Hybrid stochastic simulations of intracellular reaction-diffusion systems

Computational Biology and Chemistry

Volumn 33, Issue 3, 2009, Pages 205-215

  Kalantzis, Georgios ^a  

^a UNIVERSITY OF TEXAS MEDICAL SCHOOL   (United States)

Author keywords

Biochemical networks; Calcium dynamics; Chemical master equation; Hybrid algorithm; Stochastic simulation

Indexed keywords

BIOCHEMICAL NETWORKS; CALCIUM DYNAMICS; CHEMICAL MASTER EQUATION; HYBRID ALGORITHM; STOCHASTIC SIMULATION;

ALGORITHMS; BIOLOGICAL SYSTEMS; CALCIUM; CALCIUM ALLOYS; CIRCUIT THEORY; DIFFUSION IN LIQUIDS; DISCRETE EVENT SIMULATION; DYNAMICS; MOLECULAR STRUCTURE; RANDOM PROCESSES; SIMULATORS; STOCHASTIC CONTROL SYSTEMS; STOCHASTIC MODELS; SYSTEMS ANALYSIS;

HYBRID SYSTEMS;

CALCIUM;

ALGORITHM; ARTICLE; BIOCHEMISTRY; BIOLOGICAL MODEL; CELL; COMPUTER SIMULATION; DENDRITIC SPINE; DIFFUSION; KINETICS; METABOLISM; STATISTICS; VIROLOGY;

ALGORITHMS; BIOCHEMICAL PROCESSES; CALCIUM; CELLS; COMPUTER SIMULATION; DENDRITIC SPINES; DIFFUSION; KINETICS; MODELS, BIOLOGICAL; STOCHASTIC PROCESSES;

EID: 67349145400     PISSN: 14769271     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.compbiolchem.2009.03.002     Document Type: Article

References (52)

1. Alfonsi A., Cances E., Turinici G., Ventura B.D., and Huisinga W. Exact simulation of hybrid stochastic and deterministic models for biochemical systems. ESAIM Proc. 14 (2005) 1-13
2. Arkin A., Ross J., and McAdams H.H. Stochastic kinetic analysis of developmental pathway bifurcation in phage λ-infected Escherichia coli cells. Genetics 149 (1998) 1633-1648
3. Baras F., and Mansour M.M. reaction-diffusion master equation: a comparison with microscopic simulations. Phys. Rev. E 54 (1996) 6139
4. Bernstein D. Simulating mesoscopic reaction-diffusion systems using the gillespie algorithm. Phys. Rev. E 71 (2005) 041103
5. Bhalla U.S. Signaling in small subcellular volume ii. stochastic and diffusion effects on synaptic network properties. Biophys. J. 87 (2004) 745-753
6. Cao Y., Gillespie D., and Petzold L. The slow scale stochastic simulation algorithm. J. Chem. Phys. 122 (2005) 014116
7. Cao Y., Li H., and Petzold L.R. Efficient formulation of the stochastic simulation algorithm for chemically reacting systems. J. Phys. Chem. 105 (2004) 1876-1889
8. Cao Y., and Petzold L. Accuracy limitations and the measurement of errors in the stochastic simulation of chemically reacting systems. J. Comp. Phys. 212 (2006) 6-24
9. Chatterjee A., Katsoulakis M., and Vlachos D. Binomial distribution based tau -leap accelerated stochastic simulation. J. Chem. Phys. 122 (2005) 024112
10. Chiam K.H., Tan C.M., Bhargava V., and Rajagopal G. Hybrid simulations of stochastic reaction-diffusion processes for modeling intracellular signaling pathways. Phys. Rev. E 74 (2006) 051910
11. Erreger K., Shashank M.D., Banke T., Wyllie D., and Traynelis S. Subunit-specific gating controls rat nr1/nr2a and nr1/nr2b nmda channel kinetics and synaptic signaling profiles. J. Physiol. 563 (2005) 345-358
12. Franks K.M., Bartol T.M., and Sejnowski T.J. A monte carlo model reveals independent signaling at central glutamatergic synapse neuromuscular junction. Biophys. J. 83 (2001) 2333-2348
13. Franks K.M., Bartol T.M., and Sejnowski T.J. A monte carlo model reveals independent signaling at central glutamatergic synapses. Biophys. J. 83 (2002) 2333-2348
14. Frenkel D., and Smith B. Understanding molecular simulation: from algorithms to applications (1996), Elsevier, San Diego
15. Gibson M.A., and Bruck J. An efficient formulation of the stochastic simulation of chemical systems with many species and many channels. J. Phys. Chem. 104 (2000) 1876-1889
16. Gillespie D.T. A general method for numerically simulating the stochastic evolution of coupled chemical reactions. J. Comput. Phys. 22 (1976) 403-434
17. Gillespie D.T. Approximate accelerated stochastic simulation of chemically reacting systems. J. Chem. Phys. 115 (2001) 1716-1733
18. Gold J., and Bear M. A model of dendritic spine calcium concentration exploring possible bases for a sliding synaptic modification threshold. Proc. Natl. Acad. Sci. U.S.A. 91 (1993) 3941-3945
19. Goutsias J. Quasiequilibrium approximation of fast reaction kinetics in stochastic biochemical systems. J. Chem. Phys. 122 (2005) 184102
20. Griffith M., Courtney T., Peccoud J., and Sanders W.H. Dynamic partitioning for hybrid simulation of the bistable hiv-1 transactivation network. Bioinofrmatics 22 (2006) 2782-2789
21. Haseltine E.L., and Rawlings J.B. Approximate simulation of coupled fast and slow reactions for stochastic chemical kinetics. J. Chem. Phys. 117 (2002) 6959-6969
22. Holcman D., and Schuss Z. Modelling calcium dynamics in dendritic spines. SIAM J. Appl. Math. 65 (2005) 1006-1026
23. Holmes W. Is the function of dendritic spines to concentrate calcium?. Brain Res. 519 (1990) 338-342
24. Ichikawa K. Localization of activated Ca2+/calmodulin-dependent protein kinase ii within a spine: modeling and computer simulation. Neurocomputing 58 (2004) 443-448
25. Kampa B.M., Clements J., Jonas P., and Stuart G.J. Kinetics of mg+2 unblock of nmda receptors implications for spike-timing dependent synaptic plasticity. ESAIM Proc. 14 (2005) 1-13
26. Keller D., Franks K., Bartol T., and Sejnowski T. Calmodulin activation by calcium transients in the postsynaptic density of dendritic spines. PLOS One 3 4 (2008) e2045
27. Kesmir C., and De Boer R.J. A mathematical model on germinal center kinetics and termination. J. Immunol. 163 (1999) 2463-2469
28. Kiehl T., Mattheyses R., and Simmons M. Hybrid simulation of cellular behavior. Bioinofrmatics 20 (2004) 316-322
29. Knipe D.M., and Howley M. Fields virology (2001), Lippincott Williams and Wilkins, Philadelphia
30. Manninen T., Linne M., and Ruohonen K. Developing ito stochastic differential equation models for neuronal signal transduction pathways. Comp. Biol. Chem. 30 (2006) 280-291
31. McColluma M., Peterson G.D., Cox C.D., Simpson M.L., and Samatova N.F. The sorting direct method for stochastic simulation of biochemical systems with varying reaction execution behavior. J. Comput. Biol. Chem. 30 (2005) 39-49
32. Morishita Y., and Aihara K. Noise-reduction through interaction in gene expression and biochemical reaction processes. J. Theor. Biol. 228 (2004) 315-325
33. Naoki H., Sakumura Y., and Ishii S. Local signaling with molecular diffusion as a decoder of calcium signals in synaptic plasticity. Mol. Syst. Biol. 1 (2005) 0027
34. Perelson A.S. Modelling viral and immune system dynamics. Nature Rev. Immun. 2 (2002) 28-36
35. Poranen M.M., Daugelavicius R., and Bamford D.H. Common principles in viral entry. Ann. Rev. Microbiol. 56 (2002) 521-538
36. Pornillos O., Garrus J.E., and Sunquist W.I. Mechanisms of enveloped rna virus budding. Trends Cell Biol. 12 (2002) 569-579
37. Puchalka J., and Kierzek A.M. Bridging the gap between stochastic and deterministic regimes in the kinetic simulations of the biochemical reaction networks. Biophys. J. 86 (2004) 1357-1372
38. Rao C.V., Wolf D.M., and Arkin A.P. Control, exploitation and tolerance of intracellular noise. Nature 420 (2002) 237-321
39. Rathinam M., Petzold L.R., Cao Y., and Gillespie D.T. Stiffness in stochastic chemically reacting systems: the implicit tau-leaping method. J. Chem. Phys. 119 (2003) 12784-12794
40. Risken H. The Fokker-Planck equation: methods of solution and applications (1989), Springer, Berlin
41. Rudiger S., Shuai J.W., Huisinga W., Nagaiah C., Wamecke G., Parker I., and Falcke M. Hybrid stochastic and deterministic simulations of calcium blips. Biophys. J. 93 (2007) 1847-1857
42. Salis H., and Kaznessis Y. Accurate hybrid stochastic simulation of a system of coupled chemical or biochemical reactions. J. Chem. Phys. 122 (2005) 54103
43. Shouval H.Z., and Kalantzis G. Stochastic properties of synaptic transmission affect the shape of spike time dependent plasticity curves. J. Neurophys. 93 (2005) 1069-1073
44. Smith A.E., and Helenius A. How viruses enter animal cells. Science 304 (2001) 237-242
45. Srivastava R., You L., Summers J., and Yin J. Stochastic vs. deterministic modeling of intracellular viral kinetics. J Theor Biol. 218 (2002) 309-321
46. Takahashi K., Kaizu K., Hu B., and Tomita M. A multi-algorithm multi-timescale method for cell simulation. Bioinformatics 20 4 (2004) 538-546
47. Tuckwell H.C., and Wan F.Y.M. On the behaviour of solutions in viral dynamical models. BioSystems 73 (2004) 157-161
48. Vargas-Caballero M., and Robinson H.P. Fast and slow voltage-dependent dynamics of magnesium block in the nmda receptor: the asymmetric trapping block model. J. Neurosci. 24 (2004) 6171-6180
49. Volfobsky N., Parnas H., Segal M., and Korkotian E. Geometry of dendritic spines affects calcium dynamics in hippocampal neurons: Theory and experiments. J. Neurophys. 82 (1999) 450-462
50. Wodarz D., and Nowak M.A. Mathematical models of hiv pathogenesis and treatment. BioEssays 24 (2002) 1178-1187
51. Wylie D., Hori Y., Dinner A., and Chakraborty A.K. A hybrid deterministic-stochastic algorithm for modelling cell signaling dynamics in spatially ingomogeneous environment and under the influence of external fields. J. Phys. Chem. 110 (2006) 12749-12765
52. Zucker R.S. Calcium and activity-dependent synaptic plasticity. Curr. Opin. Neurobiol. 9 (1999) 305-313