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

Подождите немного. Документ загружается.

5.9 On the Efficiency of Consilient Protein-based Machines

205

tration step used

(0.1

N -

1.0N),

these numbers

are slightly different from the values in Table

5.4 for the concentration step of (ON -

1.0N).

The concentration step of a factor of 10

(0.1

- 1.0 N) is chosen so that the chemical energy

input at physiological temperature, 37°C

(310°K), would be 2.3RT log(lO) = 1.42 kcal/

mole, for utilization in the denominator of

Equation (5.25). Therefore,

ecM[poly(GVGVP),NACl] =

0.50kcal/mole/l.42kcal/mole = 0.35 (5.26)

For CaCl2 there is as yet no experimental

value for AHt(0.1N - l.ON) determined from

calorimetry.Thus, to have an estimate, the same

slope will be assumed as for NaCl, that is,

AGH[poly(GVGVP), CaCl2(0.1N - l.ON)] =

(0.50/12.5)(6.6

0.9) = 0.24. Under this approx-

imation,

ecM = [poly(GVGVP), CaCl2] =

0.24 cal/mole/1.42 cal/mole = 0.17 (5.27)

In this approximate way, the efficiency limit

when using the increment of

(0.1

N - l.ON)

with a chemical energy per mole of 1.42 kcal at

37°C is 0.35 for NaCl and an even smaller value

of 0.17 for CaCl2. The effectiveness of salt in

driving hydrophobic association increases dra-

matically when there are charged side chains

with which to ion pair.

5,9.3.2 CaCh and NaCl as Chemical

Energy Inputs to a Charged Model

Protein: Impact of Ion Pairing on Driving

Hydrophobic Association

In the absence of titration data for accurate

A|LI

and An values, in the absence of corrections

to activities (see above), and without direct

calorimetry data to estimate AHt for the specific

salt and model protein systems of interest, gross

comparison derives from the AGHA(salt) values

Usted in Table 5.4A, as determined in section

5.3.4.

5.9.3.2.1 For Model Protein i Using CaCl2 as

the Chemical Energy Input

For Model Protein i in Table 5.5 and from data

in Figure 5.10 and Table 5.3, the protonation of

-COQ-

(E70F) to give -COOH (E70F) gives a

slope of (9kcal/mole)/(380°C). As ion pairing

constitutes partial neutralization, we will

assume this slope. For CaCl2, in the 0.0125 N to

0.05 N concentration interval and as shown in

Figure 5.12A and listed in Table 3e of Luan and

Urry,^^ at low ion concentrations the steepest

slope is estimated to have a AT/N value of

-618°C/N, which gives

AGHA

= -14.6kcal/mole-

pentamer/N-calcium ion.

It should be emphasized that this value is rel-

evant in only a very narrow concentration range,

causing only partial folding and unfolding of

the model protein. Nonetheless, a sense of the

increased effectiveness of ion pairing in driving

hydrophobic association derives on division of

14.6 by 0.27 from Table 5.4. By this estimate,

calcium ion pairing with polymer carboxylate as

compared with the calcium chloride salt effect on

an uncharged polymer approximates to be some

50 times more efficient in the use of chemical

energy to produce a change in the Gibbs free

energy for hydrophobic association,

AGHA-

5.9.3.2.2 For Model Protein i Using NaCl as

the Chemical Energy Input

For NaCl in the 0.15 N to 0.25 N concentration

interval and also as shown in Figure 5.12A and

Usted in Table 3e of Luan and Urry,^^ at low ion

concentrations the steepest slope is estimated to

have a AT/N value of-395° C/N.This gives AGHA

= -9.35 kcal/mole-pentamer/N-sodium ion.

Division by 0.57 for NaCl with poly(GVGVP)

of Table 5.4 provides an estimate of better than

a 15'fold increase in the effectiveness ofNa^ ion

pairing with -COO~, that

is,

Glu-COO~ ... Na^,

in driving hydrophobic association than when

there is no site for ion pairing.

5.9.3.2.3 For Model Protein x' and

Poly[0.76(GVGVP),0.24(GKGVP)] Using the

NaCl Energy Input

First an estimate of the lowering of the Gibbs

free energy of hydrophobic association,

AGHA,

obtained for poly[0.76(GVGVP),0.24

(GK^GVP)],

derives from the data in Table 3d

of Luan and Urry.^^ The steepest slope, AT(/N,

(0.05

N to 0.20 N) arising from ion pairing of

-NHs^

with Cr, gives a value for NaCl of

206

Consilient Mechanisms for Diverse Protein-based Machines

-177° C/N. Next, the value for AT/AGHA of

12.5kcal/mole/230°C derives from Figure 5.10

using Model Protein x' of Table 5.5. On multi-

plication, AGHA(Lys-NH3^ ... CI"; steepest ion-

pairing slope) ~ - 9.6kcal/mole-pentamer/N-

chloride ion. Division of this number by 0.57 of

Table 5.4 for NaCl with poly(GVGVP) gives a

relative effectiveness of approximately 17.

Again, we see the dramatic effect of ion pairing

on driving hydrophobic association.

5.9.3.3 Acid as Energy Input for Model

Protein with Titrable Functional Groups

The acid-base titration curve is sigmoid in

shape as is commonly the case for equilibrium

processes wherein fraction of completion of the

reaction is plotted versus log[C]. In the case of

the acid-base titration, pH = -log[H^]. Because

of this, some basis must be decided upon for the

measurement of the relative proton chemical

energy required to drive from 0% to 100%

completion. Here we utilize the steepest part of

the sigmoid and talk of the efficiency for oper-

ating in this linear range, which would give the

maximal efficiency for the process. The curve

for a dilute weak acid, described by the

Henderson-Hasselbalch equation, exhibits a

steepest slope of 0.9 pH units for going from

degree of ionization, a, of 0 to 1, that is, from

the protonated to the charged state.

To make comparisons with the above salt

effects, however, accurate values of An from

acid-base titrations and correction of concen-

trations to activities should be considered. At

this time, however, several different graphical

representations of relative efficiencies are pos-

sible.

These include comparison of the relative

effectiveness of changes in chemical potential,

A|i,

to drive Tt from just above to below the oper-

ating temperature, comparison of the relative

A|iAn areas determined from acid-base titration

curves,

and comparison of the significance of

dif-

ferent degrees of positive cooperativity, that is,

the impact of changes in the Hill coefficient.

5.9.4 Graphical Insights into

Relative Efficiencies for Chemical

Energy Input

Three different graphical representations

provide insight into relative efficiency in

response to a chemical energy input. The first

shows the relative amount of chemical energy

required to lower the onset temperature for

hydrophobic association from just above the

operating temperature to a temperature just

sufficient to cross the width of the transition

zone of Figure 5.5. For (GVGVP)n that

would be to lower Tt from the physiological

temperature of 37°C where the polymer is

hydrophobically dissociated to 25°C where

the model protein would be almost completely

hydrophobically associated, as depicted in

Figure 5.33.

A second representation comes from the per-

spective of acid-base titration curves. The rela-

tive efficiency, for example, of two different

proton-driven molecular machines becomes

apparent by the relative areas of AjiixAn, where

A|Li

(= -2.3RT ApH) is measured by a step along

the pH axis and An by a step along the y-axis,

in terms of the change in number of moles

required to convert from one state to the other.

This is demonstrated in Figure 5.34.

A third measure of relative efficiency derives

from comparison of the Hill coefficients where

the larger Hill coefficient indicates a more

efficient conversion of chemical energy into

the hydrophobically associated state. This is

demonstrated in the inset in Figure 5.34.

5.9.4.1 Relative Efficiency Limits for

Chemical Energy Inputs Using the

Consilient Mechanism

The efficiency limit of the consilient mechanism

for a chemical energy input is written as

ecM =AGHA/A^An (5.28)

AjiAn is the chemical energy where A|i is the

change in chemical potential and is the Gibbs

free energy per mole of the chemical used

to drive hydrophobic association, given by

2.3RT log{[C2]} - log{[Ci]} or equivalently

2.3RT log{[C2]/[Ci]} where the approximation

of concentration is used for activity and the

change in chemical potential is positive when

[C2] >

[Ci].

An is the change in number of moles

of the chemical used to achieve the hydropho-

bic association, for example, the number of

moles of functional groups titrated.

5.9 On the Efficiency of Consilient Protein-based Machines

207

The relative efficiency of two systems,

r|(system-l)/r|(system-2) = T|I/T|2, can be

expressed as the ratio of efficiency limits for the

two systems when being compared using the

same chemical energy.

^i/^i

=T|

(system-1)/T|(system-2) =

ecM

(system-l)/ecM (system-2)

ili/tl2 =(AGHA/AnAn)^/(AGHA/AnAn)2

(5.29)

5.9.4.2 Relative Efficiencies by Chemical

Energy Required to Move the Cusp

of Insolubility Across Biology's

Transition Zone

When concerned with the physiological operat-

ing temperature of 37°C, a model protein with

its Tt(b)-value at 37°C will not have appreciably

hydrophobically associated. Any variable that

lowers the Tt(b)-value to

25°C,

which is the width

of the transition zone for (GVGVP)25i, will

have essentially completed the transition to the

hydrophobically associated state, as depicted in

Figure 5.33. The variable will have moved the

cusp of insolubility across the transition zone

for biology. In particular, the interest is in

the variable of the chemical energy per mole

required for a ATt just sufficient to traverse the

transition zone from hydrophobically dissoci-

ated at 37°C to hydrophobically associated at

25°C.

Two examples are represented in Figure 5.15

for Model Proteins I and ii of Table 5.5, where

the TfValue is plotted as a function of an

increase in chemical energy, that is, in this case

an increase in the concentration of calcium ion.

Section

5.4.3.2

considered the relative efficien-

cies on the basis of graphical comparisons. With

respect to Equation (5.29), that comparison

assumed the values of (AGHA)I and (AGHA)2 and

of Aui and An2 to be equivalent. The approxi-

mation becomes T|I/T|2 ~ A|X2/A|ii, which gives

the ratio of 0.116/1.12 -

0.1.

With adequate

dif-

ferential calorimetry and titration data, the rel-

ative efficiencies in terms of relative efficiency

limits can be determined accurately. Actual effi-

ciency ratios for converting chemical energy

into mechanical work using cross-linked

matrices are calculated below in section 5.9.5.3.

5.9.4.3 Relative Efficiencies by AjiAn

Areas of Acid-base Titration Curves

Another ready visual means of approximating

relative efficiencies is given in Figure 5.34 for

the series of Model Proteins i through v. In par-

ticular, Model Proteins i and v are compared by

the boxes indicated. When the titrations are

carried out with the same concentration of car-

boxyls for each model protein and the same

concentration of titrant, the vertical displace-

ment is proportional to An and the horizontal

displacement is proportional to A|i. Accord-

ingly, comparison of the area, AjiiAUi, as indi-

cated for Model Protein i with the area, A|XvAnv,

approximated for Model Protein v gives the

relative efficiencies more accurately than was

done above for the data in Figure 5.15.

Improved accuracy here would require choos-

ing accurately the same interval for the degree

of ionization, a, for example, the interval of 0.1

to 0.9.

5.9.4.4 Relative Efficiencies by

Comparison of Hill Coefficients

The most efficient operational design would be

for the machine to operate over the range of

the acid-base titration curve with the steepest

An/A|i slope. Because the Hill coefficient, n,

as defined in Equation (5.20) is a measure of

the slope, it provides for ready comparison of

efficiencies. The Hill coefficients for Model

Proteins i through v are listed in Figure 5.34,

and the slopes are plotted in the inset. Accord-

ingly, the comparison of the efficiencies of

Model Proteins i and v simply becomes T|i/T|v =

1.5/8.0

0.19.

Thus,

by increasing the hydropho-

bicity by the replacement of five Val (V)

residues by five Phe (F) residues, as indicated

in Table 5.5, increases the efficiency of the

protein-based machine by just over fivefold.

5.9.5 Relative Chemomechanical

Transductional Efficiencies of the

Electrostatic Charge-Charge

Repulsion and Consilient Mechanisms

by Experimental Determination of

A|LI,

An, and fAL

The comparison of relative efficiencies above

considered only those polymers functioning by

208

Consilient Mechanisms for Diverse Protein-based Machines

the consiUent mechanism. This involved the

inverse temperature transition for hydrophobic

association. Using the same functional group,

the carboxyl, and its interconversion between

-COO"

to -COOH, it is now possible to

compare directly the chemomechanical trans-

ductional efficiencies of poly(methacrylic acid),

[_CH2-(CH3)C(COOH)-]n, abbreviated as

PMA, to that of Model Protein iv in Table 5.5.

PMA utilizes the electrostatic charge-charge

repulsion mechanism, and Model Protein iv uti-

lizes the apolar-polar repulsive free energy of

hydration of the inverse temperature transition

developed in this chapter.

The same graphical insights utilized above

can be used to obtain insight into relative effi-

ciency. These can then be compared with the

direct experimental determination of the effi-

ciency of each polymeric system and of the rel-

ative efficiencies. The relative A|iAn areas can

be observed for the polymers as well as their

Hill coefficients. Finally, the acid-base titration

curves are given for the cross-linked elastic

matrices held at fixed force and the change in

length determined.

5.9.5.1 Relative Efficiencies by A^An

Areas and Hill Coefficients of Polymer

Acid-Base Titration Curves

5.9.5.1.1 Comparison of the AjiiAn Areas

The acid-base titration curve for PMA is given

in Figure 5.35A, where the change in degree of

ionization and change in pH are given as the

box or AjLiAn area over which the polymer func-

tions effectively in contraction/relaxation. In

Figure 5.35B occurs the acid-base titration for

Model Protein v and the A|LiAn box for its con-

traction/relaxation cycle. The AjiiAn box for

Model Protein v in Figure 5.35B is transposed

as a small shaded box onto the box for PMA in

Figure 5.35A, with a gross correction for the

difference in An. Even so, the difference in effi-

ciencies can be visually appreciated. This visual

comparison would more accurately carry over

to relative efficiencies if the change in length at

the same fixed force resulted in similar fAL

terms for the mechanical work performed.

5.9.5.1.2 Comparison of the Hill Coefficients

As shown in the inset of Figure 5.34, the Hill

coefficient for PMA is 0.5, whereas that of

Model Protein v is 2.7. Thus, without consider-

ation of differences in An, the relative efficiency

would be 0.5/8.0 = 0.06 or one-sixteenth as effi-

cient as the model protein. After the statement

of efficiency for chemomechanical transduction

immediately below, the relative efficiency of

the two mechanisms will be given using Model

Protein iv as the representative of the con-

silient mechanism. The ratio of Hill coefficients

for the latter model protein is 0.5/2.7 or differ-

ing only by a factor of 5 rather than 16. The

experimentally determined relative efficiency is

still very large.

5.9.5.2 Statement of Efficiency for

Chemomechanical Transduction

The proper expression for the efficiency of a

chemomechanical engine is

fAL/A|LiAn (5.30)

where f is the fixed force or weight being lifted

and AL is the distance that the weight is raised.

The quantities A|x and An, as considered above,

are the change in chemical potential and the

change in number of moles of proton required

during the energy conversion. In what follows

a stress-strain/acid-base titration apparatus is

used to obtain the information required for

Equation (5.30).

5.9.5.3 Relative Chemomechanical

Efficiencies of Electrostatic Repulsion and

Consilient (Inverse Temperature

Transition) Mechanisms

The quantity that we wish to calculate is given

by Equation (5.31) where the subscript ap

stands for the apolar-polar repulsive free

energy of hydration mechanism and cc stands

for the charge-charge repulsion mechanism:

r\^Jr\cc=[fAL{ap)/A\iAniap)]/

[fAL{cc)/A\iAn{cc)] (5.31)

The experimental data for AL and AJLI are

obtained from the graph in Figure 5.36 for a con-

5.9 On the Efficiency

Consilient Protein-based Machines

209

1.0

^PMA

Z 0.50

Q 0.25

0.0

COOH

-C-CH2-

Henderson-Hasselbalch

eqn:

pH = pKa +

log[cx/(l-a)]

yy P0LYMETHACRYLIC ACID

4.0

pH=pKa+

1-a

ZkTl^lp

n—

8.0

10.0

1.0

Ani;

0.75

0.50

0.25

0.0

(GEGVPGVGVPGVGVP

GVGVPGVGVPGVGVP)n

— Henderson-Hasselbalch

equation

•

(GEGFPGVGVPGVGFP

GFGFPGVGVPGVGFP)n

FIGURE

5.35.

VisuaUzation of

the

relative efficiencies

of the electrostatic charge-charge repulsion and

the

apolar-polar repulsion mechanisms

comparison

of acid-base titration curves

for

poly(methacrylic

acid),

which exhibits charge-charge repulsion (neg-

ative cooperativity),

and for the

Model Proteins

and

which exhibit apolar-posar repulsion (positive

cooperativity).

The

polymers

are

each compared

with the Henderson-Hasselbalch curve as reference.

Chemical energy

A[i*An,

where

Ap,

2.3RTApH for

the change

go from one state

the other,

and An is the number

moles

go from

degree

stant force

grams.

For the

calculation

the

steepest slope is used

for

both systems. Because

PMA exhibits

lower slope over

considerable

range of the

versus pH plot, this gives the best

working range for PMA and uses its most favor-

able efficiency

range.

As the slopes are taken for

the common AL

9 mm length changes, the

dif-

ferences

are

readily seen

in the

relative

ApH

required

achieve

the

common length change

with a

ApHpMA

of 2.24 and a

APHEMF

of 0.59. Also

the An values are 6.86

10"^

for

PMA and 6.12

10.0

of ionization,

a, of

zero

one.

Accordingly, the area

of an acid-base titration curve as indicated in

and

corrected for the difference in number of moles

required

to go

from one state

another, gives

the

relative amounts

input energy used. These areas

are indicated separately in

and in B, and then with

the correction

for

An,

the

small shaded area

in the

larger area

part

demonstrates how much less

energy

required for the apolar-polar repulsive free

energy

hydration with its positive cooperativity

perform

similar amount

work.

for

Model Protein

iv,

also indicated

in the

subscript as

E/4F.

Accordingly,

Tlap/Tlcc=[(2.24)(6.86xl0-^)]/

[(0.59)(6.12xl0-^)]-40

(5.32)

The result

dramatic!

The

efficiency

of the

charge-charge repulsion mechanism

very

limited indeed.

For years

the

common discussion

mecha-

nism even

proteins has centered

the inter-

210

Consilient Mechanisms for Diverse Protein-based Machines

2g constant force-

PMA

E4F

compact

conformation

unfolds

cp qoO\

3 4

T I I

9 10 11 12

FIGURE

5.36. Experimental plots of cross-hnked

matrices, each loaded with a 2 gram weight, that con-

tract on lowering pH to lift the weight through the

distances, AL, as indicated. These data provide a

direct experimental comparison with the relative

efficiencies for chemomechanical transduction of

Tjcc (charge-charge repulsion mechanism) using

poly(methacrylic acid) and of Tjap (apolar-polar

repulsion mechanism) using elastic Model Protein iv

of Table 5.5. The An values are 6.86 x 10"^ mole for

PMA and 6.12 x 10"^ mole for E/4F, Model Protein

iv. The calculation given in the lower part demon-

strates the apolar-polar repulsion mechanism of the

model protein to be about 40 times more efficient

than the charge-charge repulsion mechanism of

PMA, poly(methacrylic acid). See text for further

discussion. (Unpublished data of D.W. Urry, L.

Hayes, and J. Lee.)

action of charges, the attraction of opposite

charges and the repulsion of like charges. In

dominantly aqueous systems, however, salts dis-

solve to become ions because the free energy

of separated hydrated ions is more favorable

than the ion-pair associations in the crystal. The

phase separation process of inverse tempera-

ture transitions occurs in the absence of any

charge at all, but charge under the influence

of a hydrophobic domain regains its affinity

for association even in a dominantly aqueous

system and becomes a most potent means of

controlling phase separation.

It seems quite evident that the function of

biological macromolecules, and proteins in par-

ticular with their ease to evolve the most effi-

cient mechanism for accessing and utilizing its

energy sources biological systems as discussed

in Chapter 6, would utilize the inverse tem-

perature transition mechanism developed and

demonstrated in this chapter.

Clearly, it would seem not unreasonable to

propose the consilient mechanism as the domi-

nant mechanism in protein structure formation

and function. The comprehensive hydrophobic

effect should be the foundation from which to

engineer protein materials for medical and non-

medical uses.

References

E.O.Wilson, Consilience, The Unity of Knowl-

edge. Alfred E.

Knopf,

New York, 1998, page 8,

gives a definition of the word consilience as pro-

viding a "common groundwork of explanation."

Following E.O. Wilson, we speak of a consilient

mechanism as a "common groundwork of ex-

planation" for each of two interlinked physical

processes in the function of protein-based

machines of

biology.

The first physical process is

that of hydrophobic association, herein devel-

oped as the comprehensive hydrophobic effect

(CHE).

CHE derives its consiHence from being

the dominant mechanism capable of achieving

all of the diverse energy conversions for which

biology is renown and more general yet from

being relevant to all amphiphilic polymeric

systems, that

is,

for all polymers that contain both

oil-like (hydrophobic) and polar (e.g., charged)

constituents. The second physical process is that

of entropic elastic force development, which is

essential to efficient energy conversion, espe-

cially when motion is involved; this force devel-

opment is most evident as an increase in elastic

force under isometric conditions. The elastic

consilient mechanism derives its consilience

from being relevant to all polymeric systems, of

whatever composition, whenever deformation

results in a decrease in chain backbone mobility,

for example, the damping of internal chain

dynamics on extension. This second physical

process, which constitutes a consiHent mecha-

nism for ideal or entropic elastic, will be delin-

eated as the elastic consilient mechanism.

E.O. Wilson, Consilience: The Unity of Knowl-

edge. Alfred E.

Knopf,

New York, 1998, pp. 4-5.

D.W. Urry, "Physical Chemistry of Biological

Free Energy Transduction as Demonstrated by

Elastic Protein-based Polymers." / Phys. Chem.

101,11007-11028,1997.

5. ''Concepts Introduced During Development

of Elastic Protein-based Polymers for Free

References 211

Energy Transduction: The conclusions of this

article can also be given in terms of the follow-

ing chronological listing of the concepts

introduced during the development of elastic

protein-based polymers for free energy trans-

duction: (1) the concept of the damping of inter-

nal chain dynamics on extension as the source of

entropic elastomeric force, called the librational

entropy mechanism of elasticity, (2) the concept

of Tt, the temperature of the hydrophobic

folding and assembly transition, being used as

the fundamental measure of hydrophobicity and

providing a practical on-off switching capacity;

(3) the generally obvious concept that raising the

temperature from below to above Tt is a means

of performing mechanical work by cross-linked

elastic protein-based polymers; (4) the concept

of the ATt-mechanism wherein the value of Tt is

changed, rather than the temperature, as a

means of achieving free energy transduction; (5)

the concept of energy conversion by means of

the coupling of different functional moieties by

being part of the same hydrophobic folding and

assembly domain arising out of, for example, (a)

hydrophobic-induced pKa shifts, (b) hydropho-

bic-induced shift in redox potential, and (c)

demonstrated coupling of carboxyl and redox

functions to result in electrochemical trans-

duction; (6) the concept of the competition for

hydration between apolar (hydrophobic) and

polar (e.g., charged) moieties to give rise to pKa

shifts and positive cooperativity; (7) the concept

of 'poising' for achieving higher efficiencies;

(8) essential equivalence of the inverse tem-

perature transition of a phase separation and

the intramolecular phase separation of the

hydrophobic folding of a globular protein or

assembly of the protomer subunits to form a

multisubunit globular protein such as phospho-

fructose kinase, that

is,

the extension to globular

proteins; and (9) extension to all polymers

where, however, the degree of expression of the

above effects is limited due to the lack of the

many advantages of protein-based polymers of

Table I." (From Urry.4)

6. D.W. Urry, "Molecular Machines: How Motion

and Other Functions of Living Organisms Can

Result from Reversible Chemical Changes."

Angew. Chem. [German], 105, 859-883, 1993;

Angew. Chem. Int. Ed. Engl, 32,819-841,1993.

D.W. Urry, "Elastic Biomolecular Machines:

Synthetic Chains of Amino Acids, Patterned

After Those in Connective Tissue, can Trans-

form Heat and Chemical Energy into Motion."

Sci. Am. January 1995, 64-69.

8. D.W. Urry, "The Change in Gibbs Free Energy

for Hydrophobic Association: Derivation and

Evaluation by means of Inverse Temperature

Transitions." Chem. Phys. Letters, 399,177-183,

2004.

9. D.W. Urry and T.M. Parker, "Mechanics of

Elastin: Molecular Mechanism of Biological

Elasticity and its Relevance to Contraction." /.

Muscle Res. Cell Motil., 23, issue 5-6 (2002);

Special Issue: Mechanics of Elastic Biomole-

cules, H. Granzier, M. Kellermayer, W Linke,

Eds.

10.

Recall that oil-like groups contain hydrocar-

bon; the classic example is the CH2 unit, the

most common chemical grouping of oil. The

principal ingredient of vinegar is acetic acid,

which when negatively charged is written as

CH3-COO", but our use of the term vinegar-

like also includes positively charged species like

amine functions, for example, -NHs^, and it can

even include very polar groups like oxygen and

the peptide group

itself.

Of particular interest

in protein function are the vinegar-like groups

that can exist in either of two or more states,

such as charged or uncharged.

11.

The vinegar-Uke side chains can exist in either

of two different states, for example, the car-

boxyl/carboxylate, COOH/COO", chemical

couple and the amino/ammonium, -NH2/NH3^,

chemical couple. As demonstrated below, the

uncharged state of the couple favors associa-

tion of oil-like domains, whereas the charged

state of the couple disrupts association of oil-

like domains by having destroyed the special

hydration of oil-like groups in the process of

achieving its own hydration.

12.

The word consilient is used as the adjective

form of the noun consilience. As listed in

Webster's Third New International Dictionary,

consilience contains the sense that there exist

pervasive, fundamental laws of nature underly-

ing related disciplines that provide a common

groundwork of understanding. Here we refer to

the consiUent mechanism related to hydropho-

bic association as a water-dependent, pervasive,

and fundamental process by which the macro-

molecules of living organisms function in pro-

viding the essential diverse energy conversions

of Life. In general, if we speak of the consilient

mechanism without further delineation, it will

be the consilient mechanism of hydrophobic

association. When referring to elastic, reference

will be to the consilient mechanism for entropic

(ideal) elasticity or simply to the elastic con-

silient mechanism.

212

Consilient Mechanisms for Diverse Protein-based Machines

13.

(GVGVP)n uses the single letter amino acid

residue abbreviation for the repeating pen-

tapeptide sequence (glycyl-valyl-glycyl-valyl-

prolyl)n. Also, the three letter abbreviation

would be (Gly-Val-Gly-Val-Pro)n. The peptide

residue is given in general as -NH-CHR-CO-

and the R-group side chain is -H for G,

-CH-(CH3)2 for V, and -CH2-CH2-CH2- for P,

with the three CH2 moieties bridging from the

N (replacing the H) to the central atom of the

backbone of the peptide residue, C. Thus the V

and P residues contain the oil-like groupings

of atoms, which are in fact the hydrocarbon

moieties of oil. The interconnecting peptide

group

itself,

-CO-NH-, formed between the

defined residues represents a vinegar-hke

grouping, even though it is without a net charge.

It is considered polar, as there are substantial

partial charges on the atoms, but the sum of the

partial charges of the four atoms in the peptide

moiety is essentially zero. These structural

considerations were introduced in Chapter 2

and are treated in more detail below in section

5.2.

14.

For a comparison per gram with the transitions

of melting and vaporization of water, these

numbers per pentamer would need to be

divided by 23, which is (409 grams/mole-

pentamer divided by

grams/mole-water).

15.

Franks, "Protein Destabilization at Low Tem-

peratures."

^^v.

Protein Chem.,46,107-139,1995.

16.

PL. Privalov, "Cold Inactivation of Enzymes."

Crit.

Rev. Biochem. Mol BioL,25,281-305,1990.

17.

The term inverse transition was first used in con-

nection with the increase in order of the antibi-

otic stendomycin on raising the temperature

(D.W. Urry and A. Ruiter, "Conformation of

Polypeptide Antibiotics. VL Circular Dichroism

of Stendomycin." Biochem. Biophys. Res.

Commun., 38,800-806,1970). The term became

specifically inverse temperature transition in

relation to coacervation of elastin fragments

that exhibited a phase separation with

increased order on raising the temperature

(B.C.

Starcher, G. Saccomani, and D.W. Urry,

"Coacervation and Ion-Binding Studies on

Aortic Elastin." Biochim. Biophys. Acta, 310,

481^86,1973,

and D.W. Urry, B. Starcher, and

S.M. Partridge, "Coacervation of Solubilized

Elastin Effects a Notable Conformational

Change." Nature, 222, 795-796,1969).

18.

P.J. Flory, Principles of Polymer Chemistry.

Cornell University Press, Ithaca, New York,

1953,

Figure 121.

19.

M. Manno, A. Emanuele,

Martorana, PL. San

Biagio, D. Bulone, M.B. Palma-Vitorelh, D.T.

McPherson, J. Xu, T.M. Parker, and D.W. Urry,

"Interaction of Processes on Different/time

scales in a bioelastomer capable of performing

energy conversion." Biopolymers,

59,51-64,2001.

20.

F. Sciortino, K.U. Prasad, D.W. Urry, and

M.U. Palma, "Self-Assembly of Bioelastomeric

Structures From Solutions: Mean Field Critical

Behavior and Flory-Huggins Free-Energy of

Interaction." Biopolymers, 33,743-52,1993.

21.

B.A. Cox,B.C. Starcher, and

D.W.

Urry,"Coacer-

vation of a-Elastin Results in Fiber Formation."

Biochim. Biophys. Acta., 317,209-213,1973.

22.

B.A. Cox, B.C. Starcher, and D.W. Urry, "Coac-

ervation of Tropoelastin Results in Fiber For-

mation." /. Biol. Chem., 249, 997-998,1974.

23.

D.W. Urry, M.M. Long, and H. Sugano, "Cychc

Analog of Elastin Polyhexapeptide Exhibits an

Inverse Temperature Transition Leading to

Crystallization."/. Biol. Chem.,253, 6301-6302,

1978.

24.

W.J. Cook, H.M. Einspahr, T.L. Trapane, D.W.

Urry, and C.E. Bugg, "Crystal Structure and

Conformation of the CycHc Trimer of a Repeat

Pentapeptide of Elastin, Cyclo-(L-Valyl-L-

prolylglycyl-L-valylglycyl)3."/.Am. Chem. Soc,

102,

5502-5505,1980.

25.

J.A.V. Butler, "The energy and entropy of

hydration of organic compounds." Transaction

Faraday Society, 33, 229-238,1937.

26.

H.S. Frank and M.E. Evans, "Free Volume and

Entropy in Condensed Systems: III. Entropy in

Binary Liquid Mixtures; Partial Molal Entropy

in Dilute Solutions; Structure and Thermody-

namics in Aqueous Electrolytes." /. Chem.

Phys., 13, 507-532,1945.

27.

A convenient estimate of the value of Tt is

shown in Figure 5.IB, where an increase in tur-

bidity of the solution is plotted with an increase

in temperature and the 50% point for maximal

turbidity measures

Tj.

As shown in Figure 5.1C,

this measure of Tt occurs near the onset of the

transition as measured by differential scanning

calorimetry (DSC), where it is referred to as

Tb and the shaded area of the curve gives

the exothermic heat of the transition, AHt, for

(GVGVP)25i. It should be further noted that a

more accurate, but not yet precise measure of

ASt uses a mean temperature for the transition,

which we may denote as T^. The accurate

measure of ASt sums over the DSC curve in

small increments of heat released divided by

the mean temperature for the increment. For

References 213

convenience, we refer to Tt, but the differences

should be kept in mind when carrying out cal-

culations as in 5.1.3.4.

28.

D.W. Urry, T.L. Trapane, and K.U. Prasad,

"Phase-Structure Transitions of the Elastin

Polypentapeptide-Water System Within the

Framework of Composition-Temperature

Studies." Biopolymers, 24, 2345-2356,1985.

29.

D.W. Urry, D.T McPherson, J. Xu, H. Daniell,

C. Guda, D.C. Gowda, N. Jing, and T.M. Parker,

"Protein-Based Polymeric Materials: Syntheses

and Properties." In The Polymeric Materials

Encyclopedia: Synthesis, Properties and Appli-

cations, CRC Press, Boca Raton, pp. 7263-7279,

1996.

See Figure 6.

30.

As dialysis membranes are calibrated against

globular proteins and as below Tj these protein-

based polymers are unfolded and disassembled,

it was expected that the polymer that could pass

through the membrane by a process of reptition

(reptilian motion) would be much larger than

50,000 Da. After preparing the polymers by

recombinant DNA technology, where the chain

length was precisely known, for example, just

over 100,000Da for (GVGVP)25i, it was appar-

ent that the chemically synthesized protein-

based polymers retained by the 50,000 cut-off

membranes were over 100,000 Da.

31.

F Sciortino, M.U. Palma, D.W. Urry, and K.U.

Prasad, "Nucleation and Accretion of Bioelas-

tomeric Fibers at Biological Temperatures and

Low Concentrations," Biochem. Biophys. Res.

Commun. 157,1061-1066,1988.

32.

Several points require consideration on identi-

fication of AHt(CH2) - Tt(GVGIP)ASt(CH2) as

-AGHA(CH2).

The points include the separabil-

ity assumption of Equations (5.3) and (5.4), the

relevance of the model protein to such identifi-

cation, and the choice of reference state in

order that the nonlinearity of hydrophobic-

induced pKa shifts be included. From the data

of Butler,^^ the separability is reasonable for a

simple CH2 group, but examination of the cal-

culated result is required to be satisfied

whether or not extension to more complex sub-

stituents is warranted. As the inverse tempera-

ture transition of (GVGVP)n has been

experimentally shown to involve no Raman

detectable changes in secondary structure,^^ the

elastic-contractile model proteins of focus here

reasonably represent the best known model

available for such an effort. It should be noted,

however, that NMR studies on the temperature

and solvent dependence of peptide NH and

^^CO chemical shifts suggest minor changes in

the exposure of peptide NH and CO groups to

solvent during the transition'^^'^^ To include the

nonlinear effects, such as the hydrophobic-

induced pKa shifts, where pKa = AG/2.3RT, the

choice of reference state becomes important.

For situations where these nonlinear effects are

significant, ASt(GXGVP) is the preferred refer-

ence state. This requires extrapolation of

ASt(GXGVP) given for fx = 0.2 in Table 5.1 to

fx = 1, as was done for Tj. Also this requires

DSC data for the modified composition that is

not always easy to obtain. When DSC data is

not available for the perturbed state. Equation

(5.8) can yet be used with ASt(GVGVP) =

ASt(ref), for certain comparison such as ratios

of interest. The complete derivation of Equa-

tion (5.10b) and its evaluation by means of

dif-

ferential scanning calorimetry (DSC) data is

given in reference 8, which should be sought for

a more in depth treatment.

33.

Bioluminescence presents an interesting case

where a chemiluminescence occurs in which

the build up of the chemical required many

stepwise energy inputs. Also there could possibly

be a stretch-induced component, for example, as

seen at night in the wake of ships at sea.

34.

If this were not the case we would be faced with

the puzzhng question. Since the value of T, is

higher when there are fewer CH2 units in the

polymer, and therefore less hydrophobic

hydration, why should a higher temperature be

required to melt the lesser amount of more

poorly structured hydrophobic hydration? The

thermally-induced inverse temperature transi-

tion does not result from a thermal destructuring

of hydrophobic hydration, as we, with others,

have indicated in the past (See for example the

upper right illustration in Figure 2.8).^

35.

D.W.

Urry, S-Q. Peng,

Xu, and

D.T.

McPherson,

"Characterization of Waters of Hydrophobic

Hydration by Microwave Dielectric Relax-

ation."/.y4m6r. Chem. 5'oc.,119,1161-1162,1997.

36.

20 Mrad means a radiation-absorbed dose of 20

million Roentgens.

37.

To be an ideal elastic band means that the

energy expended during stretching of the band

is entirely recovered on relaxation of the

deforming force.

38.

This aspect of the consilient mechanism has

been called the ATt-mechanism, because the

energy conversion occurs not by a change in

temperature but rather by a change in the tran-

sition temperature.

214

Consilient Mechanisms for Diverse Protein-based Machines

39.

Here we note more general terms: polar for

vinegar-like or for charged or ionized and

apolar for oil-like or hydrophobic, but recog-

nize that there exist a continuum of groups

from polar to apolar.

40.

D.W. Urry, D.C. Gowda, S.-Q. Peng, and T.M.

Parker, "Non-linear Hydrophobic-induced pKa

Shifts: Implications for Efficiency of Conver-

sion to Chemical Energy." Chem. Phys. Lett,

239,

67-74,1995.

41.

D.W. Urry, S.Q. Peng, L.C. Hayes, D.T.

McPherson, Jie Xu, T.C. Woods, D.C. Gowda,

and A. Pattanaik, "Engineering Protein-based

Machines to Emulate Key Steps of Metabolism

(Biological Energy Conversion)." Biotechnol

5/o^«g., 58,175-190,1998.

42.

D.W. Urry, L. Hayes, C.X. Luan, D.C. Gowda,

McPherson, J. Xu, and T. Parker, "ATt-

Mechanism in the Design of Self-Assembling

Structures," In Self-assembling Peptide Systems

in Biology, Medicine and Engineering. A.

Aggeli, N. Boden, S. Zhang, Eds., Kluwer Aca-

demic Publishers, Dordrecht, The Netherlands,

2001,

pp. 323-340.

43.

Energy is the product of two quantities, the

change in the intensive variable times the change

in the corresponding extensive variable. For

mechanical energy, the intensive variable is the

applied force, f, and the extensive variable is

the distance over which the force is applied, AL.

The amount of mechanical energy involved in a

process becomes the product of the force to

produce the change in motion times the change

in length or position, that is, fAL. Chemical

energy is the product of the extensive variable,

the number of a molecular species,

such as that

of a particular ion utilized in the process and the

intensive variable, called chemical potential (|x =

RT Ina where a is the activity, which becomes

concentration at low concentrations that limit

effects of ion-ion interactions).

44.

D.W. Urry and M.M. Long, "Conformations of

the Repeat Peptides of Elastin in Solution: An

AppHcation of Proton and Carbon-13 Magnetic

Resonance to the Determination of Polypep-

tide Secondary Structure." CRC Crit. Rev. Bio-

chemistry, 4,1-45,1976.

45.

D.W. Urry, "Characterization of Soluble

Peptides of Elastin by Physical Techniques." In

Methods in Enzymology, 82, 673-716, 1982,

(L.W Cunningham and D.W. Frederiksen, Eds.)

Academic Press, Inc., New York, New York.

46.

D.W. Urry, CM. Venkatachalam, M.M. Long,

and K.U. Prasad, "Dynamic p-Spirals and A

Librational Entropy Mechanism of Elasticity."

In Conformation in Biol. (R. Srinivasan and R.H.

Sarma, Eds.) G.N. Ramachandran Festschrift

Volume, Adenine Press, USA, 11-27,1982.

47.

D.W. Urry, "Thermally Driven Self-assembly,

Molecular Structuring and Entropic Mecha-

nisms in Elastomeric Polypeptides." In Mol.

Conformation and Biol. Interactions (P.

Balaram and

Ramaseshan, Eds.) Indian Acad,

of Sci., Bangalore, India, pp. 555-583,1991.

48.

D.W Urry, T. Hugel, M. Seitz, H. Gaub, L.

Sheiba, J. Dea, J. Xu, and T Parker, "Elastin: A

Representative Ideal Protein Elastomer." Phil.

Trans. R. Soc.

Lond.,

B 357,169-184, 2002.

49.

D.W. Urry, T. Hugel, M. Seitz, H. Gaub, L.

Sheiba,

Dea,

Xu, L. Hayes,

Prochazka, and

T Parker, In Ideal Protein Elasticity: The Elastin

Model, P. Shewry and A. Bailey, Eds., Cam-

bridge University Press, (in press)

2003.

50.

L.B. Sandberg, J.G Leslie, C.T. Leach, V.L.

Torres, A.R. Smith, and D.W. Smith, "Elastin

Covalent Structure as Determined by Solid

State Amino Acid Sequencing." Pathol. Biol.,

33,

266-274,1985.

51.

H. Yeh, N. Ornstein-Goldstein, Z. Indik, P

Sheppard, N. Anderson, J.C. Rosenbloom, G.

Cicila, K. Yoon, and J. Rosenbloom, "Sequence

Variation of Bovine Elastin mRNA due to

Alternative Splicing." /. Collagen Rel. Res., 1,

235-247,1987.

52.

When the number of repeats is large,

poly(GVGVP) is equivalent to poly(VPGVG),

because the polymers differ only by the partic-

ular 2 or 3 residues that begin or terminate the

polymer. For the remainder of the 1,000 or so

residues, the polymers are identical.

53.

G.J. Thomas, Jr., B. Prescott, and D.W Urry,

"Raman Amide Bands of Type-II P-Turns

in Cyclo-(VPGVG)3 and Poly(VPGVG), and

Implications for Protein Secondary Structure

Analysis." Biopolymers, 26, 921-934,1987.

54.

D. Volpin, D.W. Urry, I. Pasquali-Ronchetti,

and L. Gotte, "Studies by Electron Microscopy

on the Structure of Coacervates of Synthetic

Polypeptides of Tropoelastin." Micron, 1, 193-

198,1976.

55.

D.W Urry, CM. Venkatachalam, M.M. Long,

and K.U. Prasad, "Dynamic P-Spirals and a

Librational Entropy Mechanism of Elasticity."

In Conformation in Biology, R. Srinivasan and

R.H. Sarma,Eds., G.N. Ramachandran Festschrift

Volume, Adenine Press, USA, 11-27,1982.

56.

D.K. Chang and D.W. Urry, "Polypentapeptide

of Elastin: Damping of Internal Chain Dynam-

ics on Extension." /. Computational Chem., 10,

850-855,1989.