... Chemical Principles. (network/cycling theorem/axiomatic organic chemistry/
Kirchhofrs current law/ ... principles, synthetic organic chemists have developed a
high degree of .... Problems, New Applications (The University of Chicago. Press
...
Proc. Nat. Acad. Sci. USA
Vol. 71, No. 6, pp. 2335-2336, June 1974
The Derivation of Ecological Relationships from Physical and Chemical Principles (network/cycling theorem/axiomatic organic chemistry/Kirchhofrs current law/ nonequilibrium thermodynamics)
HAROLD J. MOROWITZ Department of Molecular Biophysics and Biochemistry, Yale University, New Haven, Connecticut 06520
Communicated by G. Evelyn Hutchinson, ApriLl, 1974 ABSTRACT Organic reaction networks are formalized by representing chemical species as points in a space and representing reactions by connectivity rules. Using the generalized network, the behavior of the system is investigated under conditions of electronically exciting input and output to a thermal reservoir. Under steady-state conditions the system undergoes material cycles of the type shown by the major ecological cycles. A consideration of the attractor nature of the equilibrium state of the system leads to the conclusion that the energetically lowest-lying molecules must be inputs into the material cycles. Certain general features of the ecological system are thus shown to follow from the physical and chemical properties of an organic reaction network.
reactions by combinations of the operations shown in Figure 1. The points represent molecular descriptions and the lines represent reaction pathways. Whether or not reaction lines can be drawn between points depends on conservation rules as well as on detailed quantum mechanical considerations. While such relations are not generally available from first principles, synthetic organic chemists have developed a high degree of predictive ability in studying such problems. In any case, the space of organic molecules is clearly representable by a graph as outlined above. The graph can be made directed by assigning arrows in the direction of decreasing standard free energy of the reactions (AGo). Network theory representations of systems of chemical reactions have previously been formulated for a number of cases (6-9). The input of electronic energy can now be represented by a charging operation in parallel with a reaction line in the graph, as is shown in Figure 2. Consider next a model system closed to the flow of matter and in contact with an infinite isothermal reservoir. For definiteness, assume that the system contains a collection of molecules made up of the atoms C, H, N, 0, P,
Two essential features of global ecology are the existence of major material cycles and the presence of a pool of thermodynamic ground-state molecules as points in the cycle. In this paper we shall show that these two features are a necessary consequence of the physics and chemistry of nonequilibrium systems undergoing electronic excitations by an energy flux. The overall behavior of ecosystems is thus, in a sense, independent of the detailed interactions within the system. Our discussion will necessitate first establishing the outlines of a general formalism for dealing with networks of organic reactions. We will then derive a cycling theorem which states that steady-state organic networks maintained away from equilibrium by the input of electronic excitation will be characterized by flows of matter around closed loops in the network. We will then focus on the special role of the thermodynamic ground state as an attractor in directing the flow properties of the network. In recent years a number of workers (1-5) have attempted to establish organic chemistry on a more axiomatic foundation or to provide a set of algorithms to analyze synthetic or degradative pathways in a complex reaction network. A feature of these studies has been the necessity of representing an organic molecule as a linear array of symbols. These programs have indicated that any organic molecule whose structure is known can be so represented. As a result, a molecule can be represented as an n-tuple or a point in an abstract ndimensional space. Given this representation, we can now form a graph from the set of points by connecting valid subsets of reactants and products by lines. Rather than the edges of graph theory, we need a more complex line structure to represent chemical reactivity. By allowing short-lived -W intermediates as points in our space (part of the n-tuple FIG. 1. Graph representation of the types of elementary could be the energy state of the molecule) and dividing reacchemical reactions used to generate the reaction network. Shown tion sequences into unit steps, we can represent chemical are isomerization, condensation, and condensation splitting. 2335
2336
Biophysics: Morowitz
Representation of high-frequency inputs causing FIG. 2. transition to an electronically excited state.
Proc. Nat. Acad. Sci. USA 71 (1974)
a
and S. For homogeneous systems, the complete phenomenological description consists of specifying all the concentrations and reaction rates. In terms of the graph described above, we now think of the graph as a network, assigning concentration values to the points (which roughly correspond to a voltage assignment in electrical network theory) and flow values to the lines (which correspond to currents in electrical network theory). The input of electronic energy is analogous to the introduction of voltage sources in the electrical case. Next, consider a constant flux of excitation energy into the model system. This can be in the form of photons, ionizing radiation, very high-temperature thermal sources, spark discharge, or any other source that causes electronic transitions from lower-lying to higher-lying energy states. Under the constant energy flux the system will assume new values of concentrations and flows. The system will age and form a steady state where the time derivatives of the concentrations will vanish. For this condition, Kirchhoff's current law will hold at every point in the chemical network. This balance requires that the flows of material generated by the electronic transitions return to the points in the network where they originated. Thus, the steady state is of necessity characterized by cyclic flows of material around loops in the reaction network. As the material flows around the cycles, the input energy flows as heat into the isothermal reservoir. Thus, material cycling is seen to be a very general feature of chemical networks kept at a far from equilibrium steady state by the constant influx of energy in a form capable of electronic excitation. The relation of the model system to a planetary surface is clear. Such a surface is closed to the flow of matter and is exposed to a time-averaged constant flux of solar radiation. Outer space serves as an isothermal reservoir for the flow of heat, which is transferred in the form of infra-red radiation. Global ecology is thus an example of a general principle. Cycling is not uniquely biological; rather the biological example is special case of a more general principle. To introduce the special role of low-lying energy states, consider the previous model system after it has come to a a
steady state in an energy flux and remove the energy source, leaving the system in contact with the isothermal reservoir. The system will decay to an equilibrium state which, in the case of a biological atomic composition, will be characterized by CO2, H20, and N2 (10, 11). Eventually the entire system will consist almost entirely of these lowest-lying energy states. The equilibrium state is thus a powerful attractor in the molecular space in the topological sense of an attractor as introduced by Thom (12). The attractor nature exhibited by the equilibrium distribution is a property of the network, and not only a property of the equilibrium state. Therefore, during the dynamic states of the system the low-lying states are also acting as attractors directing flows in the network toward those points. Dynamic states of the system in which low-lying molecules are not pumped up to higher states will tend to disappear as the highenergy material drains into the sinks established by the attractors. For steady states to be maintained in the network, the energetically pumped cycles must involve the low-lying states. Thus, there is the necessity that photosynthetic processes operate on molecules such as water and carbon dioxide. Again, this is not a uniquely biological result but follows from the analysis of chemical networks. We have thus demonstrated that our previously stated features of global ecology have their origin in very general properties of networks of reacting molecules. We have previously demonstrated a generalized cycling of states for nonequilibrium systems (13) based on statistical mechanics. The present treatment demonstrates the consequences of that cycling on a more specified system. This work was supported by the National Aeronautic and Space Administration. 1. Smith, E. G. (1968) The Wisswesser Line-Formula Chemical Notation (McGraw Hill Inc., New York). 2. Ugi, I., Marquarding, D., Klusacek, H., Gokel, G. & Gillespie, P. (1970) Angew. Chem. Int. Ed. 9, 703-730. 3. Lederberg, J. (1972) Chapter 7 from Biochemical Applications- of Mass Spectrometry, ed. Waller, R. (John Wiley and Sons, New York), pp. 193-207. 4. Hendrickson, J. B. (1971) J. Amer. Chem. Soc. 93, 68476854. 5. Corey, E. J. (1971) Quart. Rev. (London) 25, 455-482. 6. Newman, S. A. & Rice, S. A. (1971) Proc. Nat. Acad. Sci. USA 68, 92-96. 7. Shear, D. (1967) J. Theor. Biol. 16, 212-228. 8. Gavalas, G. (1968) Non-Linear Differential Equations of Chemically Reacting Systems (Springer Verlag, New York). 9. Oster, G. F., Perelson, A. S. & Katchalsky, A. (1973) Quart. Rev. Biophys. 6, 1-134. 10. Dayhoff, M. O., Lippincott, E. R. & Eck, R. V. (1964) Science 146, 1461-1463. 11. Rider, K. & Morowitz, H. J. (1968) J. Theor. Biol. 21, 278-291. 12. Thom, R. (1972) in Statistical Mechanics New Concepts, New Problems, New Applications (The University of Chicago Press, Chicago), Chap. II, p. 6. 13. Morowitz, H. J. (1966) J. Theor. Biol. 13, 60-62.
