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

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6.3 Mutations

and

Evolution

Protein-based Machines

TABLE

6.2. The genetic

code.

225

Firsl

•

end>

(;

luuu

uuc

UUA

UUG

CUU

cue

CUA

CUG

AUU

AUG

AUA

AUG

Phe 9"2

rii

Leu

Leu CH

H3C CH3

lie H3C-(j)H

CH2

CH3

Met**

H3C—S—CH2—GH2

GUU

GUC

GUA

GUG

Va, /H

H3C CH3

Second position

lucu

ucc

Ser

lUCA

UCG

ecu

cec

Pro

CCA

CCG

ACU

ACC

Thr

ACA

ACG

GCU

GCC

Ala

GCA

GCG

CH2

HO CH3

CH3

UAU

UAC

I'AA

UAc;

CAU

CAC

CAA

CAG

AAU

AAC

AAA

AAG

HjN*-

1^^

'>i%^i^

sroi'

HO—NH

0\n CH*

^C-0 i

CH2

Asn

1 ^

HjN

Lys

CH,—CHi—CHj—CH,

/• "0 •'

uou

UGC

VGA

UGG

CGU

CGC

CGA

COG

AGU

AGC

AGA

AGG

GGU

GGC

GGA

GGG

Cyt

srop

Trp CI

Arg

Ser

Arg

Gly

CHa

CHo

j ^

C==NH2

' i

NH2

(jJHj

1 Third

position

(.Tend)

! u

(;

Aoiipol.ii .imiiio .n

111

tt sulius .u»- t.uj h.iNiv trsuiiUN .irr hhu .u uiu r»

NUIIH

.IK ud .itul pol.u iitu h.it

j'.rti

r« suitu

an pitrpU

AI Ci li

Ills p,ut t>l

In- imli.itii'H sii;n.«l as wtW as t miiui; lor mirnial Mi i n suluis

Source: D. voet, J. Voet, and C. Pratl, Fundamentals of Biochemistry, John Wiley and Sons, New Tork, 1990.

The set of codons that encode for the same

residue, however, do not occur at random.

Instead, a set of four codons that may encode

for the same amino acid residue is such that the

third base in the triplet codon can change

without changing the amino acid residue. Of the

four codons for

valine,

for example, the first two

bases are always GU and the third base can be

any one of the four bases, U (uracil), C (cyto-

sine),

A (adenine), or G (guanine). Thus, this

residue has a factor in favor of its occurrence,

and because of this changes in the third base of

226 6. On the Evolution of Protein-based Machines

the triplet do not result in a mutation. These are

fundamental issues relating to the origin and

evolution of self-replicating Life.

As reviewed above and demonstrated in

Chapter 5, substitutions of the Val residue by

another residue allowed access to a new energy

source and/or a more efficient use of a given

energy source. Here we simply look at the

genetic code and observe whether the critical

process for this particular evolution of molecu-

lar machines is difficult or easy to achieve by

means of the changes dictated by the genetic

code. As argued by Behe, evolution of biology's

molecular machines presents a bewildering

enigma to the graduaUsm required of

Darwinian evolution.^ As we will note below,

quite the opposite obtains. When considering

the consiUent mechanism, functional relation-

ship emerges between the genetic code and

achieving diverse and more efficient protein-

based machines.

Clearly, the capacity to access energy avail-

able in the environment and to convert that

energy to useful function was key to survival of

primitive Life, once established. In fact, perhaps

the most remarkable and central characteristic

of Life is its evolutionary capacity to access

virtually every available energy source and to

adapt to utilize each energy source more effi-

ciently. Accordingly, it is central to evolution to

understand how simple or complex the process

of accessing a new energy source may be on the

basis of what we have learned about protein-

based machines functioning by the considered

hydrophobic consilient mechanism.

6.3.2 General Relationship of the

Genetic Code to the Consilient

Mechanism

Using the genetic code for all living organisms

given in Table 6.2, we now address whether a

coherence or a consilience can be identified

within the genetic code. In approaching this

issue, the genetic code may be looked upon as

families of amino acid residues. A family would

be that set of amino acid residues that has the

same base for the second position of the triplet

codon, and a member of the family would have

any one of the other four bases in the first posi-

tion. Now we ask if a family exists for which

there is good coherence in the property of the

R-groups of the family. By this we mean that a

change in the first and third base of the triplet

codons for the family would have only a quali-

tative effect on the resulting protein sequence.

In other words, does a family exist for which

any mutation, any change, involving the first

and/or third base of the triplet codon would not

fundamentally change or destroy function of

the resulting protein. If only one such family

exists,

then it might be called iht primary family

of the genetic code.

By considering the Tfbased hydrophobicity

scale noted in Chapter 2 and developed in

Chapter 5 (see Table 5.1), the primary family is

readily recognized; it is valine (Val, V), methio-

nine (Met, M), isoleucine (He, I), leucine (Leu,

L),

and phenylalanine (Phe, F). These are all

hydrophobic residues without any other

functional capacity. The residues valine and

methionine exhibit a similar degree of oil-like

character. Substitution of one by the other

would hardly change the temperature of the

inverse temperature transition at all. Conver-

sion from Val to He or Leu results in the simple

addition of a CH2 group, which constitutes a

modest increase in oil-like character. Conver-

sion of Val to Phe does involve a substantial

increase in oil-like character, but adds no other

physical property, only an increase in oil-like

character.

It is important to note that tyrosine (Tyr, Y)

and tryptophan

(Trp,

W) are more hydrophobic

than valine in the Tfbased hydrophobicity

scale. Therefore, Y and W would be candidates

for the primary, the hydrophobic, family of the

genetic code, except that these residues add

additional physical properties. Both have large

dipole moments and exhibit chemical reactivi-

ties that can dramatically change their oil-like

character. Most notably, tyrosine can be a site

for phosphorylation, which converts it to a

supervinegar-like residue and dramatically dis-

rupts hydrophobic folding, assembly, and asso-

ciated functions. On our scale, based directly on

the hydrophobic association event, tryptophan

is the most hydrophobic residue, whereas other

scales that utilize less direct means of assessing

functional hydrophobicity place trytophan at

much less hydrophobic positions. Thus, these

residues, tyrosine and tryptophan, would not

6.3 Mutations and Evolution of Protein-based Machines

227

constitute part of a family that is unambigu-

ously oil-like in its function.

The other three famihes of the genetic code

encode for less homogeneous sets of amino

acid residues. Perhaps the second most

coherent family would be that with C (cyto-

sine) in the second position of the triplet.

These residues occupy a neutral range in the

hydrophobicity scale. These are alanine (Ala,

A),

serine (Ser, S), proline (Pro, P), and threo-

nine (Thr, T), but S and T can be phosphory-

lated to become supervinegar-like residues. The

most diverse family would appear to be that

with A (adenine) in position two of the triplet

codon. These residues span from the most polar

glutamic acid residue with a negative charge, to

lysine with the opposite signed charge, to the

very hydrophobic tyrosine with a site for phos-

phorylation, to histidine, which, due to its struc-

ture,

provides key functionaUty in active sites

of many enzymes, and finally to glutamine

and asparagine, which are relatively unstable

and with time can break down to glutamic

and aspartic acids. The remaining family with

G (guanine) in position two is also a mixed

bag containing glycine, cysteine, trytophan,

arginine, and, again, serine. Clearly, the most

homogeneous and coherent family is the unam-

biguously hydrophobic family with U (uracil) in

position two.

Starting with the primary (hydrophobic)

family of amino acid residues with U as the

second base of the triplet codon, only a change

in the second base provides the opportunity to

change to a less oil-like, more vinegar-like

residue. Among the more vinegar-like residues

are the negatively charged and positively

charged residues that provide direct access to

new energy sources, as noted above and seen in

Chapter 5.

6.3.3 Mutations That Create New and

More Efficient Molecular Machines

The capacity to access a new energy source

constitutes the cardinal step in the evolution of

an organism. As we will discuss, it represents

but a trivial step in structural modification at

the DNA level. The capacity to access a new

energy source or to more efficiently use a

source of energy renders an organism more fit

to survive whenever an energy source becomes

limiting or wherever a different energy source

is available. This symbolizes natural selection

and survival of the fittest in terms of molecular

machines.

6.3.3.1

Changing Val to Glu

(a Step Toward Diversity and

Greater Complexity)

The mutation, the change in base sequence of

DNA to insert a different amino acid residue

in the resulting protein, required to access a

new energy source is remarkably minimal. A

single base change in the codon encoding for

valine allows the change from a thermally

driven protein-based machine to a more effi-

cient chemically driven protein-based machine.

The mutation from a Val residue to a carboxy-

late-containing Glu or Asp residue requires but

a single base change in the triplet codon, and it

can occur with any of the four codons for the

Val residue.

Changing the second base of two of the four

triplet codons for Val, namely, GUA and GUG

to GAA and GAG, respectively, are two ways

to convert Val to Glu. Changing the second

base of the other two triplet codons for Val, for

example, GUU to GAU and GUC to GAC,

converts Val to

Asp.

Thus,

the Val triplet codons

are such that a single base change of the second

base from U to A results in amino acid residues

with carboxylate side chains. A single mutation

converts a thermally driven (and also a poor

chemically driven) protein-based machine into a

more efficient chemically driven protein-based

machine. How trivial and likely the diversifica-

tion of biology's molecular machines, especially

because it costs no more energy (of biosynthe-

sis) to produce the new or improved protein-

based machine.

6.3.3.2

Changing Val to Phe (Another

Step Toward Diversity and Complexity)

The mutation from the Val residue to the more

oil-like Phe residue again requires but a single

base change in the triplet codon, and it can

occur with either of two codons. Instead of

changing the second base of GUU and GUC to

A to get aspartic acid, the first base, G, is

changed to U to give the very hydrophobic

228

6. On the Evolution of Protein-based Machines

phenylalanine

residue.

The change of Val to Phe

results in more efficient chemically driven

protein-based machines as well as accesses

pressure energy, as discussed above (also see

Figures 1.2, 1.3, and 5.34). More modest

increases in hydrophobicity and in resulting

efficiency occur by changing the first base in the

valine triplet codons from G to C, for example,

to give leucine, and to A to give isoleucine from

any three of valine's four triplet codons. For the

fourth triplet codon of valine, GUG, conversion

of the first base to A gives methionine with an

insignificant change in oil-like character from

that of valine.

6J.3.3 Replacing Oil-Like Residues

by Positively Charged Residues

(Further Steps Toward Diversity and

Greater Complexity)

As indicated above, isoleucine (He, I) is only

slightly more hydrophobic than valine, and

methionine (Met, M) is very similar to valine

when compared using the T^based hydropho-

bicity scale. Thus these are functionally equiva-

lent, or nearly so, to the valine residue. The

AUA triplet codon for isoleucine and the AUG

triplet codon for methionine convert to codons

for lysine by changing the second base in these

triplet codons to A. A single base change from

these hydrophobic residues gives lysine (Lys,

K).

Changing the same isoleucine and methio-

nine codons to G in the second position gives

the positively charged arginine residue, as does

the same change to four CUX leucine codons.

As noted above, the presence of lysine provides

entry to electromechanical and electrochemical

transduction by the capacity of the positively

charged lysyl side chain to bind the negatively

charged nicotinamide and flavin mononu-

cleotides, for example. This added structural

complexity provides for electrically(redox)-

driven protein-based molecular machines.

6.3.3.4

Providing Sites

for Phosphorylation

It is remarkable that the above identified

primary family of amino acids of the genetic

code can, by single base mutations, give rise to

the full range of protein-based machines for the

conversion of one form of energy to another.

Another fundamental energy conversion is

from one form of chemical energy to another.

The central energy conversion between chemi-

cal energies in biology involves phosphoryla-

tion.

The required mutations to provide sites for

attachment of phosphate are those that result

in amino acid residues with the -OH group

available. The residues with the OH functional

group are tyrosine, serine, and threonine. Con-

verting the second, the central, U of phenylala-

nine to A accesses tyrosine. On the other hand,

conversion of the central U of phenylalanine to

C gives serine. Finally, threonine derives from

conversion of the central U of the triplet codon

of isoleucine and methionine to C.

6.3.4 Single Base Mutations Access

New and/or More Efficient Machines

In short, the primary (hydrophobic) family of

the genetic code, which provides for the

hydrophobic phase separation mechanism, also

provides the capacity to access all classes of

protein-based machines, that is, all energy

sources, by a single base change. This is the

nature of the genetic code. In this

regard,

the

genetic code becomes understood in terms of

Tt-type protein-based machines. Might protein

machines based on inverse temperature transi-

tional behavior be fundamental for Life to exist?

6.4 Energy Inputs Create Order

Out of Chaos (Biology's

Reversal of Time's Arrow for

the Universe)

From the Preface of Order Out of Chaos^:

Our scientific heritage includes two basic questions

which till now no answer was provided. One is the

relation between order and

disorder.

The

famous law

of increase of entropy describes the world as evolv-

ing from order to disorder; still, biological or social

evolution shows us the complex emerging from the

simple.

How is this possible? How can structure arise

from disorder? Great progress has been realized in

this question. We know now that nonequilibrium,

6.4 Energy Inputs Create Order

Out of

Chaos

229

the flow

matter

and

energy,

may be a

source

order.

to the

point,

we now see

biology's access

to energy

means

the consiUent mechanism

of energy conversion, combined with readily

available mutations

improve protein-based

machines,

as the

source

increased structural

order

and

functional diversity.

Again drawing from Toffler's Forward

for

Order

Out of

Chaos^:

In classical

mechanistic science, events begin with

"initial conditions,"

and

their atoms

particles

follow "world lines"

trajectories. These

can be

traced either backward into

the

past

forward into

the future. This is just

the

opposite

certain chem-

ical reactions,

for

example,

which

two

liquids

poured into

the

same

pot

diffuse until

the

mixture

is uniform

homogenous. These hquids

do not

de-diffuse themselves.

each moment

time

the mixture

different,

the

entire process

"time

oriented."

The time orientation

relentlessly

in the

direc-

tion

maximal disorder.

While indeed

the two

hquids

do not of

them-

selves de-diffuse,

we are

familiar with energy

inputs that drive de-mixing. During Prohibition

the

United States,

the

so-called revenoors

were bent

shutting down

the

stills

in the

backwoods.

this process known

distilla-

tion, the

two

Hquids

are

water

and

ethanol. With

sufficient input

thermal energy,

the

alcohol

could

largely separated from water

and

other components

of the

fermentation process

to make "moonshine." The demand

for

"moon-

shine" more than paid

for the

heat energy

required

distill

the

ferment. Thus, given

suf-

ficient energy

the

chaos

of the

mixture

reversed.

The phase separation mechanism

biology,

the separation

oil-like groups

protein

from water,

such that

it has the

capacity

take

energy efficiently

and

thereby

reverse

the flow toward disorder. Given appropriate

protein machines

and

energy sources, each

being accessible

by a

simple single base muta-

tion,

the

phase separation mechanism

biology

can,

with sufficiently reliable inputs

energy,

used

create ever-increasing order

and complexity.

6.4.1 Input

Energy Reverses Chaos

Mixture

6.4.1.1

Heating (Thermal Energy)

Achieves De-mixing

and

Self-assembly

Two protein-based polymers with different tem-

peratures

for

their inverse temperature transi-

tions,

for

example. Polymer

(GVGVP)25i with

Tt of

25° C,

and

Polymer

XII,

(GVGIP)26o(GVGVP) with

10° C,

can be

thoroughly mixed

and

dissolved

in a

solution

below 10° C.

The

protein-based polymers

whichever composition

are

completely disor-

dered

one

with respect

to the

other. Chains

of Polymer

XII are

completely randomly

dispersed with respect

themselves

and

with

respect

to the

chains

Polymer

There

complete chaos

in the

relationship among

the

polymers

solution.

Remember that

the

difference between

these polymers

quite modest. They differ

only

one CH2 in

each five residues. However,

because they exhibit inverse temperature

transitions

different onset temperatures,

one

polymer

can be

separated from

the

other

and

self-assembled into

ordered structure with

minimal input

energy.

For example,

the

completely disordered

and

mixed solution

Polymers

I and XII can be

heated from below 10°

C to

20° C,

and the

model protein with

the

lower transition

temperature will de-mix completely;

will

self-

separate

and

self-assemble

(see

Figure 6.2A).^^

Because

of the

nature

of the

phase separation

mechanism

(the

inverse temperature transi-

tion),

the

energy required

de-mix

and self-

assemble

small.

On a per

gram basis

it is

very

much less than

the

energy required

distil

spirits, that

is, to

separate alcohol from

fer-

mentation mixture. Remember also

the

simpler

cyclic analogue that

can be

dissolved

solution,

but

which

raising

the

temperature

reversibly forms crystals

(see

Figure

2.7).

This

is the

ultimate example

of an

increase

order,

and it

occurs

raising

the

temperature.

Of course,

the

essential player

in the self-

separation process

is the

structured water

surrounding oil-Uke groups when dissolved

solution.

230

6. On the Evolution of Protein-based Machines

T 2.5 m cal/sec-gram

a. Poly(IPGVG)

b. Poly(VPGVG)

-i^

Poly(IPGVG)

Poly[0.5(VPGVG) • 0.5(IPGVG)]

Poly[0.82(IPQVQ),0.18(IPQEG)] In H2O

pH2.3

FIGURE 6.2. Differential scanning

calorimetry data of elastic-

contractile model proteins. (A)

Phase separation transition for Poly-

mers I and XII, alone in solution

(curves a and c) and when mixed in

the same solution (curve b). Even

when mixed, the individual polymers

separate from each other; they de-

mix due to the input of thermal

energy during a slow increase in

temperature. Also a polymer was

synthesized that contained equal

amounts of the two pentamers, and

its phase transition is found at an

intermediate temperature (curve d).

(B) With a composition having a

carboxylate function, the input of

chemical energy of protons (addi-

tion of acid to lower the pH) drives

the phase separation to lower tem-

peratures. See text for discussion.

(Reproduced with permission from

Urry et al.'')

30 40 50

Temperature °C

6.4,1.2

Chemical Energy Achieves

De-mixing and Self-assembly

Continuing with the mixed solution of Poly-

mers I and XII as defined in Table 6.1, separa-

tion and self-assembly can also be achieved

with the addition of chemical energy at con-

stant temperature. The addition of a chemical

energy, such as the addition of salt at 25° C to a

solution of poly(GVGVP) plus poly(GVGIP),

just sufficient to lower the temperature of the

polymer with the lower transition temperature,

Polymer XII, to below the operating tempera-

ture,

can cause that polymer to self-separate.^^

Again, the energy input leads to the decrease in

entropy represented by de-mixing and by the

ordering, the self-assembly, of Polymer XII, in

analogy to Figure 6.2A, but the input energy

now is increasing salt concentration rather than

increasing temperature.

Addition of more salt can cause the Polymer

I with the higher transition temperature also to

separate out of solution. Even with one phase-

separated polymer layered over the other, these

molecules do not again become significantly re-

scrambled. Replacement of the overlying salt

6.4 Energy Inputs Create Order Out of Chaos

231

solution with pure water results in the slow

dissolution and re-mixing of the two poly-

mer compositions. Thus, this is a completely

reversible open system when there is an appro-

priate energy change.

The amount of energy required for de-mixing

and assembly sets biological macromolecular

systems apart from other molecular systems.

De-mixing of water and alcohol is a much more

difficult problem. Distillation, for example, is

itself an energy-demanding process, and the

separation of alcohol from water is not com-

plete because the alcohol distillate still contains

a fixed amount of water. This alcohol and water

distil as an azeotrope, with a set ratio of water

to alcohol. Further energy input is yet required

to achieve complete separation. On the other

hand, the complete de-mixing of our two

protein-based polymers requires but a small

amount of energy. Furthermore, we should note

that each separates from the other with their

own predetermined water composition.

6A.13 Heating Assembles Different But

Complementary Model Proteins from the

Chaos of Solution

Polymer V, (GVGVP GVGFP GEGFP

GVGVP GVGFP GVGFP)n(GVGVP), with 1

Glu (E) and 4 Phe (F) per 30 residues, and

Polymer VII, (GVGVP GVGVP GKGVP

GVGVP GVGVP GVGVP)n(GVGVP), with 1

Lys (K) and no Phe (F) per 30 residues, will

each dissolve in solution at room temperature

and physiological pH to become completely

mixed in solution. As with Polymers I and XII

above, they become completely and randomly

dispersed, each polymer chain exhibiting no

relation with respect to all others. If the tem-

perature is then raised above a critical temper-

ature of 13°

the positive charge of Polymer

VII pairs with the negative charge of Polymer

V in a pairwise self-assembly and separation

from solution, as shown in Figure 6.3B.^^ The

polymers communicate with each other to form

a more complex structure, shown in Figure 6.4.

Because in each case the charge has destruc-

tured a significant part of the ordered water

around the oil-like groups of each polymer in

solution, the amount of energy required to

achieve this striking organization is even

less than that required for the association of

uncharged polymers. Heating causes these com-

plementary model proteins to proceed efficiently

from the chaos of solution to form a specific

organized structure. The time's arrow for this

system, solution of water plus two hydrated

model proteins, however, as a whole continues

toward disorder. Under the circumstances

described, heating provides for formation of an

ordered structure containing the two comple-

mentary model proteins in Figure 6.4, but the

more structured water surrounding the oil-like

Val and Phe groups of the dissolved model pro-

teins becomes less ordered bulk water, such

that the overall change is toward disorder.

6.4.2 Poised Complementary Model

Proteins Each Contribute Energy for

Creating Order Out of Chaos

Let us again consider Polymers V and VII as

above, but in this example they are each dis-

solved in separate solutions with Polymer I.

At room temperature and physiological pH,

Polymer I is completely mixed in solution with

Polymer V in one vial, and in a second vial

Polymer I is mixed in solution with Polymer

VII.

With regard to the polymers, chaos reigns

in both solutions. When the solutions of the two

vials are mixed, however, instead of increasing

the chaos further, Polymer V assembles with

Polymer VII to form the organized structure in

Figure 6.4, leaving Polymer I alone in solution.

This association to form the structuring in

Figure 6.4 occurred without the addition of any

external energy. These two different solutions

poured into the same pot do not "diffuse until

the mixture is uniform or homogenous."

Energy, arising out of the sequence, resides

within each of the dissolved polymers. Polymer

V and VII. Each model protein has effectively

contributed energy to the other polymer for the

mutual assembly of the specifically complemen-

tary polymers. By virtue of complementary

structures, these molecules communicate with

one another to create order out of chaos! The

energy input for this ordering process was the

energy expended during protein synthesis. All

of the polymers, however, cost the same amount

232

6. On the Evolution of Protein-based Machines

K/OF 70OC

K/2F 36°C

K/3F 26° C

K/4F IS'^C

K/OF -E/OF 350C

K/OF -E/2F 24°C

K/0F-E/3F17°C

K/0F-E/4F 13°C

K/0F-E/5F 7°C

E/OF - K/OF 350C

E/OF - K/2F 22°C

E/OF

K/3F 14°C

•h E/0F-K/4F 8°C

30 40 50

Temperature, ^C

FIGURE

6.3. Temperature profiles for assembly of a

series of elastic-contractile model proteins contain-

ing one charged residue in a 30 residue repeat, either

a Lys (K) residue with the -(CH2)4NH3^ charged side

chain or a Glu (E) residue with the -(CH2)2COO"

charged side chain, and containing increasing

hydrophobicity by Val residue replacement with

more oil-like Phe (F) residues. These polymers are

defined in Table 6.1 as Polymers II though XI. Con-

ditions are 40mg/ml polymer at pH 7.5 in 0.01 M

phosphate. (A) Temperature-elicited self-assembly

of Polymers VII through X, identified as K/OF, K/2F,

K/3F and K/4F. (B) Temperature-driven association

of oppositely charged (complementary) polymers

with a constant Lys (K)-containing polymer, K/OF,

and varying hydrophobicity of the Glu (E)-con-

taining polymers, E/OF, E/2F, E/3F, E/4F, and E/5F.

charged (complementary) polymers with a constant

Glu (E)-containing polymer, E/OF, and varying

hydrophobicity of the Lys (K)-containing polymers,

K/OF, K/2F, K/3F, and K/4F. Under the conditions

used, the self-assembly of E/0°F is greater than 80° C

(not shown) and that of K/OF occurs at 70° C (shown

in A) such that individually at 37° C both polymers

form clear solutions. On combining the two solutions

above 13° C, they associate. Each complementary

polymer provides the chemical energy to the other

for structure formation. See text for imphcations.

(Reproduced with permission from Urry et al.^^)

6.4 Energy Inputs Create Order Out of Chaos

233

Self-assembly of protein-based polymers

by ion-pairing of hydrophobically poised charges

Phe

residues

FIGURE 6.4. Ion-paired complementary structure

formed on combining solutions of two model pro-

teins,

E/4F and K/OF, that is, Polymers V and VII,

respectively, as defined in Table 6.1. The data are

given in Figure 6.3B. See text for discussion.

of energy to produce by biosynthesis, but com-

plementary sequences caused two to combine

and create order out of chaos.

6.4.2.1

Within Each Model Protein There

Exists a Repulsive Free Energy Between

Charged Groups and Oil-like Groups as

Each Reaches for Water of Hydration

Unperturbed by the Other

Conventional wisdom would say that the addi-

tion of a charged group to a generally oil-like

model protein would increase its solubility, and

this is correct. Conventional wisdom would not

recognize, however, that the charged groups

of these fully dissolved and generally unstruc-

tured model proteins before mixing would

be at increased free energy. After all, in the

conventional view, increases in free energy of

a charged species arise either from charge-

charge repulsion or by charge being con-

strained in some way to exist in a medium of

low dielectric constant, as being forced by a

"conformational change." Neither of these con-

ventional arguments is applicable to this case of

1 charge per 30 residues and generally disor-

dered dissolved model protein.

As developed in Chapter 5, the interaction

energy that is applicable is a repulsive free

energy of hydration between the charged

groups and the oil-like groups arising out of a

competition for hydration between the charged

and oil-like groups. This we have called an

apolar-polar repulsive free energy of hydra-

tion, AGap, as approximated by hydrophobic-

induced pKa shifts (see Figures 1.2 and 5.20).

Furthermore, when there is no charge-charge

repulsion, AGap = -5AGHA, the Gibbs free

energy of hydrophobic association (see

Chapter 5 for the derivations).

For Polymers II through XI, AGap measures

the increase in free energy of the carboxylate,

-COO",

or of the charged amino, -NHs^, which

is reflected in systematic increases in pKa shifts

(see Figures 1.2 and 5.20). This results from an

increase in oil-like hydration due to replace-

ment of Val (V) by Phe (F), which, by com-

petition for hydration, limits hydration of the

charged species. In an entirely analogous way,

we beUeve that the free energy of a phosphate,

-OPO3",

can be increased, that is, energized,

due to a face-off between extremely polar phos-

phate and oil-like domains. As argued in

Chapter 8, we beUeve this to be relevant to the

function of ATP synthase and to the myosin II

motor of muscle contraction.

6.4.2.2

By Protein Biosynthesis, Polymers

/, V, and VII Each Requires the Same

Energy to Produce Chains of

the Same Length

As was discussed in Chapter 4, the energy

required to produce a specific protein sequence

234

6. On the Evolution of Protein-based Machines

is independent of the sequence. Therefore, it

requires no more energy to produce a 1,000

residue sequence of Polymer V or of Polymer

VII than it does to produce a 1,000 residue

sequence of Polymer

Yet Polymers V and VII

are at higher energy due to the repulsive free

energy of interaction between the oil-Uke and

charged residues. The higher energies are

directly measurable from the magnitudes of

their hydrophobic-induced pKa shifts exhibited

by their charged -COO" and -NHs^ groups.

Because of their energized complementary

sequences. Polymers V and VII are poised for

hydrophobic association induced by ion-pair

formation.^^ They are energized for structure

formation due to the large apolar-polar repulsion,

AGap, within the separated chains that relaxes

on ion pairing with hydrophobic association.

In an analogous manner, mutations in hom-

ologous protein domains result in new asso-

ciations of the protein domains with the result

of new structure and new function. From

the emerging data on the human genome, it

appears that as many as half of the human

genes were derived in this way from the genes

of lower species to result in diversity of struc-

ture and improved function required of higher

species.

6A23 ''Order Out of Chaos'' by

Combining Complementary Protein

Domains with Each Separately Being

at Equilibrium

To provide broader impUcations of this associ-

ation of complementary model proteins, we

turn to Prigogine and Stengers' Order Out of

Chaos'''.

On the other hand, far from equilibrium there

appears

variety of mechanisms corresponding to the

possibility of occurrence of various types of dissipa-

tive structures. For example, far from equilibrium

we ... may also have processes of self-organization

leading to nonhomogeneous structures to nonequi-

librium

crystals....

can speak of

a new

coherence,

of a mechanism of "communication" among mole-

cules.

But this type of communication can arise only

in far from equilibrium conditions. It is quite inter-

esting that such communication seems to be the rule

in the world of

biology.

It may in fact be taken as the

very basis of the definition of a biological system.

In our example of communication among

molecules, the source of the communication

resides within the energetics of each dissolved

polymer sequence. We considered in Chapter 4

the biosynthesis of protein of specified

sequence. The biosynthesis of protein requires

a great deal of energy, and thereby a protein

sequence might be considered a "dissipative

structure." More correct, however, would be to

consider a protein sequence as a unique storage

device with the distinctive propensity for orga-

nization of structure and specialized function.

Nor would the many small energy steps, taken

during biosynthesis, be reasonably representa-

tive of far-from-equilibrium conditions. Nor

would the individual Polymer V or VII sepa-

rately in solution be reasonably considered as

existing under conditions far from equilibrium,

because their AGap values would generally be

less than 8 to lOkcal/mole. Therefore, it would

seem that proteins of unique sequence, even

when energized by an apolar-polar repulsive

free energy and capable of forming ordered

structures of complex function by virtue of their

sequence, are not well-represented by terms

such as dissipative

Sind

far from equilibrium.

Importantly, for polymers of the same length,

the energy required for biosynthesis of Poly-

mers V and VII would be no different from

the energy to produce Polymer I, and yet only

Polymers V and VII exhibited this particular

propensity to self-organize. Directing time's

arrow relentlessly toward synthesis utilizes, in

sum, the simple doubling of the energy re-

quired for each step by the trick of removing

the pyrophosphate reaction product (see

Chapter 4). Thus, biological creation of struc-

tures would not seem to require far-from-

equilibrium conditions.

Instead, biology creates new structures and

functions by employing relatively small packets

of energy, using approximately 8kcal/mole

steps,

derived ultimately from the energy of

sunlight. In particular, the energy of the sun as

trapped by biology's photosynthetic process

creates the glucose structure; the glucose struc-

ture through the energy conversions of biology

results in the universal biological energy cur-

rency ATP (adenosine triphosphate), and ATP

and its equivalents provide the energy for