{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,14]],"date-time":"2026-09-14T18:09:11Z","timestamp":1789409351123,"version":"build-2803163510"},"reference-count":48,"publisher":"MathDoc\/Centre Mersenne","issue":"10","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"abstract":"<jats:title>Purpose<\/jats:title>\n                  <jats:p id=\"spar0005\">Statistical mechanics establishes a link between microscopic properties of matter and its bulk properties. A.\u00a0Huxley's equations (1957) [1] provide the necessary phenomenological formalism to use statistical mechanics.<\/jats:p>\n                  <jats:sec>\n                    <jats:title>Methods<\/jats:title>\n                    <jats:p id=\"spar0010\">\n                      We compared statistical mechanics in rat diaphragm in tetanus (tet;\n                      <jats:italic>n<\/jats:italic>\n                      \u2005=\u200510) and twitch (tw;\n                      <jats:italic>n<\/jats:italic>\n                      \u2005=\u200512) modes, in heart in twitch mode (\n                      <jats:italic>n<\/jats:italic>\n                      \u2005=\u200520), and in tracheal smooth muscle in tetanus mode (TSM;\n                      <jats:italic>n<\/jats:italic>\n                      \u2005=\u200510). This powerful tool makes it possible to determine: (i) statistical entropy (S) which is related to the dispersal of energy and represents a measure of the degree of disorder in muscular system; (ii) thermodynamic force A\/T (chemical affinity A and temperature T); (iii) thermodynamic flow (\u03c5); (iv) entropy production rate (A\/T\u2005\u00d7\u2005\u03c5), which quantifies irreversible chemical processes generated by myosin crossbridge (CB) molecular motors.\n                    <\/jats:p>\n                  <\/jats:sec>\n                  <jats:sec>\n                    <jats:title>Results<\/jats:title>\n                    <jats:p id=\"spar0015\">All muscles studied operated near equilibrium, i.e., A\u2005&lt;&lt;\u20052500\u2005J\/mol and in a stationary linear regime, i.e., A\/T varied linearly with \u03c5. The heart operated farther from equilibrium than both diaphragm (tet and tw) and TSM, as attested by its high entropy production rate. S was of the same order of magnitude in heart and TSM but lower in diaphragm (tet and tw).<\/jats:p>\n                  <\/jats:sec>\n                  <jats:sec>\n                    <jats:title>Conclusion<\/jats:title>\n                    <jats:p id=\"spar0020\">CB kinetics derived from A.\u00a0Huxley's equations conferred a characteristic profile in terms of statistical mechanics on each muscle type. All studied muscles differed in terms of statistical entropy, chemical affinity, and entropy production rate. Stimulation mode (tet and tw) modulated CB kinetics and statistical mechanics. All muscle types operated near equilibrium and in a stationary linear regime.<\/jats:p>\n                  <\/jats:sec>","DOI":"10.1016\/j.crvi.2011.08.001","type":"journal-article","created":{"date-parts":[[2011,9,15]],"date-time":"2011-09-15T13:45:39Z","timestamp":1316094339000},"page":"725-736","source":"Crossref","is-referenced-by-count":5,"title":["Comparative statistical mechanics of myosin molecular motors in rat heart, diaphragm and tracheal smooth muscle"],"prefix":"10.5802","volume":"334","author":[{"given":"Yves","family":"Lecarpentier","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Victor","family":"Claes","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"\u00c9douard","family":"Lecarpentier","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Fran\u00e7ois-Xavier","family":"Blanc","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Thierry","family":"Joseph","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Bart","family":"Geraets","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"X\u00e9nophon","family":"Krokidis","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Jean-Louis","family":"H\u00e9bert","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"3842","published-online":{"date-parts":[[2011,9,13]]},"reference":[{"key":"key2025102316335911401_1","doi-asserted-by":"crossref","first-page":"255","DOI":"10.1016\/S0096-4174(18)30128-8","article-title":"Muscle structure and theories of contraction","volume":"7","author":"Huxley, A.F.","year":"1957","unstructured":"[1] Huxley, A.F. Muscle structure and theories of contraction, Prog. Biophys. Biophys. Chem., Volume 7 (1957), pp. 255-318","journal-title":"Prog. Biophys. Biophys. Chem."},{"key":"key2025102316335911401_2","author":"Atkins, P.W.","year":"1990","unstructured":"[2] Atkins, P.W. Physical Chemistry, Oxford University Press, Oxford\/Melbourne\/Tokyo, 1990","journal-title":"Physical Chemistry"},{"key":"key2025102316335911401_3","author":"Kondepudi, D.","year":"1999","unstructured":"[3] Kondepudi, D.; Prigogine, I. Modern thermodynamics from heat engines to dissipative structures, Wiley & Sons, New York, 1999","journal-title":"Modern thermodynamics from heat engines to dissipative structures"},{"key":"key2025102316335911401_4","doi-asserted-by":"crossref","first-page":"4617","DOI":"10.1021\/bi00801a004","article-title":"Mechanism of adenosine triphosphate hydrolysis by actomyosin","volume":"10","author":"Lymn, R.W.","year":"1971","unstructured":"[4] Lymn, R.W.; Taylor, E.W. Mechanism of adenosine triphosphate hydrolysis by actomyosin, Biochemistry, Volume 10 (1971), pp. 4617-4624","journal-title":"Biochemistry"},{"key":"key2025102316335911401_5","doi-asserted-by":"crossref","first-page":"87","DOI":"10.1016\/S0301-4622(02)00069-8","article-title":"Thermodynamics and bioenergetics","volume":"97","author":"Demirel, Y.","year":"2002","unstructured":"[5] Demirel, Y.; Sandler, S.I. Thermodynamics and bioenergetics, Biophys. Chem., Volume 97 (2002), pp. 87-111","journal-title":"Biophys. Chem."},{"key":"key2025102316335911401_6","doi-asserted-by":"crossref","first-page":"659","DOI":"10.1073\/pnas.78.2.659","article-title":"Symmetry breaking and pattern selection in far-from-equilibrium systems","volume":"78","author":"Nicolis, G.","year":"1981","unstructured":"[6] Nicolis, G.; Prigogine, I. Symmetry breaking and pattern selection in far-from-equilibrium systems, Proc. Natl Acad. Sci. U S A, Volume 78 (1981), pp. 659-663","journal-title":"Proc. Natl Acad. Sci. U S A"},{"key":"key2025102316335911401_7","doi-asserted-by":"crossref","first-page":"381","DOI":"10.1016\/j.jtbi.2005.01.018","article-title":"Statistical mechanics of myosin molecular motors in skeletal muscles","volume":"235","author":"Lecarpentier, Y.","year":"2005","unstructured":"[7] Lecarpentier, Y.; Blanc, F.X.; Quillard, J.; Hebert, J.L.; Krokidis, X.; Coirault, C. Statistical mechanics of myosin molecular motors in skeletal muscles, J. Theor. Biol., Volume 235 (2005), pp. 381-392","journal-title":"J. Theor. Biol."},{"key":"key2025102316335911401_8","doi-asserted-by":"crossref","first-page":"92","DOI":"10.1016\/j.jtbi.2007.09.022","article-title":"Increased entropy production in diaphragm muscle of PPAR alpha knockout mice","volume":"250","author":"Lecarpentier, Y.","year":"2008","unstructured":"[8] Lecarpentier, Y.; Krokidis, X.; Martin, P.; Pineau, T.; Hebert, J.L.; Quillard, J.; Cortes-Morichetti, M.; Coirault, C. Increased entropy production in diaphragm muscle of PPAR alpha knockout mice, J. Theor. Biol., Volume 250 (2008), pp. 92-102","journal-title":"J. Theor. Biol."},{"key":"key2025102316335911401_9","doi-asserted-by":"crossref","first-page":"L83","DOI":"10.1152\/ajplung.2002.282.1.L83","article-title":"Myosin cross-bridge kinetics in airway smooth muscle: a comparative study of humans, rats, and rabbits","volume":"282","author":"Lecarpentier, Y.","year":"2002","unstructured":"[9] Lecarpentier, Y.; Blanc, F.X.; Salmeron, S.; Pourny, J.C.; Chemla, D.; Coirault, C. Myosin cross-bridge kinetics in airway smooth muscle: a comparative study of humans, rats, and rabbits, Am. J. Physiol. Lung Cell Mol. Physiol., Volume 282 (2002), p. L83-L90","journal-title":"Am. J. Physiol. Lung Cell Mol. Physiol."},{"key":"key2025102316335911401_10","doi-asserted-by":"crossref","first-page":"136","DOI":"10.1098\/rspb.1938.0050","article-title":"The heat of shortening and the dynamic constants of muscle","volume":"126","author":"Hill, A.V.","year":"1938","unstructured":"[10] Hill, A.V. The heat of shortening and the dynamic constants of muscle, Proc. R. Soc. Lond. Biol. Sci., Volume 126 (1938), pp. 136-195","journal-title":"Proc. R. Soc. Lond. Biol. Sci."},{"key":"key2025102316335911401_11","doi-asserted-by":"crossref","first-page":"981","DOI":"10.1096\/fasebj.12.11.981","article-title":"Mechanics, energetics, and crossbridge kinetics of rabbit diaphragm during congestive heart failure","volume":"12","author":"Lecarpentier, Y.","year":"1998","unstructured":"[11] Lecarpentier, Y.; Chemla, D.; Blanc, F.X.; Pourny, J.C.; Joseph, T.; Riou, B.; Coirault, C. Mechanics, energetics, and crossbridge kinetics of rabbit diaphragm during congestive heart failure, FASEB J., Volume 12 (1998), pp. 981-989","journal-title":"FASEB J."},{"key":"key2025102316335911401_12","author":"Woledge, R.C.","year":"1985","unstructured":"[12] Woledge, R.C.; Curtin, A.N.; Homsher, E. Energetic aspects of muscle contraction, Academic Press, London, 1985","journal-title":"Energetic aspects of muscle contraction"},{"key":"key2025102316335911401_13","doi-asserted-by":"crossref","first-page":"533","DOI":"10.1038\/233533a0","article-title":"Proposed mechanism of force generation in striated muscle","volume":"233","author":"Huxley, A.F.","year":"1971","unstructured":"[13] Huxley, A.F.; Simmons, R.M. Proposed mechanism of force generation in striated muscle, Nature, Volume 233 (1971), pp. 533-538","journal-title":"Nature"},{"key":"key2025102316335911401_14","doi-asserted-by":"crossref","first-page":"50","DOI":"10.1126\/science.8316857","article-title":"Three-dimensional structure of myosin subfragment-1: a molecular motor","volume":"261","author":"Rayment, I.","year":"1993","unstructured":"[14] Rayment, I.; Rypniewski, W.R.; Schmidt-Base, K.; Smith, R.; Tomchick, D.R.; Benning, M.M.; Winkelmann, D.A.; Wesenberg, G.; Holden, H.M. Three-dimensional structure of myosin subfragment-1: a molecular motor, Science, Volume 261 (1993), pp. 50-58","journal-title":"Science"},{"key":"key2025102316335911401_15","doi-asserted-by":"crossref","first-page":"559","DOI":"10.1016\/S0092-8674(00)81598-6","article-title":"Crystal structure of a vertebrate smooth muscle myosin motor domain and its complex with the essential light chain: visualization of the pre-power stroke state","volume":"94","author":"Dominguez, R.","year":"1998","unstructured":"[15] Dominguez, R.; Freyzon, Y.; Trybus, K.M.; Cohen, C. Crystal structure of a vertebrate smooth muscle myosin motor domain and its complex with the essential light chain: visualization of the pre-power stroke state, Cell, Volume 94 (1998), pp. 559-571","journal-title":"Cell"},{"key":"key2025102316335911401_16","doi-asserted-by":"crossref","first-page":"175","DOI":"10.1113\/jphysiol.1923.sp002115","article-title":"A quantitative comparison between the energy liberated and the work performed by the isolated sartorius muscle of the frog","volume":"58","author":"Fenn, W.O.","year":"1923","unstructured":"[16] Fenn, W.O. A quantitative comparison between the energy liberated and the work performed by the isolated sartorius muscle of the frog, J. Physiol. Lond., Volume 58 (1923), pp. 175-203","journal-title":"J. Physiol. Lond."},{"key":"key2025102316335911401_17","doi-asserted-by":"crossref","first-page":"677","DOI":"10.1085\/jgp.62.6.677","article-title":"Energetics of shortening muscles in twitches and tetanic contractions. II. Force-determined shortening heat","volume":"62","author":"Homsher, E.","year":"1973","unstructured":"[17] Homsher, E.; Mommaerts, W.F.; Ricchiuti, N.V. Energetics of shortening muscles in twitches and tetanic contractions. II. Force-determined shortening heat, J. Gen. Physiol., Volume 62 (1973), pp. 677-692","journal-title":"J. Gen. Physiol."},{"key":"key2025102316335911401_18","first-page":"H1","article-title":"Sense and nonsense about the Fenn effect","volume":"242","author":"Rall, J.A.","year":"1982","unstructured":"[18] Rall, J.A. Sense and nonsense about the Fenn effect, Am. J. Physiol., Volume 242 (1982), p. H1-H6","journal-title":"Am. J. Physiol."},{"key":"key2025102316335911401_19","doi-asserted-by":"crossref","first-page":"427","DOI":"10.1152\/physrev.1969.49.3.427","article-title":"Energetics of muscular contraction","volume":"49","author":"Mommaerts, W.F.","year":"1969","unstructured":"[19] Mommaerts, W.F. Energetics of muscular contraction, Physiol. Rev., Volume 49 (1969), pp. 427-508","journal-title":"Physiol. Rev."},{"key":"key2025102316335911401_20","doi-asserted-by":"crossref","first-page":"341","DOI":"10.1536\/ihj.31.341","article-title":"Energetics of the time-varying elastance model, a visco-elastic model, matches Mommaerts\u2019 unifying concept of the Fenn effect of muscle","volume":"31","author":"Suga, H.","year":"1990","unstructured":"[20] Suga, H. Energetics of the time-varying elastance model, a visco-elastic model, matches Mommaerts\u2019 unifying concept of the Fenn effect of muscle, Jpn Heart J., Volume 31 (1990), pp. 341-353","journal-title":"Jpn Heart J."},{"key":"key2025102316335911401_21","doi-asserted-by":"crossref","first-page":"98","DOI":"10.1038\/368098a0","article-title":"Molecular motors. Clamping down on myosin","volume":"368","author":"Howard, J.","year":"1994","unstructured":"[21] Howard, J. Molecular motors. Clamping down on myosin, Nature, Volume 368 (1994), pp. 98-99","journal-title":"Nature"},{"key":"key2025102316335911401_22","doi-asserted-by":"crossref","first-page":"113","DOI":"10.1038\/368113a0","article-title":"Single myosin molecule mechanics: piconewton forces and nanometre steps","volume":"368","author":"Finer, J.T.","year":"1994","unstructured":"[22] Finer, J.T.; Simmons, R.M.; Spudich, J.A. Single myosin molecule mechanics: piconewton forces and nanometre steps, Nature, Volume 368 (1994), pp. 113-119","journal-title":"Nature"},{"key":"key2025102316335911401_23","author":"Prigogine, I.","year":"1967","unstructured":"[23] Prigogine, I. Introduction to thermodynamics of irreversible processes, Wiley\u00a0J, New York, 1967","journal-title":"Introduction to thermodynamics of irreversible processes"},{"key":"key2025102316335911401_24","author":"Levine, I.N.","year":"2003","unstructured":"[24] Levine, I.N. Physical chemistry, Mc\u00a0Graw Hill, New York, 2003","journal-title":"Physical chemistry"},{"issue":"Suppl.\u00a02","key":"key2025102316335911401_25","first-page":"21","article-title":"Efficiency of cardiac muscle: thermodynamic and statistical mechanical considerations","volume":"88","author":"Backx, P.","year":"1993","unstructured":"[25] Backx, P. Efficiency of cardiac muscle: thermodynamic and statistical mechanical considerations, Basic Res. Cardiol., Volume 88 (1993) no. Suppl.\u00a02, pp. 21-28","journal-title":"Basic Res. Cardiol."},{"key":"key2025102316335911401_26","doi-asserted-by":"crossref","first-page":"60","DOI":"10.1161\/01.RES.83.1.60","article-title":"Relation between crossbridge structure and actomyosin ATPase activity in rat heart","volume":"83","author":"Weisberg, A.","year":"1998","unstructured":"[26] Weisberg, A.; Winegrad, S. Relation between crossbridge structure and actomyosin ATPase activity in rat heart, Circ. Res., Volume 83 (1998), pp. 60-72","journal-title":"Circ. Res."},{"key":"key2025102316335911401_27","doi-asserted-by":"crossref","first-page":"48","DOI":"10.1139\/y85-008","article-title":"Force-velocity constants in smooth muscle: afterloaded isotonic and quick-release methods","volume":"63","author":"Stephens, N.L.","year":"1985","unstructured":"[27] Stephens, N.L. Force-velocity constants in smooth muscle: afterloaded isotonic and quick-release methods, Can. J. Physiol. Pharmacol., Volume 63 (1985), pp. 48-51","journal-title":"Can. J. Physiol. Pharmacol."},{"key":"key2025102316335911401_28","doi-asserted-by":"crossref","first-page":"348","DOI":"10.1152\/ajplegacy.1954.177.3.348","article-title":"Dependence of isometric tension and isotonic shortening of uterine muscle on temperature and on strength of stimulation","volume":"177","author":"Csapo, A.","year":"1954","unstructured":"[28] Csapo, A. Dependence of isometric tension and isotonic shortening of uterine muscle on temperature and on strength of stimulation, Am. J. Physiol., Volume 177 (1954), pp. 348-354","journal-title":"Am. J. Physiol."},{"key":"key2025102316335911401_29","doi-asserted-by":"crossref","first-page":"1243","DOI":"10.1152\/ajplegacy.1971.221.5.1243","article-title":"Mechanical properties of smooth muscle. I. Length-tension and force-velocity relations","volume":"221","author":"Gordon, A.R.","year":"1971","unstructured":"[29] Gordon, A.R.; Siegman, M.J. Mechanical properties of smooth muscle. I. Length-tension and force-velocity relations, Am. J. Physiol., Volume 221 (1971), pp. 1243-1249","journal-title":"Am. J. Physiol."},{"key":"key2025102316335911401_30","doi-asserted-by":"crossref","first-page":"111","DOI":"10.1113\/jphysiol.1953.sp004983","article-title":"Measurements of oxygen consumption in smooth muscle","volume":"122","author":"Bulbring, E.","year":"1953","unstructured":"[30] Bulbring, E. Measurements of oxygen consumption in smooth muscle, J. Physiol., Volume 122 (1953), pp. 111-134","journal-title":"J. Physiol."},{"key":"key2025102316335911401_31","doi-asserted-by":"crossref","first-page":"58","DOI":"10.1126\/science.8316858","article-title":"Structure of the actin-myosin complex and its implications for muscle contraction","volume":"261","author":"Rayment, I.","year":"1993","unstructured":"[31] Rayment, I.; Holden, H.M.; Whittaker, M.; Yohn, C.B.; Lorenz, M.; Holmes, K.C.; Milligan, R.A. Structure of the actin-myosin complex and its implications for muscle contraction, Science, Volume 261 (1993), pp. 58-65","journal-title":"Science"},{"key":"key2025102316335911401_32","doi-asserted-by":"crossref","first-page":"825","DOI":"10.1023\/A:1005489501357","article-title":"A 7-amino-acid insert in the heavy chain nucleotide binding loop alters the kinetics of smooth muscle myosin in the laser trap","volume":"19","author":"Lauzon, A.M.","year":"1998","unstructured":"[32] Lauzon, A.M.; Tyska, M.J.; Rovner, A.S.; Freyzon, Y.; Warshaw, D.M.; Trybus, K.M. A 7-amino-acid insert in the heavy chain nucleotide binding loop alters the kinetics of smooth muscle myosin in the laser trap, J. Muscle Res. Cell. Motil., Volume 19 (1998), pp. 825-837","journal-title":"J. Muscle Res. Cell. Motil."},{"key":"key2025102316335911401_33","doi-asserted-by":"crossref","first-page":"1109","DOI":"10.1161\/01.RES.82.10.1109","article-title":"How actin-myosin interactions differ with different isoforms of myosin","volume":"82","author":"Winegrad, S.","year":"1998","unstructured":"[33] Winegrad, S. How actin-myosin interactions differ with different isoforms of myosin, Circ. Res., Volume 82 (1998), pp. 1109-1110","journal-title":"Circ. Res."},{"key":"key2025102316335911401_34","doi-asserted-by":"crossref","first-page":"587","DOI":"10.1007\/BF00121066","article-title":"Role of myosin light chains","volume":"15","author":"Trybus, K.M.","year":"1994","unstructured":"[34] Trybus, K.M. Role of myosin light chains, J. Muscle Res. Cell. Motil., Volume 15 (1994), pp. 587-594","journal-title":"J. Muscle Res. Cell. Motil."},{"key":"key2025102316335911401_35","doi-asserted-by":"crossref","first-page":"515","DOI":"10.1038\/372515a0","article-title":"How molecular motors work","volume":"372","author":"Spudich, J.A.","year":"1994","unstructured":"[35] Spudich, J.A. How molecular motors work, Nature, Volume 372 (1994), pp. 515-518","journal-title":"Nature"},{"key":"key2025102316335911401_36","doi-asserted-by":"crossref","first-page":"99","DOI":"10.1111\/j.1749-6632.1974.tb20557.x","article-title":"Nonequilibrium problems in biological phenomena","volume":"231","author":"Prigogine, I.","year":"1974","unstructured":"[36] Prigogine, I.; Nicolis, G.; Babloyantz, A. Nonequilibrium problems in biological phenomena, Ann. N Y Acad. Sci., Volume 231 (1974), pp. 99-105","journal-title":"Ann. N Y Acad. Sci."},{"key":"key2025102316335911401_37","doi-asserted-by":"crossref","first-page":"6538","DOI":"10.1016\/S0021-9258(18)50401-4","article-title":"Cytosolic phosphorylation potential","volume":"254","author":"Veech, R.L.","year":"1979","unstructured":"[37] Veech, R.L.; Lawson, J.W.; Cornell, N.W.; Krebs, H.A. Cytosolic phosphorylation potential, J. Biol. Chem., Volume 254 (1979), pp. 6538-6547","journal-title":"J. Biol. Chem."},{"key":"key2025102316335911401_38","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/0304-4165(74)90046-4","article-title":"Measured and calculated NAD+-NADH ratios in human erythrocytes","volume":"354","author":"Marshall, W.E.","year":"1974","unstructured":"[38] Marshall, W.E.; Omachi, A. Measured and calculated NAD+-NADH ratios in human erythrocytes, Biochim. Biophys. Acta, Volume 354 (1974), pp. 1-10","journal-title":"Biochim. Biophys. Acta"},{"key":"key2025102316335911401_39","doi-asserted-by":"crossref","first-page":"20321","DOI":"10.1016\/S0021-9258(17)30507-0","article-title":"The Gibbs-Donnan near-equilibrium system of heart","volume":"265","author":"Masuda, T.","year":"1990","unstructured":"[39] Masuda, T.; Dobson, G.P.; Veech, R.L. The Gibbs-Donnan near-equilibrium system of heart, J. Biol. Chem., Volume 265 (1990), pp. 20321-20334","journal-title":"J. Biol. Chem."},{"key":"key2025102316335911401_40","doi-asserted-by":"crossref","first-page":"241","DOI":"10.1080\/15216540215678","article-title":"The energetics of ion distribution: the origin of the resting electric potential of cells","volume":"54","author":"Veech, R.L.","year":"2002","unstructured":"[40] Veech, R.L.; Kashiwaya, Y.; Gates, D.N.; King, M.T.; Clarke, K. The energetics of ion distribution: the origin of the resting electric potential of cells, IUBMB Life, Volume 54 (2002), pp. 241-252","journal-title":"IUBMB Life"},{"key":"key2025102316335911401_41","doi-asserted-by":"crossref","first-page":"405","DOI":"10.1103\/PhysRev.37.405","article-title":"Reciprocal relations in irreversible processes II","volume":"38","author":"Onsager, L.","year":"1931","unstructured":"[41] Onsager, L. Reciprocal relations in irreversible processes II, Phys. Rev., Volume 38 (1931), pp. 405-426","journal-title":"Phys. Rev."},{"key":"key2025102316335911401_42","doi-asserted-by":"crossref","first-page":"117","DOI":"10.1016\/S0005-2728(98)00051-6","article-title":"Flux-force relationships in intact cells: a helpful tool for understanding the mechanism of oxidative phosphorylation alterations?","volume":"1365","author":"Rigoulet, M.","year":"1998","unstructured":"[42] Rigoulet, M.; Devin, A.; Espie, P.; Guerin, B.; Fontaine, E.; Piquet, M.A.; Nogueira, V.; Leverve, X. Flux-force relationships in intact cells: a helpful tool for understanding the mechanism of oxidative phosphorylation alterations?, Biochim. Biophys. Acta, Volume 1365 (1998), pp. 117-124","journal-title":"Biochim. Biophys. Acta"},{"key":"key2025102316335911401_43","doi-asserted-by":"crossref","first-page":"269","DOI":"10.1111\/j.1432-1033.1980.tb04792.x","article-title":"The optimal efficiency and the economic degrees of coupling of oxidative phosphorylation","volume":"109","author":"Stucki, J.W.","year":"1980","unstructured":"[43] Stucki, J.W. The optimal efficiency and the economic degrees of coupling of oxidative phosphorylation, Eur. J. Biochem., Volume 109 (1980), pp. 269-283","journal-title":"Eur. J. Biochem."},{"key":"key2025102316335911401_44","doi-asserted-by":"crossref","first-page":"197","DOI":"10.1098\/rspb.1991.0070","article-title":"Non-equilibrium thermodynamic sensitivity of oxidative phosphorylation","volume":"244","author":"Stucki, J.W.","year":"1991","unstructured":"[44] Stucki, J.W. Non-equilibrium thermodynamic sensitivity of oxidative phosphorylation, Proc. R. Soc. Lond. B Biol. Sci., Volume 244 (1991), pp. 197-202","journal-title":"Proc. R. Soc. Lond. B Biol. Sci."},{"key":"key2025102316335911401_45","first-page":"413","article-title":"Thermodynamic analysis of the permeability of biological membranes to non-electrolytes, 1958","volume":"1000","author":"Kedem, O.","year":"1989","unstructured":"[45] Kedem, O.; Katchalsky, A. Thermodynamic analysis of the permeability of biological membranes to non-electrolytes, 1958, Biochim. Biophys. Acta, Volume 1000 (1989), pp. 413-430","journal-title":"Biochim. Biophys. Acta"},{"key":"key2025102316335911401_46","doi-asserted-by":"crossref","first-page":"211","DOI":"10.1073\/pnas.64.1.211","article-title":"Oxidative phosphorylation: thermodynamic criteria for the chemical and chemiosmotic hypotheses","volume":"64","author":"Caplan, S.R.","year":"1969","unstructured":"[46] Caplan, S.R.; Essig, A. Oxidative phosphorylation: thermodynamic criteria for the chemical and chemiosmotic hypotheses, Proc. Natl Acad. Sci. U S A, Volume 64 (1969), pp. 211-218","journal-title":"Proc. Natl Acad. Sci. U S A"},{"key":"key2025102316335911401_47","doi-asserted-by":"crossref","first-page":"593","DOI":"10.1006\/jtbi.1998.0724","article-title":"Non-equilibrium thermodynamics of molecular evolution","volume":"193","author":"Dewey, T.G.","year":"1998","unstructured":"[47] Dewey, T.G.; Delle Donne, M. Non-equilibrium thermodynamics of molecular evolution, J. Theor. Biol., Volume 193 (1998), pp. 593-599","journal-title":"J. Theor. Biol."},{"key":"key2025102316335911401_48","doi-asserted-by":"crossref","first-page":"107","DOI":"10.1017\/S0033583500000615","article-title":"Biological order, structure and instabilities","volume":"4","author":"Prigogine, I.","year":"1971","unstructured":"[48] Prigogine, I.; Nicolis, G. Biological order, structure and instabilities, Q. Rev. Biophys., Volume 4 (1971), pp. 107-148","journal-title":"Q. Rev. Biophys."}],"container-title":["Comptes Rendus. 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