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 Consilient Mechanism of Energy Conversion 135

aggregation as the result of increasing the free

energy of the hydrophobically associated state!

Therefore, within the practical approach of

the Tfbased hydrophobicity scale, we argue

that any R-group capable of increasing the tem-

perature for aggregation is more vinegar-like

than the R-group it replaced. Therefore, we

evaluate each of the naturally occurring R-

groups by these criteria. Recall that oil-like

groups lower the temperature interval for

aggregation, in our view, due to increasing the

amount of hydrophobic hydration surrounding

them. (Refer to the discussion in sections

5.1.3.3,

5.1.3.4, and

5.7.7)

In our interpretation

below, charged groups raise the temperature

interval by destructuring the pentagonally

arranged hydrophobic hydration surrounding

oil-Hke groups in the unfolded and disassoci-

ated model protein, that is, by decreasing the

total number of molecules of hydrophobic

hydration possible in the disassociated model

protein.

53.2,7 Systematic Comparison of All 20

R-groups of Proteins

Meaningful comparison of the relative oil-like

character of all of the 20 naturally occurring R-

groups of Table 5.1, including the different

states of functional R-groups, requires adher-

ence to stringent criteria and conditions. These

experimental conditions, discussed above, are

given by footnote here.^^ The criteria and

conditions are remarkably met by the elastic

repeating peptide sequence that originated in

the mammaUan elastic fiber, (GVGVP)n.

Axiom 1, given above and the first of five

axioms Hsted below in section 5.6.3, becomes

the basis for consideration of protein function

and for the design of protein-based materials

for the future (see Chapter 9). As simply inter-

preted below, when there are more water mol-

ecules surrounding oil-like groups, the phase

separation of the oil-like groups from water

occurs at a lower temperature.

5.3.2,8 The Continuous Nature of the

Tt-based Hydrophobicity Scale

The terms oil-like and vinegar-like provide

good insight into the basic issues, but they are

limited when addressing particular issues. To

overcome preconceptions and to limit the need

for clarifications of what is oil-like and what is

vinegar-like when discussing the practical Tt-

based hydrophobicity scale, more general

terms prove helpful. Thus, the term apolar

often replaces oil-like, and the term polar often

replaces vinegar-like. Although the Tt-based

hydrophobicity scale warrants much discussion,

only a few issues are noted here.

5.3.2.8.1 A Scale from Apolar to Polar

As shown in Table

5.1,

tryptophan (Trp, W) has

the most apolar R-group, and glutamic acid

(Glu, E), when ionized, has the most polar

R-group. Between these two extremes exists

an essentially continuous set of values. The

side chain of glutamine, -CH2-CH2-CO-NH2,

though uncharged is quite polar, the most polar

uncharged side chain. This indicates that the

peptide moiety

itself,

-CO-NH-, is polar and

suggests that some half-dozen peptide moieties

could sum to be as effective as a single car-

boxylate. It would seem that the hydrogen

bonding of peptide moieties with water could

limit the amount of hydrophobic hydration and

raise the value of Tt. Also when the oil-like

residues dominate, even though the CO or NH

may be at the interface with water, they would

be at a higher free energy due to limited hydro-

gen bonding with water. This would lower the

free energy for formation of secondary struc-

ture,

that is, intramolecular and intermolecular

hydrogen bonding becomes favored by the

presence of more hydrophobic residues. In our

view, this factor contributes to the growth of

amyloid deposits of Alzheimer's disease and

assists in driving prions into insoluble aggre-

gates (see Chapter 7).

5.3.2.8.2 Comparison of Negative and

Positive Ions

The Tt-based hydrophobicity scale shows the

side chain of aspartic acid, -CH2-COO~, to be

significantly less polar than that of glutamic

acid, -CH2-CH2-COO~. This is not as expected

from the number of CH2 groups in the side

chains and likely arises from steric-dependent

hydrogen bonding interactions with nearby

136

Consilient Mechanisms for Diverse Protein-based Machines

peptide groups. Significant also is the difference

between the effectiveness of -NHs^, and

-COO",

in raising the value of Tf These

delineations are relevant to protein function

and dysfunction in Chapters 7 and 8 and

are explored further below once estimates

for AGHA(E-) and AGHACK-") have been

obtained.

5.3.3 The Tt-based Hydrophobicity

Scale for Additional Biologically

Relevant Chemical Groups

5.3.3.1 The Special

Position

the

Phosphate Group^-OPOs^

Many chemical groups in addition to the amino

acid side chains are important in biology

because of their attachment to proteins. Most

notable is the phosphate group, -OPO3", the

most important chemical entity in biological

energy conversion. The phosphate group is also

the most important chemical entity in the con-

silient mechanism for the function of protein-

based machines. The most polar chemical entity

of all those examined for inclusion in the Tj-

based hydrophobicity scale is the phosphate

group. As shown in Table 5.2, phosphate

attached to a Ser OH constitutes the most

polar, the most supra-vinegar-like chemical

group attachable to our model proteins; it is the

least oil-like. The removal of a phosphate most

dramatically makes the model protein more oil-

Uke and most emphatically drives hydrophobic

association.

5.3.3.2 Effects on Tt of Oxidation and

Reduction of Redox Functional Groups

Nicotinamide plays a central role in both pho-

tosynthesis and respiration, as introduced in

Chapter 2. In photosynthesis, light effectively

splits water molecules into electrons, protons,

and oxygen, O2. The protons, H^, drive the

rotary ATP synthase motor to produce ATP

from ADP and Pi. The electrons reduce nicoti-

namide, which then provides for reduction of

CO2 to result in glucose. In respiration, nicoti-

namides and flavins become reduced in the

process of glucose oxidation to form CO2. This

occurs by the reactions of glycolysis, the transi-

tion reaction, and the Krebs cycle of inter-

mediary metabolism. Subsequent oxidation of

nicotinamides and flavins in the inner mito-

chondrial membrane results in the pumping of

protons across the inner mitochondrial mem-

brane to the intermembrane space between the

inner and outer mitochondrial membranes (see

Chapter 8 and specifically section 8.3). In this

process oxidation of nicotinamide results in

50%

more protons pumped across the mem-

brane than the oxidation of flavin. The higher

concentration of protons in the inner mem-

brane space then drives the ATP synthase that

combines ADP and Pi to produce 32 of the 36

ATP molecules for each molecule of glucose

oxidized.

The change of the glutamic acid side chain

from -COO" to -COOH resuhs in the largest

change in Tt (ATt = -220) of all of the vinegar-

like side chains of the natural amino acid

residues (see Table 5.1). As reported in Table

5.2, the model nicotinamide, N-methyl nicoti-

namide (NMeN) used for its relative stability,

exhibits a ATt of -250° C on reduction to the

dihydro-NMeN. The ATt decreases to -105° C

on subsequent reaction that adds a water mol-

ecule to give the more polar 6-OH tetrahydro-

NMeN. Reduction of nicotinamide adenine

dinucleotide (NAD^ -> NADH) results in a ATt

of -150° C, and that of flavin adenine dinu-

cleotide (FAD -^ FADH2) results in a ATt of

-95° C. The relative ATt values of -150° C for

NAD^

and -95° C for FAD are consistent with

their relative contributions to the pumping of

protons across the inner mitochondrial

membrane.

5.3.3.3 Nitration and Sulfation of the

Aromatic Side Chain of Tyrosine

From Table 5.1 the Tt of tyrosine is -55° C and

in Table 5.2 that of sulfated tyrosine is 140° C.

This gives a large ATt of -195° C. The ATt due

to nitration of tyrosine is an even larger 275° C.

These are large effects, but only one-third to

one-fourth of the magnitude due to phospho-

rylation. It is no surprise, therefore, that

phosphorylation/dephosphorylation became

biology's primary process for energy conver-

sion, biology's universal energy currency.

5.3 Cataloging the Energy Resources Available to the Consilient Mechanism of Energy Conversion 137

TABLE

5.2. Hydrophobicity scale (preliminary Tt and

AGHA

values) for chemical modifications and prosthetic

groups of proteins^.

Residue X

AGHA

from Figure 5.10 (kcal/mol)^ T,, linearly extrapolated to /x = 1 (°C)

Lys(dihydro NMeN)'=

Glu(NADH)''

Lys(6-OH tetrahydro NMeN)'=

Glu(FADH2)

Glu(AMP)

Ser(—O—SO3H)

Thr(—O—SO3H)

Glu(NAD)'^

Lys(NMeN, oxidized)''

Glu(FAD)

Tyr(—O—SOsH)^

Tyr(—O—NO2-)'

Ser(POl)

-7.0

-5.5

-3.0

-2.5

+1.0

+1.5

+2.0

+2.5

+3.5

+8.0

-130

-30

100

120

140

220

860

^ The usual conditions are for 40mg/ml polymer, 0.15N NaCl and 0.01 M phosphate at pH 7.4. T, = Temperature of inverse

temperature transition for poly[/v(VPGVG),/x(VPGXG)].

'' Gross estimates of

AGHA

using the Tt-values in the right column in combination with the Tb versus

AGHA

values from

Figure 5.10.

NMeN is for an N-methyl nicotinamide pendant on a lysyl side chain, that is, N-methyl-nicotinate attached by amide

linkage to the e-NH2 of Lys.The most hydrophobic reduced state is N-methyl-l,6-dihydronicotinamide (dihydro NMeN),

and the second reduced state is N-methyl-6-OH 1,4,5,6-tetrahydronicotinamide or (6-OH tetrahydro NMeN). For the oxi-

dized and reduced N-methyl nicotinamide, the conditions were 0.5mg/ml polymer, 0.1 M potassium bicarbonate buffer at

pH 9.5, and 0.1 M potassium chloride.

'^ For the oxidized and reduced nicotinamide adenine dinucleotides, the conditions were 2.5mg/ml polymer, 0.2 M sodium

bicarbonate buffer at pH 9.2.

' The pKa of polymer bound —O—SO3H is 8.2.

' The pKa of Tyr(—O—NO2) is 7.2.

Source: Adapted with permission from Urry et al."*^

5.3.3,4

Cinnamide

Cinnamide undergoes a light-driven geometri-

cal isomerization, which is a simple conversion

from a trans to a cis configuration. This raises

the value of Tt such that the effect of the

absorption of light is a modest shift toward

hydrophobic unfolding/^

5.3.4 Energy Resources of the

Consilient Mechanism: Changing the

Free Energy (AGHA) for Hydrophobic

Association

5.3.4.1

Different Estimates of Transition

Temperature Used in Calculating the

Gibbs Free Energy for Hydrophobic

Association, AGHA, by Equation (5.10a)

When estimating the value of AGHA, as derived

in section

5.1.3.4

and defined in Equation

(5.10a), AGHA(X) = [Tt(ref)ASt(ref) -

Tt(x)ASt(x)], three different ways are noted

to represent the temperature of the transition,

and they lead to different levels of accuracy for

the calculated value. The first of course is Tt, the

simplest measurement, which actually is the

temperature of the onset of turbidity repre-

senting the initial aggregation event of the

phase transition (see Figure 5.IB). When cal-

culating AGHA using Tt, the error will be greater

as the widths of the transitions of the two states

differ more significantly.

The second representation of the transition

temperature,

Tb,

utilizes the onset of the transi-

tion as estimated from the differential scanning

calorimetry (DSC) curve in Figure 5.1C, as esti-

mated by the intersection of the initial baseline

and the initial rise of the curve.

The third representation of the transition

temperature utilizes the extremum (in this case

138

Consilient Mechanisms

for

Diverse Protein-based Machines

the maximal value)

the DSC curve

Figure

5.1C. This estimate will

designated

as T^.

Use

of Tm

would normally result

in a

accurate AGnA-This, however, requires accurate

DSC data

both states. Such data

are not as

easily obtained because

of the

small heats

the transitions,

the

long time required

for

com-

pleting the association

the transition, and

the

higher value

of T^.

5.3.4.2 AGHA'

The

Change

Gibbs Free

Energy

for

Hydrophobic Association

Due

to Change

Amino Acid Composition

With AG„A(Gly)

= 0

5.3.4.2.1 Calculation

AGHA

and

Choice

Reference State

Equation (5.10b),

AGHA(%)

[AHt(ref)

AHt(x)],

utilizes

the AHt

values

for the

phase

transition. Because

for the

inverse temperature

transition,

AHt =

TtASt,

the

heat

this transi-

tion

to the

hydrophobically associated state

becomes

measure

the change

Gibbs free

energy

for

the transition,

AGHA-

now becomes

necessary

define

appropriate reference

state

achieve meaningful comparisons. This

involves both

the

fraction

composition

well

as the

specific amino acid composition

be referenced.

For the

former,

the AHt

values

reported

Table

5.1 for fx = 0.2 are

extrapo-

lated

to fx = 1 and for the

latter

the Gly (G)

residue

taken

as the

amino acid

reference,

because

its

side chain,

single hydrogen atom,

is neither oil-like

nor

vinegar-like. This change

in Gibbs free energy

for

hydrophobic associa-

tion

substitution

of Gly (G) in

GGGVP

the guest amino acid residue

may

written

AGHA(GGGVP

GXGVP), but is indicated

reference value

by the

superscript.

5.3.4.2.2 Estimated Values

for

AGHA(GGGVP

-^ GXGVP)

For

the

following estimates,

values

are

available

for

guest amino acid residues without

functional groups.^^ With Equation (5.10b),

the calculated values

for the

residues more

hydrophobic than glycine

(Gly, G),

that

is,

AGHA(GGGVP

GXGVP) substitutions,

units

kcal/mol-pentamer become

AGHA(GGGVP

GWGVP)

-7.00,

AGHA(GGGVP

GYGVP)

-5.85,

AGHA(GGGVP

GFGVP)

-6.15,

AGHA(GGGVP

GLGVP)

-4.05,

AGHA(GGGVP

GIGVP)

-3.65,

AGHA(GGGVP

GVGVP)

-2.50,

AGHA(GGGVP

GMGVP)

-1.50,

AGHA(GGGVP

GEGVP)

-1.30,

AGHA(GGGVP

GPGVP)

-1.10,

AGHA(GGGVP

GAGVP)

-0.75,

AGHA(GGGVP

GTGVP)

-0.60,

AGHA(GGGVP

GD°GVP)

-0.40,

AGHA(GGGVP

GK°GVP)

-0.05,

AGHA(GGGVP

GNGVP)

-0.05,

and AGHA(GGGVP

GGGVP)

0.00, Thus,

we have

measure

the favorable decrease

free energy

of the

hydrophobically associated

state

for

those residues more hydrophobic

than

For residues less hydrophobic,

more polar,

than glycine, AGHA(GGGVP

GSGVP)

+0.55,

AGHA(GGGVP

GQGVP)

+0.75,

AGHA(GGGVP

GYGVP)

+1.95,

AGHA(GGGVP

^ GDGVP) - +2.6,

AGHA(GGGVP

GK^GVP)

+2.94,

and

AGHA(GGGVP

GEGVP)

+3.72.

positive

AGHA

disfavors

the

hydrophobically

associated state,

and a

negative

AGHA

favors

hydrophobic association. The values

are

plotted

in Figure

5.10 and

listed

Table

5.3.

In Figure

5.10 a

sigmoid curve

drawn

through

the

data points, which

on the

hydro-

phobic side follows closely

the

hydrophobic

residues W, F,

L, I,

V, P,

and A to the

neutral

residue. Those residues with mixed,

but

uncharged, hydroxyl, carboxyl, amino,

and so

forth, functional substituents fall

off of the

sigmoid.

On the

polar side

the

sigmoid curves

around until

takes

the

slope defined

the

data points. Interestingly, continuing

the

- E"

slope

860° C,

the

TfValue resulting

from

phosphate attached

to a

serine (Ser,

residue, gives

value

for

AGHA(P04")

approximately

kcal/mole-phosphate.

Another interesting point about Figure

5.10

is provided

by the

diagonal straight line though

the data points. This line illustrates

the

approx-

imation

of the

Tb(Tt)-based hydrophobicity

scale, which provides

the

most directly usable

5.3 Cataloging the Energy Resources Available to the Consilient Mechanism of Energy Conversion 139

^ 40 ^

FIGURE 5.10. An embodiment of the comprehensive

hydrophobic effect in terms of a plot of the temper-

ature for the onset of phase separation for hydropho-

bic association, Tb, versus AGHA, the Gibbs free

energy of hydrophobic association for the amino

acid residues, calculated by means of Equation

(5.10b) using the heats of the phase (inverse tem-

perature) transition (AHt). Values were taken from

Table

5.3.

and Tt were determined from the onset

of the phase separation as defined in Figure 5.1C,B,

respectively. The estimates of

AGHA

utilized the AHt

data listed in Table 5.1 for fx = 0.2 but extrapolated

to fx = 1, and the Gly (G) residue was taken as the

zero reference. Identification of the delineated

slopes: (a) The diagonal straight line gives the

approximation of the Tb(Tt)-based hydrophobicity

scale, as developed from the data in Figure 5.9 and

Usted in Table

5.1.

(b) The slope for aliphatic hydro-

carbons defined by Leu (L), He

(I),

Val

(V), Pro (P),

Ala (A), and Gly (G). (c) The slope, as defined by

charged Lys (K^) and Glu (E"), for charged species

in competition for hydration with the hydrophobic

residues of the host model protein, (d) An approxi-

mate slope for the aromatic hydrocarbons defined by

Phe (F) and Trp (W). (Adapted from Urry.«)

information in terms of achieving function by

turning on and off hydrophobic association.

Equation (5.9), AGHA(X) « -AT,(x)ASt(ref),

expresses the approximation of the Tb(T|)-

based hydrophobicity scale wherein the mean

value of ASt(ref), as obtained from the diagonal

line of Figure 5.10, would be approximately

30 cal/mole-pentamer-deg.

Perhaps most significant in Figure 5.10 is the

delineation of the sigmoid into three slopes that

group in terms of the classes of side chains,

slope b for those amino acid residues contain-

ing only aliphatic groups, slope d for those

amino acid residues containing aromatic

groups, and slope c for those amino acid

residues containing charged groups.

It should also be noted that the data in Table

5.3 in parentheses were obtained on microbially

prepared Model Proteins i and x' in Table 5.5

(p.

153) and that the values for AGHA(D~) and

AGHA(P04") were obtained by using the exper-

imentally derived Tt-values and reading the

corresponding AGHA values from the sigmoid of

Figure 5.10 or extensions

thereof.

140

Consilient Mechanisms

for

Diverse Protein-based Machines

TABLE

5.3. Hydrophobicity Scale in terms of

AGHA,

the change

Gibbs free energy

for

hydrophobic

association, for amino acid residue (X)

chemically

synthesized poly[fv(GVGVP), fx(GXGVP)], 40mg/

ml,

100 kDa

0.15 N

NaCl,

0.01 M

phosphate,

using the

net

heat

the inverse temperature transi-

tion,

AGHA

[AHt(GGGVP)

AHt(GXGVP)]

for

the fx = 0.2 data extrapolated

fx =

Residue

Trp

Phe

Tyr

His

Leu

Val

Met

His^

Cys

Glu(COOH)

Pro

Ala

Thr

Asp(COOH)

Lys(NH2)

Asm

Gly

Ser

Arg

Gin

Tyr((t)-0-)

Asp(COO-)

Lys(NH^)

Glu(COO-)

Ser(P04=)

Tb°C

-105

-45

-75

-10 (TO

30 (TO

20(2)

40 (38)

60 (TO

140

170 (Tt)

(104)

(218)

860 (TO

AGHA(X)/l^<^^l/niol

pentamer

-7.00

-6.15

-5.85

-4.80 (from graph)

-4.05

-3.65

-2.50

-1.50

-1.90 (from graph)

-1.30 (-1.50)

-1.10

-0.75

-0.60

-0.40

-0.05 (-0.60)

-0.05

0.00

+0.55

+0.80 (from graph)

+0.75

+1.95

~ +3.4 (from graph)

(+2.94)

(+3.72)

= +8.0 (from graph)

Data within parentheses utilized microbial preparations

poly(30-mers),

e.g.,

(GVGVP GVGVP GXGVP GVGVP

GVGVP

GVGVP)n,

with

n «

40.

The notation (from graph) indicates that

the

value

of Tt

from Table

5.1 was

used with

the

sigmoid curve

Figure

5.10 to

estimate

AGHA(X).

Source: Adapted from Urry.^

5.3.4.2.3 Considerations

of the

Experimental

Conditions for the Evaluation of

AGHA

and

Their Relevance

to the Use of the

Values

Table

5.3

Appropriate

use of the

values

Table

5.3

begins with

understanding

of the

conditions

for obtaining

the

experimental data.

At a

tem-

perature below

the

onset

of the

inverse tem-

perature transition,

the

side chains

are

fully

exposed

to and

surrounded

water; they have

their complete complement

hydration.

At a

temperature above

the

transition interval,

the

packing

of the

folded state determines

the

extent

loss

of the

hydration shell. Because

the barrier

mobility

of the

model protein,

poly(GVGVP),

is a

very

low 1 to

1.5kcal,

seems reasonable

expect that

the

transition

to hydrophobic association would

essentially

complete,

packing would

not be

limited

the energetics

association

more rigid

interfaces. Fortunately,

the

reference values

are

not

significantly compromised

such

considerations.

Use

the values

Table

5.3 to

estimate

the

hydrophobicity

given surfaces,

will

done

Chapters

7 and 8,

requires

estimate

the

surface exposure

of a

particular side

chain

water

at the

interface

interest.

Crude estimates

surface exposure

can be

made

for

hydrophobic residues,

and

future cal-

culations should

able

improve those esti-

mates.

regards charged residues,

the key

issue

whether

or not

they

are ion

paired

involved

"salt bridges," which

is the

term

commonly used

crystallographers. Experi-

mental results

on the

effect

of ion

pairing

the heat

of the

inverse temperature transition

suggest

reduction

in the

heat

about

one-

half.

Accordingly, when

the

structure suggests

ion pairing,

the

value

AGHA

for a

particular

residue will

divided

two. Interestingly,

for

those surfaces where there

opportunity

for

complete exposure

water,

the

residues with

charged side chains

are

fully extended

and

jutting

out

into

the

water.

It is as

though

the

charged component

was

trying

stay

as far

away

possible from

the

hydrophobic chain

on which

it is

often perched. This

especially

apparent

for the

side chains

lysine

(-CH2_CH2_CH2-CH2-NH3^), arginine

(-CH2-CH2-CH2-NH-C[NH]-NH2^),

and

glu-

tamic acid (-CH2-CH2-COO-). We believe this

another reflection

of the

component

AGHA

referred

to as an

apolar-polar repulsive

free energy

hydration, AGap

(see

Equation

[5.13]

section

5.7.9.2

below). TTius, when

the

side chain

fully erect,

seen

for

certain

residues

in the

crystal structures

of the

molec-

ular chaperone, GroEL/GroES,

and

especially

of the y-rotor

ATP synthase,

the

full value

AGHA should

used

for

that residue.

5.3 Cataloging the Energy Resources Available to the Consilient Mechanism of Energy Conversion 141

5.3.4.3 Determination of AG

for a

Change in Functional State of Naturally

Occurring Vinegar-like Side Chain

5.3.4.3.1 The AG^ArOlu-COOH->

GhkCOO)

Using Equation (5.10b) and differential

calorimetry data on Model protein i of Table

5.5 as listed in Table 5.3 with a Tb(Glu-COOH)

2° C,

a Tb(Glu-COO-) of

218° C,

a AGHA(G1U-

COOH) of -1.50kcal/mole, and a AGHA(G1U-

COO") of +3.72kcal/mole, the calculated

increase in Gibbs free energy of hydrophobic

association on ionization of the carboxyl func-

tion, AGHA(G1U-COOH -> Glu-COO) = [+

3.72 - (-1.50)] = +5.22 kcal/mole-pentamer. This

quantity is of interest in connection with that

calculated below for AGHA(Lys-NH2 -^ Lys-

NHs^) for the purpose of estimating effects of

ion pairing between model proteins.

Additional questions can be addressed. For

example, how does AGHA(G1U-COOH -^ Glu-

COO") compare with the AGHA of other func-

tional groups in the same model protein, for

example, functional groups that are coupled

with proton pumping in oxidative phosphoryla-

tion of the mitochondria, such as nicoti-

namides? This question is answered in section

5.3.4.4. Another question is, how does the mag-

nitude of AGHA(G1U-COOH -^ Glu-COO)

compare with that of an opposite signed

vinegar-like functional group, for example, the

quantity AGHA(Lys-NH2 -^ Lys-NHg^)? The

latter is given immediately below.

5.3.4.3.2 The AGHA(Lys-NH2 -^ Lys-NHj^)

Using Equation (5.10b) and differential

calorimetry data at pH 7.5 on Model Protein x'

of Table 5.5 with a Tb(Lys-NH2) of 38° C, a

Tb(Lys-NH3^) of 104° C, a AGHA(Lys-NH2) of

-0.60kcal/mole-(GKGVP), and a AGHA(Lys-

NHs^) of

-h2.94

kcal/mole-(GK^GVP), the

calculated increase in Gibbs free energy for

hydrophobic association on protonation of the

amine function, AGHA(Lys-NH2 -^ Lys-NHs^)

= +3.54 kcal/mole-pentamer. The effect on

AGHA of forming the charged Lys-NHs^ is less

than on forming the charged Glu-COO", that is,

AGHA(G1U-COOH -^ Glu-COO) of +5.22

kcal/mole-pentamer. Thus, one might under-

stand when using ion pairing to lower Tt and

AGHA that a thermodynamic equivalence could

require more positively charged groups than

negatively charged groups. In this regard, data

on the allosteric protein hemoglobin are rele-

vant. The allosteric binding, of biphosphoglyc-

erate with five negative charges to eight

positively charged groups at the diad axis of

hemoglobin, enhances oxygen release. This ion

pairing favors the more hydrophobically asso-

ciated deoxyhemoglobin state, with the charge

stoichiometry such that there are to be antici-

pated more positive charges than negative

charges (see Chapter 7).

5.3.4.3.3 Calculation of the Effect of Ion

Pairing Between Chains, AGHA[(G1U-COO-;

Lys-NHs^) -^ (COO- NHs^)]

Using Equation (5.10b) and differential

calorimetry data on the COO" state of Model

Protein i of Table 5.5 with a Tb(Glu-COO-) of

218° C yields a value for AGHA(GIU-COO-) of

3.72kcal/mole-(GE-GVP). Similarly for Model

Protein x' of Table 5.5 with a Tb(Lys-NH3^) of

104° C yields a value for AGHA(Lys-NH3^) of

+2.94kcal/mole-(GK^GVP). The AGHA(COO-

NHs^) value, obtained for a pH 7.5 solution con-

taining equimolar (Glu-COO") and (Lys-NHs"^)

functional groups, is 0.36 kcal/mole. This means

that the decrease in Gibbs free energy for

hydrophobic association due to the ion-pair

formation between Model proteins i and x' is

approximately 3 kcal/mole-pentamer, that is,

AGHA[(G1U-COO-;

Lys-NHs^)

-^ (COO"

NHs^)],

becomes [0.36 - (3.72 + 2.94)/2] - -3.0

kcal/mole-pentamer. This exemplifies the

power of ion pairing in lowering the Gibbs free

energy for hydrophobic association, which

increases with increasing hydrophobicity.

5.3.4.4 Calculation of

AGHA

for a Change

in the State of Bound Biologically

Relevant Functional Groups

5.3.4.4.1 The

AGHA

Due to the Reduction of

Oxidized N-methyl Nicotinamide (NMeN^)

Tt is equivalent to Tb, a direct means of esti-

mating values of AGHA[GK(NMeN^)GVP],

of AGHA[GK(dihydroNMeN)GVP], and of

142

Consilient Mechanisms for Diverse Protein-based Machines

AGHA[GK(NMeN)GVP] is to use the values of

Tt in Table 5.2 and the plot of Tb versus AGHA

of Figure 5.10. The Gibbs free energy of

hydrophobic hydration, obtained in this way, is

given in Table 5.2 to be +2.0, -3.0, and -7.0,

respectively. Therefore, an estimate of the

change in Gibbs free energy for hydrophobic

association on reduction of the N-methyl nico-

tinamide, AGHAINMCN"^ -> NMeN] becomes

[-7.0 - [+2.0]] = -9.0kcal/mole-pentamer.

Comparison of the change in free energy for

hydrophobic association on reduction of this

nicotinamide, AGHA[NMeN^ -^ NMeN], to the

decrease in free energy of hydrophobic asso-

ciation due to protonation of the carboxylate

of Glu,

AGHA[G1U-COO-

Glu-COOH]

-5.22kcal/mole, gives insight into the maximal

efficiency for the coupling of these functional

groups. Accordingly, the coupling of the two

reactions, wherein reduction drives the uptake

of a proton by a Glu-COO", could be expected

to occur in the particular model protein with a

60%

efficiency of energy conversion. A similar

number for efficiency is obtainable on calculat-

ing the carboxyl/carboxylate pKa shift due to

reduction in the same polymer containing both

functional groups by comparing the free energy

change on reduction with the observed pKa

shift (see section 5.9, below).^^

5.3.4.4.2 The

AGHA

Due to the Reduction

of Oxidized Nicotinamide Adenine

Dinucleotide (NAD)

Following the same process as used above for

N-methyl nicotinamide, involving the data in

Table 5.2 and the plot in Figure 5.10, an esti-

mate of the change in Gibbs free energy for

hydrophobic association on reduction of nicoti-

namide adenine dinucleotide, AGHA(NAD -^

NADH) becomes [-5.5 - (+2.0)] = -7.5kcal/

mole-pentamer.

5.3.4.4.3 The

AGHA

Due to the Reduction of

Oxidized Flavin Adenine Dinucleotide (FAD)

Continuing as immediately above using the

data in Table 5.2 and in Figure 5.10, an estimate

of the change in Gibbs free energy for

hydrophobic association on reduction of flavin

adenine dinucleotide, AGHA(FAD -^ FADH2)

becomes [-2.5 - (+2.0)] = ^.Skcal/mole-

pentamer. The qualitative relationship between

AGHA(NAD -> NADH) of -7.5kcal/mole-

pentamer and AGHA(FAD -^ FADH2) of

-4.5kcal/mole-pentamer is consistent with the

resulting relative proton translocation due to

these molecules on oxidation in the electron

transport chain of the inner mitochondrial

membrane where the proton transport ratio for

FADH2:NADHis2:3.

5.3.4.4.4 The

AGHA

Due to Phosphorylation

Phosphorylation by the cardiac cyclic AMP-

dependent protein kinase at the serine (Ser, S)

residue of the polymer poly[30(GVGIP),

(RGYSLG)] resulted in an estimated Tt-value

in Table 5.2 of 860° C.^'*'^^ The equilibrium con-

stant for the reaction

ATP + poly [30(G

VGIP),

(RGYSLG)] =

ADP + poly(30[GVGIP],[RGYS]

{-OPOjJLG])

(5.11)

was essentially 1. In particular, the average

phosphorylation from many phosphorylation

attempts was

47%.^'^^

This means that the

change in free energy of the phosphate on

going from the terminal position of ATP

to poly(30[GVGIP],[RGYS{-OPO3=}LG]) is

effectively

zero.

The conclusion is that the phos-

phate in poly(30[GVGIP],[RGYS{-OPO3=}

LG]) is at the same high free energy state as it

is in the y-position of ATP.

Because hydrophobic association does not

occur until the temperature is above Tt for the

phosphorylated state, the phosphate cannot be

folded into a low dielectric constant site, but

instead would be fully exposed to the solvent.

It is fundamental to the consilient mechanism

of protein-based machines to understand how

this can be! As discussed in section 5.7, the

high-energy state of the phosphate is due to

competition for hydration between the phos-

phate and the hydrophobic groups, as reflected

in the large change in Tt.

Following the above approach of combining

the data in Table 5.2 with the relationship

5.3 Cataloging

the

Energy Resources Available

to the

Consilient Mechanism

Energy Conversion

143

between

Tb and

AGHA

Figure

5.10 and the

realization that

Tb ~ Tt, it

becomes possible

achieve

estimate

AGHAC-OPOS").

The

charged species,

K^ and E",

determine

slope

with which

extrapolate from

100° C to the

value

860°

determined

for the

phosphory-

lation discussed above. This gross means

estimation results

in the

remarkable value

AGHA(-0P03=)

= +8kcal/mole.

This free energy

interaction occurs

in the

unfolded state

and

serves

raise

the

free

energy

for

formation

of the

hydrophobically

associated state. Because

the

high-energy state

the

unfolded polymer,

cannot

be due to

charge-charge repulsion; there

only

phos-

phate

about

300

residues.

The

high-energy

state cannot

be due to the

phosphate being

the

low

dielectric region

of a

folded protein.

our view,

represents

clear measure

of the

apolar-polar repulsive free energy

hydration

arising

out of the

competition

for

hydration

between

the

oil-like side chains

of the

isoleucine

(He, I) and

valine (Val,

residues

and

the

phosphate

in the

unfolded model

protein.

Phosphate removal drives hydrophobic asso-

ciation, that

is,

contraction, more effectively

than

any

other chemical change measured thus

far.

The

binding

of ATP,

adenosine triphos-

phate, the universal energy currency

biology,

could even more effectively increase

the

value

Tt, but

this

can be

modified

by the

associa-

tions

of the ATP at the

binding site. Also,

as in

Table

5.2, the

estimate

AGHA[G1U(AMP)]

modest -i-l kcal/mole,

and the

addition

each phosphate would

add

approximately

8kcal/mole. Furthermore,

expect that

the

state

greatest apolar-polar repulsion would

result from

the

presence

ADP plus

Pi.

5.3.4.5 Using

ATf Due to

Addition

Salts

to Calculate Change

Free Energy

(AGHA)

for

Hydrophobic Association

Neutral Poly(GVGVP)

The dependence

for

poly(GVGVP)

on the

addition

of a

series

salts

(the

Hoffmeister

series)

shown

Figure 5.11A. With

the

exceptions

and

SCN",

the

addition

salts

to poly(GVGVP) lowers

the

value

of T^

With

the

AHt

data from Table

I of

Luan

al.^^

for

use

Equation (5.10b), calculation

AGHA

N ^ 1.0 N

NaCl) yields

value

of -0.57

kcal/mole. Calorimetry

(AHt)

data

are not yet

available

for the

other salts.

If we

assume

the

values

to be

proportional

ATt with

the

NaCl

data providing

the

proportionality constant,

however, estimates

AGHA(0

N -^ 1.0 N

salt)

can

obtained

for a

series

salts. These

are

listed below

and in

Table 5.4A. The decrease

Tt(GVGVP)

due to the

addition

of 1

mole

salt

found

Table

3c of

Luan

and

Urry.^^

what follows, after identification

the polymer

composition

and

salt, listed

are the

numbers

for

ATt

increasing

the

amount

salt from

0 to

1.0 N and the

calculated value

AGHA

kcal/mole based

on a

proportionality

to the

NaCl data: NasPO^pH

> 8), -140° C, -5.7;

(NH4)250,, -69° C, -2.8; Na2C05(pH

8),

-28°

C, -1.1; NaCl, -13.9° C, -0.57; CaCls, -6.6° C,

-0.27;

NaBr, -3.5° C, -0.14;

Nal and

NaSCN,

+3.5° C,+0.14.

5.3.4.6 Using

ATt Due to

Ion-Pairing

Salts with Functional Groups

Estimate

Change

Free Energy (AGHA)

for

Hydrophobic Association

As shown

comparison

of the

data

Figure

5.12A with those

Figure 5.11A,

the

effect

of salts

lowering

the

free energy

of the

hydrophobically associated state

the protein-

based polymer

much greater when

the

polymer contains

charged side chain.

esti-

mate

AGHA(G1U-COO"

•••

Na"^; steepest

ion-pair slope), that is, the change

Gibbs free

energy

for ion

pairing over

the

change

salt

concentration with

the

steepest slope,

may be

obtained using the

slopes,

ATJ/AGHA established

in Figure 5.10

for the

ionization

the carboxyl

-^ E") to be

380°/9 kcal/mole. Table

Luan

and Urry^^ provides

the

data points used

Figure

5.12A

from which

the

steepest slope

(0.15

N to

0.25

N) is

obtained

give

the

value

of ATt/N NaCl

to be

-395°

C/N. The

result

AGHA(G1U-COO"

•••

Na^; steepest ion-pair

slope)

-9.4kcal/mole-pentamer/N. The effect

ion

pairing

of Na^

with

COO"

lowers

the

free energy

of the

hydrophobically associated

state

more than

order

magnitude when

144

Consilient Mechanisms for Diverse Protein-based Machines

compared with the NaCl interaction with the

neutral polymer, that is, AGHA[poly(GVGVP);

0 N -> 1 N NaCl] = -0.57kcal/mole. Further-

more, once the effect of ion pairing is com-

pleted above 1 N NaCl, the effect of the salt for

the step from 1 N to 2 N reduces to -0.7

kcal/mole. This estimate of the powerful effect

of ion pairing on lowering the free energy of

hydrophobic association is greater for Ca^^

(-15 kcal/mole) and greater yet as the polymer

30 H

20 i

10 -I

Nal,

NaSCN

60 -

50 -

40 -

30 -

20 -

1 Sodium Dodecyl Sulfate 1

/ Guanldlne HClJ

/ ^ Urea J

1—^^=^^

Ethylene Glycol |

-^ .._____^^ Glycerol j

Trifluoroethanoi "—'

i~" • 1 ' r • 1 • I " 1

0.2

0.4 0.6

Molarity

0.8 1.0

FIGURE 5.11. Dependences of Tj-values for

poly(GVGVP) as a function of salt concentration,

(A) and of organic solvents and solutes (B). These

data are used in Table 5.4 on a per mole (normality)

basis to calculate the AGHA(solute) in terms of

kcal/mole solute. (Adapted with permission from

Urry^)

becomes more hydrophobic by replacement of

Val by Phe and He (see Figure 5.15).

For calculation of the lowering of

AGHA

due

to the ion pairing of -NHs^ with CI", within

poly[0.76(GVGVP),0.24(GK^GVP)] the data

in Table 3d of Luan and Urry^^ provide the

steepest slope (0.05 N to 0.20 N) to give the

value of ATt/N NaCl, that is, -177° C/N. From

Figure 5.10 the ATI/AGHA value established for

the ionization of the amino (K -^ K^) is

230°/12.5 kcal/mole. Accordingly, AGHA(Lys-

NHs^

••• CI"; steepest ion-pairing slope) ~ -9.6

kcal/mole-pentamer/N. After the effect of ion

pairing is complete, that is, for the slope above

1 N NaCl, this reduces to AGHA(Lys-NH3^ •••

CI";

0.5 N -^ 1.5 N salt) = -36. Again, the effect

of ion pairing to stabilize the hydrophobically

associated state of the model protein is seen to

be large.

Figure 5.12B demonstrates the effect of

adding a CH2 group, as for the more hydropho-

bic (GVGIP) repeat, on increasing the magni-

tude of the favorable change in the Gibbs free

energy for hydrophobic association as the

result of ion pairing. Also shown in Figure

5.12B is the greater capacity of calcium ion over

sodium ion in lowering the free energy for

hydrophobic association. This effect will be cal-

culated below in relation to the data in Figure

5.15.

5.3.4.7 Limited Relevance of AT^ Due to

Addition of Organic Solvents and Solutes

to Calculate Change in Free Energy

(AGHA)

for Hydrophobic Association of

Neutral Poly(GVGVP)

The dependence of Tt for poly(GVGVP) on the

addition of a series of organic solutes and sol-

vents is shown in Figure 5.1

IB.

Additional data

are given by Luan and Urry,^^ who also include

the thermodynamic values used below in com-

bination with Equation (5.10b) to estimate

AGHA,

as indicated in the footnotes of Table

5.4B. The solute with the steepest initial slope

for increasing the value of Tt on adding the

organic solute is SDS. One expects, therefore,

that it would be most effective in raising the

free energy of the hydrophobically folded state.

There is no calorimetry data available for SDS,