Information Thermodynamics of Turing Patterns

被引：65

作者：

Falasco, Gianmaria ^{[1
]}

Rao, Riccardo ^{[1
]}

Esposito, Massimiliano ^{[1
]}

机构：

[1] Univ Luxembourg, Phys & Mat Sci Res Unit, Complex Syst & Stat Mech, L-1511 Luxembourg, Luxembourg

来源：

PHYSICAL REVIEW LETTERS | 2018年 / 121卷 / 10期

基金：

欧洲研究理事会;

关键词：

We presented the nonequilibrium thermodynamics of RDSs and exemplified the theory with the application to the Brusselator model. We went beyond the conventional treatment of classical nonequilibrium thermodynamics [47] in two respects: avoiding to linearize the chemistry; i.e; to oversimplify reaction affinities to currents times Onsager coefficients; explicitly building thermodynamic potentials that act as Lyapunov functions in the relaxation to equilibrium provide minimum work principles and reveal the existence of nonequilibrium phase transitions. As demonstrated by the paradigmatic case of the Brusselator model; the framework can be directly applied to quantify the energy cost of pattern manipulations in complex biochemical systems [48–50] and paves the way to study information transmission in signal transduction [51; quorum sensing [52; and chemotaxis [53] . We acknowledge funding from the National Research Fund of Luxembourg (AFR Ph.D. Grant 2014-2; No. 9114110) and the European Research Council project NanoThermo (ERC-2015-CoG Agreement No. 681456). [1] 1 V. Castets; E; Dulos; J; Boissonade; and P. De Kepper; Phys; Rev; Lett; 64; 2953 ( 1990 ). PRLTAO 0031-9007 10.1103/PhysRevLett.64.2953 [2] 2 Q. Ouyang and H. L. Swinney; Nature; (London); 352; 610 ( 1991 ). NATUAS 0028-0836 10.1038/352610a0 [3] 3 A. N. Zaikin and A. M. Zhabotinsky; 225; 535; 1970; NATUAS; 0028-0836; 10.1038/225535b0; 4; A. T; Winfree; Science; 175; 634; 1972; SCIEAS; 0036-8075; 10.1126/science.175.4022.634; 5; P. J; Ortoleva; Geochemical Self-Organization ( Oxford University Press; New York; 1994; 6; J. D; Murray; Mathematical Biology. II Spatial Models and Biomedical Applications; 3rd ed; Springer-Verlag; Berlin 2001 ). [7] 7 S. Kondo and T. Miura; 329; 1616 ( 2010 ). SCIEAS 0036-8075 10.1126/science.1179047 [8] 8 D. Iber and D. Menshykau; Open Biol. 3; 130088 ( 2013 ). 10.1098/rsob.130088 [9] 9 S. Kretschmer and P. Schwille; Curr. Opin. Cell Biol. 38; 52; 2016; COCBE3; 0955-0674; 10.1016/j.ceb.2016.02.005; 10; M; Falcke; Adv; 53; 255; 2004; ADPHAH; 0001-8732; 10.1080/00018730410001703159; 11; K; Thurley; A; Skupin; R; Thul; and M. Falcke; Biochim; Biophys; Acta; 1820; 1185 ( 2012 ). BBACAQ 0006-3002 10.1016/j.bbagen.2011.10.007 [12] 12 I. Prigogine and G. Nicolis; Q; 107 ( 1971 ). QURBAW 0033-5835 10.1017/S0033583500000615 [13] 13 G. Nicolis and I. Prigogine; Self-Organization in Nonequilibrium Systems: From Dissipative Structures to Order Through Fluctuations ( Wiley-Blackwell; 1977 ). [14] 14 M. C. Cross and P. C. Hohenberg; Mod; 65; 851; 1993; RMPHAT; 0034-6861; 10.1103/RevModPhys.65.851; 15; Ross; Thermodynamics and Fluctuations Far from Equilibrium ( Springer; 2008; Chap. 5; 16; F; Rossi; S; Ristori; Rustici; N; Marchettini; and E. Tiezzi; Theor; Biol; 404 ( 2008 ). JTBIAP 0022-5193 10.1016/j.jtbi.2008.08.026 [17] 17 B. A. Grzybowski and W. T. Huck; Nat; Nanotechnol; 585; NNAABX; 1748-3387; 10.1038/nnano.2016.116; 18; Adamatzky; B. De Lacy Costello; and T. Asai; Reaction-Diffusion Computers ( Elsevier; 2005; 19; C; Jarzynski; Annu. Rev. Condens. Matter Phys. 2; 329 ( 2011 ). ARCMCX 1947-5454 10.1146/annurev-conmatphys-062910-140506 [20] 20 C. Van den Broeck and M. Esposito; Physica; (Amsterdam); 418A; 2015; PHYADX; 0378-4371; 10.1016/j.physa.2014.04.035; 21; G; Verley; Esposito; T; Willaert; and C. Van den Broeck; Commun; 4721; 2014; NCAOBW; 2041-1723; 10.1038/ncomms5721; 22; U; Seifert; Rep; Prog; 75; 126001; 2012; RPPHAG; 0034-4885; 10.1088/0034-4885/75/12/126001; 23; J. M. R; Parrondo; J.&thi;

D O I：

10.1103/PhysRevLett.121.108301

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

We set up a rigorous thermodynamic description of reaction-diffusion systems driven out of equilibrium by time-dependent space-distributed chemostats. Building on the assumption of local equilibrium, nonequilibrium thermodynamic potentials are constructed exploiting the symmetries of the chemical network topology. It is shown that the canonical (resp. semigrand canonical) nonequilibrium free energy works as a Lyapunov function in the relaxation to equilibrium of a closed (resp. open) system, and its variation provides the minimum amount of work needed to manipulate the species concentrations. The theory is used to study analytically the Turing pattern formation in a prototypical reaction-diffusion system, the one-dimensional Brusselator model, and to classify it as a genuine thermodynamic nonequilibrium phase transition.

引用

页数：6

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