxylate, COO", is the special case of a proton,

H^, the transition zone can occur at very low

concentrations, for example, between a concen-

tration-1 (Ci) of 0.000001 and concentration-2

(C2) of

0.00001

N HCl. Another way to write this

small concentration difference is to use powers

of 10, that is, Ci = 10"' N HCl and C2 = 10"^ N

HCl. Yet another way to write this difference is

to use logarithms to express the increase in con-

centration, for example, log(C2) - log(Ci) =

(-5) - (-6) =

The change in chemical energy,

AE,

required to drive a process is the product of

the change in chemical potential,

A|LI,

times

the change in number of moles. An, that

is,

AE =

AjLiAn. For simpUcity, the present argument

focuses on chemical potential such that AE/An

= 2.3RT[log(C2) - log(Ci)] = 1420cal/mole,

where R = 1.987 cal/mole-deg and at physiolog-

ical temperature (e.g., 37° C such that T = 310

K).

Pumping iron, performing mechanical work,

by the mechanism of charge neutralization, for

example, ion pairing, requires less chemical

energy to do the same amount of mechanical

work than if the model protein had no charged

functional group or if the charged group of the

model protein were already neutralized. This

comparison is graphically demonstrated below.

5.4.3.2 Relationship Between Temperature

Interval and Transition Zone for Chemical

Energy Input

5.4.3.2.1 Relationship Between Changing the

Temperature Interval and Moving Through

the Transition Zone for Contraction Using

Carboxylate (-COO") Functional Side Chains

and Calcium ion (Ca^^)

The temperature interval for poly(GVGVP)

begins at 25° C and ends at 37° C. The same

temperature interval is considered for two

different microbially prepared analogues of

poly(GVGVP), namely. Model protein I:

(GVGIP GFGEP GEGFP GVGVP GFGFP

GFGIP)26 and Model Protein ii: (GVGVP

GVGFP GEGFP GVGVP GVGVP

GVGVP)4o of Table 5.5. Figure 5.15 contains

the dependence on the logarithm of the calcium

ion concentration, log[Ca^^], of the value of Tj

for both model proteins in water. For Model

Protein ii aggregation of the model protein in

solution and contraction of the cross-linked

band in the absence of a load begin at 37° C, as

the calcium chloride reaches a concentration of

0.034 mole/liter (log[Ca'T = -1.47), and

hydrophobic association is complete as the

calcium chloride concentration increases to

0.446 mole/Hter (log[Ca2^] = -0.351). Thus, the

temperature interval of 25° to 37° C corre-

sponds to a transition zone for the independent

variable of calcium ion concentration of 0.034

to 0.446 mole/liter. This is a change in concen-

tration of 0.412 mole/liter, but, more to the

point, on the log scale, the difference is

1.12.The

chemical energy divided by the number of

moles of calcium ion consumed in the process

of driving contraction of Model Protein ii in the

limit of zero load is AE/An == 2.3RT[1.12] «

1,580 cal/mole. For Model Protein I the transi-

tion zone is narrower with a difference on the

log scale of only 0.116. The chemical energy

per mole required to drive the contraction of

Model Protein I is AE/An - 2.3RT[0.116] - 164

cal/mole. The two carboxyls of Model Protein I

would reasonably bind a single calcium ion in a

bidentate manner, and this is less Ukely for

Model Protein ii where the carboxyls are sepa-

rated by 30 residues instead of two residues.

5.4 Visual Observation of Elastic Protein-based Machines at Work

153

TABLE

5.5. Model Proteins and Protein-based Polymers.

A. Microbially-produced Model Proteins

(GVGIP GFGEP GEGFP GVGVP GFGFP GFGIP)26(GVGVP) 2E/5F/2I

(GVGVP GVGVP GEGVP GVGVP GVGVP GVGVP)36(GVGVP) E/OF

(GVGVP GVGFP GEGFP GVGVP GVGVP GVGVP)4o(GVGVP) E/2F

(GVGVP GVGVP GEGVP GVGVP GVGFP GFGFP)39(GVGVP) E/3F

(GVGVP GVGFP GEGFP GVGVP GVGFP GVGFP)i5(GVGVP) E/4F

(GVGVP GVGFP GEGFP GVGVP GVGFP GFGFP)42(GVGVP) E/5F

(GVGVP GVGFP GK(NMeN}GFP GVGVP GVGVP GVGVP)22(GVGVP) K/2F

(GVGVP GVGVP GK(NMeN}GVP GVGVP GVGFP GFGFP)22(GVGVP) K/3F

(GVGVP GVGFP GK{NMeN}GFP GVGVP GVGFP GVGFP)2i(GVGVP) K/4F

(GVGVP GVGFP GK(NMeN)GFP GVGVP GVGFP GFGFP)2i(GVGVP) K/5F

(GVGVP GVGFP GEGFP GVGVP GVGVP GK(CnAm}GVpi.(GVGVP^ E-K/2F

(GVGVP GVGFP GEGFP GVGVP GVGFP GK{CnAinlGVP)2i(GVGVP) E-K/2F

(GVGVP GVGK{CnAm}P GEGFP GVGVP GVGVP GFGVP)22(GVGVP) E-K/2F

(GVGVP GVGK{CnAm}P GEGFP GVGVP GVGFP GFGVP)2i(GVGVP) E-K/3F

(GVGVP GVGVP GKGWF GVGVP GVGVP GVGVP)22(GVGVP) K/OF

(GVGVP GVGFP GKGFP GVGVP GVGVP GVGVP)22(GVGVP) K/2F

(GVGVP GVGVP

GA:GVP

GVGVP GVGFP GFGFP)22(GVGVP) K/3F

(GVGVP GVGFP GKGFP GVGVP GVGFP GVGFP)2i(GVGVP) K/4F

(GVGVP GVGFP GKGFP GVGVP GVGFP GFGFP)2i (GVGVP) K/5F

Model Protein

iii

ii'

iii'

iv'

vi'

vii'-

viii':

ix':

x':

xi':

xii':

xiii':

xiv':

Chemically-synthesized Protein-based Polymers

(Mean molecular weights approximately 100 kDa)

Poly(GDGFP GVGVP GVGVP GFGVP GVGVP GVGK{NMeN|P^ DK/IF

Poly(GVGVP GVGVP GDGVP GVGVP GVGVP GVGVP) D/OF

Poly(GVGVP GVGFP GDGFP GVGVP GVGVP GVGVP) D/2F

Poly(GVGVP GVGVP GDGVP GVGVP GVGFP GFGFP) D/3F

Poly(GVGVP GVGFP GDGFP GVGVP GVGFP GVGFP) D/4F

Poly(GVGVP GVGFP GDGFP GVGVP GVGFP GFGFP) D/5F

Poly(GVGVP GVGVP GEGVP GVGVP GVGVP GVGVP) E/OF

Poly(GVGVP GVGFP GEGFP GVGVP GVGVP GVGVP) E/2F

Poly(GVGVP GVGVP GEGVP GVGVP GVGFP GFGFP) E/3F

Poly(GVGVP GVGFP GEGFP GVGVP GVGFP GVGFP) E/4F

Poly(GVGVP GVGFP GEGFP GVGVP GVGFP GFGFP) E/5F

Poly(GFGFP GVGVP GDGVP GFGFP GFGVP GVGVP) D/5F

Poly(GFGFP GVGVP GEGVP GFGFP GFGVP GVGVP) E/5F

Polymer

II:

III:

IV:

VI:

VII:

VIII:

IX:

XI:

XII:

Accordingly, the values for An are likely to

differ by significantly less than a factor of tv^o

for the two model proteins. Thus, simply by

changing the composition from that of Model

Protein ii to that of Model Protein I, the con-

traction v^ith which to perform mechanical

work could possibly occur using one-tenth the

amount of the chemical energy and certainly

with no more than one-fifth the amount of the

chemical energy. (See section

5.9.5.1

for further

discussion of the relative efficiencies of Model

Proteins I and ii in Table 5.5.)

5.4.3.2.2 Relationship Between Width of

Transition Zone (Plotted Using the Log

Scale),

Efficiency of Energy Conversion,

Energy Required for Biological Production of

the Model Proteins, and Evolution of More

Efficient Machines

The log scale shown in Figure 5.15 was chosen

because when concentration is plotted in this

way the width of the transition zone is propor-

tional to chemical energy. Thus simply by

looking at Figure 5.15, it is apparent that Model

154

Consilient Mechanisms for Diverse Protein-based Machines

FIGURE 5.15. Plot of Tt as a function of

log(calcium ion concentration), log[Ca^^],

which is proportional to chemical energy.

Considering the biological transition zone

of lowering Tt from 37°C to 25°C, it is

possible visually to gain a sense of how the

amount of chemical energy differs as the

composition of the model protein changes.

Clearly, as the hydrophobicity increases

per carboxylate, the chemical energy

required to drive hydrophobic association

decreases, and it further decreases by

having the carboxylates of the Glu (E)

residues proximal for bidentate interaction

with the doubly charged calcium ion. (D.

Urry and C.-H. Luan, unpublished results.)

Log[Ca++]

Protein I is on the order of 10 times more

efficient in converting the chemical energy of

calcium ion into mechanical work. Yet, as was

discussed in Chapter 4 for proteins of the same

chain length, it cost the organism the same

amount of energy to produce the more efficient

molecular machine as to produce the less effi-

cient machine. As argued in Chapter 6, the

evolution of Model Protein ii into the more

efficient machine of Model Protein I can occur

by single base mutations, and each mutation

would step by step increase the efficiency of the

protein for calcium driven energy conversion.

Given the consilient mechanism of energy con-

version by single base mutations it is apparent

that more complex and more efficient molecular

machines would evolve due to natural selection.

5.4.3.3 Contraction by Moving Through

the Transition Zone and Its Equivalent

of Moving the Temperature Interval for

Heat-driven Contraction

5.4.3.3.1 Addition of Acid can Drive

Contraction by Lowering Temperature

Interval for Heat-driven Contraction,

Which Moves the Elastomer Through the

Transition Zone

Adding acid (proton, H^) converts the nega-

tively charged vinegar-like R-group (-CH2-

CH2-COO ) of the glutamic acid residue to

-CH2-CH2-COOH. In the model protein,

poly[4(GVGVP),(GEGVP)] with a ratio of

four GVGVP pentamers to one GEGVP pen-

tamer, there is one glutamic acid residue, des-

ignated by the letter E, in 25 residues. This

model protein remains soluble in neutral or

alkaline water; it will not aggregate no matter

how high the temperature, and the rubber-like

band formed by cross-linking this model

protein will not contract. The temperature

interval for this composition is above 100° C.

If acid is added to the solution of polymer,

then aggregation begins at 28° C and is com-

plete by 40° C, that is, the temperature interval

is from 28° to 40° C. Similarly, for the cross-

linked elastomer, contraction occurs as the

temperature is raised through the tempera-

ture interval. Protonation of the charged

(-CH2-CH2-COO~) R-group 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 increasing acid

concentration transforms into the mechanical

energy of lifting a weight. By increasing the

concentration of acid through the range of the

transition zone contraction occurs and results

in the performance of mechanical work with

lifting of a weight.