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Origin of the Species
Chapter 8: Thermodynamics and the Origins of Life
Peter Molton has defined life as "regions of order which use energy to maintain
their organization against the disruptive force of entropy."1 In
Chapter 7 it has been shown that energy and/or mass flow through a system can
constrain it far from equilibrium, resulting in an increase in order. Thus, it
is thermodynamically possible to develop complex living forms, assuming the
energy flow through the system can somehow be effective in organizing the simple
chemicals into the complex arrangements associated with life.
In existing living systems, the coupling of the energy flow to the organizing
"work" occurs through the metabolic motor of DNA, enzymes, etc. This is
analogous to an automobile converting the chemical energy in gasoline into
mechanical torque on the wheels. We can give a thermodynamic account of how
life's metabolic motor works. The origin of the metabolic motor (DNA, enzymes,
etc.) itself, however, is more difficult to explain thermodynamically, since a
mechanism of coupling the energy flow to the organizing work is unknown for
prebiological systems. Nicolis and Prigogine summarize the problem in this way:
Needless to say, these simple remarks cannot suffice to solve the problem of
biological order. One would like not only to establish that the second law
0) is compatible with a decrease in overall entropy (dS < 0), but also to
indicate the mechanisms responsible for the emergence and maintenance of
Without a doubt, the atoms and molecules which comprise living cells
individually obey the laws of chemistry and physics, including the laws of
thermodynamics. The enigma is the origin of so unlikely an organization of these
atoms and molecules. The electronic computer provides a striking analogy to the
living cell. Each component in a computer obeys the laws of electronics and
mechanics. The key to the computer's marvel lies, however, in the highly
unlikely organization of the parts which harness the laws of electronics and
mechanics. In the computer, this organization was specially arranged by the
designers and builders and continues to operate (with occasional frustrating
lapses) through the periodic maintenance of service engineers.
Living systems have even greater organization. The problem then, that molecular
biologists and theoretical physicists are addressing, is how the organization of
living systems could have arisen spontaneously. Prigogine et al., have
All these features bring the scientist a wealth of new problems. In the
first place, one has systems that have evolved spontaneously to extremely
organized and complex forms. Coherent behavior is really the characteristic
feature of biological systems.3
In this chapter we will consider only the problem of the origin of
living systems. Specifically, we will discuss the arduous task of using simple
biomonomers to construct complex polymers such as DNA and protein by means of
thermal, electrical, chemical, or solar energy. We will first specify the nature
and magnitude of the "work" to be done in building DNA and enzymes.
[NOTE: Work in physics normally refers to force times displacement. In this
chapter it refers in a more general way to the change in Gibbs free energy
of the system that accompanies the polymerization of monomers into
In Chapter 9 we will describe the various theoretical models which attempt to
explain how the undirected flow of energy through simple chemicals can
accomplish the work necessary to produce complex polymers. Then we will review
the experimental studies that have been conducted to test these models. Finally
we will summarize the current understanding of this subject.
How can we specify in a more precise way the work to be done by energy flow
through the system to synthesize DNA and protein from simple biomonomers? While
the origin of living systems involves more than the genesis of enzymes and DNA,
these components are essential to any system if replication is to occur. It is
generally agreed that natural selection can act only on systems capable of
replication. This being the case, the formation of a DNA/enzyme system by
processes other than natural selection is a necessary (though not sufficient)
part of a naturalistic explanation for the origin of life.
[NOTE: A sufficient explanation for the origin of life would also require a
model for the formation of other critical cellular components, including
membranes, and their assembly].
Order vs. Complexity in the Question of Information
Only recently has it been appreciated that the distinguishing feature of living
systems is complexity rather than order.4 This distinction has come
from the observation that the essential ingredients for a replicating
system---enzymes and nucleic acids---are all information-bearing molecules. In
contrast, consider crystals. They are very orderly, spatially periodic
arrangements of atoms (or molecules) but they carry very little information.
Nylon is another example of an orderly, periodic polymer (a polyamide) which
carries little information. Nucleic acids and protein are aperiodic
polymers, and this aperiodicity is what makes them able to carry much more
information. By definition then, a periodic structure has order. An
aperiodic structure has complexity. In terms of information, periodic
polymers (like nylon) and crystals are analogous to a book in which the same
sentence is repeated throughout. The arrangement of "letters" in the book is
highly ordered, but the book contains little information since the information
presented---the single word or sentence---is highly redundant.
It should be noted that aperiodic polypeptides or polynucleotides do not
necessarily represent meaningful information or biologically useful
functions. A random arrangement of letters in a book is aperiodic but contains
little if any useful information since it is devoid of meaning.
[NOTE: H.P. Yockey, personal communication, 9/29/82. Meaning is extraneous
to the sequence, arbitrary, and depends on some symbol convention. For
example, the word "gift," which in English means a present and in
German poison, in French is meaningless].
Only certain sequences of letters correspond to sentences, and only certain
sequences of sentences correspond to paragraphs, etc. In the same way only
certain sequences of amino acids in polypeptides and bases along polynucleotide
chains correspond to useful biological functions. Thus, informational
macro-molecules may be described as being and in a specified sequence.5
Living organisms are distinguished by their specified complexity.
Crystals fail to qualify as living because they lack complexity; mixtures of
random polymers fail to qualify because they lack specificity.6
Three sets of letter arrangements show nicely the difference between order and
complexity in relation to information:
1. An ordered (periodic) and therefore specified arrangement:
THE END THE END THE END THE END
Example: Nylon, or a crystal.
[NOTE: Here we use "THE END" even though there is no reason to suspect
that nylon or a crystal would carry even this much information. Our
point, of course, is that even if they did, the bit of information would
be drowned in a sea of redundancy].
2. A complex (aperiodic) unspecified arrangement:
AGDCBFE GBCAFED ACEDFBG
Example: Random polymers (polypeptides).
3. A complex (aperiodic) specified arrangement:
THIS SEQUENCE OF LETTERS CONTAINS A MESSAGE!
Example: DNA, protein.
Yockey7 and Wickens5 develop the same distinction, that
"order" is a statistical concept referring to regularity such as could might
characterize a series of digits in a number, or the ions of an inorganic
crystal. On the other hand, "organization" refers to physical systems and the
specific set of spatio-temporal and functional relationships among their parts.
Yockey and Wickens note that informational macromolecules have a low degree of
order but a high degree of specified complexity. In short, the redundant order
of crystals cannot give rise to specified complexity of the kind or magnitude
found in biological organization; attempts to relate the two have little future.
Information and Entropy
There is a general relationship between information and entropy. This is
fortunate because it allows an analysis to be developed in the formalism of
classical thermodynamics, giving us a powerful tool for calculating the work to
be done by energy flow through the system to synthesize protein and DNA (if
indeed energy flow is capable of producing information). The information content
in a given sequence of units, be they digits in a number, letters in a sentence,
or amino acids in a polypeptide or protein, depends on the minimum number of
instructions needed to specify or describe the structure. Many instructions are
needed to specify a complex, information-bearing structure such as DNA.
Only a few instructions are needed to specify an ordered structure such
as a crystal. In this case we have a description of the initial sequence or unit
arrangement which is then repeated ad infinitum according to the
Orgel9 illustrates the concept in the following way. To describe a
crystal, one would need only to specify the substance to be used and the way in
which the molecules were to be packed together. A couple of sentences would
suffice, followed by the instructions "and keep on doing the same," since the
packing sequence in a crystal is regular. The description would be about as
brief as specifying a DNA-like polynucleotide with a random sequence. Here one
would need only to specify the proportions of the four nucleotides in the final
product, along with instructions to assemble them randomly. The chemist could
then make the polymer with the proper composition but with a random sequence.
It would be quite impossible to produce a correspondingly simple set of
instructions that would enable a chemist to synthesize the DNA of an E. coli
bacterium. In this case the sequence matters. Only by specifying the
sequence letter-by-letter (about 4,000,000 instructions) could we tell a chemist
what to make. Our instructions would occupy not a few short sentences, but a
large book instead!
Brillouin,10 Schrodinger,11 and others12 have
developed both qualitative and quantitative relationships between information
and entropy. Brillouin,13 states that the entropy of a system is
S = k ln
where S is the entropy of the system, k is Boltzmann's constant, and
corresponds to the number of ways the energy and mass in a system may be
We will use Sth and Sc to refer to the thermal and
configurational entropies, respectively. Thermal entropy, Sth, is
associated with the distribution of energy in the system. Configurational
entropy Sc is concerned only with the arrangement of mass in the
system, and, for our purposes, we shall be especially interested in the
sequencing of amino acids in polypeptides (or proteins) or of nucleotides in
polynucleotides (e.g., DNA). The symbols
refer to the number of ways energy and mass, respectively, may be arranged in a
Thus we may be more precise by writing
S = k lnth
= k lnth
+ k lnc
= Sth + Sc
Sth = k lnth
Sc = k lnc
Determining Information: From a Random Polymer to an Informed
If we want to convert a random polymer into an informational molecule, we can
determine the increase in information (as defined by Brillouin) by finding the
difference between the negatives of the entropy states for the initial random
polymer and the informational molecule:
I = - (Scm - Scr)
I = Scr - Scm
= k lncr
- k lncm
In this equation, I is a measure of the information content of an aperiodic
(complex) polymer with a specified sequence, Scm represents the
configurational "coding" entropy of this polymer informed with a given message,
and Scr represents the configurational entropy of the same polymer
for an unspecified or random sequence.
[NOTE: Yockey and Wickens define information slightly differently than
Brilloum, whose definition we use in our analysis. The difference is
unimportant insofar as our analysis here is concerned].
Note that the information in a sequence-specified polymer is maximized when the
mass in the molecule could be arranged in many different ways, only one of which
communicates the intended message. (There is a large Scr from eq.
is large, yet Scm = 0 from eq. 8-2c since
= 1.) The information carried in a crystal is small because Sc is
small (eq. 8-2c) for a crystal. There simply is very little potential for
information in a crystal because its matter can be distributed in so few ways.
The random polymer provides an even starker contrast. It bears no
information because Scr, although large, is equal to Scm
(see eq. 8-3b).
In summary, equations 8-2c and 8-3c quantify the notion that only specified,
aperiodic macromolecules are capable of carrying the large amounts of
information characteristic of living systems. Later we will calculate "c"
for both random and specified polymers so that the configurational entropy
change required to go from a random to a specified polymer can be determined. In
the next section we will consider the various components of the total work
required in the formation of macromolecules such as DNA and protein.
DNA and Protein Formation:
Defining the Work
There are three distinct components of work to be done in assembling simple
biomonomers into a complex (or aperiodic) linear polymer with a specified
sequence as we find in DNA or protein. The change in the Gibbs free energy,
of the system during polymerization defines the total work that must be
accomplished by energy flow through the system. The change in Gibbs free energy
has previously been shown to be
where a decrease in Gibbs free energy for a given chemical reaction near
equilibrium guarantees an increase in the entropy of the universe as demanded by
the second law of thermodynamics.
Now consider the components of the Gibbs free energy (eq. 8-4b) where the change
in enthalpy (H)
is principally the result of changes in the total bonding energy (E),
with the (P
term assumed to be negligible. We will refer to this enthalpy component (H)
as the chemical work. A further distinction will be helpful. The change
in the entropy (S)
that accompanies the polymerization reaction may be divided into two distinct
components which correspond to the changes in the thermal energy distribution (Sth)
and the mass distribution (Sc),
eq. 8-2. So we can rewrite eq. 8-4b as
(Gibbs free energy) = (Chemical work) - (Thermal entropy work) -
(Configurational entropy work)
It will be shown that polymerization of macromolecules results in a decrease in
the thermal and configurational entropies (Sth
0). These terms effectively increase
and thus represent additional components of work to be done beyond the chemical
Consider the case of the formation of protein or DNA from biomonomers in a
chemical soup. For computational purposes it may be thought of as requiring two
steps: (1) polymerization to form a chain molecule with an aperiodic but
near-random sequence, and (2) rearrangement to an aperiodic, specified
[NOTE: Some intersymbol influence arising from differential atomic bonding
properties makes the distribution of matter not quite random. (H.P. Yockey,
1981. J. Theoret. Biol. 91,13)].
The entropy change (S)
associated with the first step is essentially all thermal entropy change (Sth),
as discussed above. The entropy change of the second step is essentially all
configurational entropy reducing change (Sc).
In fact, as previously noted, the change in configurational entropy (Sc)
"coding" as one goes from a random arrangement (Scr) to a specified
sequence (Scm) in a macromolecule is numerically equal to the
negative of the information content of the molecule as defined by Brillouin (see
In summary, the formation of complex biological polymers such as DNA and protein
involves changes in the chemical energy,
the thermal entropy,
and the configurational entropy,
of the system. Determining the magnitudes of these individual changes using
experimental data and a few calculations will allow us to quantify the magnitude
of the required work potentially to be done by energy flow through the system in
synthesizing macromolecules such as DNA and protein.
Quantifying the Various Components of Work
1. Chemical Work
The polymerization of amino acids to polypeptides (protein) or of nucleotides to
polynucleotides (DNA) occurs through condensation reactions. One may calculate
the enthalpy change in the formation of a dipeptide from amino acids to be 5-8
kcal/mole for a variety of amino acids, using data compiled by Hutchens.14
Thus, chemical work must be done on the system to get polymerization to occur.
Morowitz15 has estimated more generally that the chemical work, or
average increase in enthalpy, for macromolecule formation in living systems is
16.4 cal/gm. Elsewhere in the same book he says that the average increase in
bonding energy in going from simple compounds to an E. coli bacterium
is 0.27 ev/atom. One can easily see that chemical work must be done on the
biomonomers to bring about the formation of macromolecules like those that are
essential to living systems. By contrast, amino acid formation from simple
reducing atmosphere gases (methane, ammonia, water) has an associated enthalpy
of -50 kcal/mole to -250 kcal/ mole,16 which means energy is released
rather than consumed. This explains why amino acids form with relative ease in
prebiotic simulation experiments. On the other hand, forming amino acids from
less-reducing conditions (i.e., carbon dioxide, nitrogen, and water) is known to
be far more difficult experimentally. This is because the enthalpy change (H)
is positive, meaning energy is required to drive the energetically unfavorable
chemical reaction forward.
2. Thermal Entropy Work
Wickens17 has noted that polymerization reactions will reduce the
number of ways the translational energy may be distributed, while generally
increasing the possibilities for vibrational and rotational energy. A net
decrease results in the number of ways the thermal energy may be distributed,
giving a decrease in the thermal entropy according to eq. 8-2b (i.e.,
0). Quantifying the magnitude of this decrease in thermal entropy (Sth
) associated with the formation of a polypeptide or a polynucleotide is
best accomplished using experimental results.
Morowitz18 has estimated that the average decrease in thermal entropy
that occurs during the formation of macromolecules of living systems in 0.218
cal/deg-gm or 65 cal/gm at 298oK. Recent work by Armstrong et
al.,19 for nucleotide oligomerization of up to a pentamer
values of 11.8 kcal/mole and 15.6 kcal/mole respectively, at 294K. Thus the
decrease in thermal entropy during the polymerization of the macromolecules of
life increases the Gibbs free energy and the work required to make these
molecules, i.e., -T
3. Configurational Entropy Work
Finally, we need to quantify the configurational entropy change (Sc)
that accompanies the formation of DNA and protein. Here we will not get much
help from standard experiments in which the equilibrium constants are determined
for a polymerization reaction at various temperatures. Such experiments do not
consider whether a specific sequence is achieved in the resultant polymers, but
only the concentrations of randomly sequenced polymers (i.e., polypeptides)
formed. Consequently, they do not measure the configurational entropy (Sc)
contribution to the total entropy change (S).
However, the magnitude of the configurational entropy change associated with
sequencing the polymers can be calculated.
Using the definition for configurational "coding" entropy given in eq. 8-2c, it
is quite straightforward to calculate the configurational entropy change for a
given polymer. The number of ways the mass of the linear system may be arranged
can be calculated using statistics. Brillouin20 has shown that the
number of distinct sequences one can make using N different symbols and
Fermi-Dirac statistics is given by
If some of these symbols are redundant (or identical), then the number of unique
or distinguishable sequences that can be made is reduced to
= N! / n1!n2!n2!...ni!
where n1 + n2 + ... + ni = N and i defines the
number of distinct symbols. For a protein, it is i =20, since a subset of twenty
distinctive types of amino acids is found in living things, while in DNA it is i
= 4 for the subset of four distinctive nucleotides. A typical protein would have
100 to 300 amino acids in a specific sequence, or N = 100 to 300. For DNA of the
bacterium E. coli, N = 4,000,000. In Appendix 1, alternative approaches
are considered and eq. 8-7 is shown to be a lower bound to the actual value.
For a random polypeptide of 100 amino acids, the configurational entropy, Scr,
may be calculated using eq. 8-2c and eq. 8-7 as follows:
Scr = k lncr
= N! / n1!n2!...n20! = 100! / 5!5!....5! = 100!
= 1.28 x 10115
The calculation of equation 8-8 assumes that an equal number of each type of
amino acid, namely 5, are contained in the polypeptide. Since k, or Boltzmann's
constant, equals 1.38 x 10-16 erg/deg, and ln [1.28 x 10115]
Scr = 1.38 x 10-16 x 265 = 3.66 x 10-14
If only one specific sequence of amino acids could give the proper
function, then the configurational entropy for the protein or specified,
aperiodic polypeptide would be given by
Scm = k lncm
= k ln 1
Going from a Random Polymer to an Informed Polymer
The change in configurational entropy,
as one goes from a random polypeptide of 100 amino acids with an equal number of
each amino acid type to a polypeptide with a specific message or sequence is:
= Scm - Scr
= 0 - 3.66 x 10-14 erg/deg-polypeptide
= -3.66 x 10-14 erg/deg-polypeptide
The configurational entropy work (-T
at ambient temperatures is given by
= - (298oK) x (-3.66 x 10-14) erg/deg-polypeptide
= 1.1 x 10-11 erg/polypeptide
= 1.1 x 10-11 erg/polypeptide x [6.023 x 1023
molecules/mole] / [10,000 gms/mole] x [1 cal] / 4.184 x 107 ergs
= 15.8 cal/gm
where the protein mass of 10,000 amu was estimated by assuming an average amino
acid weight of 100 amu after the removal of the water molecule. Determination of
the configurational entropy work for a protein containing 300 amino acids
equally divided among the twenty types gives a similar result of 16.8 cal/gm.
In like manner the configurational entropy work for a DNA molecule such as for
E. coli bacterium may be calculated assuming 4 x 106
nucleotides in the chain with 1 x 106 each of the four distinctive
nucleotides, each distinguished by the type of base attached, and each
nucleotide assumed to have an average mass of 339 amu. At 298oK:
= -T (Scm - Scr)
= T ( Scr - Scm)
= kT ln (cr
= kT ln [(4 x 106)! / (106)!(106)!(106)!(106)!]
- kT ln 1
= 2.26 x 10-7 erg/polynucleotide
= 2.39 cal/gm
It is interesting to note that, while the work to code the DNA molecule with 4
million nucleotides is much greater than the work required to code a protein of
100 amino acids (2.26 x 10-7 erg/DNA vs. 1.10 x 10-11
erg/protein), the work per gram to code such molecules is actually less in DNA.
There are two reasons for this perhaps unexpected result: first, the nucleotide
is more massive than the amino acid (339 amu vs. 100 amu); and second, the
alphabet is more limited, with only four useful nucleotide "letters" as compared
to twenty useful amino acid letters. Nevertheless, it is the total work that is
important, which means that synthesizing DNA is much more difficult than
It should be emphasized that these estimates of the magnitude of the
configurational entropy work required are conservatively small. As a practical
matter, our calculations have ignored the configurational entropy work involved
in the selection of monomers. Thus, we have assumed that only the proper subset
of 20 biologically significant amino acids was available in a prebiotic oceanic
soup to form a biofunctional protein. The same is true of DNA. We have assumed
that in the soup only the proper subset of 4 nucleotides was present and that
these nucleotides do not interact with amino acids or other soup ingredients. As
we discussed in Chapter 4, many varieties of amino acids and nucleotides would
have been present in a real ocean---varieties which have been ignored in our
calculations of configurational entropy work. In addition, the soup would have
contained many other kinds of molecules which could have reacted with amino
acids and nucleotides. The problem of using only the appropriate optical isomer
has also been ignored. A random chemical soup would have contained a 50-50
mixture of D- and L-amino acids, from which a true protein could incorporate
only the Lenantiomer. Similarly, DNA uses exclusively the optically active sugar
D-deoxyribose. Finally, we have ignored the problem of forming unnatural links,
assuming for the calculations that only CL-links occurred between amino acids in
making polypeptides, and that only correct linking at the 3', 5'-position of
sugar occurred in forming polynucleotides. A quantification of these problems of
specificity has recently been made by Yockey.21
The dual problem of selecting the proper composition of matter and then
coding or rearranging it into the proper sequence is analogous to writing a
story using letters drawn from a pot containing many duplicates of each of the
22 Hebrew consonants and 24 Greek and 26 English letters all mixed together. To
write in English the message,
HOW DID I GET HERE?
we must first draw from the pot 2 Hs, 2 Is, 3 Es, 2 Ds, and one each of the
letters W, 0, G, T, and R. Drawing or selecting this specific set of letters
would be a most unlikely event itself. The work of selecting just these 14
letters would certainly be far greater than arranging them in the correct
sequence. Our calculations only considered the easier step of coding while
ignoring the greater problem of selecting the correct set of letters to be
coded. We thereby greatly underestimate the actual configurational entropy work
to be done.
In Chapter 6 we developed a scale showing degrees of investigator interference
in prebiotic simulation experiments. In discussing this scale it was noted that
very often in reported experiments the experimenter has actually played a
crucial but illegitimate role in the success of the experiment. It
becomes clear at this point that one illegitimate role of the investigator is
that of providing a portion of the configurational entropy work, i.e., the
"selecting" work portion of the total -T
It is sometimes argued that the type of amino acid that is present in a protein
is critical only at certain positions---active sites---along the chain, but not
at every position. If this is so, it means the same message (i.e., function) can
be produced with more than one sequence of amino acids.
This would reduce the coding work by making the number of permissible
in eqs. 8-9 and 8-10 for Scm greater than 1. The effect of
overlooking this in our calculations, however, would be negligible compared to
the effect of overlooking the "selecting" work and only considering the "coding"
work, as previously discussed. So we are led to the conclusion that our estimate
is very conservatively low.
Calculating the Total Work: Polymerization of Biomacromolecules
It is now possible to estimate the total work required to combine biomonomers
into the appropriate polymers essential to living systems. This calculation
using eq. 8-5 might be thought of as occurring in two steps. First, amino acids
polymerize into a polypeptide, with the chemical and thermal entropy work being
Next, the random polymer is rearranged into a specific sequence which
constitutes doing configurational entropy work (-T
For example, the total work as expressed by the change in Gibbs free energy to
make a specified sequence is
may be assumed to be 300 kcal/mole to form a random polypeptide of 101 amino
acids (100 links). The work to code this random polypeptide into a useful
sequence so that it may function as a protein involves the additional component
"coding" work, which has been estimated previously to be 15.9 cal/gm, or
approximately 159 kcal/mole for our protein of 100 links with an estimated mass
of 10,000 amu per mole. Thus, the total work (neglecting the "sorting and
selecting" work) is approximately
= (300 + 159) kcal/mole = 459 kcal/mole
with the coding work representing 159/459 or 35% of the total work.
In a similar way, the polymerization of 4 x 106 nucleotides into a
random polynucleotide would require approximately 27 x 106 kcal/mole.
The coding of this random polynucleotide into the specified, aperiodic sequence
of a DNA molecule would require an additional 3.2 x 106 kcal/mole of
work. Thus, the fraction of the total work that is required to code the
polymerized DNA is seen to be 8.5%, again neglecting the "sorting and selecting"
The Impossibility of Protein Formation under Equilibrium Conditions
It was noted in Chapter 7 that because macromolecule formation (such as amino
acids polymerizing to form protein) goes uphill energetically, work must be done
on the system via energy flow through the system. We can readily see the
difficulty in getting polymerization reactions to occur under equilibrium
conditions, i.e., in the absence of such an energy flow.
Under equilibrium conditions the concentration of protein one would obtain from
a solution of 1 M concentration in each amino acid is given by:
K= [protein] x [H2 0] / [glycine] [alanine]...
where K is the equilibrium constant and is calculated by
K = exp [ -
/ RT ]
An equivalent form is
= -RT ln K
We noted earlier that
= 459 kcal/mole for our protein of 101 amino acids. The gas constant R = 1.9872
cal/deg-mole and T is assumed to be 298oK. Substituting these values
into eqs. 8-15 and 8-16 gives
protein concentration = 10-338 M
This trivial yield emphasizes the futility of protein formation under
equilibrium conditions. In the next chapter we will consider various theoretical
models attempting to show how energy flow through the system can be useful in
doing the work quantified in this chapter for the polymerization of DNA and
protein. Finally, we will examine experimental efforts to accomplish
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