Multi-scale modeling in biology: How to bridge the gaps between scales?

Progress in Biophysics and Molecular Biology

Volumn 107, Issue 1, 2011, Pages 21-31

  Qu, Zhilin ^a   Garfinkel, Alan ^a   Weiss, James N ^a   Nivala, Melissa ^a  

^a UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

Computational biology; Multi scale modeling; Systems biology

Indexed keywords

ANIMAL; BIOLOGICAL MODEL; BIOLOGY; HUMAN; METHODOLOGY; NONLINEAR SYSTEM; REVIEW; STATISTICS; SYSTEMS BIOLOGY;

ANIMALS; BIOLOGY; HUMANS; MODELS, BIOLOGICAL; NONLINEAR DYNAMICS; STOCHASTIC PROCESSES; SYSTEMS BIOLOGY;

EID: 80053608521     PISSN: 00796107     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.pbiomolbio.2011.06.004     Document Type: Review

References (138)

1. Achuthan S., Canavier C.C. Phase-resetting curves determine synchronization, phase locking, and clustering in networks of neural oscillators. J. Neurosci. 2009, 29:5218-5233.
2. Aon M.A., Cortassa S., O'Rourke B. Percolation and criticality in a mitochondrial network. Proc. Natl. Acad. Sci. U S A 2004, 101:4447-4452.
3. Baker R.E., Simpson M.J. Correcting mean-field approximations for birth-death-movement processes. Phys. Rev. E 2010, 82:041905.
4. Bankes S.C. Agent-based modeling: a revolution?. Proc. Natl. Acad. Sci. U S A 2002, 99(Suppl. 3):7199-7200.
5. Bassingthwaighte J.B., Chizeck H.J., Atlas L.E., Qian H. Multiscale modeling of cardiac cellular energetics. Ann. N. Y Acad. Sci. 2005, 1047:395-424.
6. Bishop L.M., Qian H. Stochastic bistability and bifurcation in a mesoscopic signaling system with autocatalytic kinase. Biophys. J. 2010, 98:1-11.
7. Bornholdt S. Boolean network models of cellular regulation: prospects and limitations. J. R Soc. Interface 2008, 5:S85-S94.
8. Bradley C., Bowery A., Britten R., Budelmann V., Camara O. OpenCMISS: a multi-physics & multi-scale computational infrastructure for the VPH/Physiome project. Prog. Biophys. Mol. Biol. 2011, 101:32-47.
9. Brady N.R., Elmore S.P., van Beek J.J., Krab K., Courtoy P.J., Hue L., Westerhoff H.V. Coordinated behavior of mitochondria in both space and time: a reactive oxygen species-activated wave of mitochondrial depolarization. Biophys. J. 2004, 87:2022-2034.
10. 2+ sparks evoked by action potentials in mouse ventricular myocytes. J. Physiol. 1999, 518:469-478.
11. Camazine S., Deneuboug J.-L., Franks N.R., Sneyd J., Theraulaz G., Bonabeau E. Self-organization in Biological Systems 2001, Princeton University Press, Princeton.
12. Cao Y., Gillespie D.T., Petzold L.R. The slow-scale stochastic simulation algorithm. J. Chem. Phys. 2005, 122:14116.
13. Cheng H., Lederer W.J. Calcium sparks. Physiol. Rev. 2008, 88:1491-1545.
14. i waves in cardiac myocytes. Am. J. Physiol. 1996, 270:C148-C159.
15. Chialvo D.R., Gilmour R.F., Jalife J. Low dimensional chaos in cardiac tissue. Nature 1990, 343:653-657.
16. Chu J.W., Ayton G.S., Izvekov S., Voth G.A. Emerging methods for multiscale simulation of biomolecular systems. Mol. Phys. Int. J. Interface Between Chem. Phys. 2007, 105:167-175.
17. Clancy C.E., Rudy Y. Linking a genetic defect to its cellular phenotype in a cardiac arrhythmia. Nature 1999, 400:566-569.
18. Clay J.R., DeFelice L.J. Relationship between membrane excitability and single channel open-close kinetics. Biophys. J. 1983, 42:151-157.
19. Clute P., Pines J. Temporal and spatial control of cyclin B1 destruction in metaphase. Nat. Cell Biol. 1999, 1:82-87.
20. Coffey W., Kalmykov Y., Waldron J. The Langevin equation. Series in Contemporary Chemical Physics 2004, World Scientific Publishing, Singapore. M. Evans (Ed.).
21. Cortassa S., Aon M.A., Marban E., Winslow R.L., O'Rourke B. An integrated model of cardiac mitochondrial energy metabolism and calcium dynamics. Biophys. J. 2003, 84:2734-2755.
22. Courtemanche M., Glass L., Keener J.P. Instabilities of a propagating pulse in a ring of excitable media. Phys. Rev. Lett. 1993, 70:2182-2185.
23. Coveney P.V., Fowler P.W. Modelling biological complexity: a physical scientist's perspective. J. R Soc. Interface 2005, 2:267-280.
24. Cui X., Rovetti R.J., Yang L., Garfinkel A., Weiss J.N., Qu Z. Period-doubling bifurcation in an array of coupled stochastically excitable elements subjected to global periodic forcing. Phys. Rev. Lett. 2009, 103:44102-44104.
25. 2+ concentration. Proc. Natl. Acad. Sci. U S A 1992, 89:9895-9899.
26. Deane C.M., Salwinski L., Xenarios I., Eisenberg D. Protein interactions: two methods for assessment of the reliability of high throughput observations. Mol. Cell Proteomics 2002, 1:349-356.
27. Dodson G.G., Lane D.P., Verma C.S. Molecular simulations of protein dynamics: new windows on mechanisms in biology. EMBO Rep. 2008, 9:144-150.
28. Echebarria B., Karma A. Amplitude equation approach to spatiotemporal dynamics of cardiac alternans. Phys. Rev. E 2007, 76:051911.
29. Emonet T., Macal C.M., North M.J., Wickersham C.E., Cluzel P. AgentCell: a digital single-cell assay for bacterial chemotaxis. Bioinformatics 2005, 21:2714-2721.
30. Engler A.J., Humbert P.O., Wehrle-Haller B., Weaver V.M. Multiscale modeling of form and function. Science 2009, 324:208-212.
31. Gardner T.S., Cantor C.R., Collins J.J. Construction of a genetic toggle switch in Escherichia coli. Nature 2000, 403:339-342.
32. Garfinkel A., Tintut Y., Petrasek D., Bostrom K., Demer L.L. Pattern formation by vascular mesenchymal cells. Proc. Natl. Acad. Sci. U S A 2004, 101:9247-9250.
33. Garfinkel A. Forms of Explanation 1981, Yale Univ. Press, New Haven.
34. Gerhardt M., Schuster H., Tyson J.J. A cellular automation model of excitable media including curvature and dispersion. Science 1990, 247:1563-1566.
35. Gillespie D.T. Exact stochastic simulation of coupled chemical reactions. J. Phys. Chem. 1977, 81:2340-2361.
36. Gillespie D.T. Stochastic simulation of chemical kinetics. Annu. Rev. Phys. Chem. 2007, 58:35-55.
37. Girard S., Luckhoff A., Lechleiter J., Sneyd J., Clapham D. Two-dimensional model of calcium waves reproduces the patterns observed in Xenopus oocytes. Biophys. J. 1992, 61:509-517.
38. Goldbeter A. A model for circadian oscillations in the Drosophila period protein (PER). Proc. Biol. Sci. 1995, 261:319-324.
39. Goodwin B. An entrainment model for timed enzyme synthesis in bacteria. Nature 1966, 209:479-481.
40. Greenstein J.L., Winslow R.L. Integrative systems models of cardiac excitation-contraction coupling. Circ. Res. 2011, 108:70-84.
41. Grima R. Multiscale modeling of biological pattern formation. Curr. Top. Dev. Biol. 2008, 81:435-460.
42. Guevara M.R., Glass L., Shrier A. Phase locking, period-doubling bifurcations, and irregular dynamics in periodically stimulated cardiac cells. Science 1981, 214:1350-1353.
43. Haken H. Synergetics, an Introduction: Nonequilibrium Phase Transitions and Self-organization in Physics, Chemistry, and Biology 1983, Springer-Verlag, New York.
44. Hilborn R.C. Chaos and Nonlinear Dynamics 1994, Oxford University Press, New York.
45. Hodgkin A.L., Huxley A.F. A quantitative description of membrane current and its application to conduction and excitation in nerve. J. Physiol. 1952, 117:500-544.
46. Horsthemke W., Lefever R. Noise-induced transitions. Springer Series in Synergetics 1984, Springer, Berlin. H. Haken (Ed.).
47. Hu G., He K. Bistable systems subject to a singular stochastic force. Phys. Rev. A 1992, 45:5447-5454.
48. Hu G., Nicolis G., Nicolis C. Periodically forced Fokker-Planck equation and stochastic resonance. Phys. Rev. A 1990, 42:2030-2041.
49. Hunter P., Nielsen P. A strategy for integrative computational physiology. Physiology (Bethesda) 2005, 20:316-325.
50. Hunter P.J., Pullan A.J., Smaill B.H. Modeling total heart function. Annu. Rev. Biomed. Eng. 2003, 5:147-177.
51. Inoue M., Bridge J.H. Variability in couplon size in rabbit ventricular myocytes. Biophys. J. 2005, 89:3102-3110.
52. Joshi H., Singharoy A.B., Sereda Y.V., Cheluvaraja S., Ortoleva P.J. Multiscale simulation of microbe structure and dynamics. Prog. Biophys. Mol. Biol. 2011, 107:200-217.
53. Kadanoff L.P. Statistical Physics: Statics, Dynamics and Renormalization 2000, World Scientific, Singapore.
54. Kamerlin S.C., Vicatos S., Dryga A., Warshel A. Coarse-grained (multiscale) simulations in studies of biophysical and chemical systems. Annu. Rev. Phys. Chem 2010.
55. Kaneko K. Overview of coupled map lattices. Chaos 1992, 2:279-282.
56. Karplus M., Kuriyan J. Molecular dynamics and protein function. Proc. Natl. Acad. Sci. U S A 2005, 102:6679-6685.
57. Karplus M., Petsko G.A. Molecular dynamics simulations in biology. Nature 1990, 347:631-639.
58. Karsenti E. Self-organization in cell biology: a brief history. Nat. Rev. Mol. Cell Biol. 2008, 9:255-262.
59. Kauffman S.A. Metabolic stability and epigenesis in randomly constructed genetic nets. J. Theor. Biol. 1969, 22:437-467.
60. Kawai R., Sailer X., Schimansky-Geier L., Van den Broeck C. Macroscopic limit cycle via pure noise-induced phase transitions. Phys. Rev. E 2004, 69:051104.
61. Keener J.P., Sneyd J. Mathematical physiology. Interdisciplinary Applied Mathematics 1998, 766. Springer, New York.
62. Keener J.P. Invariant manifold reductions for Markovian ion channel dynamics. J. Math. Biol. 2009, 58:447-457.
63. Kholodenko B.N. Negative feedback and ultrasensitivity can bring about oscillations in the mitogen-activated protein kinase cascades. Euro J. Biochem. 2000, 267:1583-1588.
64. Kholodenko B.N. Four-dimensional organization of protein kinase signaling cascades: the roles of diffusion, endocytosis and molecular motors. J. Exp. Biol. 2003, 206:2073-2082.
65. Kitano H. Systems biology: a brief overview. Science 2002, 295:1662-1664.
66. Klepeis J.L., Lindorff-Larsen K., Dror R.O., Shaw D.E. Long-timescale molecular dynamics simulations of protein structure and function. Curr. Opin. Struct. Biol. 2009, 19:120-127.
67. Kohl P., Crampin E.J., Quinn T.A., Noble D. Systems biology: an approach. Clin. Pharmacol. Ther. 2010, 88:25-33.
68. Kondo S., Miura T. Reaction-diffusion model as a framework for understanding biological pattern formation. Science 2010, 329:1616-1620.
69. Lechleiter J., Girard S., Peralta E., Clapham D. Spiral calcium wave propagation and annihilation in Xenopus laevis oocytes. Science 1991, 252:123-126.
70. Lett P., Gage E., Chyba T. Colored-noise-induced first-order phase transition in a single-mode dye laser. Phys. Rev. A 1987, 35:746-751.
71. Levin M.D., Morton-Firth C.J., Abouhamad W.N., Bourret R.B., Bray D. Origins of individual swimming behavior in bacteria. Biophys. J. 1998, 74:175-181.
72. Lewis T.J., Guevara M.R. Chaotic dynamics in an ionic model of the propagated cardiac action potential. J. Theor. Biol. 1990, 146:407-432.
73. Li F., Long T., Lu Y., Ouyang Q., Tang C. The yeast cell-cycle network is robustly designed. Proc. Natl. Acad. Sci. U S A 2004, 101:4781-4786.
74. Liang J., Qian H. Computational cellular dynamics based on the chemical master equation: a challenge for understanding complexity. J. Comput. Sci. Technol. 2010, 25:154-168.
75. Lipp P., Niggli E. Microscopic spiral waves reveal positive feedback in subcellular calcium signaling. Biophys. J. 1993, 65:2272-2276.
76. Loew S., Hinderliter A., May S. Stability of protein-decorated mixed lipid membranes: the interplay of lipid-lipid, lipid-protein, and protein-protein interactions. J. Chem. Phys. 2009, 130:045102.
77. 2+ handling. Am. J. Physiol. 1997, 273:C717-C733.
78. 2+ clock in cardiac pacemaker cells. Biophys. J. 2011, 100:271-283.
79. 2+ oscillations. Embo J. 2001, 20:65-76.
80. May R.M. Simple mathematical models with very complicated dynamics. Nature 1976, 261:459-467.
81. Meier-Schellersheim M., Fraser I.D., Klauschen F. Multiscale modeling for biologists. Wiley Interdiscip. Rev. Syst. Biol. Med. 2009, 1:4-14.
82. Meinhardt H., Gierer A. Pattern formation by local self-activation and lateral inhibition. Bioessays 2000, 22:753-760.
83. Michaelis L., Menten M. Die kinetik der invertinwirkung. Biochem. Z. 1913, 49:333-369.
84. Miller C.A., Beard D.A. The effects of reversibility and noise on stochastic phosphorylation cycles and cascades. Biophys. J. 2008, 95:2183-2192.
85. Murray J.D. Mathematical Biology 1993, Springer-Verlag, Berlin.
86. Murtola T., Bunker A., Vattulainen I., Deserno M., Karttunen M. Multiscale modeling of emergent materials: biological and soft matter. Phys. Chem. Chem. Phys. 2009, 11:1869-1892.
87. Nadell C.D., Foster K.R., Xavier J.o.B. Emergence of Spatial structure in cell groups and the evolution of cooperation. PLoS Comput. Biol. 2010, 6:e1000716.
88. Naundorf B.R., Wolf F., Volgushev M. Unique features of action potential initiation in cortical neurons. Nature 2006, 440:1060-1063.
89. Neves S.R., Tsokas P., Sarkar A., Grace E.A., Rangamani P., Taubenfeld S.M., Alberini C.M., Schaff J.C., Blitzer R.D., Moraru, Iyengar R. Cell shape and negative links in regulatory motifs together control spatial information flow in signaling networks. Cell 2008, 133:666-680.
90. Nicolis G., Prigogine I. Self-organization in Nonequilibrium Systems. From Dissipative Strucutre to Order through Fluctuations 1977, Wiley, New York.
91. Nolasco J.B., Dahlen R.W. A graphic method for the study of alternation in cardiac action potentials. J. Appl. Physiol. 1968, 25:191-196.
92. Nordsletten D.A., Niederer S.A., Nash M.P., Hunter P.J., Smith N.P. Coupling multi-physics models to cardiac mechanics. Prog. Biophys. Mol. Biol. 2011, 104:77-88.
93. Oppo G.-L., Politi A. Center-manifold reduction for laser equations with detuning. Phys. Rev. A 1989, 40:1422.
94. Pines J. Four-dimensional control of the cell cycle. Nat. Cell Biol. 1999, 1:E73-E79.
95. Prigogine I. Time, structure, and fluctuations. Science 1978, 201:777-785.
96. Qian H., Saffarian S., Elson E.L. Concentration fluctuations in a mesoscopic oscillating chemical reaction system. Proc. Natl. Acad. Sci. U S A 2002, 99:10376-10381.
97. Qu Z., Hu G. Spatiotemporally periodic states, periodic windows and intermittency in coupled-map lattices. Phys. Rev. E 1994, 49:1099-1108.
98. Qu Z., Hu G., Ma B. Relaxation from an intrinsically unstable state to the metastable state in a colored-noise-driven system. Phys. Rev. E 1993, 47:2361-2365.
99. Qu Z., Weiss J.N., MacLellan W.R. Regulation of the mammalian cell cycle: a model of the G1-to-S transition. Am. J. Physiol. Cell Physiol. 2003, 284:C349-C364.
100. Qu Z., Shiferaw Y., Weiss J.N. Nonlinear dynamics of cardiac excitation-contraction coupling: an iterated map study. Phys. Rev. E 2007, 75:011927.
101. Qu Z., Xie Y., Garfinkel A., Weiss J.N. T-wave alternans and arrhythmogenesis in cardiac diseases. Front. Physiol. 2010, 1:154.
102. Risken H. The Fokker-Plank equation. Springer Series in Synergetics 1989, Springer, Berlin. H. Haken (Ed.).
103. Rovetti R., Cui X., Garfinkel A., Weiss J.N., Qu Z. Spark-induced sparks as a mechanism of intracellular calcium alternans in cardiac myocytes. Circ. Res. 2010, 106:1582-1591.
104. Samoilov M., Plyasunov S., Arkin A.P. Stochastic amplification and signaling in enzymatic futile cycles through noise-induced bistability with oscillations. Proc. Natl. Acad. Sci. U S A 2005, 102:2310-2315.
105. Schnell S., Grima R., Maini P.K. Multiscale modeling in biology. Am. Scientist 2007, 95:134-142.
106. Scianna M., Munaron L., Preziosi L. A multiscale hybrid approach for vasculogenesis and related potential blocking therapies. Progress in Biophysics and Molecular Biology 2011, 106:450-462.
107. Sha W., Moore J., Chen K., Lassaletta A.D., Yi C.S., Tyson J.J., Sible J.C. Hysteresis drives cell-cycle transitions in Xenopus laevis egg extracts. Proc. Natl. Acad. Sci. U S A 2003, 100:975-980.
108. 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., Wriggers W. Atomic-level characterization of the structural dynamics of proteins. Science 2010, 330:341-346.
109. Shiferaw Y., Watanabe M.A., Garfinkel A., Weiss J.N., Karma A. Model of intracellular calcium cycling in ventricular myocytes. Biophys. J. 2003, 85:3666-3686.
110. Singhania R., Sramkoski R.M., Jacobberger J.W., Tyson J.J. A hybrid model of Mammalian cell cycle regulation. PLoS Comput. Biol. 2011, 7:e1001077.
111. Smythe J., Moss F., McClintock P. Observation of a noise-induced phase trasition with an analog simulator. Phys. Rev. Lett. 1983, 51:1062-1065.
112. Sneddon M.W., Faeder J.R., Emonet T. Efficient modeling, simulation and coarse-graining of biological complexity with NFsim. Nat. Meth. 2011, 8:177-183.
113. 2+ sparks: an investigative mathematical model of calcium-induced calcium release. Biophys. J. 2002, 83:59-78.
114. Southern J., Pitt-Francis J., Whiteley J., Stokeley D., Kobashi H., Nobes R., Kadooka Y., Gavaghan D. Multi-scale computational modelling in biology and physiology. Prog. Biophys. Mol. Biol. 2008, 96:60-89.
115. Stein M., Gabdoulline R.R., Wade R.C. Bridging from molecular simulation to biochemical networks. Curr. Opin. Struct. Biol. 2007, 17:166-172.
116. Stoneham A.M., Harding J.H. Not too big, not too small: the appropriate scale. Nat. Mater. 2003, 2:77-83.
117. Sutterlin T., Huber S., Dickhaus H., Grabe N. Modeling multi-cellular behavior in epidermal tissue homeostasis via finite state machines in multi-agent systems. Bioinformatics 2009, 25:2057-2063.
118. Ten Tusscher K.H., Hren R., Panfilov A.V. Organization of ventricular fibrillation in the human heart. Circ. Res. 2007, 100:e87-101.
119. Torquato S. Toward an Ising model of cancer and beyond. Phys. Biol. 2011, 8:015017.
120. Tsai T.Y., Choi Y.S., Ma W., Pomerening J.R., Tang C., Ferrell J.E. Robust, tunable biological oscillations from interlinked positive and negative feedback loops. Science 2008, 321:126-129.
121. Tsien R.Y. Constructing and exploiting the fluorescent protein paintbox (Nobel Lecture). Angew. Chem. Int. Edition 2009, 48:5612-5626.
122. Turing A.M. The chemical basis of morphogenesis. Phil. Roy. Soc. Lond. B. 1952, 237:37-72.
123. Tyson J.J., Chen K.C., Novak B. Sniffers, buzzers, toggles and blinkers: dynamics of regulatory and signaling pathways in the cell. Curr. Opin. Cell Biol. 2003, 15:221-231.
124. Uetz P., Giot L., Cagney G., Mansfield T.A., Judson R.S., Knight J.R., Lockshon D., Narayan V., Srinivasan M., Pochart P., Qureshi-Emili A., Li Y., Godwin B., Conover D., Kalbfleisch T., Vijayadamodar G., Yang M., Johnston M., Fields S., Rothberg J.M. A comprehensive analysis of protein-protein interactions in Saccharomyces cerevisiae. Nature 2000, 403:623-627.
125. Vellela M., Qian H. A quasistationary analysis of a stochastic chemical reaction: Keizer's paradox. Bull. Math. Biol. 2007, 69:1727-1746.
126. Vellela M., Qian H. Stochastic dynamics and non-equilibrium thermodynamics of a bistable chemical system: the Schlogl model revisited. J. R Soc. Interface 2009, 6:925-940.
127. Wang S., Xie Y., Qu Z. Coupled iterated map models of action potential dynamics in a one-dimensional cable of coupled cardiac cells. New J. Phys. 2007, 10:055001.
128. Weiss J., Nivala M., Garfinkel A., Qu Z. Alternans and arrhythmias: from cell to heart. Circ. Res. 2011, 108:98-112.
129. 2+ 'sparks' and waves in intact ventricular muscle resolved by confocal imaging. Circ. Res. 1997, 81:462-469.
130. Wolfram S. Statistical mechanics of cellular automata. Rev. Mod. Phys. 1983, 55:601.
131. Wu F., Yang F., Vinnakota K.C., Beard D.A. Computer modeling of mitochondrial tricarboxylic acid cycle, oxidative phosphorylation, metabolite transport, and electrophysiology. J. Biol. Chem. 2007, 282:24525-24537.
132. Wylie D.C., Hori Y., Dinner A.R., Chakraborty A.K. A hybrid deterministic-stochastic algorithm for modeling cell signaling dynamics in spatially inhomogeneous environments and under the influence of external fields. J. Phys. Chem. B. 2006, 110:12749-12765.
133. Xie F., Qu Z., Yang J., Baher A., Weiss J.N., Garfinkel A. A simulation study of the effects of cardiac anatomy in ventricular fibrillation. J. Clin. Invest. 2004, 113:686-693.
134. Xie X.S., Yu J., Yang W.Y. Living cells as test tubes. Science 2006, 312:228-230.
135. Xiong W., Ferrell J.E. A positive-feedback-based bistable 'memory module' that governs a cell fate decision. Nature 2003, 426:460-465.
136. Yang L., Han Z., Robb MacLellan W., Weiss J.N., Qu Z. Linking cell division to cell growth in a spatiotemporal model of the cell cycle. J. Theor. Biol. 2006, 241:120-133.
137. Yang L., Korge P., Weiss J.N., Qu Z. Mitochondrial oscillations and waves in cardiac myocytes: insights from computational models. Biophys. J. 2010, 98:1428-1438.
138. Zima A.V., Picht E., Bers D.M., Blatter L.A. Partial inhibition of sarcoplasmic reticulum ca release evokes long-lasting ca release events in ventricular myocytes: role of luminal Ca in termination of Ca release. Biophys. J. 2008, 94:1867-1879.