Hostname: page-component-cd9895bd7-8ctnn Total loading time: 0 Render date: 2024-12-23T11:04:11.707Z Has data issue: false hasContentIssue false
  • English
  • Français

Network thermodynamics: dynamic modelling of biophysical systems

Published online by Cambridge University Press:  17 March 2009

George F. Oster ,
Alan S. Perelson  and
Aharon Katchalsky
George F. Oster
Affiliation:
Donner Laboratory, Lawrence Berkeley Laboratory, University of California, Berkeley, California 94720
Alan S. Perelson
Affiliation:
Group in Biophysics and Medical Physics, Donner Laboratory, Lawrence Berkeley Laboratory, University of California, Berkeley, California 94720
Aharon Katchalsky
Affiliation:
Polymer Department, Weizman Institute of Science, and Donner Laboratory, Lawrence Berkeley Laboratory, University of California, Berkeley, California 94720
Get access Rights & Permissions [Opens in a new window]

Extract

The success of equilibrium thermodynamics in describing static phenomena has inspired many attempts to develop a rigorous thermodynamics of rate processes.

Type
Research Article
Information
Quarterly Reviews of Biophysics , Volume 6 , Issue 1 , February 1973 , pp. 1 - 134
Copyright
Copyright © Cambridge University Press 1973

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Aranow, R. H. (1963). Periodic behavior in charged membranes and its physical and biological implications. Proc. natn. Acad. Sci. (U.S.A.) 50, 1066.CrossRefGoogle ScholarPubMed
Aris, R. (1969). Elementary Chemical Reactor Analysis. Englewood Cliffs, New Jersey: Prentice-Hall.Google Scholar
Aris, R. & Mah, R. H. S. (1963). Independence of chemical reactions. Ind. & Chem. Fundam. 2, 901.CrossRefGoogle Scholar
Arnold, V. I. (1967). Characteristic class entering in quantization conditions. Funct. Anal. & Appl. 1, 1.CrossRefGoogle Scholar
Arnold, V. I. & Avez, A. (1968). Ergodic Problems of Classical Mechanics. New York: Benjamin.Google Scholar
Bearman, R. J. & Kirkwood, J. G. (1958). Statistical mechanics of transport processes. XI. Equations of transport in multi-component systems. J. chem. Phys. 28, 136.CrossRefGoogle Scholar
Berge, C. (1962). The Theory of Graphs and Its Applications. New York: Wiley.Google Scholar
Berge, C. & Ghouila-Houri, A. (1965). Programming, Games, and Transportation Networks. New York: Wiley.Google Scholar
Blackwell, W. A. (1968). Mathematical Modelling of Physical Networks. New York: Macmillan.Google Scholar
Blumenthal, R. & Katchalsky, A. (1969). The effect of the carrier association—dissociation rate on membrane permeation. Biochim. biophys. Acta 173, 357.CrossRefGoogle ScholarPubMed
Branin, F. (1962). Machine analysis of networks and its applications. IBM Tech. Rept. TR 00.855.Google Scholar
Branin, F. (1966). The algebraic-topological basis for network analogies and the vector calculus. In Proceedings of the Symposium on Generalized Networks. Brooklyn, New York: Polytechnic Press of the Polytechnic Institute of Brooklyn.Google Scholar
Brayton, R. K. (1969). Nonlinear reciprocal networks. IBM Research Rept. RC 2606 (no. 12427).Google Scholar
Brayton, R. K. & Moser, J. K. (1964). A theory of nonlinear networks, I and II. Q. appl. Math. 22, 1; 22, 81.CrossRefGoogle Scholar
Callen, H. (1960). Thermodynamics. New York: Wiley.Google Scholar
Caplan, S. R. & Mikulecky, D. C. (1966). Transport processes in membranes. In Ion Exchange, vol. 1 (ed. Marinsky, J. A.). New York: Marcel DekkerGoogle Scholar
Cherry, C. (1951). Some general theorems for nonlinear systems possessing reactance. Phil. Mag. 42, 1161.CrossRefGoogle Scholar
Chua, L. (1971). Memristor – the missing circuit element. IEEE Trans. Circuit Theory CT-18, 507.CrossRefGoogle Scholar
Chua, L. O. & Lam, Y. F. (1971). Nonlinear n-ports. I. Characterization, classification, and representation. University of California, Berkeley, Electronics Research Laboratory Memorandum ERL-M307.Google Scholar
Cole, K. (1968). Membranes, Ions and Impulses. Berkeley: University of California Press.CrossRefGoogle Scholar
Cullis, C. E. (1913). Matrices and Determinoids, vol. 2, p. 165. London: Cambridge University Press.Google Scholar
De Donder, Th. & Van Rysselberghe, P. (1936). Affinity. Stanford, California: Stanford University Press.Google Scholar
de Groot, S. (1951). Thermodynamics of Irreversible Processes. Amsterdam: North-Holland.Google Scholar
de Groot, S. R. & Mazur, P. (1962). Nonequilibrium Thermodynamics. Amsterdam: North-Holland.Google Scholar
De Simone, J. A. & Caplan, S. R. (1972). Symmetry and the stationary state behaviour of enzyme membranes. J. theor. Biol.(in the Press).Google Scholar
Desoer, C. (1970). Notes for a Second Course on Linear Systems. New York: Van Nostrand–Reinhold.Google Scholar
Desoer, C. & Kuh, E. (1969). Basic Circuit Theory. New York: McGraw-Hill.Google Scholar
Desoer, C. & Oster, G. (1973). Globally reciprocal stationary systems. Int. J. Eng. Sci. (in the Press).CrossRefGoogle Scholar
Desoer, C. & Wu, F. (1971). Networks viewed as flows on manifolds. In Proceedings of the International Network Theory Conference. London.Google Scholar
Desoer, C. & Wu, F. (1972). Trajectories of nonlinear RLC networks: A geometric approach. IEEE Trans. Circuit Theory CT-19, 562.CrossRefGoogle Scholar
Fleming, W. (1965). Functions of Several Variables. Reading, Mass.: Addison-Wesley.Google Scholar
Franck, U. F. (1963). Über da Electrochemische Verhalten von Porösen Ionenanstauschenmembranen, Ber. BunsenGes. Phys. Chem. 67, 657.CrossRefGoogle Scholar
Friedlander, S. K. & Keller, K. H. (1965). Mass transfer in reacting systems near equilibrium. Chem. Engng Sci. 20, 121.CrossRefGoogle Scholar
Glansdorff, P. & Prigogine, I. 1954 Sur le propriétés différentielles de la production d'entropie. Physica's Grav. 20, 773.Google Scholar
Glansdorff, P. & Prigogine, I. (1964). On a general evolution criterion in macroscopic physics. Physica's Grav. 30, 351.Google Scholar
Glansdorff, P. & Prigogine, I. (1970). Nonequilibrium stability theory. Physica's Grav. 46, 344.Google Scholar
Glansdorff, P. & Prigogine, I.Thermodynamic Theory of Structure, Stability and Fluctuations. London: Wiley-Interscience.CrossRefGoogle Scholar
Haldane, J. B. S. (1930). Enzymes. London: Longmans, Green and Co.Google Scholar
Harary, F. (1969). Graph Theory. Reading, Mass.: Addison-Wesley.CrossRefGoogle Scholar
Hermann, R. (1971). Vector Bundles in Mathematical Physics, vols. 1 and 2. New York: Benjamin.Google Scholar
Karnopp, D. & Rosenberg, R. (1968). Analysis and Simulation of Multiport Systems. Cambridge, Mass.: MIT Press.Google Scholar
Katchalsky, A. & Oster, G. (1969). Chemico-diffusional coupling in biomembranes. In The Molecular Basis of Membrane Function, ed. Tosteson, D. C.. Englewood Cliffs, New Jersey: Prentice-Hall.Google Scholar
Katchalsky, A. & Spangler, R. (1968). Dynamics of membrane processes. Q. Rev. Biophys. 1, 127.CrossRefGoogle ScholarPubMed
Kedem, O. & Katchalsky, A. (1961). A physical interpretation of the phenomenological coefficients of membrane permeability. J. gen. Physiol. 45, 143.CrossRefGoogle ScholarPubMed
Killingbeck, J. & Cole, G. H. A. (1971). Mathematical Techniques and Physical Applications. New York: Academic Press.Google Scholar
Kobatake, Y. & Fugita, H. (1964). Flow through charged membranes. 1: Flip-flop currents vs. voltage relation. J. chem. Phys. 40, 2212; 2: Oscillation phenomena. J. chem. Phys. 40, 2219.CrossRefGoogle Scholar
Koenig, H., Tokad, Y. & Kevasan, H. K. (1969). Analysis of Discrete Physical Systems. New York: McGraw-Hill.Google Scholar
Kron, G. (1943). Equivalent circuits to represent the electromagnetic field equations. Phys. Rev. 64, 126.CrossRefGoogle Scholar
Kron, G. (1944 a). Equivalent circuits of the field equations of Maxwell. Proc. Instn Radio Engrs Aust. 32, 289.Google Scholar
Kron, G. (1944 b). Equivalent circuits of the elastic field. J. appl. Mech. 11, 149.CrossRefGoogle Scholar
Kron, G. (1945 a). Electric circuit models of the Schrödinger equation. Phys. Rev. 67, 39.CrossRefGoogle Scholar
Kron, G. (1945 b). Equivalent circuits of compressible and incompressible fluid flow fields. J. aeronaut. Sci. 12, 221.CrossRefGoogle Scholar
Kron, G. (1946). Electric circuit models for the vibration spectrum of polyatomic molecules. J. Chem. Phys. 14, 19.CrossRefGoogle Scholar
Kron, G. (1948). Electric circuit models of partial differential equations. Electron. Engng 67, 672.CrossRefGoogle Scholar
LaMer, V. K., Foss, O. & Reiss, H. (1949). Some new procedures in the thermodynamic theory inspired by the recent work of J. N. Brønsted. Ann. N.Y. Acad. Sci. 51, 605.CrossRefGoogle Scholar
Li, J. C. M. (1958). Thermodynamics for nonisothermal systems. The classical formulation. J. chem. Phys. 29, 747.CrossRefGoogle Scholar
Loomis, L. H. & Sternberg, S. (1968). Advanced Calculus. Reading, Mass.: Addison-Wesley.Google Scholar
MacFarlane, A. G. J. (1970). Dynamical System Models. London: Harrap.Google Scholar
MacLane, S. (1968). Geometrical Mechanics. (Lecture Notes.) Department of Mathematics, University of Chicago.Google Scholar
Mal'cev, A. I. (1963). Foundation of Linear Algebra. San Francisco: Freeman.Google Scholar
Martens, H. & Allen, D. (1969). Introduction to Systems Theory. Columbus, Ohio: Merrill.Google Scholar
Meixner, J. (1941). Zür Thermodynamik der Thermodiffusion. Ann. Physik. 39, 333.CrossRefGoogle Scholar
Meixner, J. (1942). Reversible Bewegungen von Flüssigkeiten und Gasen. Ann. Physik 41, 409.CrossRefGoogle Scholar
Meixner, J. (1943). Zür Thermodynamik der irreversiblen Prozesse in Gasen mit chemisch reagierenden, dissoziierenden und anregbaren Komponenten. Annln Phys. 43, 244.CrossRefGoogle Scholar
Meixner, J. (1963). Thermodynamics of electrical networks and the Onsager–Casmir reciprocal relations. J. math. Phys. 4, 154.CrossRefGoogle Scholar
Meixner, J. (1964). On the theory of linear passive systems. Archs ration. Mech. Analysis 17, 278.CrossRefGoogle Scholar
Meixner, J. (1965). Linear passive systems. In Proceedings of the International Symposium on Statistic al Mechanics and Thermodynamics, pp. 52–68. Amsterdam: North-Holland.Google Scholar
Meixner, J. (1966 b). Network theory in its relation to thermodynamics. In Proceedings of the Symposium on Generalized Networks, pp. 13–25. New York: Polytechnic Press of the Polytechnic Institute of Brooklyn.Google Scholar
Millar, W. (1951). Some general theorems for nonlinear systems possessing resistance. Phil. Mag. 42, 1150.CrossRefGoogle Scholar
Morowitz, H. J., Higinbotham, W. A., Matthysse, S. W., & Quastler, H. (1964). Passive stability in a metabolic network. J. theor. Biol. 7, 98.CrossRefGoogle Scholar
Newman, S. & Rice, S. (1971). Model for constraint and control in biochemical networks. Proc. natn. Acad. Sci. (U.S.A.) 68, 92.CrossRefGoogle ScholarPubMed
Olson, H. (1958). Dynamical Analogies, 2nd ed.Princeton, New Jersey: D. Van Nostrand.Google Scholar
Onsager, L. (1931). Reciprocal relations in irreversible processes, I and II. Phys. Rev. 37, 405; 38, 2265.CrossRefGoogle Scholar
Oster, G. & Auslander, D. (1971). Topological representations of thermodynamic systems. I: Basic concepts. J. Franklin Inst. 292, 1. II: Some elemental subunits for irreversible thermodynamics. J. Franklin Inst. 292, 77.CrossRefGoogle Scholar
Oster, G. & Desoer, C. (1971). Tellegen's theorem and thermodynamic inequalities. J. theor. Biol. 32, 219.CrossRefGoogle ScholarPubMed
Oster, G., Perelson, A. & Katchalsky, A. (1971). Network thermodynamics. Nature (Lond.) 234, 393.CrossRefGoogle Scholar
Oster, G. & Perelson, A. (1973). Chemical reaction dynamics. (Submitted for publication.)Google Scholar
Othmer, H. G. & Scriven, L. E. (1971). Instability and dynamic pattern in cellular networks. J. theor. Biol. 32, 507.CrossRefGoogle ScholarPubMed
Paynter, H. (1961). Analysis and Design of Engineering Systems. Cambridge, Mass.: MIT Press.Google Scholar
Penfield, P. & Haus, H. (1967). Electrodynamics of Moving Media. Cambridge, Mass.: MIT Press.Google Scholar
Penfield, P., Spence, R. & Duinker, S. (1970). Tellegen's Theorem and Electrical Networks. Cambridge, Mass.: MIT Press.Google Scholar
Perelson, A. (1973). Bond graph sign conventions. (Submitted for publication.)Google Scholar
Perelson, A. (1972). A Network Thermodynamic Treatment of Chemical and Diffusional Processes. Ph.D. dissertation. University of California, Berkeley.Google Scholar
Perelson, A. & Katchalsky, A. (1972). The relationship between the thermodynamic and kinetic reaction diffusion parameters. Chem. Engng Sci. 27, 1190.CrossRefGoogle Scholar
Pings, C. J. & Nebeker, E. B. (1965). Thermodynamics of chemical coupling. Ind. & Eng. Chem. Fundam. 4, 376.CrossRefGoogle Scholar
Pitzer, K. S. (1961). Irreversible thermodynamics. Pure appl. Chem. 2, 207.CrossRefGoogle Scholar
Prigogine, I. (1947). Étude thermodynamique des phénomènes irreversibles Liége: Desoer.Google Scholar
Prigogine, I. (1967). Thermodynamics of Irreversible Processes, 3rd ed.New York: Wiley-Interscience.Google Scholar
Redlich, O. (1970). Intensive and extensive properties. J. chem. Educ. 47, 154.CrossRefGoogle Scholar
Roth, J. P. (1955). An application of algebraic topology to numerical analysis: On the existence of a solution to the network problem. Proc. natn. Acad. Sci. (U.S.A.) 41, 518.CrossRefGoogle Scholar
Seshu, S. & Reed, M. (1961). Linear Graphs and Electrical Networks. Reading, Mass.: Addison-Wesley.Google Scholar
Shearer, J., Murphy, A. & Richardson, H. (1967). Introduction to System Dynamics. Reading, Mass.: Addison-Wesley.Google Scholar
Smale, S. (1972). On the mathematical foundations of circuit theory. J. Different. Geometry (in the Press).CrossRefGoogle Scholar
Smith, O. J. M. (1950). Thermistors. I: Static characteristics. Rev. Scient. Instrum. 21, 344. II: Dynamic characteristics. Rev. Scient. Instrum. 21, 351.CrossRefGoogle Scholar
Spiegler, K. S. (1958). Transport processes in ionic membranes. Trans. Faraday Soc. 54, 1408.CrossRefGoogle Scholar
Spivak, M. (1965). Calculus on Manifolds. New York: Benjamin.Google Scholar
Sudarshan, E. C. G. (1962). The structure of dynamical theories. Brandeis Summer Institute, 1961. Lectures in Theoretical Physics, vol. 2. New York: Benjamin.Google Scholar
Takakashi, Y., Auslander, D. & Rabins, M. (1970). Control. Reading, Mass.: Addison-Wesley.Google Scholar
Tellegen, B. D. H. (1952). A general network theorem, with applications. Philips Res. Rep. 7, 259.Google Scholar
Teorell, T. (1962). Excitability phenomena in artificial membranes. Biophys. J. 2, (2), part 2, 27.CrossRefGoogle ScholarPubMed
Trent, H. M. (1955). Isomorphisms between oriented linear graphs and lumped physical systems. J. acoust. Soc. Am. 27, 500.CrossRefGoogle Scholar
Truesdell, C. (1969). Rational Thermodynamics. New York: McGraw-Hill.Google Scholar
Van Rysselberghe, P. (1958). Reaction rates and affinities. J. chem. Phys. 29, 640.CrossRefGoogle Scholar