Thermodynamics of Living Systems
It is widely
held that in the physical sciences the laws of thermodynamics have had a
unifying effect similar to that of the theory of evolution in the biological sciences.
What is intriguing is that the predictions of one seem to contradict the
predictions of the other. The second law of thermodynamics suggests a
progression from order to disorder, from complexity to simplicity, in the
physical universe. Yet biological evolution involves a hierarchical progression
to increasingly complex forms of living systems, seemingly in contradiction to
the second law of thermodynamics. Whether this discrepancy between the two
theories is only apparent or real is the question to be considered in the next
three chapters. The controversy which is evident in an article published in the
American Scientist 1 along with the replies it provoked
demonstrates the question is still a timely one.
The
First Law of Thermodynamics
Thermodynamics
is an exact science which deals with energy. Our world seethes with
transformations of matter and energy. Be these mechanical or chemical, the
first law of thermodynamics---the principle of the Conservation of
Energy---tells us that the total energy of the universe or any isolated part of
it will be the same after any such transformation as it was before. A major
part of the science of thermodynamics is accounting---giving an account of the
energy of a system that has undergone some sort of transformation. Thus, we
derive from the first law of thermodynamics that the change in the energy of a
system (
E) is equal to the work
done on (or by) the system (W) and the heat flow into
(or out of) the system (Q) Mechanical work and
energy are interchangeable, i.e., energy may be converted into mechanical work
as in a steam engine, or mechanical work can be converted into energy as in the
heating of a cannon which occurs as its barrel is bored. In mathematical terms
(where the terms are as previously defined):
E = Q + W 
(7-1)
The
Second Law of Thermodynamics
The second law
of thermodynamics describes the flow of energy in nature in processes which are
irreversible. The physical significance of the second law of thermodynamics is
that the energy flow in such processes is always toward a more uniform
distribution of the energy of the universe. Anyone who has had to pay utility
bills for long has become aware that too much of the warm air in his or her
home during winter escapes to the outside. This flow of energy from the house
to the cold outside in winter, or the flow of energy from the hot outdoors into
the air-conditioned home in the summer, is a process described by the second
law of thermodynamics. The burning of gasoline, converting energy
"rich" compounds (hydrocarbons) into energy "lean"
compounds, carbon dioxide (CO2) and water (H20), is a
second illustration of this principle.
The concept of entropy (S) gives us a more quantitative way to describe the
tendency for energy to flow in a particular direction. The entropy change for a
system is defined mathematically as the flow of energy divided by the
temperature, or,
S 
[Q / T] (7-2)
where S is the change in entropy,
Q is the heat flow into or
out of a system, and T is the absolute temperature in degrees Kelvin (K).
[Note: For a
reversible flow of energy such as occurs under equilibrium conditions, the
equality sign applies. For irreversible energy flow, the inequality applies.]
A Driving
Force
If we consider heat flow from a warm house to the outdoors on a cold winter
night, we may apply equation 7-2 as follows:
ST = Shouse + Soutdoors - Q / T1 + Q / T2 (7-3)
where Sr is the total
entropy change associated with this irreversible heat flow, T1 is
the temperature inside the house, and T2 is the temperature
outdoors. The negative sign of the first term notes loss of heat from the
house, while the positive sign on the second term recognizes heat gained by the
outdoors. Since it is warmer in the house than outdoors (T1 > T2),
the total entropy will increase (Sr > 0) as a
result of this heat flow. If we turn off the heater in the house, it will
gradually cool until the temperature approaches that of the outdoors, i.e., T1
= T2. When this occurs, the entropy change (S) associated with heat
flow (Q) goes to zero. Since
there is no further driving force for heat flow to the outdoors, it ceases;
equilibrium conditions have been established.
As this simple example shows, energy flow occurs in a direction that causes the
total energy to be more uniformly distributed. If we think about it, we can
also see that the entropy increase associated with such energy flow is
proportional to the driving force for such energy flow to occur. The second law
of thermodynamics says that the entropy of the universe (or any isolated system
therein) is increasing; i.e., the energy of the universe is becoming more
uniformly distributed.
It is often noted that the second law indicates that nature tends to go from
order to disorder, from complexity to simplicity. If the most random
arrangement of energy is a uniform distribution, then the present arrangement
of the energy in the universe is nonrandom, since some matter is very rich in
chemical energy, some in thermal energy, etc., and other matter is very poor in
these kinds of energy. In a similar way, the arrangements of mass in the
universe tend to go from order to disorder due to the random motion on an
atomic scale produced by thermal energy. The diffusional processes in the solid,
liquid, or gaseous states are examples of increasing entropy due to random
atomic movements. Thus, increasing entropy in a system corresponds to
increasingly random arrangements of mass and/or energy.
Entropy and Probability
There is another way to view entropy. The entropy of a system is a measure of
the probability of a given arrangement of mass and energy within it. A
statistical thermodynamic approach can be used to further quantify the system
entropy. High entropy corresponds to high probability. As a random arrangement
is highly probable, it would also be characterized by a large entropy. On the
other hand, a highly ordered arrangement, being less probable, would represent
a lower entropy configuration. The second law would tell us then that events
which increase the entropy of the system require a change from more order to
less order, or from less-random states to more-random states. We will find this
concept helpful in Chapter 9 when we analyze condensation reactions for DNA and
protein.
Clausius2, who formulated the second law of thermodynamics,
summarizes the laws of thermodynamics in his famous concise statement:
"The energy of the universe is constant; the entropy of the universe tends
toward a maximum." The universe moves from its less probable current
arrangement (low entropy) toward its most probable arrangement in which the
energy of the universe will be more uniformly distributed.
Life
and the Second Law of Thermodynamics
How does all of
this relate to chemical evolution? Since the important macromolecules of living
systems (DNA, protein, etc.) are more energy rich than their precursors (amino
acids, heterocyclic bases, phosphates, and sugars), classical thermodynamics
would predict that such macromolecules will not spontaneously form.
Roger Caillois has recently drawn this conclusion in saying, "Clausius and
Darwin cannot both be right."3 This prediction of classical
thermodynamics has, however, merely set the stage for refined efforts to
understand life's origin. Harold Morowitz4 and others have suggested
that the earth is not an isolated system, since it is open to energy flow from
the sun. Nevertheless, one cannot simply dismiss the problem of the origin of
organization and complexity in biological systems by a vague appeal to open-system
non-equilibrium thermodynamics. The mechanisms responsible for the emergence
and maintenance of coherent (organized) states must be defined. To clarify the
role of mass and energy flow through a system as a possible solution to
this problem, we will look in turn at the thermodynamics of (1) an isolated
system, (2) a closed system, and (3) an open system. We will then discuss the
application of open-system thermodynamics to living systems. In Chapter 8 we
will apply the thermodynamic concepts presented in this chapter to the
prebiotic synthesis of DNA and protein. In Chapter 9 this theoretical analysis
will be used to interpret the various prebiotic synthesis experiments for DNA
and protein, suggesting a physical basis for the uniform lack of success in synthesizing
these crucial components for living cells.
Isolated Systems
An isolated system is one in which neither mass nor energy flows in or out. To
illustrate such a system, think of a perfectly insulated thermos bottle (no heat
loss) filled initially with hot tea and ice cubes. The total energy in this
isolated system remains constant but the distribution of the energy changes
with time. The ice melts and the energy becomes more uniformly distributed in
the system. The initial distribution of energy into hot regions (the tea) and
cold regions (the ice) is an ordered, nonrandom arrangement of energy, one not
likely to be maintained for very long. By our previous definition then, we may
say that the entropy of the system is initially low but gradually increases
with time. Furthermore, the second law of thermodynamics says the entropy of
the system will continue to increase until it attains some maximum value, which
corresponds to the most probable state for the system, usually called
equilibrium.
In summary, isolated systems always maintain constant total energy while
tending toward maximum entropy, or disorder. In mathematical terms,
E / t = 0
(isolated system)
S / t 0 (7-4)
where E and S are the changes in the
system energy and system entropy respectively, for a time interval t. Clearly the emergence of
order of any kind in an isolated system is not possible. The second law of
thermodynamics says that an isolated system always moves in the direction of
maximum entropy and, therefore, disorder.
It should be noted that the process just described is irreversible in the sense
that once the ice is melted, it will not reform in the thermos. As a matter of
fact, natural decay and the general tendency toward greater disorder are so
universal that the second law of thermodynamics has been appropriately dubbed
"time's arrow."5
Closed Systems near Equilibrium
A closed system is one in which the exchange of energy with the outside world
is permitted but the exchange of mass is not. Along the boundary between the
closed system and the surroundings, the temperature may be different from the
system temperature, allowing energy flow into or out of the system as it moves
toward equilibrium. If the temperature along the boundary is variable (in
position but not time), then energy will flow through the system,
maintaining it some distance from equilibrium. We will discuss closed systems
near equilibrium first, followed by a discussion of closed systems removed from
equilibrium next.
If we combine the first and second laws as expressed in equations 7-1 and 7-2
and replace the mechanical work term W by P V, where P is pressure and V is volume change, we
obtain,
[NOTE: Volume
expansion (V> 0) corresponds to the
system doing work, and therefore losing energy. Volume contraction
(V 0) corresponds to work
being done on the system].
S [E + P V] / [T] (7-5)
Algebraic manipulation gives
E + P V - T S 
0 or G 0 (7-6)
where
G = E + P V - T S
The term on the left side of the
inequality in equation 7-6 is called the change in the Gibbs free energy (G). It may be thought of as
a thermodynamic potential which describes the tendency of a system to
change---e.g., the tendency for phase changes, heat conduction, etc. to occur.
If a reaction occurs spontaneously, it is because it brings a decrease in the
Gibbs free energy (G 0). This requirement is
equivalent to the requirement that the entropy of the universe increase. Thus,
like an increase in entropy, a decrease in Gibbs free energy simply means that
a system and its surroundings are changing in such a way that the energy of the
universe is becoming more uniformly distributed.
We may summarize then by noting that the second law of thermodynamics requires,
G / t 0, (closed system) (7-7)
where t indicates the time period
during which the Gibbs free energy changed.
The approach to equilibrium is characterized by,
G / t 
0, (closed system) (7-8)
The physical significance of equation 7-7
can be understood by rewriting equations 7-6 and 7-7 in the following form:
[S / t] - [ 1 / T (E / t + P V / t)] 0 (7-9)
or
(S / t ) - (1 / T H / t ) 0
and noting that the first term represents
the entropy change due to processes going on within the system and the second
term represents the entropy change due to exchange of mechanical and/or thermal
energy with the surroundings. This simply guarantees that the sum of the
entropy change in the system and the entropy change in the surroundings will be
greater than zero; i.e., the entropy of the universe must increase. For the
isolated system, E + P V = 0 and equation 7-9
reduces to equation 7-4.
A simple illustration of this principle is seen in phase changes such as water
transforming into ice. As ice forms, energy (80 calories/gm) is liberated to
the surrounding. The change in the entropy of the system as the amorphous water
becomes crystalline ice is -0.293 entropy units (eu)/degree Kelvin (K). The
entropy change is negative because the thermal and configuration entropy (or
disorder) of water is greater than that of ice, which is a highly ordered
crystal.
[NOTE:
Confirgurational entropy measures randomness in the distribution of matter in
much the same way that thermal entropy measures randomness in the distribution
of energy].
Thus, the
thermodynamic conditions under which water will transform to ice are seen from
equation 7-9 to be:
-0.293 - (-80 / T) > 0 (7-l0a)
or
T 273oK (7-l0b)
For condition of T 273oK
energy is removed from water to produce ice, and the aggregate disordering of
the surroundings is greater than the ordering of the water into ice crystals.
This gives a net increase in the entropy of the universe, as predicted by the
second law of thermodynamics.
It has often been argued by analogy to water crystallizing to ice that simple
monomers may polymerize into complex molecules such as protein and DNA. The
analogy is clearly inappropriate, however. The E + P V term (equation 7-9) in
the polymerization of important organic molecules is generally positive (5 to 8
kcal/mole), indicating the reaction can never spontaneously occur at or near
equilibrium.
[NOTE: If E + P V is positive, the entropy
term in eq 7 9 must be negative due to the negative sign which preceeds it. The
inequality can only be satisfied by S being sufficiently
positive, which implies disordenng].
By contrast the E + P V term in water changing to
ice is a negative, -1.44 kcal/mole, indicating the phase change is spontaneous
as long as T 273oK, as previously noted. The atomic bonding forces
draw water molecules into an orderly crystalline array when the thermal
agitation (or entropy driving force, T S) is made sufficiently
small by lowering the temperature. Organic monomers such as amino acids resist
combining at all at any temperature, however, much less in some orderly
arrangement.
Morowitz6 has estimated the increase in the chemical bonding energy
as one forms the bacterium Escherichia coli from simple precursors to be
0.0095 erg, or an average of 0.27 ev/ atom for the 2 x 1010 atoms in
a single bacterial cell. This would be thermodynamically equivalent to having
water in your bathtub spontaneously heat up to 360oC, happily a most
unlikely event. He goes on to estimate the probability of the spontaneous
formation of one such bacterium in the entire universe in five billion years under
equilibrium conditions to be 10-1011. Morowitz summarizes the
significance of this result by saying that "if equilibrium processes alone
were at work, the largest possible fluctuation in the history of the universe
is likely to have been no longer than a small peptide."7 Nobel
Laureate I. Prigogine et al., have noted with reference to the same
problem that:
The probability
that at ordinary temperatures a macroscopic number of molecules is assembled to
give rise to the highly ordered structures and to the coordinated functions
characterizing living organisms is vanishingly small. The idea of spontaneous
genesis of life in its present form is therefore highly improbable, even on the
scale of billions of years during which prebiotic evolution occurred.8
It seems safe to
conclude that systems near equilibrium (whether isolated or closed) can never
produce the degree of complexity intrinsic in living systems. Instead, they
will move spontaneously toward maximizing entropy, or randomness. Even the
postulate of long time periods does not solve the problem, as "time's
arrow" (the second law of thermodynamics) points in the wrong direction;
i.e., toward equilibrium. In this regard, H.F. Blum has observed:
The second law
of thermodynamics would have been a dominant directing factor in this case [of
chemical evolution]; the reactions involved tending always toward equilibrium,
that is, toward less free energy, and, in an inclusive sense, greater entropy.
From this point of view the lavish amount of time available should only have
provided opportunity for movement in the direction of equilibrium.9
(Emphasis added.)
Thus, reversing
"time's arrow" is what chemical evolution is all about, and this will
not occur in isolated or closed systems near equilibrium.
The possibilities are potentially more promising, however, if one considers a system
subjected to energy flow which may maintain it far from equilibrium, and its
associated disorder. Such a system is said to be a constrained system,
in contrast to a system at or near equilibrium which is unconstrained. The
possibilities for ordering in such a system will be considered next.
Closed Systems Far from Equilibrium
Energy flow through a system is the equivalent to doing work continuously on
the system to maintain it some distance from equilibrium. Nicolis and
Prigoginelo have suggested that the entropy change (S) in a system for a time
interval (t) may be divided into two
components.
S = Se + Si (7-11)
where Se is the entropy
flux due to energy flow through the system, and Si is the
entropy production inside the system due to irreversible processes such as
diffusion, heat conduction, heat production, and chemical reactions. We will
note when we discuss open systems in the next section that Se includes the
entropy flux due to mass flow through the system as well. The second law of
thermodynamics requires,
Si 0 (7-12)
In an isolated system, Se = 0 and
equations 7-11 and 7-12 give,
S =Si 0 (7-13)
Unlike Si, Se in a closed system
does not have a definite sign, but depends entirely on the boundary constraints
imposed on the system. The total entropy change in the system can be negative
(i.e., ordering within system) when,
Se 0 and | Se | > Si (7-14)
Under such conditions a state that would
normally be highly improbable under equilibrium conditions can be maintained
indefinitely. It would be highly unlikely (i.e., statistically just short of
impossible) for a disconnected water heater to produce hot water. Yet when the
gas is connected and the burner lit, the system is constrained by energy flow
and hot water is produced and maintained indefinitely as long as energy flows
through the system.
An open system offers an additional possibility for ordering---that of
maintaining a system far from equilibrium via mass flow through the system, as
will be discussed in the next section.
An open system is one which exchanges both energy and mass with the
surroundings. It is well illustrated by the familiar internal combustion
engine. Gasoline and oxygen are passed through the system, combusted, and then
released as carbon dioxide and water. The energy released by this mass flow
through the system is converted into useful work; namely, torque supplied to
the wheels of the automobile. A coupling mechanism is necessary, however, to
allow the released energy to be converted into a particular kind of work. In an
analagous way the dissipative (or disordering) processes within an open system
can be offset by a steady supply of energy to provide for (S) Se type work.
Equation 7-11, applied earlier to closed systems far from equilibrium, may also
be applied to open systems. In this case, the Se term
represents the negative entropy, or organizing work done on the system as a
result of both energy and mass flow through the system. This work done to the
system can move it far from equilibrium, maintaining it there as long as the
mass and/or energy flow are not interrupted. This is an essential
characteristic of living systems as will be seen in what follows.
Thermodynamics
of Living Systems
Living systems are
composed of complex molecular configurations whose total bonding energy is less
negative than that of their chemical precursors (e.g., Morowitz's estimate of E = 0.27 ev/atom) and whose
thermal and configurational entropies are also less than that of their chemical
precursors. Thus, the Gibbs free energy of living systems (see equation 7-6) is
quite high relative to the simple compounds from which they are formed. The formation
and maintenance of living systems at energy levels well removed from
equilibrium requires continuous work to be done on the system, even as
maintenance of hot water in a water heater requires that continuous work be
done on the system. Securing this continuous work requires energy and/or mass
flow through the system, apart from which the system will return to an
equilibrium condition (lowest Gibbs free energy, see equations 7-7 and 7-8)
with the decomposition of complex molecules into simple ones, just as the hot
water in our water heater returns to room temperature once the gas is shut off.
In living plants, the energy flow through the system is supplied principally by
solar radiation. In fact, leaves provide relatively large surface areas per
unit volume for most plants, allowing them to "capture" the necessary
solar energy to maintain themselves far from equilibrium. This solar energy is
converted into the necessary useful work (negative Se in equation
7-11) to maintain the plant in its complex, high-energy configuration by a
complicated process called photosynthesis. Mass, such as water and carbon
dioxide, also flows through plants, providing necessary raw materials, but not
energy. In collecting and storing useful energy, plants serve the entire
biological world.
For animals, energy flow through the system is provided by eating high energy
biomass, either plant or animal. The breaking down of this energy-rich biomass,
and the subsequent oxidation of part of it (e.g., carbohydrates), provides a
continuous source of energy as well as raw materials. If plants are deprived of
sunlight or animals of food, dissipation within the system will surely bring
death. Maintenance of the complex, high-energy condition associated with life
is not possible apart from a continuous source of energy. A source of energy
alone is not sufficient, however, to explain the origin or maintenance of
living systems. The additional crucial factor is a means of converting this
energy into the necessary useful work to build and maintain complex living
systems from the simple biomonomers that constitute their molecular building
blocks.
An automobile with an internal combustion engine, transmission, and drive chain
provides the necessary mechanism for converting the energy in gasoline into
comfortable transportation. Without such an "energy converter,"
however, obtaining transportation from gasoline would be impossible. In a
similar way, food would do little for a man whose stomach, intestines, liver,
or pancreas were removed. Without these, he would surely die even though he
continued to eat. Apart from a mechanism to couple the available energy to the
necessary work, high-energy biomass is insufficient to sustain a living system
far from equilibrium. In the case of living systems such a coupling mechanism
channels the energy along specific chemical pathways to accomplish a very
specific type of work. We therefore conclude that, given the availability of
energy and an appropriate coupling mechanism, the maintenance of a
living system far from equilibrium presents no thermodynamic problems.
In mathematical formalism, these concepts may be summarized as follows:
(1) The second law of thermodynamics requires only that the entropy production
due to irreversible processes within the system be greater than zero; i.e.,
Si > 0 (7-15)
(2) The maintenance of living systems
requires that the energy flow through the system be of sufficient magnitude
that the negative entropy production rate (i.e., useful work rate) that results
be greater than the rate of dissipation that results from irreversible
processes going on within the systems; i.e.,
| Se | > Si (7-16)
(3) The negative entropy generation must
be coupled into the system in such a way that the resultant work done is
directed toward restoration of the system from the disintegration that occurs
naturally and is described by the second law of thermodynamics; i.e.,
- Se = Si (7-17)
where Se and Si refer not
only to the magnitude of entropy change but also to the specific changes that
occur in the system associated with this change in entropy. The coupling must
produce not just any kind of ordering but the specific kind required by the
system.
While the maintenance of living systems is easily rationalized in terms of
thermodynamics, the origin of such living systems is quite another
matter. Though the earth is open to energy flow from the sun, the means of
converting this energy into the necessary work to build up living systems from
simple precursors remains at present unspecified (see equation 7-17). The
"evolution" from biomonomers of to fully functioning cells is the
issue. Can one make the incredible jump in energy and organization from raw
material and raw energy, apart from some means of directing the energy flow
through the system? In Chapters 8 and 9 we will consider this question, limiting
our discussion to two small but crucial steps in the proposed evolutionary
scheme namely, the formation of protein and DNA from their precursors.
It is widely agreed that both protein and DNA are essential for living systems
and indispensable components of every living cell today.11 Yet they
are only produced by living cells. Both types of molecules are much more energy
and information rich than the biomonomers from which they form. Can one
reasonably predict their occurrence given the necessary biomonomers and an
energy source? Has this been verified experimentally? These questions will be
considered in Chapters 8 and 9.
References
1. Victor F. Weisskopf, 1977. Amer. Sci. 65, 405-11.
2. R. Clausius, 1855. Ann. Phys. 125, 358.
3. R. Caillois, 1976. Coherences Aventureuses.
4. H.J. Morowitz, 1968. Energy Flow in Biology.
5. H.F. Blum, 1951. Time's Arrow and Evolution. Princeton:
6. H.J. Morowitz, Energy Flow, p.66.
7. H.J. Morowitz, Energy Flow, p.68.
8.
9. H.F. Blum, 1955. American Scientist 43, 595.
10. G. Nicolis and
11. S.L. Miller and L.E. Crgel, 1974. The Origins of Life on the Earth. Englewood
Cliffs,
Thermodynamics and the Origin 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 (dSi 0) is compatible with a
decrease in overall entropy (dS < 0), but also to indicate the mechanisms
responsible for the emergence and maintenance of coherent states.2
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
noted:
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 polymers].
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 Orgel notes:
Living organisms
are distinguished by their specified complexity.
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
packing instructions.
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
given by
S = k ln 
(8-1)
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 arranged.
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 th and c refer to the
number of ways energy and mass, respectively, may be arranged in a system.
Thus we may be more precise by writing
S = k lnth c = k lnth + k lnc = Sth
+ Sc (8-2A)
where
Sth = k lnth (8-2b)
and
Sc = k lnc (8-2c)
Determining Information: From a Random
Polymer to an Informed Polymer
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) (8-3A),
I = Scr - Scm (8-3b),
= k lncr - k lncm (8-3c)
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.
8-2c since cr is large, yet
Scm = 0 from eq. 8-2c since cm = 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, G, 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
G = E + P