Urry D.W. (Ed.) What Sustains Life? : Consilient Mechanisms for Protein-Based Machines and Materials
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4.3 Protein Sequence as a Biosynthetic Construct
95
pletely specified sequence of 100 residues
would be (1/20)^^^, assuming an equal probabil-
ity for the incorporation of each amino acid.
Tliis is one chance in
10^^^.
On this basis, the
chance that a mixture of amino acids would
assemble spontaneously into a specified protein
sequence, even with catalyst and abundant
energy to activate the assembly reaction, is
essentially nonexistent. This is in part why argu-
ments arise in relation to biology for extraordi-
nary circumstances beyond those of common
experience to chemists and physicists. In order
to convey some sense of the magnitude of this
improbability, we next consider mass.
4.2.2 Probability in Terms of Mass of
100 Residue Protein Molecule
For a mean residue weight of 100 grams per
mole, 1 mole of a 100 residue protein would
weigh about
10
kg.
With the number of mole-
cules in a mole being Avogadro's number of
6.023 X 10^^ « 10^"^ molecules/mole, one mole-
cule of a 100 residue protein would weigh about
10"^^
grams. A quantity of 10^^^ distinct protein
molecules of 100 residues with an average
residue weight of 100 would weigh 10^^^ grams.
This is the mass that would result for one
molecule each of the possible 10^^^ distinct
sequences of a 100 residue protein.
To illustrate the magnitude, this quantity of
10^^^
grams can be compared with the total mass
of the earth. The mean density of the earth is
given as 5.5 grams/cm^, and the volume of the
earth is approximately
10^^
cm^ The total mass
of the earth becomes approximately 10^^ grams.
Thus,
if the total mass of the earth were made
up only of proteins of 100 residues of different
sequences, the chance of finding a specified
sequence would be no more than 1 chance in
10^^.
When any 1 of 20 residues can be in each
position in a 100 residue protein, the occur-
rence of a single molecule of specified sequence
is so improbable that finding the specified
sequence would still be unhkely, even if the
known universe were comprised of nothing but
100 residue protein sequences.
How, then, can there be tens of thousands
of unique and usually much longer protein
sequences in living organisms? The answer, of
course, comes from an understanding of the
process and energetics of protein biosynthesis.
4.2.3 Reaching the Extraordinary
Potential of such Enormous
Structural Diversity
Proteins have no rival in the world of polymers.
The difference is not small; rather, comparisons
involve the enormous numbers of improbabil-
ity noted above. Diversity in petroleum-based
polymers utilizes a number of different repeat-
ing units, but compositional variation within a
single polymer has been limited largely to so-
called block copolymers.
Taking the most meaningful advantage of
the enormous structural diversity of proteins
requires some sense of the physical basis of
function. Finding the way by a random selection
of sequences poses no option, because the pos-
sibilities are too many. Knowledge of the laws
that control structure and function, however,
does provide access to the potential of such
structural diversity. As presented in Chapter 5,
the consiUent mechanism offers the required
insight, that is, the emerging comprehensive
hydrophobic effect, and more specifically the
apolar-polar repulsive free energy of hydra-
tion, systematizes progress that has been
made in designing diverse and relatively effi-
cient elastic-contractile model protein-based
machines.
4.3 Protein Sequence as a
Biosynthetic Construct
With detailed knowledge of the biological
process of protein synthesis,^ it becomes pos-
sible to estimate a minimal amount of energy
required for biosynthesis of a specific protein
sequence. We have just seen that a specific
protein sequence is an extremely unlikely struc-
ture,
because each position in the sequence
could be occupied by any 1 of 20 of the natu-
rally occurring amino acid residues. Surpris-
ingly, as shown below, not only is the product of
the biological synthesis very probable, but ener-
getically biological synthesis of protein appears
to be a wasteful process. The required fidelity
96
4.
Likelihood of Life's Protein Machines:
Extravagant
in
Construction
Yet Efficient in Function
of a precise protein sequence comes at an extra-
ordinary cost in energy.
Biosynthesis of protein can be seen in three
steps:
repHcation, the production of the DNA
for a daughter cell; transcription, the conver-
sion of the DNA into the equivalent sequence
of RNA; and translation, the conversion of the
ribonucleic acid sequence into the specified
protein sequence, that is,
1.
DNA -^ replication -> DNA
2.
DNA -> transcription -^ RNA
3.
RNA -> translation -> protein
4.3.1 DNA Replication
4.3.1.1 Energy Cost to Produce DNA of
the Required Length
Production of a DNA sequence that encodes
for a 100 amino acid residue protein requires
300 bases (three for each triplet codon specify-
ing a particular amino acid at a specific posi-
tion) plus 3 bases for a start codon. (The table
of the genetic code specifying the sequence of
three bases [the triplet codon] that encodes
for each amino acid residue is given in Chapter
6.) The bases of the nucleic acids begin as
the triphosphates—adenosine triphosphates
(ATP),
guanosine triphosphates (GTP), thymi-
dine triphosphates (TTP), and cytosine triphos-
phates (CTP). The structures of these
nucleoside triphosphates (NTPs) may be
gleaned from Figures 3.13 and 3.14. The equa-
tion for the conversion of nucleoside triphos-
phates into the DNA polymer can be written as
follows:
p ATP
-h
qGTP + rTTP + sCTP =
DNA
-h
(p + q+r + s)PP (4.1a)
This utilizes nATP equivalents where n = (p +
q + r + s). As written. Equation (4.1a) is a
reversible reaction. The key element of irre-
versibility results from Equation (4.1b), the
removal of the side product, PP, which is an
inorganic diphosphate called pyrophosphate.
The enzyme pyrophosphatase catalyses the fol-
lowing very important reaction:
(p + q-h r + s)PP -^ pyrophosphatase -^
2(p-Hq-hr + s)P (4.1b)
Thus,
another nATP equivalents are required
where n = (p-hq-i-r-hs). One equivalent of ATP
is required to convert a nucleoside monophos-
phate (NMP) into a nucleoside diphosphate
(NDP) and a second is required to convert
the nucleoside diphosphate into a nucleoside
triphosphate (NTP). Accordingly, two equiva-
lents of ATP are required for the addition of
each base to the growing DNA polymer.
If the interest is in producing a 100 residue
protein, then a 300 base DNA would be
required, that
is,
n = 300
-1-2x3,
where one three
is due to a triplet stop codon and the second
three is due to the triplet start codon (AUG),
which encodes for methionine but which is
usually processed off. Therefore, 2n or 612 ATP
equivalents are required to duplicate a 306 base
strand of DNA to encode for a 100 residue
protein.
A key feature of the above equations is that
the reactions in Equation (4.1a) are reversible,
but those represented in Equation (4.1b) are
irreversible. This represents the very significant
means whereby synthesis of the gene, the
poly(deoxyribonucleic acid) encoding for
protein, is an irreversible process. Another
important expense of energy is that only inter-
mittent parts, called exons, of the DNA
sequence (the gene) actually encode for
protein. For the DNA that encodes elastin, less
than 20% is exon, the remainder, called introns,
does not encode for the protein. In addition,
there is much "junk" DNA carried along during
replication that appears to serve no useful
purpose.
4.3.1.2 Improbability of the Specified 306
Base Sequence of DNA
It is in fact more improbable to have a 306 base
sequence of DNA, poly(deoxyribonucleic
acid),
of an exactly specified sequence of bases
than it is to have a 100 residue protein of spec-
ified sequence. In the case of DNA, any one of
four bases can exist in each of the 306 base posi-
tions.
The chance of any single position being of
one of the four bases would be 1/4. Thus the
chance that each position contains the specified
base would be (l/4)^^^ which is
lO'^'^
Recall
that the number for the 100 residue protein was
4.3 Protein Sequence as a Biosynthetic Construct
97
10"^^^.
This result, however, requires modifica-
tion due to redundancy where several codons
can encode for a given amino acid residue. This
comes from the fact that, given four different
bases and a triplet codon, there are 64 different
triplet codons to encode for 20 amino acid
residues. (Table 6.2 shows how the 64 codons
are used.)
4.3,1.3 Probability of DNA Sequence in
Terms of an Equilibrium Constant
Writing the probability in terms of an equilib-
rium constant, K, uses the change in Gibbs free
energy, AG, in the form K = e""^^^^^, where R is
the gas constant, 1.98cal/mole-degree, and T is
the temperature in degrees Kelvin, for example,
310 for body temperature. Because the equilib-
rium constant is expressed as the ratio of re-
actants over products, it can be seen as a
statement of probability, that is, an equilibrium
constant of 1 indicates that reactant and prod-
ucts are equally likely. Now, K may be written
for the combined reactions represented by
Equations (4.1a) and (4.1b) as follows:
p ATP
-H
qGTP
-h
rTTP
-h
sCTP =
DNA-h2(p-hq-hr-hs)P (4.1')
Because the equilibrium constant for Equation
(4.1a) is approximately 1, that is, AG = 0, and
we know that the AG for hydrolysis of PP is
-8,000 cal/mole,^ each base addition of the
overall reaction of Equation (4.1') would have
an equiUbrium constant of K = e^'^^^^^^ = e^^ =
4.4 X 10^ = 10^^ Because there are 306 base
additions, the overall equilibrium constant
would be the product of 306 such reactions, that
is,
(10^^)^^ = W'^\ The reaction for DNA for-
mation is irreversible, not because of far-from-
equilibrium conditions, but rather because
energy is thrown away in Skcal/mole steps. The
result is that DNA is produced irreversibly at
an extraordinarily high cost in energy.
4.3.2 Transcription: DNA -^ RNA
4.3.2.1 Energy Cost to Produce RNA of
the Required Length
The following sets of analogous reactions
transcribe the DNA, deoxyribonucleic acid
sequence, into RNA, a ribonucleic acid
sequence. In RNA the DNA base of thymine
(T) is replaced by uracil (U), and, of course, the
ribose of the RNA replaces the deoxyribose of
DNA.
p ATP + qGTP + rUTP
+
sCTP = RNA
+
(p
-K
q
-h
r
-H
s)PP; nATP equivalents (4.2a)
(p +
q-i-
r + s)PP -^ pyrophosphatase -^
2(p
-h
q
-h
r
-h
s)P;
nATP equivalents (4.2b)
where n = (p-i-q4-r-i-s). Again, for a 300 (n)
base sequence of mRNA, and for the three base
start codon, which becomes translated into a
methionine residue, 2(300 + 3) equivalents of
ATP are required, that is, another 606 ATP
equivalents are utilized.
4.3.2.2 Improbability of the Specified 303
Base Sequence of RNA
The same argument applies for RNA as for
DNA except that there are 303 bases in the
sequence. Again, any one of four bases may
occur in each position of the 303 base sequence.
Thus we would write, (1/4)^^^ = 10"^^l Of course,
this again is more improbable than the 100
residue protein into which the RNA sequence
is translated, but this number is again not quite
so small due to codon redundancy.
4.3.2.3 Probability of RNA Sequence in
Terms of an Equilibrium Constant
Now, by adding Equations (4.2a) and (4.2b), we
have the equivalent overall reaction to that of
Equation (4.1') given above, that is,
p ATP + qGTP
+
rUTP
+
sCTP
= RNA
-H
2(p + q+r
-F
s)P (4.2')
Again by analogy to the argument used above
for DNA, we have for each base addition of
Equation (4.2') that K =
Q^^^'^^
= W\ Now
with the slightly fewer, 303, base additions, the
overall equilibrium constant would be (10^^)^^^
=
10^'^^^.
The reaction for RNA formation is irre-
versible, again because each addition is paid
for by a relatively small Skcal/mole packet of
energy. Thus, RNA is also produced, not by
far-from-equilibrium conditions, but, rather.
4.
Likelihood of Life's Protein Machines: Extravagant in
Construction
Yet Efficient in Function
from the summation of stepwise base-by-base
additions, due to an extraordinarily high overall
expenditure of energy.
4.3.3 Translation: RNA -^ Protein
4.3.3.1 Energy Cost of Loading Amino
Acids on tRNA
Before aligning the amino acids along the
messenger ribonucleic acid (mRNA) template,
the amino acid (AA) is activated by reaction
to form AMP-AA and transferred to a small
nucleic acid called tRNA, transfer ribonucleic
acid, that is tRNA-AA, which contains the
triplet codon for base pairing along the mRNA
sequence. This two-step reaction is shown as
Equations (4.3'a) and (4.3'b) below.
r| ATP
-H
r| AA = r| AMP-AA
-\-
r|PP (4.3'a)
TjAMP-AA-htRNA
= r| AMP + tRNA-AA (4.3'b)
where AMP is adenosine monophosphate and
ri is 100 for the 100 amino acids to be incorpo-
rated into the 100 residue protein. Reactions
indicated by Equations (4.3'a) and (4.3'b)
are reversible with the equiUbrium constant
for their sum being equal to 1. It is again the
removal of the PP byproduct of the reactions
that makes the activation and attachment of
the amino acids to tRNA an irreversible
process.
r|PP -^ pyrophosphatase -> 2r|P (4.3'c)
Accordingly, 2r| ATP equivalents are required,
which adds another 200 ATP equivalents.
4.3.3.2 Energy Cost of Binding and
Translocation oftRNA-AAs to
Form Protein
The final steps in achieving the growth of a
protein chain of specified sequence involve the
binding of tRNA-AAs to position 1 of the ribo-
some and aUgning along mRNA followed by
translocation to position 2 of ribosome with
incorporation into the growing peptide chain.
These reactions can be indicated by the follow-
ing equations:
TjtRNA-AA
+ K]
ribosome(position
1) +
rjGTP
-^ TjtRNA-AA-ribosome(position 1)
+ r|GDP-hr|P (4.3a)
r|tRNA-AA-ribosome(position 1)-H
r| ribosome(position 2)
-\-
r|GTP -^ TjtRNA-
AA-ribosome(position 2)-h r| ribosome
(position
1) -h
r|GDP
-h
r|P (4.3b)
ri(tRNA-AA-ribosome(position 2) -^
TjtRNA-h r|AA in protein (4.3c)
Because GTP is energetically equivalent to
ATP,
this requires r| (100) ATP equivalents
for Equation (4.3a) and another r| (100) ATP
equivalents for Equation (4.3b) to give another
200 ATP equivalents.
4.3.3.3 Probability of Protein Sequence
Arising from Translation Alone
Adding the reactions indicated by Equations
(4.3'a),
(4.3'b), and (4.3'c) again gives the oppor-
tunity to calculate a statement of probability
from the expression of the overall equilibrium
constant for addition of an amino acid to its
tRNA in terms of the change in Gibbs free
energy, K = e^'^^^^^^ =
10^
^ the ratio of product
to reactant favors product by a factor of some
100,000.
Thus, the activation of each amino acid
for selective alignment at the ribosome is essen-
tially an irreversible process.
The processes at the ribosome, required to
add a single amino acid of tRNA-AA to the
growing protein chain, results in the conversion
of two molecules of GTP to two molecules of
GDP plus two molecules of
P.
The standard free
energy of hydrolysis of ATP to ADP and P is
given as -7,290 cal/mole,^ and this same value
can be used for the hydrolysis of GTP to
GDP plus P. Thus for the equilibrium constant
we can estimate K = (e^'29o/RT)2 ^
^QH.S
Qf
course again the reaction goes to completion,
but irreversibility always occurs as a result of a
step by step loss of energy packets of about
8kcal/mole.
4.3.3.4 The Cost of Producing Scores of
tRNA Molecules
The tRNA that contains the anticodon for
alanine (Ala, A), tRNA^^^ has 76 bases such
4.4 Protein Machines: Improbable or Extravagant Constructs
99
that 75 bonds must be formed to assemble the
tRNA molecule with each bond utilizing 2 ATP
equivalents. This requires 150 ATP equivalents.
Furthermore, there are as many as 64 different
tRNA molecules. If we assume a codon redun-
dancy in a given species sufficient to require
40 different anticodons, the result would be
40
X
150 or 6,000 ATP equivalents.
4.3.3.4 The Cost of Producing
the Ribosome
The total mass of the Escherichia coli ribosome
is 2,520,000 Da. Considering only the protein
that constitutes only one third of the ribosome,
the molecular weight of the protein is 857,000
Da. Assuming the mean residue weight to be
100,
there are some
8,570
residues. The forma-
tion of
8,570
peptide bonds alone would cost
17,000 ATP equivalents. Thus, the assembly
of only the tRNA and protein components
required for translation at the ribosome
number requires much more than 23,000 ATP
equivalents. Of course, a ribosome can be used
for the synthesis of many copies of protein, but,
even with synthesis of a large number of pro-
teins before the ribosome would have to be
replaced, the number of ATP equivalents is
significant.
4.3.4 Summary of Minimal Energy
Expenditure to Produce Protein
The biosynthesis of the DNA sequence, repli-
cation, to encode for a 100 residue protein
requires 612 ATP equivalents. Transcription,
the biosynthesis of the RNA sequence to
encode for a 100 residue protein requires an
additional 606 ATP equivalents. The activation
of the amino acids and their attachment to the
correct tRNA requires another 200 ATP equiv-
alents,
and, finally, translation into the specified
100 residue protein requires yet another 200
ATP equivalents. The total number of ATPs
required is
1^618.
On the one hand, this overall
number does not recognize that a single strand
of DNA may produce many strands of RNA
and that a single strand of RNA may be used
to produce many protein chains. On the other
hand, this sum does not include the ATP
expense for producing the unused introns, the
junk DNA, the complex nuclear and ribosomal
structures, and all of the enzymes, for example,
pyrophosphatase and RNA polymerase, that
are necessary. In addition, there are other
expenses, for example, the many housekeeping
chores such as controUing the supercoiling of
nucleic acids by type II topoisomerases and
refolding of improperly folded protein by mol-
ecular chaperones. Thus, even by considering
individually the replication of DNA, or the
transcription to RNA, or the production of a
protein chain, the production of biology's poly-
mers occurs at an enormous cost in energy.
4.4 Protein Machines:
Improbable or Extravagant
Constructs
4.4.1 Comparison of Improbabilities
and Minimal Energy Costs
The probabilities of product formation arising
out of the individual processes of replication,
transcription, and translation were considered
separately above. Nonetheless, there remains
a curiosity to obtain some overall number to
compare with the factor of
10"^^^
arising out of
the probability of a specific sequence for a
protein when there are any of 20 residues pos-
sible for each position of a 100 residue protein.
A sense of the sort of number might be
obtained if the total energy were put in an equi-
librium expression relevant to the overall
process. Thus, the total energy consumed was
1,618 ATP equivalents. Thus we might write,
-8kcal/mole-ATP x 1,618 ATP = -12,944,000
cal/mole and K - e^^'^^^'^^^^^^ -
10^'^^^
Of course,
such numbers are so large as to have almost no
meaning, except perhaps to justify the state-
ment that the first copy of a 100 residue protein
of specified sequence was paid for by an enor-
mously extravagant expenditure of energy.
It is perhaps easier to discuss such biological
overkill in the drive toward synthesis in terms
of the addition of a single selected amino acid
residue at a given position in the growing
protein chain. The factor of 1/20 equals
10"^
^.
Putting this in terms of K =
IQ-^^/^^^^,
AG =
100
4.
Likelihood of Life's Protein Machines: Extravagant in
Construction
Yet Efficient in Function
1.8kcal/mole, yet the AG expenditure was ap-
proximately 30kcal/mole. Favoring the selec-
tive addition by a factor of 1 million, seemingly
an ample amount to ensure synthesis, would
require 8.4kcal/mole. Yet there are another
22kcal/mole expended for this individual step.
Therefore, this "creation of structure" did
not require "far-from-equiUbrium" conditions;
rather, it simply required an extravagant use
of the energy coin of biology. "Order Out of
Chaos" in terms of the production of the bio-
logical molecular machines occurs not under
classic irreversible conditions but rather simply
by the removal of a side product at the expense
of an extraordinary amount of free energy.
4.4.2 Comparison of Energy Required
to Form a 100 Residue Protein w^ith
that Released on Return of the
Residues to Free Amino Acids
There is another way to compare the two prob-
abilities. This is to compare the energy required
to combine amino acids into a protein with that
recovered when the protein of 99 peptide
bonds is hydrolyzed to return to amino acid
residues. In short, 1,618 ATP equivalents were
required to form 99 peptide bonds of the 100
residue protein, which is just over 16 ATPs per
peptide bond. This is a free energy cost of 8 x
16 = 128kcal/mole. As hydrolysis of a peptide
bond yields no more than
3
kcal/mole, the effi-
ciency of energy conversion would be about
2%.
Protein synthesis without considering pro-
duction of the required DNA and RNA, but
only the positioning of a single amino acid in
the correct position, could properly be called
extravagant as well.
4.4.3 Sun's Energy Required to
Produce a Small Protein
We now continue further consideration of the
biological machinery for production of protein.
Because more than 50 photons are required to
produce one glucose molecule, and one glucose
molecule results in 36 ATPs, and 1,618 ATP
equivalents (44.9 glucose molecules) are
required to produce the 100 residue protein,
some 2,250 photons would be required to
produce this small protein. This is about 23
photons per peptide bond. Based on a value of
70
kcal/mole of photons, this means much more
than 156,000 kcal is required to produce 1 mole
of a 100 amino acid residue protein worth about
300
kcal on hydrolysis to free amino acids. In
terms of energy recovered, this is an efficiency
of 0.2%. The quantity, 156,000
kcal,
is sufficient
energy to bring to a boil from room tempera-
ture more than 500 gallons of water. Overall
the biological process for creating a single
small protein from the energy available is
enormously extravagant.
This calculation assumes that the complex
apparatus of the enzymes and nucleic acids of
the ribosome appeared at no cost. The actual
cost should take into consideration the number
of times the individual components are used
before replacement is required, that is, the
so-called turnover number for each required
component of the ribosome, of the t RNA, of
the enzymes to carry out all of the syntheses of
the nucleic acids, to break down the pyrophos-
phates, to catalyze the polymerizations, to
correct errors, and so forth.
Despite this enormous expense, because the
photons from the sun are free and the products
such as glucose made with the sun's energy are
so inexpensive, utilizing the biological mecha-
nism to produce protein is orders of magnitude
more efficient than man's capacity to produce
protein by chemical synthesis. Based on large-
scale chemical synthesis, $20/gram would be
an optimistic cost for the synthesis of
poly(GVGVP), whereas less than $20/kg has
been indicated as possible with microbial
biosynthesis. It becomes quite obvious how
much we depend on the sun's energy reaching
the earth's surface and the photosynthetic
apparatus to harvest the sun's energy. This
simply reinforces our recognition of the essen-
tial role of the photosynthesis of the world's
forests and grasslands.
4.4.4 Implied Importance in Control
of Protein Sequence
Surely the occurrence and maintenance of such
a profuse process for protein biosynthesis
demonstrate an unequivocal need for complete
References 101
control of sequence and the continuing manda-
tory requirement of twenty diverse amino acids.
Why should this be the case? In the non-
biological world of petroleum-derived polymers
with limited residues available and without
control of sequence, function is much more
limited. One presumes that diverse function of
protein machines, by whatever means, requires
complete control of such diverse sequence.
From the viewpoint of required energy, the
biosynthetic process is extravagant indeed, yet
protein machines can be remarkably efficient in
spite of diverse function. For example the effi-
ciency of the Fi-ATPase in rotating an actin fil-
ament has been estimated to approach 100%.^
Why are these twenty amino acid residues
required and why, for example, are leucine and
valine residues functionally different from an
isoleucine residue? Such questions raise the
issue as to whether there might be a common
groundwork with which to understand protein
function using these twenty amino acid
residues. Might there be a consilient mechanism
wherein an understanding of otherwise subtle
differences among certain of the twenty amino
acids would become recognized as essential for
diverse function. These issues are addressed in
subsequent chapters.
References
1.
See for example
D.
Voet and J.
Voet,
Biochemistry,
Second Edition, John Wiley & Sons, Inc., New
York,
1995,
Chapter
V.
The Expression and Trans-
mission of Genetic Information, pp 830-1019.
2.
See for example
D.
Voet and J. Voet, Biochemistry.
Second Edition, John Wiley & Sons, Inc., New
York, 1995, standard free energies of phosphate
hydrolysis, Table
15-3,
page 430.
3.
K. Kinosita, Jr., R. Yasuda, and H. Noji, "Fi-
ATPase: a highly efficient rotary ATP machine."
In "Essays in Biochemistry: Molecular Motors'',
35,
3-18, 2000, Edited by G. Banting and S.J.
Higgins, Portland Press Ltd 59 Portland Place,
London, WIN 3AJ, U.K.
Consilient Mechanisms for Diverse
Protein-based Machines: The Efficient
Comprehensive Hydrophobic Effect
5.1 Introduction
The machines of biology are of a mechanism
more elemental than those of man's design.
Consider, for example, the intermittent internal
combustion (e.g., gasoline-reciprocating piston)
engine that performs the work of putting a
vehicle in motion. Fuel is injected in a timely
manner into a series of chambers; the fuel
vapors are ignited in each chamber; a series of
explosions of hot expanding gasses occur in
properly timed sequence; the hot expanding
gasses supply the energy that drives the pistons,
that by means of connecting rods rotates the
crankshaft, that through a clutch assembly
and speed-changing gears rotates the drive
shaft, that by means of a differential gear box
rotates the wheels, that puts the vehicle in
motion.
The fundamental process is simpler for
protein-based engines of biology. An energy
input drives spatially separated oil-like
domains of the protein into association and
thereby produces the motion of a contraction.
In our view, the protein-based engines of
biology function by shifting oil-like domains
between being water soluble and water insolu-
ble.
This perspective forms "a common ground-
work of explanation" for diverse functions of
protein machines; therefore, the perspective is
that of a consilient mechanism.^'^
Due to the diverse molecular compositions
of protein, different energy inputs cause the oil-
like regions to come together or to separate.
Because the many different energy inputs func-
tion by the same process of changing water
solubility of the oil-like regions, energy outputs
in addition to motion occur, and, because the
association/dissociation of oil-like domains is
generally reversible, energy inputs and energy
outputs can exchange roles. How a given energy
input changes the energy of the hydrophobi-
cally associated state becomes central to the
consihent mechanism of protein-based
machines.
In this chapter, we (1) note the structure and
elasticity of our unadorned model protein-
based machine, (2) catalog diverse energy
resources available to this consilient mecha-
nism as a function of model protein composi-
tion, (3) describe visual demonstration of
contraction and relaxation of elastic protein
bands functioning as engines that produce
motion with diverse energy inputs, (4) demon-
strate energy conversions not involving the
work of motion by means of the coupling of
functions through shared interaction with
hydrophobic hydration, (5) review the kinds of
work performed by these protein-based
machines, (6) establish the physical basis for
protein-based machines functioning by the
consilient mechanism, (7) establish a general
basis for positive cooperativity (Monod's
"second secret of life"), and (8) relate 6 and 7
to provide an understanding of the remarkable
efficiency made possible by the consilient
mechanism.
For many coworkers, and
myself,
this chapter
unfolds an ongoing journey of personal enlight-
enment, even of personal Ionian enchantment,^
102
5.1 Introduction
103
of longer than three decades. Developments
presented here generally follow the sequence in
which they occurred. The concluding paragraph
of the most complete scientific review to date
of the basic science aspects of our work,
chronologically lists the sequence of develop-
ments."^ That paragraph is quoted here
separately.^
In this section, we introduce key thoughts
and arguments in preparation for more com-
plete discussions in sections 5.2 through 5.9. For
even more detailed description and for differ-
ent vantage points of examination of what we
here call the consilient mechanism, please refer
to original reviews at more"^'^ and less^ techni-
cal levels and to the references listed therein
and herein. First reported in this chapter,
however, are thermodynamic derivations^'^ and
analyses (included in sections 5.1.3.4, 5.3, and
5.9). A developing general formaUsm for
energy conversion by the consilient mechanism
is begun in section 5.8.4. Those with a more
general background in this area need not
belabor these details in order to grasp the
essential point of this chapter. The elemental
message becomes a general sense of how one
achieves diverse energy conversions by the
design of model elastic-contractile protein-
based machines wherein the key becomes
control of hydrophobic association.
5.1.1 The Consilient Mechanism
for Controlhng Association of
Oil-hke Domains
5.1.1.1 Changes in Folding and
Association of Oil-like Domains of
Protein Chains Give Rise to Protein-
catalyzed Energy Conversion
5.1.1.1.1 Energy Conversions Sustain Life
The living organism itself accesses energies
available in its environment and converts those
energies into the energies needed for the full
range of biological functions. Machines convert
energy from one form to another, and proteins,
functioning as molecular machines, catalyze the
energy conversions of biology.
5.1.1.1.2 Oil-like and Vinegar-like
Parts of Proteins
In our
view,
an essential element of the many
dif-
ferent protein-catalyzed energy conversions of
biology resides in the old adage "oil and vinegar
don't mix." We apply the adage to oil-like and
vinegar-like parts^^ arising from different amino
acid residues constrained by sequence to coexist
along the protein chain. Key facets reside in the
repulsive forces that cause the oil-like parts and
vinegar-like parts of proteins to distance them-
selves one from the other and in the forces that
cause oil-like parts of protein chain molecules
to separate from water. These forces, between
oil-hke and changeable vinegar-like side chains
(also referred to as R-groups as in Figure
2.1
and
related text) distributed along the protein chain,
control whether or not oil-like regions separate
from water by association.
5.1.1.1.3 Sequence of Oil-like and
Vinegar-like Parts Control Folding and
Assembly of Proteins
Figure 2.1 provides example of the sequence-
dependent interplay between oil-like and
vinegar-hke residues of our elastic-contractile
model proteins that directs chain folding and
association of folded chains. The relative posi-
tion of oil-hke and vinegar-hke R-groups along
a sequence and the state of the vinegar-like
R-groups^^ determine when and in what
arrangement the oil-like R-groups separate
from water. In this chapter, we design diverse
molecular machines of elastic-contractile
model proteins. Repulsive interactions between
oil-like and changeable vinegar-hke R-groups
attached to the model proteins build up on
becoming more polar and relax on becoming
less polar, and thereby they reversibly catalyze
the many energy conversions exhibited by
living organisms.
5.1.1.2 A Consilient Mechanism Provides
a ''Common Groundwork of Explanation"
for the Diverse Energy Conversions
of Biology
The mechanism whereby oil-like groups sepa-
rate from vinegar-like groups provides a
104
5.
Consilient Mechanisms for Diverse Protein-based Machines
"common groundwork of explanation"^ for
diverse energy conversions that sustain Life; it
is a consilient mechanism for hydrophobic asso-
ciation.^^ Fundamental to this process is the
interplay of oil-like groups between being sur-
rounded by water to being separated from
water and self-associated, that is, from being
soluble to being insoluble in water.
5.1.1.2.1 Phase Separation and Its
Temperature Interval
Our model proteins provide a visible, that is,
macroscopic, demonstration of oil-like regions
going from being soluble to insoluble in water
by means of a dramatic phase change. A par-
ticular energy input causes the single phase of
a clear solution to become two visibly distinct
phases. In Figure 5.1A, the particular energy
input is heat, thermal energy, and the phase sep-
aration occurs as the temperature is raised from
room temperature, 25° C (77°
F),
to body tem-
perature, 37° C (98.6°
F).
For the parent elastic-
contractile model protein, poly(GVGVP) or
(GVGVP)n,^^ in water, the interval from 25°
to 37° C is its temperature interval for the phase
transition from solubility to insolubiUty (see
Figure 5.1C).
5.1.1.2.2 Phase Separations of Protein
Polymers Produce Motion
The fascinating phase transitions exhibited by
these elastic-contractile model proteins are
analyzed below. It is the phase transition of
these elastic model proteins that makes them
contractile model proteins and that brings in
other energy sources in addition to thermal by
virtue of the capacity of other energy sources
to change the temperature at which the phase
separation occurs. The phase diagram perspec-
tive,
therefore, provides a unifying means for
describing the many energy conversions possi-
ble by the consilient mechanism. It is the basic
process of oil-like domains gaining dominance
and then associating that drives the phase sepa-
ration and constitutes a contraction that can be
used to move an object.
To produce motion is to perform mechanical
work. In this case, mechanical work is the
energy output resulting from the particular
energy input that drove the contraction. In the
most fundamental demonstration of the con-
silient mechanism (see Section 5.1.4), thermal
energy is the input and mechanical work is the
output. First, however, we consider familiar and
not so familiar phase changes. Analysis of the
resulting phase diagrams opens the door to the
full range of energy conversions that occur in
biology, that is, opens the door to the consilient
mechanism of protein-based machines. This is a
mechanism whereby the set of energy conver-
sions of living organisms can occur.
5.1.2 Four Phase Changes
(Transitions) in Model Protein-Water
Systems
5.1.2.1 Familiar Phase Changes: Melting
of Ice and Vaporization of Water
5.1.2.1.1 Heat and Entropy Changes of Phase
Transitions
In schematic fashion. Figure 5.2 contains peaks
representing our most famihar reversible phase
transitions: the melting of ice near 0° C (32°F or
273° K) and the boiling of water near 100° C
(212° F or 373°
K).
These phase transitions in
the state of water represent changes from more
order to less order on raising the temperature.
The amount of heat required to melt ice to form
less ordered water is 80cal/gram (or, for the
molar heat of the transition, AHt[melting] =
80cal/gram x 18 gram/mole = -i-l,440cal/mole,
where the subscript t denotes transition).
The heat required to convert liquid water to
vapor is a much larger 540cal/gram, or AHt
(vaporization) = 540cal/gram x 18 gram/mole =
+9,720 cal/mole.
One way to look at this is to heat both ice-
cubes in a pan on the stove and to the same
amount of water in a second pan on a second
burner on the stove. It will take about seven
times more heat (produced by burning gas or
passing an electric current through a heating
element on a stove) to boil away the quantity
of water converting it from water to vapor
than to melt completely the same amount of
water in ice cubes at 0° C to form liquid water
atO°C.