|
[~][`] |
Scripture and Science "In
Conflict" Site Map
Back to Evolution Index
Origin of the Species
The Mystery of Life's Origin:
Reassessing Current Theories
Chapter 7 Thermodynamics of Living Systems, p113
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. Paris: Gallimard.
4. H.J. Morowitz, 1968. Energy Flow in Biology. New York: Academic
Press, p.2-3.
5. H.F. Blum, 1951. Time's Arrow and Evolution. Princeton:
Princeton University Press.
6. H.J. Morowitz, Energy Flow, p.66.
7. H.J. Morowitz, Energy Flow, p.68.
8. I. Prigogine, G. Nicolis, and A. Babloyantz, November, 1972. Physics
Today, p.23.
9. H.F. Blum, 1955. American Scientist 43, 595.
10. G. Nicolis and I. Prigogine, 1977. Self-Organization in Nonequilibrium
Systems. New York: John Wiley, p.24.
11. S.L. Miller and L.E. Crgel, 1974. The Origins of Life on the Earth.
Englewood Cliffs, New Jersey: Prentice-Hall, p.162-3.
|
|
