Stochastic Petri net models of Ca 2+ signaling complexes and their analysis

Natural Computing

Volumn 10, Issue 3, 2011, Pages 1045-1075

  Lamprecht, Ruth ^a   Smith, Gregory D ^a   Kemper, Peter ^a  

^a Dept of Economics and Thomas Jefferson Program in Public Policy at the College of William and Mary   (United States)

Author keywords

Ca 2+ release sites; Petri net; Stochastic activity networks

Indexed keywords

CALCIUM CHANNEL;

ANALYTIC METHOD; ARTICLE; BIOCHEMISTRY; CALCIUM SIGNALING; CALCIUM TRANSPORT; CELL SYNCHRONIZATION; CONTROLLED STUDY; ENDOPLASMIC RETICULUM; GENE REGULATORY NETWORK; HIDDEN MARKOV MODEL; KINETICS; MATHEMATICAL ANALYSIS; MATHEMATICAL COMPUTING; MATHEMATICAL MODEL; MEMBRANE DEPOLARIZATION; MOLECULAR DYNAMICS; MOLECULAR INTERACTION; PETRI NET; PROBABILITY; PROTEIN PROTEIN INTERACTION; SARCOPLASMIC RETICULUM; SIGNAL TRANSDUCTION; STOCHASTIC MODEL;

EID: 80054981646     PISSN: 15677818     EISSN: 15729796     Source Type: Journal    
DOI: 10.1007/s11047-009-9143-y     Document Type: Article

References (70)

1. Benoit A, Brenner L, Fernandes P, Plateau B (2004) Aggregation of stochastic automata networks with replicas. Linear Algebra Appl 386:111-136
2. Berridge MJ (1997) Elementary and global aspects of calcium signalling. J Exp Biol 499(2):291-306 (Pubitemid 27129414)
3. Berridge MJ (2006) Calcium microdomains: organization and function. Cell Calcium 40:405-412 (Pubitemid 44752611)
4. Bray D (1998) Signaling complexes: biophysical constraints on intracellular communication. Annu Rev Biophys Biomol Struct 27(1):59-75 (Pubitemid 28286009)
5. Buchholz P (1994) Exact and ordinary lumpability in finite Markov chains. J Appl Probab 31(1):59-74
6. Buchholz P (1995) Equivalence relations for stochastic automata networks. In: Stewart WJ (ed) Computation with Markov chains. Kluwer, Boston, MA, pp 197-216
7. Buchholz P (2004) Adaptive decomposition and approximation for the analysis of stochastic Petri nets. Perform Eval 56(1-4):23-52
8. Buchholz P, Dayar T (2004) Comparison of multilevel methods for Kronecker-based Markovian representations. Computing 73(4):349-371
9. Chaouiya C (2007) Petri net modelling of biological networks. Brief Bioinform 8(4):210-219 (Pubitemid 47336806)
10. Chiola G, Dutheillet C, Franceschinis G, Haddad S (1993) Stochastic well-formed colored nets and symmetric modeling applications. IEEE Trans Comput 42(11):1343-1360
11. Cho W (2006) Building signaling complexes at the membrane. Science's STKE 2006(321):pe7
12. Ciardo G (1989) Analysis of large stochastic Petri net models. PhD thesis, Duke University
13. Ciardo G, Miner AS (1999) A data structure for the efficient Kronecker solution of GSPNs. In: Proceedings of the 8th international workshop on Petri nets and performance models. IEEE CS, pp 22-31
14. Ciardo G, Trivedi KS (1993) A decomposition approach for stochastic reward net models. Perform Eval 18(1):37-59 (Pubitemid 23710402)
15. Ciardo G, Marmorstein RM, Siminiceanu R (2003) Saturation unbound. In: 9th international conference on tools and algorithms for the construction and analysis of systems, vol 2619. Springer, Berlin, pp 379-393
16. Colquhoun D, Hawkes AG (1995) A Q-matrix cookbook: how to write only one program to calculate the single-channel and macroscopic predictions for any kinetic mechanism. In: Singel-channel recording, 2nd edn. Plenum Press, New York, pp 589-633
17. Deavours DD, Clark G, Courtney T, Daly D, Derisavi S, Doyle JM, Sanders WH, Webster PG (2002) The Möbius framework and its implementation. IEEE Trans Softw Eng 28(10):956-969
18. DeRemigio H, Smith GD (2005) The dynamics of stochastic attrition viewed as an absorption time on a terminating Markov chain. Cell Calcium 38(2):73-86 (Pubitemid 41150655)
19. DeRemigio H, Kemper P, Lamar MD, Smith GD (2007) Markov chain models of couples intracellular calcium channels: Kronecker structured representations and benchmark stationary distribution calculations. Pac Symp Biocomput 13:354-365
20. DeRemigio H, Groff JR, Smith GD (2008a) Calcium release site ultrastructure and the dynamics of puffs and sparks. Math Med Biol 25(1):65-85
21. DeRemigio H, Lamar MD, Kemper P, Smith GD (2008b) Markov chain models of coupled calcium channels: Kronecker representations and iterative solution methods. Phys Biol 5(3):36003
22. Derisavi S, Hermanns H, Sanders WH (2003) Optimal state-space lumping in Markov chains. Inf Process Lett 87(6):309-315
23. Derisavi S, Kemper P, Sanders WH (2004) Symbolic state-space exploration and numerical analysis of state-sharing composed models. Linear Algebra Appl 386:137-166
24. Derisavi S, Kemper P, Sanders WH (2005) Lumping matrix diagram representations of Markov models. In: Proceedings of the 2005 international conference on dependable systems and networks. IEEE CS, pp 742-751 (Pubitemid 41538288)
25. 2+ concentration. Proc Natl Acad Sci 89:9895-9899
26. Donatelli S (1994) Superposed generalized stochastic Petri nets: definition and efficient solution. In: Proceedings of the 15th international conference on application and theory of Petri nets, Lecture Notes in Computer Science, vol 815. Springer, Berlin, pp 258-277
27. Duke TA, Bray D (1999) Heightened sensitivity of a lattice of membrane receptors. Proc Natl Acad Sci USA 96(18):10104-10108 (Pubitemid 29422519)
28. Duke TA, Novere NL, Bray D (2001) Conformational spread in a ring of proteins: a stochastic approach to allostery. J Mol Biol 308(3):541-553 (Pubitemid 33027618)
29. Fishman GS (1978) Principles of discrete event simulation. Wiley, New York, NY, USA
30. Fox BL, Glynn PW (1988) Computing Poisson probabilities. Commun ACM 31(4):440-445
31. Gillespie DT (1977) Exact stochastic simulation of coupled chemical reactions. J Phys Chem 81(25): 2340-2361
32. Gomperts BD, Tatham PE, Kramer IM (2002) Signal transduction. Academic Press, San Diego, CA
33. Goss PJ, Peccoud J (1998) Quantitative modeling of stochastic systems in molecular biology by using stochastic Petri nets. Proc Natl Acad Sci USA 95(12):6750-6755 (Pubitemid 28278052)
34. Griffith M, Courtney T, Peccoud J, Sanders WH (2006) Dynamic partitioning for hybrid simulation of the bistable HIV-1 transactivation network. Bioinformatics 22(22):2782-2789 (Pubitemid 44742399)
35. Groff JR, Smith GD (2008) Calcium-dependent inactivation and the dynamics of calcium puffs and sparks. J Theor Biol 253(3):483-499
36. Groff JR, DeRemigio H, Smith GD (2009) Markov chain models of ion channels and the collective gating of calcium release sites. In: Stochastic methods in neuroscience. Oxford University Press, Oxford, pp 29-64
37. Hardy S, Robillard PN (2007) Petri net-based method for the analysis of the dynamics of signal propagation in signaling pathway. Bioinformatics 24(2):209-217
38. Heiner M, Koch I (2004) Petri net based model validation in systems biology. In: Proceedings of the 25th international conference on application and theory of Petri nets, Lecture Notes in Computer Science, vol 3099. Springer, Berlin, pp 216-237
39. Hermanns H (2002) Interactive Markov chains and the quest for quantified quality, Lecture Notes in Computer Science, vol 2428. Springer, Berlin
40. Hill TL (1977) Free energy transduction in biology: the steady-state kinetic and thermodynamic formalism. Academic Press, New York
41. Hillston J (2005) Process algebras for quantitative analysis. In: Logic in computer science. IEEE CS, pp 239-248 (Pubitemid 41462571)
42. Jansen DN, Hermanns H (2004) Dependability checking with StoCharts: is train radio reliable enough for trains? In: Proceedings of the 1st international conference on quantitative evaluation of systems (QEST). IEEE CS, pp 250-259 (Pubitemid 40456781)
43. Kemeney JG, Snell JL (1960) Finite Markov chains. D. Van Nostrand Company, Princeton, NJ
44. Krauss G (2003) Biochemistry of signal transduction and regulation. Wiley-VCH, Weinheim
45. Law AM, Kelton WD (2000) Simulation modeling and analysis. McGraw Hill, New York
46. Lecca P (2006) A time-dependent extension of gillespie algorithm for biochemical stochastic p-calculus. In: Proceedings of the 2006 ACM symposium on applied computing. ACM, New York, NY, USA, pp 137-144 (Pubitemid 44758763)
47. Mak DOD, Foskett JK (1997) Single-channel kinetics, inactivation, and spatial distribution of inositol trisphosphate (IP3) receptors in Xenopus oocyte nucleus. J Gen Physiol 109(5):571-587 (Pubitemid 27218319)
48. Marsan MA, Balbo G, Conte G, Donatelli S, Franceschinis G (1995) Modelling with generalized stochastic Petri nets, Wiley Series in parallel computing. Wiley Inc, New York
49. Materi W, Wishart DS (2007) Computational systems biology in drug discovery and development: Methods and applications. Drug Discov Today 12(7-8):295-303 (Pubitemid 46467486)
50. Matsuno H, Li C, Miyano S (2006) Petri net based descriptions for systematic understanding of biological pathways. IEICE Trans Fundam Electron Commun Comput Sci E89-A(11):3166-3174 (Pubitemid 44934429)
51. McQuinn MG, Kemper P, Sanders WH (2007) Dependability analysis with Markov chains: how symmetries improve symbolic computations. In: Proceedings of the 4th international conference on quantitative evaluation of systems (QEST). IEEE CS, pp 151-160
52. Miner AS, Parker D (2004) Symbolic representations and analysis of large probabilistic systems. In: Validation of stochastic systems: a guide to current research, Lecture Notes in Computer Science, vol 2925. Springer, Berlin
53. 2+ channels. Bull Math Biol 67(3):393-432 (Pubitemid 40466380)
54. Obal WD II (1998) Measure-adaptive state-space construction methods. PhD thesis, University of Arizona
55. Obal WD II, McQuinn MG, Sanders WH (2007) Detecting and exploiting symmetry in discrete-state Markov models. IEEE Trans Reliab 56(4):643-654 (Pubitemid 350238635)
56. Peccoud J, Courtney T, Sanders WH (2007) Möbius: an integrated discrete-event modeling environment. Bioinformatics 23(24):3412-3414 (Pubitemid 350238902)
57. Peleg M, Yeh I, Altman RB (2002) Modelling biological processes using workflow and Petri net models. Bioinformatics 18(6):825-837 (Pubitemid 34727643)
58. Peleg M, Rubin D, Altman RB (2005) Using Petri net tools to study properties and dynamics of biological systems. J Am Med Inform Assoc 12(2):181-199 (Pubitemid 40298953)
59. Priami C (1995) Stochastic p-calculus. Comput J 38(7):578-589
60. Priese L, Wimmel H (2003) Theoretische Informatik: Petri-Netze (in German). Springer, Berlin
61. Sanders WH, Meyer JF (1991) Reduced base model construction methods for stochastic activity networks. IEEE J Sel Areas Commun, Special issue on Computer-Aided Model Anal Des Netw 9(1):25-36
62. Sanders WH, Meyer JF (2001) Stochastic activity networks: formal definitions and concepts. In: Lectures on Formal Methods and Performance Analysis, Lecture Notes in Computer Science, vol 2090. Springer, Berlin, pp 315-343 (Pubitemid 33332568)
63. Schaub MA, Henzinger TA, Fisher J (2007) Qualitative networks: a symbolic approach to analyze biological signaling networks. BMC Syst Biol 1(4)
64. Schwarick M (2008) Transient analysis of stochastic Petri nets with interval decision diagrams. In: Proceeding of the 15th German workshop on algorithms and tools for Petri nets, AWPN 2008, CEURWS. org, CEUR Workshop Proceedings, vol 380, pp 43-48
65. Sneyd J, Falcke M (2005) Models of the inositol trisphosphate receptor. Prog Biophys Mol Biol 89(3): 207-245 (Pubitemid 40793522)
66. Srivastava R, You L, Summers J, Yin J (2002) Stochastic vs. deterministic modeling of intracellular viral kinetics. J Theor Biol 218(3):309-321 (Pubitemid 35191831)
67. Steggles LJ, Banks R, Shaw O, Wipat A (2007) Qualitatively modelling and analyzing genetic regulatory networks: a Petri net approach. Bioinformatics 23(3):336-343 (Pubitemid 46323156)
68. Stewart WJ (1994) Introduction to the numerical solution of Markov chains. Princeton University Press, Princeton
69. 2+ signalling events in Xenopus oocytes. J Physiol 509(1):67-80 (Pubitemid 28252012)
70. 2+ evoked by iinositol trisphosphate in Xenopus oocytes. J Physiol 482(3):533-553