Citation Relationships

Nguyen V, Mathias R, Smith GD (2005) A stochastic automata network descriptor for Markov chain models of instantaneously coupled intracellular Ca2+ channels. Bull Math Biol 67:393-432 [PubMed]

   Stochastic automata network Markov model descriptors of coupled Ca2+ channels (Nguyen et al. 2005)

References and models cited by this paper

References and models that cite this paper

Allbritton NL, Meyer T, Stryer L (1992) Range of messenger action of calcium ion and inositol 1,4,5-trisphosphate. Science 258:1812-5 [PubMed]

Asmussen S, Bladt M (1997) Renewal theory and queueing algorithms for matrix-exponential distributions Matrix-Analytic Methods in Stochastic Models, Chakravarthy S:Alfa A, ed. pp.313

Atri A, Amundson J, Clapham D, Sneyd J (1993) A single-pool model for intracellular calcium oscillations and waves in the Xenopus laevis oocyte. Biophys J 65:1727-39 [Journal] [PubMed]

Berridge MJ (1993) Inositol trisphosphate and calcium signalling. Nature 361:315-25 [Journal] [PubMed]

Berridge MJ (1997) Elementary and global aspects of calcium signalling. J Physiol 499 ( Pt 2):291-306 [PubMed]

Berridge MJ (1998) Neuronal calcium signaling. Neuron 21:13-26 [PubMed]

Bers D (1992) Excitation-Contraction Coupling and Cardiac Contractile Force

Bertram R, Smith GD, Sherman A (1999) Modeling study of the effects of overlapping Ca2+ microdomains on neurotransmitter release. Biophys J 76:735-50 [Journal] [PubMed]

Bezprozvanny I, Ehrlich BE (1994) Inositol (1,4,5)-trisphosphate (InsP3)-gated Ca channels from cerebellum: conduction properties for divalent cations and regulation by intraluminal calcium. J Gen Physiol 104:821-56 [PubMed]

Bootman MD, Lipp P (1999) Ringing changes to the 'bell-shaped curve'. Curr Biol 9:R876-8 [PubMed]

Bugrim AE, Zhabotinsky AM, Epstein IR (1997) Calcium waves in a model with a random spatially discrete distribution of Ca2+ release sites. Biophys J 73:2897-906 [Journal] [PubMed]

Cannell MB, Cheng H, Lederer WJ (1995) The control of calcium release in heart muscle. Science 268:1045-9 [PubMed]

Cheng H, Lederer MR, Lederer WJ, Cannell MB (1996) Calcium sparks and [Ca2+]i waves in cardiac myocytes. Am J Physiol 270:C148-59

Cheng H, Lederer WJ, Cannell MB (1993) Calcium sparks: elementary events underlying excitation-contraction coupling in heart muscle. Science 262:740-4 [PubMed]

Chow CC, White JA (1996) Spontaneous action potentials due to channel fluctuations. Biophys J 71:3013-21 [Journal] [PubMed]

   Spontaneous firing caused by stochastic channel gating (Chow, White 1996) [Model]

Clay JR, DeFelice LJ (1983) Relationship between membrane excitability and single channel open-close kinetics. Biophys J 42:151-7 [Journal] [PubMed]

Colquhoun D, Hawkes AG (1995) A Q-Matric cookbook: how to write only one program to calculate single-channel and macroscopic predictions for any kinetic mechanism. Single-channel Recording, Second Edition, Sakmann B:Neher E, ed. pp.589

Dargan SL, Parker I (2003) Buffer kinetics shape the spatiotemporal patterns of IP3-evoked Ca2+ signals. J Physiol 553:775-88 [Journal] [PubMed]

de Souza e Silva E, Gail H (2000) Transient solutions for Markov chains Computational Probability, Grassmann W, ed. pp.43

De Young GW, Keizer J (1992) A single-pool inositol 1,4,5-trisphosphate-receptor-based model for agonist-stimulated oscillations in Ca2+ concentration. Proc Natl Acad Sci U S A 89:9895-9 [PubMed]

Defelice LJ (1981) Introduction to Membrane Noise

Durrett R (1999) Essentials of Stochastic Processes

Falcke M, Tsimring L, Levine H (2000) Stochastic spreading of intracellular Ca(2+) release. Phys Rev E Stat Phys Plasmas Fluids Relat Interdiscip Topics 62:2636-43 [PubMed]

Fernandes P, Plateau B, Stewart W (1998) Efficient descriptor-vector multiplications in stochastic automata networks J Acm 45:381-414

Fox RF, Lu Yn (1994) Emergent collective behavior in large numbers of globally coupled independently stochastic ion channels. Phys Rev E Stat Phys Plasmas Fluids Relat Interdiscip Topics 49:3421-3431 [PubMed]

Gabso M, Neher E, Spira ME (1997) Low mobility of the Ca2+ buffers in axons of cultured Aplysia neurons. Neuron 18:473-81 [PubMed]

Gillespie DT (1977) Exact stochastic simulation of coupled chemical reactions. Journal Of Physical Chemistry 81:2340-2361

Golub GH, van_Loan CF (1996) Matrix computations

Hagar RE, Burgstahler AD, Nathanson MH, Ehrlich BE (1998) Type III InsP3 receptor channel stays open in the presence of increased calcium. Nature 396:81-4 [Journal] [PubMed]

Hill T (1977) Free Energy Transduction in Biology: The Steady-State Kinetic and Thermodynamic Formalism

Horn R, Johnson C (1991) Topics in Matrix Analysis

Joseph SK (1996) The inositol triphosphate receptor family. Cell Signal 8:1-7 [PubMed]

Kaftan EJ, Ehrlich BE, Watras J (1997) Inositol 1,4,5-trisphosphate (InsP3) and calcium interact to increase the dynamic range of InsP3 receptor-dependent calcium signaling. J Gen Physiol 110:529-38 [PubMed]

Keizer J (1987) Statistical Thermodynamics of Nonequilibrium Processes

Keizer J, Smith GD (1998) Spark-to-wave transition: saltatory transmission of calcium waves in cardiac myocytes. Biophys Chem 72:87-100 [PubMed]

Kemeny J, Snell J (1976) Finite Markov Chains

Langville A, Stewart W (2003) A Kronecker product approximate preconditioner for SANs Numer Linear Algebra Appl 10:1-29

Langville A, Stewart W (2004) The Kronecker product and stochastic automata networks J Comput Appl Math 167:429-447

Latouche G, Ramaswami V (1999) Introduction to Matrix Analytic Methods in Stochastic Modeling

LeBeau AP, Yule DI, Groblewski GE, Sneyd J (1999) Agonist-dependent phosphorylation of the inositol 1,4,5-trisphosphate receptor: A possible mechanism for agonist-specific calcium oscillations in pancreatic acinar cells. J Gen Physiol 113:851-72 [PubMed]

Li YX, Rinzel J (1994) Equations for InsP3 receptor-mediated [Ca2+]i oscillations derived from a detailed kinetic model: a Hodgkin-Huxley like formalism. J Theor Biol 166:461-73 [Journal] [PubMed]

Mak DO, Foskett JK (1997) Single-channel kinetics, inactivation, and spatial distribution of inositol trisphosphate (IP3) receptors in Xenopus oocyte nucleus. J Gen Physiol 109:571-87 [PubMed]

Mak DO, McBride S, Raghuram V, Yue Y, Joseph SK, Foskett JK (2000) Single-channel properties in endoplasmic reticulum membrane of recombinant type 3 inositol trisphosphate receptor. J Gen Physiol 115:241-56 [PubMed]

Maranto AR (1994) Primary structure, ligand binding, and localization of the human type 3 inositol 1,4,5-trisphosphate receptor expressed in intestinal epithelium. J Biol Chem 269:1222-30 [PubMed]

Marchant JS, Parker I (1998) Kinetics of elementary Ca2+ puffs evoked in Xenopus oocytes by different Ins(1,4,5)P3 receptor agonists. Biochem J 334 ( Pt 3):505-9 [PubMed]

Marx SO, Gaburjakova J, Gaburjakova M, Henrikson C, Ondrias K, Marks AR (2001) Coupled gating between cardiac calcium release channels (ryanodine receptors). Circ Res 88:1151-8 [PubMed]

Mazzanti M, DeFelice LJ, Liu YM (1991) Gating of L-type Ca2+ channels in embryonic chick ventricle cells: dependence on voltage, current and channel density. J Physiol 443:307-34 [PubMed]

Meyer CD (1989) Stochastic complementation, uncoupling Markov chains, and the theory of nearly reducible systems Siam Rev 31:240-272

Moraru II, Kaftan EJ, Ehrlich BE, Watras J (1999) Regulation of type 1 inositol 1,4,5-trisphosphate-gated calcium channels by InsP3 and calcium: Simulation of single channel kinetics based on ligand binding and electrophysiological analysis. J Gen Physiol 113:837-49 [PubMed]

Naraghi M, Neher E (1997) Linearized buffered Ca2+ diffusion in microdomains and its implications for calculation of [Ca2+] at the mouth of a calcium channel. J Neurosci 17:6961-73 [PubMed]

Neher E (1986) Concentration profiles of intracellular calcium in the presence of a diffusible chelator Exp Brain Res 14:80-96

Neher E (1998) Usefulness and limitations of linear approximations to the understanding of Ca++ signals. Cell Calcium 24:345-57 [PubMed]

Nicola V (1998) Lumping in Markov reward processes Technical Report, RC14719

Niggli E (1999) Localized intracellular calcium signaling in muscle: calcium sparks and calcium quarks. Annu Rev Physiol 61:311-35 [Journal] [PubMed]

Norris J (1997) Markov Chains

Parker I, Choi J, Yao Y (1996) Elementary events of InsP3-induced Ca2+ liberation in Xenopus oocytes: hot spots, puffs and blips. Cell Calcium 20:105-21 [PubMed]

Plateau B, Atif K (1991) Stochastic automata network for modeling parallel systems Ieee Trans Softw Eng 17:1093-1108

Plateau B, Stewart W (2000) Stochastic automata networks Computational Probability, Grassmann W, ed. pp.113

Ramos-franco J, Fill M, Mignery G (1998) Isoform-specific function of single inositol 1,4,5-trisphosphate receptor channels Biophys J 75:834-839

Rengifo J, Rosales R, González A, Cheng H, Stern MD, Ríos E (2002) Intracellular Ca(2+) release as irreversible Markov process. Biophys J 83:2511-21 [Journal] [PubMed]

Ríos E, Stern MD (1997) Calcium in close quarters: microdomain feedback in excitation-contraction coupling and other cell biological phenomena. Annu Rev Biophys Biomol Struct 26:47-82 [Journal] [PubMed]

Sala F, Hernández-Cruz A (1990) Calcium diffusion modeling in a spherical neuron. Relevance of buffering properties. Biophys J 57:313-24 [Journal] [PubMed]

Sham JS, Song LS, Chen Y, Deng LH, Stern MD, Lakatta EG, Cheng H (1998) Termination of Ca2+ release by a local inactivation of ryanodine receptors in cardiac myocytes. Proc Natl Acad Sci U S A 95:15096-101 [PubMed]

Sherman A, Keizer J, Rinzel J (1990) Domain model for Ca2(+)-inactivation of Ca2+ channels at low channel density. Biophys J 58:985-95 [Journal] [PubMed]

Shuai JW, Jung P (2002) Stochastic properties of Ca(2+) release of inositol 1,4,5-trisphosphate receptor clusters. Biophys J 83:87-97 [Journal] [PubMed]

Shuai JW, Jung P (2003) Optimal ion channel clustering for intracellular calcium signaling. Proc Natl Acad Sci U S A 100:506-10 [Journal] [PubMed]

Shuai JW, Jung P (2003) Selection of intracellular calcium patterns in a model with clustered Ca2+ release channels. Phys Rev E Stat Nonlin Soft Matter Phys 67:031905 [Journal] [PubMed]

Smith G (2002) An extended DeYoung-Keizer-like IP3 receptor model that accounts for domain Ca2+-mediated inactivation Recent Research Developments in Biophysical Chemistry II, Condat C:Baruzzi A, ed. pp.37

Smith G (2002) Modeling the stochastic gating of ion channels Computational Cell Biology, Fall C:Marland E:Wagner J:Tyson J, ed. pp.291

Smith G, Dai L, Muira R, Sherman A (2001) Asymptotic analysis of equations for the buffered diffusion of intracellular Ca2+ Siam J Appl Math 61:1816-1838

Smith GD (1996) Analytical steady-state solution to the rapid buffering approximation near an open Ca2+ channel. Biophys J 71:3064-72 [Journal] [PubMed]

Sobie EA, Dilly KW, dos Santos Cruz J, Lederer WJ, Jafri MS (2002) Termination of cardiac Ca(2+) sparks: an investigative mathematical model of calcium-induced calcium release. Biophys J 83:59-78 [PubMed]

Steeb WH (1997) Matrix Calculus and Kronecker Product with Applications and C++ Programs

Stern MD, Song LS, Cheng H, Sham JS, Yang HT, Boheler KR, Ríos E (1999) Local control models of cardiac excitation-contraction coupling. A possible role for allosteric interactions between ryanodine receptors. J Gen Physiol 113:469-89 [PubMed]

Stewart W (1994) Introduction to the Numerical Solution of Markov Chains

Sun XP, Callamaras N, Marchant JS, Parker I (1998) A continuum of InsP3-mediated elementary Ca2+ signalling events in Xenopus oocytes. J Physiol 509 ( Pt 1):67-80 [PubMed]

Swillens S, Champeil P, Combettes L, Dupont G (1998) Stochastic simulation of a single inositol 1,4,5-trisphosphate-sensitive Ca2+ channel reveals repetitive openings during 'blip-like' Ca2+ transients. Cell Calcium 23:291-302 [PubMed]

Swillens S, Dupont G, Combettes L, Champeil P (1999) From calcium blips to calcium puffs: theoretical analysis of the requirements for interchannel communication. Proc Natl Acad Sci U S A 96:13750-5 [PubMed]

Tang Y, Othmer HG (1994) A model of calcium dynamics in cardiac myocytes based on the kinetics of ryanodine-sensitive calcium channels. Biophys J 67:2223-35 [Journal] [PubMed]

Tang Y, Stephenson JL, Othmer HG (1996) Simplification and analysis of models of calcium dynamics based on IP3-sensitive calcium channel kinetics. Biophys J 70:246-63 [Journal] [PubMed]

Wagner J, Keizer J (1994) Effects of rapid buffers on Ca2+ diffusion and Ca2+ oscillations. Biophys J 67:447-56 [Journal] [PubMed]

Wang SQ, Song LS, Xu L, Meissner G, Lakatta EG, Ríos E, Stern MD, Cheng H (2002) Thermodynamically irreversible gating of ryanodine receptors in situ revealed by stereotyped duration of release in Ca(2+) sparks. Biophys J 83:242-51 [Journal] [PubMed]

White JA, Rubinstein JT, Kay AR (2000) Channel noise in neurons. Trends Neurosci 23:131-7 [PubMed]

Yao Y, Choi J, Parker I (1995) Quantal puffs of intracellular Ca2+ evoked by inositol trisphosphate in Xenopus oocytes. J Physiol 482 ( Pt 3):533-53 [PubMed]

(84 refs)