中国物理B ›› 2016, Vol. 25 ›› Issue (1): 16401-016401.doi: 10.1088/1674-1056/25/1/016401
所属专题： TOPICAL REVIEW — 8th IUPAP International Conference on Biological Physics
• TOPICAL REVIEW—8th IUPAP International Conference on Biological Physics • 上一篇 下一篇
Uncovering the underlying physical mechanisms of biological systems via quantification of landscape and flux
Li Xu(徐丽), Xiakun Chu(楚夏昆), Zhiqiang Yan(晏致强), Xiliang Zheng(郑喜亮), Kun Zhang(张坤), Feng Zhang(张锋), Han Yan(闫晗), Wei Wu(吴畏), Jin Wang(汪劲)
- 1. State Key Laboratory of Electroanalytical Chemistry, Changchun Institute of Applied Chemistry, Chinese Academy of Sciences, Changchun 130022, China;
2. Department of Chemistry and Physics, Stony Brook University, Stony Brook, NY 11794-3400, USA
-
收稿日期:2015-05-08修回日期:2015-10-08出版日期:2016-01-05发布日期:2016-01-05 -
通讯作者:Li Xu, Jin Wang E-mail:jin.wang.1@stonybrook.edu -
基金资助:Project supported by the Natural Science Foundation of China (Grant Nos. 21190040, 11174105, 91225114, 91430217, and 11305176) and Jilin Province Youth Foundation, China (Grant No. 20150520082JH).
Uncovering the underlying physical mechanisms of biological systems via quantification of landscape and flux
Li Xu(徐丽)1, Xiakun Chu(楚夏昆)1, Zhiqiang Yan(晏致强)1, Xiliang Zheng(郑喜亮)1, Kun Zhang(张坤)1, Feng Zhang(张锋)1, Han Yan(闫晗)1, Wei Wu(吴畏)1, Jin Wang(汪劲)1,2
- 1. State Key Laboratory of Electroanalytical Chemistry, Changchun Institute of Applied Chemistry, Chinese Academy of Sciences, Changchun 130022, China;
2. Department of Chemistry and Physics, Stony Brook University, Stony Brook, NY 11794-3400, USA
-
Received:2015-05-08Revised:2015-10-08Online:2016-01-05Published:2016-01-05 -
Contact:Li Xu, Jin Wang E-mail:jin.wang.1@stonybrook.edu -
Supported by:Project supported by the Natural Science Foundation of China (Grant Nos. 21190040, 11174105, 91225114, 91430217, and 11305176) and Jilin Province Youth Foundation, China (Grant No. 20150520082JH).
摘要：
In this review, we explore the physical mechanisms of biological processes such as protein folding and recognition, ligand binding, and systems biology, including cell cycle, stem cell, cancer, evolution, ecology, and neural networks. Our approach is based on the landscape and flux theory for nonequilibrium dynamical systems. This theory provides a unifying principle and foundation for investigating the underlying mechanisms and physical quantification of biological systems.
中图分类号: (Networks)
- 64.60.aq
引用本文
徐丽, 楚夏昆, 晏致强, 郑喜亮, 张坤, 张锋, 闫晗, 吴畏, 汪劲. Uncovering the underlying physical mechanisms of biological systems via quantification of landscape and flux[J]. 中国物理B, 2016, 25(1): 16401-016401.
Li Xu(徐丽), Xiakun Chu(楚夏昆), Zhiqiang Yan(晏致强), Xiliang Zheng(郑喜亮), Kun Zhang(张坤), Feng Zhang(张锋), Han Yan(闫晗), Wei Wu(吴畏), Jin Wang(汪劲). Uncovering the underlying physical mechanisms of biological systems via quantification of landscape and flux[J]. Chin. Phys. B, 2016, 25(1): 16401-016401.
| [1] | Bryngelson J D and Wolynes P G 1987 Proc. Natl. Acad. Sci. USA 847524 |
| [2] | Bryngelson J D and Wolynes P G 1989 J. Phys. Chem. 93 6902 |
| [3] | Bryngelson J D and Wolynes P G 1990 Biopolymers 30 177 |
| [4] | Onuchic J N, Wolynes P G, Lutheyschulten Z and Socci N D 1995Proc. Natl. Acad. Sci. USA 92 3626 |
| [5] | Onuchic J N, LutheySchulten Z and Wolynes P G 1997 Annu. Rev.Phys. Chem. 48 545 |
| [6] | Dill K A and Chan H S 1997 Nat. Struct. Biol. 4 10 |
| [7] | Dobson C M, Sali A and Karplus M Š 1998 Angew. Chem. Int. Ed. 37868 |
| [8] | Wang J 2015 Adv. Phys. 64 1 |
| [9] | Wang J, Xu L and Wang E K 2008 Proc. Natl. Acad. Sci. USA 10512271 |
| [10] | Wang J, Li C H and Wang E K 2010 Proc. Natl. Acad. Sci. USA 1078195 |
| [11] | Li C H and Wang J 2014 Proc. Natl. Acad. Sci. USA 111 14130 |
| [12] | Wang J, Xu L, Wang E K and Huang S 2010 Biophys. J. 99 29 |
| [13] | Wang J, Zhang K and Wang E K 2010 J. Chem. Phys. 133 125103 |
| [14] | Wang J, Zhang K, Xu L and Wang E K 2011 Proc. Natl. Acad. Sci.USA 108 8257 |
| [15] | Feng H D and Wang J 2011 J. Chem. Phys. 135 234511 |
| [16] | Feng H D and Wang J 2012 Sci. Rep. 2 550 |
| [17] | Zhang K, Sasai M and Wang J 2013 Proc. Natl. Acad. Sci. USA 11014930 |
| [18] | Li C H and Wang J 2013 PLoS Comput. Biol. 9 e1003165 |
| [19] | Xu L, Zhang K and Wang J 2014 PLoS One 9 e105216 |
| [20] | Gerard C and Goldbeter A 2009 Proc. Natl. Acad. Sci. USA 106 21643 |
| [21] | Gerard C and Goldbeter A 2012 PLoS Comput. Biol. 8 e1002516 |
| [22] | Xu L, Zhang F, Zhang K, Wang E K and Wang J 2014 PLoS ONE 9e86746 |
| [23] | Zhang F, Xu L, Zhang K, Wang E K and Wang J 2012 J. Chem. Phys.137 065102 |
| [24] | Yan H, Zhao L, Hu L, Wang X, Wang E K and Wang J 2013 Proc. Natl.Acad. Sci. USA 110 E4185 |
| [25] | Koretke K K, Luthey-Schulten Z A and Wolynes P G 1998 Proc. Natl.Acad. Sci. USA 95 2932 |
| [26] | Wang J and Verkhivker G M 2003 Phys. Rev. Lett. 90 188101 |
| [27] | Levy Y, Wolynes P G and Onuchic J N 2004 Proc. Natl. Acad. Sci. USA101 511 |
| [28] | Wang J, Zheng X, Yang Y, Drueckhammer D, Yang W, Verkhivker Gand Wang E 2007 Phys. Rev. Lett. 99 198101 |
| [29] | Chu X, Gan L, Wang E and Wang J 2013 Proc. Natl. Acad. Sci. USA110 E2342 |
| [30] | Goldstein R A, Luthey-Schulten Z A and Wolynes P G 1992 Proc. Natl.Acad. Sci. USA 89 4918 |
| [31] | Goldstein R A, Luthey-Schulten Z A and Wolynes P G 1992 Proc. Natl.Acad. Sci. USA 89 9029 |
| [32] | Hardin C, Eastwood M P, Luthey-Schulten Z and Wolynes P G 2000Proc. Natl. Acad. Sci. USA 97 14235 |
| [33] | Takada S 2001 Proteins 42 85 |
| [34] | Fain B and Levitt M 2003 Proc. Natl. Acad. Sci. USA 100 10700 |
| [35] | Liu Z, Dominy B N and Shakhnovich E I 2004 J. Am. Chem. Soc. 1268515 |
| [36] | Yan Z and Wang J 2012 Sci. Rep. 2 309 |
| [37] | Yan Z, Guo L, Hu L and Wang J 2013 Bioinformatics 29 1127 |
| [38] | Yan Z and Wang J 2013 PloS ONE 8 e74443 |
| [39] | Li C H and Wang J 2014 J. R. Soc. Interf. 11 20140774 |
| [40] | Van Kampen N G 2007 Stochastic Processes in Physics and Chemistry(Amsterdam: Elsevier) |
| [41] | Hu G 1995 Stochastic Force and Nonlinear Systems (Shanghai: Shanghai Science Education) |
| [42] | Gardiner C W 2004 Handbook of Stochastic Methods: For Physics,Chemistry and the Natural Sciences (Berlin: Springer-Verlag) |
| [43] | Risken H 1996 The Fokker-Planck Equation: Methods of Solution andApplications (Berlin: Springer-Verlag) |
| [44] | Levinthal C 1969 Proceedings in Mossbauer Spectroscopy in Biological Systems. Mossbauer Spectroscopy in Biological Systems: Proceedings of a Meeting Held at Allerton House, Monticello, Illinois. p. 22 |
| [45] | Bryngelson J D, Onuchic J N, Socci N D and Wolynes P G 1995 Proteins 21 167 |
| [46] | Leopold P E, Montal M and Onuchic J N 1992 Proc. Natl. Acad. Sci.USA 89 8721 |
| [47] | Wang J, Onuchic J and Wolynes P 1996 Phys. Rev. Lett. 76 4861 |
| [48] | Frauenfelder H, Sligar S G and Wolynes P G 1991 Science 254 1598 |
| [49] | Tsai C J, Kumar S, Ma B Y and Nussinov R 1999 Protein Sci. 8 1181 |
| [50] | Wang J, Xu L and Wang E 2007 Biophys. J. 92 L109 |
| [51] | Oliveberg M and Wolynes P G 2005 Q. Rev. Biophys. 38 245 |
| [52] | Wolynes P G 2005 Philos. T. Roy. Soc. A 363 453 |
| [53] | Wolynes P G 2005 Q. Rev. Biophys. 38 405 |
| [54] | Wang J, Oliveira R J, Chu X, Whitford P C, Chahine J, Han W, WangE, Onuchic J N and Leite V B P 2012 Proc. Natl. Acad. Sci. USA 10915763 |
| [55] | Chu X and Wang J 2014 PLoS Comput. Biol. 10 e1003782 |
| [56] | Wang Y, Chu X, Suo Z, Wang E and Wang J 2012 J. Am. Chem. Soc.134 13755 |
| [57] | Wang J, Lu Q and Lu H P 2006 PLoS Comput. Biol. 2 e78 |
| [58] | Lu Q, Lu P H and Wang J 2007 Phys. Rev. Lett. 98 128105 |
| [59] | Wang J, Wang Y, Chu X, Hagen S J, Han W and Wang E 2011 PLoSComput. Biol. 7 e1001118 |
| [60] | Chu X, Wang Y, Gan L, Bai Y, Han W, Wang E and Wang J 2012 PLoSComput. Biol. 8 e1002608 |
| [61] | Wang Y, Chu X, Longhi S, Roche P, Han W, Wang E and Wang J 2013Proc. Natl. Acad. Sci. USA 110 E3743 |
| [62] | Wang Y, Longhi S, Roche P and Wang J 2014 Proc. Natl. Acad. Sci.USA 111 E1559 |
| [63] | Lu Q and Wang J 2008 J. Am. Chem. Soc. 130 4772 |
| [64] | Lu Q and Wang J 2009 J. Phys. Chem. B 113 1517 |
| [65] | Lai Z Z, Lu Q and Wang J 2011 J. Phys. Chem. B 115 4147 |
| [66] | Wang Y, Tang C, Wang E and Wang J 2012 PLoS Comput. Biol. 8e1002471 |
| [67] | Wang Y, Gan L, Wang E and Wang J 2013 J. Chem. Theory Comput. 984 |
| [68] | Chu X, Liu F, Maxwell B A, Wang Y, Suo Z, Wang H, Han W andWang J 2014 PLoS Comput. Biol. 10 e1003804 |
| [69] | Yan Z Q, Zheng X L, Wang E K and Wang J 2013 Chem. Sci. 4 2387 |
| [70] | Yang Y L, Li G H, Zhao D Y, Yu H Y, Zheng X L, Peng X D, ZhangX E, Fu T, Hu X Q, Niu M S, Ji X F, Zou L B and Wang J 2015 Chem.Sci. 6 2812 |
| [71] | Zheng X and Wang J 2015 PLoS Comput. Biol. 11 e1004212 |
| [72] | Graham R 1989 Macroscopic Potentials, Bifurcations and Noise inDissipative Systems in Noise in Nonlinear Dynamical Systems (Cambridge: Cambridege Unviersity Press) |
| [73] | Sasai M and Wolynes P G 2003 Proc. Natl. Acad. Sci. USA 100 2374 |
| [74] | Qian H and Reluga T C 2005 Phys. Rev. Lett. 94 028101 |
| [75] | Ao P 2005 Phys. Life Rev. 2 117 |
| [76] | Ao P 2008 Commun. Theor. Phys. 49 1073 |
| [77] | Ao P, Galas D L H and Zhu X 2008 Med Hypotheses 70 678 |
| [78] | Qian H 2014 Phys. Lett. A 378 609 |
| [79] | Feng H D, Han B and Wang J 2011 J. Phys. Chem. B 115 1254 |
| [80] | Li C H, Wang E K and Wang J 2012 J. Chem. Phys. 136 194108 |
| [81] | Wu W and Wang J 2013 J. Phys. Chem. B 117 12908 |
| [82] | Wu W and Wang J 2013 J. Chem. Phys. 139 121920 |
| [83] | Wu W and Wang J 2014 J. Chem. Phys. 141 105104 |
| [84] | Lepzelter D and Wang J 2008 Phys.Rev. E 77 041917 |
| [85] | Kumar S, Bouzida D, Swendsen R H, Kollman P A and Rosenberg J M1992 J. Comput. Chem. 13 1011 |
| [86] | Plotkin S S, Wang J and Wolynes P G 1997 J. Chem. Phys. 106 2932 |
| [87] | Shakhnovich E I 1994 Phys. Rev. Lett. 72 3907 |
| [88] | Iben I E T, Braunstein D, Doster W, Frauenfelder H, Hong M K, Johnson J B, Luck S, Ormos P, Schulte A, Steinbach P J, Xie A H and YoungR D 1989 Phys. Rev. Lett. 62 1916 |
| [89] | Wright P E and Dyson H J 1999 J. Mol. Biol. 293 321 |
| [90] | Dunker A K, Lawson J D, Brown C J, Williams R M, Romero P, Oh J S,Oldfield C J, Campen A M, Ratliff C R, Hipps K W, Ausio J, NissenM S, Reeves R, Kang C H, Kissinger C R, Bailey R W, Griswold M D,Chiu M, Garner E C and Obradovic Z 2001 J. Mol. Graph. Model. 1926 |
| [91] | Tompa P 2002 Trends. Biochem. Sci. 27 527 |
| [92] | Dyson H J and Wright P E 2002 Curr. Opin. Struct. Biol. 12 54 |
| [93] | Wright P E and Dyson H J 2009 Curr. Opin. Struct. Biol. 19 31 |
| [94] | Dunker A K, Garner E, Guilliot S, Romero P, Albrecht K, Hart J,Obradovic Z, Kissinger C and Villafranca J E 1998 Pacific Symposiumon Biocomputing. Pacific Symposium on Biocomputing 473 |
| [95] | Shoemaker B A, Portman J J and Wolynes P G 2000 Proc. Natl. Acad.Sci. USA 97 8868 |
| [96] | Dunker A K, Silman I, Uversky V N and Sussman J L 2008 Curr. Opin.Struct. Biol. 18 756 |
| [97] | Smock R G and Gierasch L M 2009 Science 324 198 |
| [98] | Tantos A, Han K H and Tompa P 2012 Mol. Cell. Endocrinol 348 457 |
| [99] | Clementi C, Nymeyer H and Onuchic J N 2000 J. Mol. Biol. 298 937 |
| [100] | Levy Y, Cho S S, Onuchic J N and Wolynes P G 2005 J. Mol. Biol. 3461121 |
| [101] | Ganguly D, Zhang W and Chen J 2013 PLoS Comput. Biol. 9 e1003363 |
| [102] | Turjanski A G, Gutkind J S, Best R B and Hummer G 2008 PLoS Comput. Biol. 4 2008 PLoS Com-put. Biol. 4 e1000060 |
| [103] | Ganguly D and Chen J 2011 Proteins: Struc. Funct. Bioinform. 791251 |
| [104] | Huang Y and Liu Z 2009 J. Mol. Biol. 393 1143 |
| [105] | Hansen D F, Zhou Z, Fen H Q, Jenkins L M M, Bai Y W and Kay L E2009 J. Mol. Biol. 387 1 |
| [106] | Pappu R V, Mao A H, Crick S L, Vitalis A and Chicoine C L 2010Proc. Natl. Acad. Sci. USA 107 8183 |
| [107] | Muller-Spath S, Soranno A, Hirschfeld V, Hofmann H, Ruegger S,Reymond L, Nettels D and Schuler B 2010 Proc. Natl. Acad. Sci. USA107 14609 |
| [108] | Haran G and England J L 2010 Proc. Natl. Acad. Sci. USA 107 14519 |
| [109] | Shaw D E, Maragakis P, Lindorff-Larsen K, Piana S, Dror R O, Eastwood M P, Bank J A, Jumper J M, Salmon J K, Shan Y, et al. 2010Science 330 341 |
| [110] | Lindorff-Larsen K, Piana S, Dror R O and Shaw D E 2011 Science 334517 |
| [111] | Narayanan R, Ganesh O K, Edison A S and Hagen S J 2008 J. Am.Chem. Soc. 130 11477 |
| [112] | Longhi S, Receveur-Bréchot V, Karlin D, Johansson K, Darbon H, Bhella D, Yeo R, Finet S and Canard B 2003 J. Biol. Chem. 278 18638 |
| [113] | Bourhis J M, Johansson K, Receveur-Bréchot V, Oldfield C J, Dunker ′K A, Canard B and Longhi S 2004 Virus Res. 99 157 |
| [114] | Bourhis J M, Receveur-Bréchot V, Oglesbee M, Zhang X, Buccellato ′M, Darbon H, Canard B, Finet S and Longhi S 2005 Protein Sci. 141975 |
| [115] | Jensen M R, Communie G, Ribeiro E A, Martinez N, Desfosses A,Salmon L, Mollica L, Gabel F, Jamin M, Longhi S et al. 2011 Proc.Natl. Acad. Sci. USA 108 9839 |
| [116] | Piana S, Lindorff-Larsen K and Shaw D E 2011 Biophys. J. 100 L47 |
| [117] | Daura X, Gademann K, Jaun B, Seebach D, van Gunsteren W F andMark A E 1999 Angew. Chem. Int. Ed. 38 236 |
| [118] | Koshland D E 1958 Proc. Natl. Acad. Sci. USA 44 98 |
| [119] | Ma B Y, Kumar S, Tsai C J and Nussinov R 1999 Protein Eng. 12 713 |
| [120] | Boehr D D, Nussinov R and Wright P E 2009 Nat. Chem. Biol. 5 789 |
| [121] | Okazaki K i, Koga N, Takada S, Onuchic J N and Wolynes P G 2006Proc. Natl. Acad. Sci. USA 103 11844 |
| [122] | Okazaki K i and Takada S 2008 Proc. Natl. Acad. Sci. USA 105 11182 |
| [123] | Whitford P C, Miyashita O, Levy Y and Onuchic J N 2007 J. Mol. Biol.366 1661 |
| [124] | Berry M B, Meador B, Bilderback T, Liang P, Glaser M and PhillipsG N 1994 Proteins 19 183 |
| [125] | Berry M B, Bae E, Bilderback T R, Glaser M and Phillips G N 2006Proteins 62 555 |
| [126] | Wong J H, Fiala K A, Suo Z and Ling H 2008 J. Mol. Biol. 379 317 |
| [127] | Ohmori H, Friedberg E, Fuchs R, Goodman M, Hanaoka F, Hinkle D,Kunkel T, Lawrence C, Livneh Z, Nohmi T, Prakash L, Prakash S, TodoT, Walker G, Wang Z and Woodgate R 2001 Mol. Cell 8 7 |
| [128] | Janin J 1995 Biochimie 77 497 |
| [129] | Havranek J J and Harbury P B 2003 Nat. Struct. Mol. Biol. 10 45 |
| [130] | Kortemme T, Joachimiak L A, Bullock A N, Schuler A D, StoddardB L and Baker D 2004 Nat. Struct. Mol. Biol. 11 371 |
| [131] | Bolon D N, Grant R A, Baker T A and Sauer R T 2005 Proc. Natl.Acad. Sci. USA 102 12724 |
| [132] | Liu Z, Zheng X, Yang X, Wang E and Wang J 2009 Biophys. J. 96 3917 |
| [133] | Li D, Liu Z, Zhao W, Zheng X, Wang J and Wang E 2013 Eur. J.Pharm. Sci. 48 658 |
| [134] | Liu Z, Li D, Zhao W, Zheng X, Wang J and Wang E 2012 PLoS ONE7 e37841 |
| [135] | Zhao W, Li D, Liu Z, Zheng X, Wang J and Wang E 2013 PLoS ONE8 e66362 |
| [136] | Zheng X, Liu Z, Li D, Wang E and Wang J 2013 Curr. Pharm. Des. 192246 |
| [137] | Liu Z, Li D, Zheng X, Wang E and Wang J 2013 Curr. Pharm. Des. 192259 |
| [138] | Zheng X, Gan L, Wang E and Wang J 2013 The AAPS. Journal 15 228 |
| [139] | Vauquelin G and Van Liefde I 2006 Trends Pharmacol. Sci. 27 355 |
| [140] | Tummino P J and Copeland R A 2008 Biochemistry 47 5481 |
| [141] | Yan Z, Zheng X, Wang E and Wang J 2013 Chem. Sci. 4 2387 |
| [142] | Socci N D, Onuchic J N and Wolynes P G 1996 J. Chem. Phys. 1045860 |
| [143] | Wang J 2006 Chem. Phys. Lett. 418 544 |
| [144] | Shoichet B K 2004 Nature 432 862 |
| [145] | Swinney D C 2004 Nat. Rev. Drug Discov. 3 801 |
| [146] | Swinney D C 2006 Lett. Drug Des. Discov. 3 569 |
| [147] | Copeland R A, Pompliano D L and Meek T D 2006 Nat. Rev. DrugDiscov. 5 730 |
| [148] | Lu H and Tonge P J 2010 Curr. Opin. Chem. Biol. 14 467 |
| [149] | Xu L F, Shi H L, Feng H D and Wang J 2012 J. Chem. Phys. 136165102 |
| [150] | Xu L, Zhang F, Wang E K and Wang J 2013 Nonlinearity 26 69 |
| [151] | V Blickle T Speck L H U S and Bechinger C 2006 Phys. Rev. Lett. 96070603 |
| [152] | Seifert U 2005 Phys. Rev. Lett. 95 040602 |
| [153] | Seifert U and Speck T 2010 Europhys. Lett. 89 10007 |
| [154] | Speck T and Seifert U 2005 J. Phys. A 38 L581 |
| [155] | Esposito M and Van den Broeck C 2010 Phys. Rev. Lett. 104 090601 |
| [156] | Esposito M and Van den Broeck C 2010 Phys. Rev. E 82 011143 |
| [157] | Esposito M and Van den Broeck C 2010 Phys. Rev. E 82 011144 |
| [158] | Ge H and Qian H 2010 Phys. Rev. E 81 051133 |
| [159] | Singhania R, Sramkoski R M, Jacobberger J W, and Tyson J J 2011PLoS Comput. Biol. 7 e1001077 |
| [160] | Han B and Wang J 2007 Biophys. J. 92 3755 |
| [161] | Waddington C H 1957 The Strategy of the Genes (London: Allen andUnwin) |
| [162] | Zhang B and Wolynes P G 2014 Proc. Natl. Acad. Sci. USA 111 10185 |
| [163] | Walczak A M, Sasai M and Wolynes P G 2005 Biophys. J. 88 828 |
| [164] | Ferrell J E 2012 Curr. Biol. 22 R458 |
| [165] | Huang S, Guo Y P, May G and Enver T 2007 Dev. Biol. 305 695 |
| [166] | Li C H and Wang J 2013 J. R. Soc. Interf. 10 20130787 |
| [167] | Feng H D, Zhang K and Wang J 2014 Chem. Sci. 5 3761 |
| [168] | Huang S, Ernberg I and Kauffman S 2009 Semin Cell Dev. Biol. 20 869 |
| [169] | Kalmar T, Lim C, Hayward P, Munoz-Descalzo S and Nichols J 2009PLoS Biol. 7 |
| [170] | Singh A M, Hamazaki T, Hankowski K E and Terada N 2007 StemCells 25 2534 |
| [171] | Onsager L and Machlup S 1953 Phys. Rev. 91 1505 |
| [172] | Hunt K L C and Ross J 1981 J. Chem. Phys. 75 976 |
| [173] | Kramers H A 1940 Physica 7 284 |
| [174] | Maier R S and Stein D L 1997 SIAM J. Appl. Math. 57 752 |
| [175] | Hanggi P, Talkner P and Borkovec M ¨ 1990 Rev. Mod. Phys. 62 251 |
| [176] | Weinberg R A 2013 The Biology of Cancer (New York: Taylor & Francis) |
| [177] | Hanahan D and Weinberg R A 2011 Cell 144 646 |
| [178] | Hanahan D and Weinberg R A 2000 Cell 100 57 |
| [179] | Kauffman S 1971 J. Theor. Biol. 31 429 |
| [180] | Lu M, Onuchic J N and Ben-Jacob E 2014 Phys. Rev. Lett. 113 078102 |
| [181] | Lu M, Jolly M K, Gomoto R, Huang B, Onuchic J N and Ben-Jacob E2013 J. Phys. Chem. B 117 13164 |
| [182] | Lu M, Jolly M K, Levine H, Onuchic J N and Ben-Jacob E 2013 Proc.Natl. Acad. Sci. USA 110 18144 |
| [183] | Jolly M K, Huang B, Lu M, Mani S A, Levine H and Ben-Jacob E 2014J. R. Soc. Interface 11 20140962 |
| [184] | Wright S 1932 Proceedings of the Sixth International Congress on Genetics 1 356 |
| [185] | Fisher R A 1930 The Genetical Theory of Natural Selection (NewYork: Clarendon and Oxford) |
| [186] | Rice S H 2004 Evolutionary Theory: Mathematical and ConceptualFoundations (Sinauer Associates) |
| [187] | Van Valen L 1973 Evol Theory 1 1 |
| [188] | Murray J 1998 Mathematical Biology (New York/Berlin: Springer) |
| [189] | Lotka A 1925 Elements of Physical Biology (Baltimore: Williams andWilkins) |
| [190] | Volterra V 1931 Lecons sur la Theorie Mathematique de la Lutte pourla Vie (Paris: Gauthier-Villars) |
| [191] | Goh B 1976 J. Math. Biol. 3 313 |
| [192] | Hastings A 1977 J. Math. Biol. 5 399 |
| [193] | Bazykin A 1985 Mathematical Biophysics of Interacting Populations(Moscow: Nauka) (in Russian) |
| [194] | Abbott L F and Regehr W G 2004 Nature 431 796 |
| [195] | Abbott L F 2008 Neuron 60 489 |
| [196] | Vogels T P, Rajan K and Abbott L F 2005 Annu. Rev. Neurosci. 28 357 |
| [197] | Hodgkin A L and Huxley A F 1952 J. Physiol. 117 500 |
| [198] | Hopfield J J 1982 Proc.Natl. Acad. Sci. USA 79 2554 |
| [199] | Hopfield J J and Tank D W 1986 Science 233 625 |
| [200] | Arnsten A F T, Wang M, Gamo N J, Yang Y, Jin L E, Wang X J,Laubach M, Mazer J A and Lee D 2011 Nature 476 210 |
| [201] | Buzsaki G and Draguhn A 2004 Science 304 1926 |
| [202] | Wang X J, Tegner J, Constantinidis C and Goldman-Rakic P S 2004Proc. Natl. Acad. Sci. USA 101 1368 |
| [203] | McCarley R W and Massaquoi S G 1986 Am. J. Physiol-Reg. I 251R1011 |
| [204] | Massaquoi S G and McCarley R W 1992 J. Sleep. Res. 1 138 |
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| [11] | 张兴雨, 王永良, 吕超林, 尤立星, 李浩, 王镇, 谢晓明. Flux-to-voltage characteristic simulation of superconducting nanowire interference device[J]. 中国物理B, 2020, 29(9): 98501-098501. |
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| [15] | 秦顺达, 葛红霞, 程荣军. A new control method based on the lattice hydrodynamic model considering the double flux difference[J]. 中国物理B, 2018, 27(5): 50503-050503. |
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