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Onsager's principle: A unifying bio-theme
J. theor. Biol. (1989) 136, 171-175
Onsager's Principle: A Unifying Bio-theme RICHARD E. MOREL AND GEORGE FLECK
Department of Chemistry, Smith College, Northampton, Massachusetts 01063, U.S.A. (Received 18 April 1988, and accepted in revised form 20 June 1988) A hitherto obscure thermodynamic principle proposed by Lars Onsager in 1931 (Phys. Rev. 37, 405) serves as a parsimonious explanation for consistencies in the rates at which biochemical events occur, consistencies not explained by existing thermodynamic laws. It also provides an underlying rationale for the observation that thermodynamic systems, including living systems, are relentlessly opportunistic with respect to increasing entropy. These consistencies and this opportunism form a broadly unifying theme for biological phenomena from molecular to organismic and evolutionary levels.
1.
Introduction
Consistencies in the direction of events over time are predicted by the First and Second Laws of Thermodynamics. The First Law (the principle of conservation of energy) states that the total amount of energy does not change during an event. The Second Law states that, within the context of the First Law, entropy always increases during an event. Locally, energy may change and entropy may increase or decrease; the First and Second Laws apply to the universe of the event, that portion of the physical universe in terms of which every thermodynamically important aspect of the event can be described (Bent, 1965). Consider a burning candle. Usable energy contained in the wax and wick is being dissipated into light and heat by the flame. Highly ordered molecules such as paratfins and cellulose are being converted to less ordered molecules such as water and carbon dioxide, and the orderly and compact arrangement of molecules in the candle (a solid) is being transformed to a less ordered arrangement of molecules (gases). As the Second Law predicts, entropy increases as the burning continues. We would not expect the products of combustion to recombine spontaneously in a candle flame to form a whole candle. Beyond the fundamental consistency in the direction of this process, toward higher entropy, we also know that an undisturbed candle burns at a consistent rate. That is, entropy increases at a consistent rate. The First and Second Laws do not address, much less explain, this consistency--a consistency so reliable that candles have been used as instruments to measure elapsed time. But experience and observation tell us that t h e r m o d y n a m i c entropy increases at remarkably consistent rates. Consistency in the rates at which thermodynamic entropy increases is a precondition for the existence o f biochemical systems and living matter. A living cell relies, for example, on consistencies in the rates at which molecules diffuse, on consistencies 171
0022-5193/89/020171 +05 $03.00/0
© 1989 Academic Press Limited
172
R.E.
MOREL
AND
G,
FLECK
in the rates enzymes catalyze reactions, and on consistencies in the rates at which protein molecules fold into their active tertiary structures. All of these rates of change depend on a fundamental consistency in how entropy increases. Although the Second Law specifies the direction of entropy changes, it is silent about the rates at which these changes occur. Yet consistencies in rates of change (that is, in the manner in which thermodynamic entropy increases) undeniably exist and are manifest features of the living world. An important step toward understanding such consistencies was taken by Onsager in 1931. Lord Rayleigh (Strutt, 1871-1873) in 1873 had introduced the dissipation function, and Onsager (1931) generalized this idea to discuss consistencies in the rates of certain processes in terms of a principle that can be expressed as an equation of the form d S / d t - I = maximum, where d S / d t is the rate of entropy change and I is the impediment to entropy increase. Under certain circumstances, Onsager was able to quantify /, and he showed in detail that I is consistently minimized in specific systems; in all the systems quantified, the rate of entropy production is a maximum. The broad implications of Onsager's equation have not been explored. His equation says that systems increase entropy at the maximum rate possible. This principle has the power to predict and explain consistencies in a wide range of biological phenomena. 2. Consistencies in Rates of Chemical Reactions
The established laws of thermodynamics do not address the existence of consistencies in rates of chemical reactions (and in the corresponding rates of entropy production). Yet the consistencies exist, and life depends on them. Onsager's principle provides a parsimonious explanation: the rates of reactions depend upon the rate at which entropy increases, and that rate is the maximum rate possible. Therefore the reaction rates will always be the same. The same principle applies nicely to a class of astonishing phenomena that .occur predictably and consistently in many far-from-equilibrium systems, the phenomena of dissipative structures. Far-from-equilibrium low-entropy systems, in which intriguing and seemingly enigmatic spatially ordered structures (dissipative structures) appear, have been studied since the 19th century. The probability that such highly ordered structures would appear in chaotic systems seems most remote, yet their occurrence is both predictable and common. For example, a regular pattern of hexagonal structures called Brnard cells consistently appears in thin layers of silicone oil heated uniformly from below and exposed to ambient air above (Koschmieder, 1974). Salt fingers (another Brnard phenomenon) form in oceans when both thermal gradients and concentration gradients are simultaneously present (Schechter et al., 1974). Other well-investigated examples include Liesegang rings (Hedges & Myers, 1926), the oscillating Belousov-Zhabotinski reaction and many analogs (Field & Burger, 1985). The thermodynamic role of dissipative structures is always the same: they enhance
ONSAGER'S
PRINCIPLE
173
the rate of entropy production. That is, they reduce the I in Onsager's equation. His principle suggests that systems will be manifestly opportunistic with regard to maximizing the rate at which they produce entropy. The regular and predictable appearance of dissipative structures, seemingly against staggering odds, reflects this opportunism.
3. Living Systems Before the advent of life, pools of low-entropy organic material were accumulating in many places on earth. Within these far-from-equilibrium aggregations of matter, reactions that increased entropy were occurring very slowly. Under these conditions, Onsager's principle would predict that, if opportunities existed to increase the rate of entropy production, they would be seized. Not only did catalysts for many entropy-increasing reactions come into existence, but the theme eventually led to the evolution of enormous arrays of enzymes, the intricate architectures housing them and the capacity of these dissipative structures to reproduce themselves. From a thermodynamic point of view, each enzyme is a dissipative structure that greatly reduces impediments (Onsager's I) to increasing entropy. Some enzymes increase reaction rates up to a million fold. The evolution of structurally elaborate selfreplicating catalytic systems (ceils) is a dramatic illustration of thermodynamic opportunism. The living cell, as an organized aggregate of catalyzed chemical reactions, is remarkably adept at transforming energy and chemicals to higher states of entropy via metabolic processes. Because of cells, thermodynamic entropy increases at rates far beyond the rates that were occurring in the lifeless environment. Without cells, potential metabolites remained intact (in states of comparatively low entropy) for much longer periods. Given the structural and functional complexity of cells, the odds against their existence would seem overwhelming. Yet the thermodynamic theme that ted to their evolution (the manifest opportunism of systems for maximizing the rate of entropy production) suggests an inevitability to the events that led from primordial cellular precursors to organized living cells. The theme of thermodynamic opportunism is further expressed in living matter when a few individuals of a species arrive in a favorable environment where there are few or no natural enemies or competitors for food. From a thermodynamic point of view, the absence of competitors in a favorable environment means, among other things, that there is matter (food) stranded in a low state of entropy. Also, from a thermodynamic perspective, "a few individuals of a species arriving" means the advent of a new dissipative opportunity. A population of pre-existing dissipative structures capable of exchanging both matter and energy with their environment and capable of reproducing themselves become part of a low-entropy environment and begin processing the low-entropy matter, increasing the entropy of matter that was previously stranded. In situations such as this, populations of dissipative structures explode, as did gypsy moths in Eastern United States and rabbits in Australia. From a thermodynamic perspective, this phenomenon reflects a fundamental consistency in the behavior of matter. If opportunities to increase the rate
174
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E.
MOREL
AND
G.
FLECK
at which entropy is produced exist, thermodynamic systems will seize those opportunities. If, for example, predators become part of the system, a dynamic interplay of predator and prey populations develops; the system as a whole organizes to increase the rate of entropy production. Whether in chemical systems or ecosystems, the production of entropy tends to be maximized. The same theme is expressed in a different way when species radiate adaptively. Adaptive radiations from a thermodynamic point of view are changes in dissipative structures that diversify their capacities to increase entropy. Consider the geospizine finches of the Galapagos Islands (Lack, 1947). When the ancestral finches arrived on the islands, they apparently found few competing species of small land birds. With little competition, they had the opportunity to exploit a variety of food sources such as seeds, fruits, buds and insects. Over the next three million years the ancestral seed-eating species diversified into a number of species, each with specialized feeding behaviors. These species eventually exploited the environment as seed eaters, insect eaters, fruit and seed eaters, and fruit and bud eaters. From a thermodynamic perspective, the food consumption of the finches can be described as dissipative behavior. This diversification of species represents specializations in the dissipative behavior of matter, leading to exploitation of a wider range of low-entropy enclaves and thus to further increases in the overall rate of entropy production in the Galapagos Island system. On even broader phyletic and time scales, the thermodynamic behavior of living matter remains consistent with the principle of opportunism. Fossil records indicate that a number of mass extinctions have occurred on this planet. Each extinction appears to have been the consequence of dramatically changed environmental conditions which resulted in the elimination of major taxonomic groups. These reductions in the diversity of species meant that arrays of low-entropy matter were no longer being exploited at former rates. Rediversification would be predicted by Onsager's equation and the theme of thermodynamic opportunism. And indeed, after each extinction, species consistently reradiated into rich and diverse biota (Simpson, 1949). In general, the diversification of dissipative behavior seems to be a unifying and fundamental thermodynamic and biological theme. The process of evolution itself appears to represent survival,, reproduction and diversification of the most effective thermodynamic entropy producers.
4. Discussion
Onsager's Principle offers a simple and satisfying explanation for observable thermodynamic phenomena at many levels of physical and biological science. Biological events are governed by three thermodynamic principles: the First and Second Laws, and Onsager's Principle. Because these are functional principles, not mechanistic principles, they offer an opportunity to understand what Wicken (1987) has called "the global direction of evolution" without necessarily comprehending details of molecular and biochemical dynamics. Organismic and evolutionary, as well as biochemical, phenomena seem to be direct reflections of the thermodynamic
ONSAGER~S PRINCIPLE
175
t h e m e e x p r e s s e d by O n s a g e r ' s e q u a t i o n . B i o l o g i c a l a d a p t a t i o n a n d d i v e r s i f i c a t i o n , v i e w e d f r o m a t h e r m o d y n a m i c p e r s p e c t i v e , are p a r s i m o n i o u s l y r a t i o n a l i z e d .
REFERENCES BENT, H. A. (1965). In: The Second Law. p. 10. New York: Oxford University Press. FIELD, R. J. & BURGER, M. (eds.) (1985). Oscillations and Traveling Waves in Chemical Systems. New York: Wiley. HEDGES, E. S. & MYERS, J. E. (1926). The Problem of Physico-Chemical Periodicity. New York: Longmans, Green. KOSCHMIEDER, E. L. (1974). Adv. chem. Phys. 26, 177. LACK, D. (1947). Darwin's Finches. Cambridge: Cambridge University Press. ONSAGER, L. (1931). Phys. Rev. 37, 405. SCHECHTER, R. S., VELARDE, M. G. & PLATTEN, J. K. (1974). Adv. Chem. Phys. 26, 265. SIMPSON, G. G. (1949). The Meaning of Evolution. New Haven: Yale University Press. STRUTT, J. W. (Lord Rayleigh) (1871-1873). Proc Lond. Math. Soc. 4, 357. WIC'KEN, J. S. (1987). In: Evolution, Thermodynamics, and Information: Extending the Darwinian Program. p. 57. New York: Oxford University Press.
Onsager's Principle: A Unifying Bio-theme RICHARD E. MOREL AND GEORGE FLECK
Department of Chemistry, Smith College, Northampton, Massachusetts 01063, U.S.A. (Received 18 April 1988, and accepted in revised form 20 June 1988) A hitherto obscure thermodynamic principle proposed by Lars Onsager in 1931 (Phys. Rev. 37, 405) serves as a parsimonious explanation for consistencies in the rates at which biochemical events occur, consistencies not explained by existing thermodynamic laws. It also provides an underlying rationale for the observation that thermodynamic systems, including living systems, are relentlessly opportunistic with respect to increasing entropy. These consistencies and this opportunism form a broadly unifying theme for biological phenomena from molecular to organismic and evolutionary levels.
1.
Introduction
Consistencies in the direction of events over time are predicted by the First and Second Laws of Thermodynamics. The First Law (the principle of conservation of energy) states that the total amount of energy does not change during an event. The Second Law states that, within the context of the First Law, entropy always increases during an event. Locally, energy may change and entropy may increase or decrease; the First and Second Laws apply to the universe of the event, that portion of the physical universe in terms of which every thermodynamically important aspect of the event can be described (Bent, 1965). Consider a burning candle. Usable energy contained in the wax and wick is being dissipated into light and heat by the flame. Highly ordered molecules such as paratfins and cellulose are being converted to less ordered molecules such as water and carbon dioxide, and the orderly and compact arrangement of molecules in the candle (a solid) is being transformed to a less ordered arrangement of molecules (gases). As the Second Law predicts, entropy increases as the burning continues. We would not expect the products of combustion to recombine spontaneously in a candle flame to form a whole candle. Beyond the fundamental consistency in the direction of this process, toward higher entropy, we also know that an undisturbed candle burns at a consistent rate. That is, entropy increases at a consistent rate. The First and Second Laws do not address, much less explain, this consistency--a consistency so reliable that candles have been used as instruments to measure elapsed time. But experience and observation tell us that t h e r m o d y n a m i c entropy increases at remarkably consistent rates. Consistency in the rates at which thermodynamic entropy increases is a precondition for the existence o f biochemical systems and living matter. A living cell relies, for example, on consistencies in the rates at which molecules diffuse, on consistencies 171
0022-5193/89/020171 +05 $03.00/0
© 1989 Academic Press Limited
172
R.E.
MOREL
AND
G,
FLECK
in the rates enzymes catalyze reactions, and on consistencies in the rates at which protein molecules fold into their active tertiary structures. All of these rates of change depend on a fundamental consistency in how entropy increases. Although the Second Law specifies the direction of entropy changes, it is silent about the rates at which these changes occur. Yet consistencies in rates of change (that is, in the manner in which thermodynamic entropy increases) undeniably exist and are manifest features of the living world. An important step toward understanding such consistencies was taken by Onsager in 1931. Lord Rayleigh (Strutt, 1871-1873) in 1873 had introduced the dissipation function, and Onsager (1931) generalized this idea to discuss consistencies in the rates of certain processes in terms of a principle that can be expressed as an equation of the form d S / d t - I = maximum, where d S / d t is the rate of entropy change and I is the impediment to entropy increase. Under certain circumstances, Onsager was able to quantify /, and he showed in detail that I is consistently minimized in specific systems; in all the systems quantified, the rate of entropy production is a maximum. The broad implications of Onsager's equation have not been explored. His equation says that systems increase entropy at the maximum rate possible. This principle has the power to predict and explain consistencies in a wide range of biological phenomena. 2. Consistencies in Rates of Chemical Reactions
The established laws of thermodynamics do not address the existence of consistencies in rates of chemical reactions (and in the corresponding rates of entropy production). Yet the consistencies exist, and life depends on them. Onsager's principle provides a parsimonious explanation: the rates of reactions depend upon the rate at which entropy increases, and that rate is the maximum rate possible. Therefore the reaction rates will always be the same. The same principle applies nicely to a class of astonishing phenomena that .occur predictably and consistently in many far-from-equilibrium systems, the phenomena of dissipative structures. Far-from-equilibrium low-entropy systems, in which intriguing and seemingly enigmatic spatially ordered structures (dissipative structures) appear, have been studied since the 19th century. The probability that such highly ordered structures would appear in chaotic systems seems most remote, yet their occurrence is both predictable and common. For example, a regular pattern of hexagonal structures called Brnard cells consistently appears in thin layers of silicone oil heated uniformly from below and exposed to ambient air above (Koschmieder, 1974). Salt fingers (another Brnard phenomenon) form in oceans when both thermal gradients and concentration gradients are simultaneously present (Schechter et al., 1974). Other well-investigated examples include Liesegang rings (Hedges & Myers, 1926), the oscillating Belousov-Zhabotinski reaction and many analogs (Field & Burger, 1985). The thermodynamic role of dissipative structures is always the same: they enhance
ONSAGER'S
PRINCIPLE
173
the rate of entropy production. That is, they reduce the I in Onsager's equation. His principle suggests that systems will be manifestly opportunistic with regard to maximizing the rate at which they produce entropy. The regular and predictable appearance of dissipative structures, seemingly against staggering odds, reflects this opportunism.
3. Living Systems Before the advent of life, pools of low-entropy organic material were accumulating in many places on earth. Within these far-from-equilibrium aggregations of matter, reactions that increased entropy were occurring very slowly. Under these conditions, Onsager's principle would predict that, if opportunities existed to increase the rate of entropy production, they would be seized. Not only did catalysts for many entropy-increasing reactions come into existence, but the theme eventually led to the evolution of enormous arrays of enzymes, the intricate architectures housing them and the capacity of these dissipative structures to reproduce themselves. From a thermodynamic point of view, each enzyme is a dissipative structure that greatly reduces impediments (Onsager's I) to increasing entropy. Some enzymes increase reaction rates up to a million fold. The evolution of structurally elaborate selfreplicating catalytic systems (ceils) is a dramatic illustration of thermodynamic opportunism. The living cell, as an organized aggregate of catalyzed chemical reactions, is remarkably adept at transforming energy and chemicals to higher states of entropy via metabolic processes. Because of cells, thermodynamic entropy increases at rates far beyond the rates that were occurring in the lifeless environment. Without cells, potential metabolites remained intact (in states of comparatively low entropy) for much longer periods. Given the structural and functional complexity of cells, the odds against their existence would seem overwhelming. Yet the thermodynamic theme that ted to their evolution (the manifest opportunism of systems for maximizing the rate of entropy production) suggests an inevitability to the events that led from primordial cellular precursors to organized living cells. The theme of thermodynamic opportunism is further expressed in living matter when a few individuals of a species arrive in a favorable environment where there are few or no natural enemies or competitors for food. From a thermodynamic point of view, the absence of competitors in a favorable environment means, among other things, that there is matter (food) stranded in a low state of entropy. Also, from a thermodynamic perspective, "a few individuals of a species arriving" means the advent of a new dissipative opportunity. A population of pre-existing dissipative structures capable of exchanging both matter and energy with their environment and capable of reproducing themselves become part of a low-entropy environment and begin processing the low-entropy matter, increasing the entropy of matter that was previously stranded. In situations such as this, populations of dissipative structures explode, as did gypsy moths in Eastern United States and rabbits in Australia. From a thermodynamic perspective, this phenomenon reflects a fundamental consistency in the behavior of matter. If opportunities to increase the rate
174
R.
E.
MOREL
AND
G.
FLECK
at which entropy is produced exist, thermodynamic systems will seize those opportunities. If, for example, predators become part of the system, a dynamic interplay of predator and prey populations develops; the system as a whole organizes to increase the rate of entropy production. Whether in chemical systems or ecosystems, the production of entropy tends to be maximized. The same theme is expressed in a different way when species radiate adaptively. Adaptive radiations from a thermodynamic point of view are changes in dissipative structures that diversify their capacities to increase entropy. Consider the geospizine finches of the Galapagos Islands (Lack, 1947). When the ancestral finches arrived on the islands, they apparently found few competing species of small land birds. With little competition, they had the opportunity to exploit a variety of food sources such as seeds, fruits, buds and insects. Over the next three million years the ancestral seed-eating species diversified into a number of species, each with specialized feeding behaviors. These species eventually exploited the environment as seed eaters, insect eaters, fruit and seed eaters, and fruit and bud eaters. From a thermodynamic perspective, the food consumption of the finches can be described as dissipative behavior. This diversification of species represents specializations in the dissipative behavior of matter, leading to exploitation of a wider range of low-entropy enclaves and thus to further increases in the overall rate of entropy production in the Galapagos Island system. On even broader phyletic and time scales, the thermodynamic behavior of living matter remains consistent with the principle of opportunism. Fossil records indicate that a number of mass extinctions have occurred on this planet. Each extinction appears to have been the consequence of dramatically changed environmental conditions which resulted in the elimination of major taxonomic groups. These reductions in the diversity of species meant that arrays of low-entropy matter were no longer being exploited at former rates. Rediversification would be predicted by Onsager's equation and the theme of thermodynamic opportunism. And indeed, after each extinction, species consistently reradiated into rich and diverse biota (Simpson, 1949). In general, the diversification of dissipative behavior seems to be a unifying and fundamental thermodynamic and biological theme. The process of evolution itself appears to represent survival,, reproduction and diversification of the most effective thermodynamic entropy producers.
4. Discussion
Onsager's Principle offers a simple and satisfying explanation for observable thermodynamic phenomena at many levels of physical and biological science. Biological events are governed by three thermodynamic principles: the First and Second Laws, and Onsager's Principle. Because these are functional principles, not mechanistic principles, they offer an opportunity to understand what Wicken (1987) has called "the global direction of evolution" without necessarily comprehending details of molecular and biochemical dynamics. Organismic and evolutionary, as well as biochemical, phenomena seem to be direct reflections of the thermodynamic
ONSAGER~S PRINCIPLE
175
t h e m e e x p r e s s e d by O n s a g e r ' s e q u a t i o n . B i o l o g i c a l a d a p t a t i o n a n d d i v e r s i f i c a t i o n , v i e w e d f r o m a t h e r m o d y n a m i c p e r s p e c t i v e , are p a r s i m o n i o u s l y r a t i o n a l i z e d .
REFERENCES BENT, H. A. (1965). In: The Second Law. p. 10. New York: Oxford University Press. FIELD, R. J. & BURGER, M. (eds.) (1985). Oscillations and Traveling Waves in Chemical Systems. New York: Wiley. HEDGES, E. S. & MYERS, J. E. (1926). The Problem of Physico-Chemical Periodicity. New York: Longmans, Green. KOSCHMIEDER, E. L. (1974). Adv. chem. Phys. 26, 177. LACK, D. (1947). Darwin's Finches. Cambridge: Cambridge University Press. ONSAGER, L. (1931). Phys. Rev. 37, 405. SCHECHTER, R. S., VELARDE, M. G. & PLATTEN, J. K. (1974). Adv. Chem. Phys. 26, 265. SIMPSON, G. G. (1949). The Meaning of Evolution. New Haven: Yale University Press. STRUTT, J. W. (Lord Rayleigh) (1871-1873). Proc Lond. Math. Soc. 4, 357. WIC'KEN, J. S. (1987). In: Evolution, Thermodynamics, and Information: Extending the Darwinian Program. p. 57. New York: Oxford University Press.