Approaches and tools for modeling signaling pathways and calcium dynamics in neurons

Journal of Neuroscience Methods

Volumn 220, Issue 2, 2013, Pages 131-140

  Blackwell, K T ^a  

^a GEORGE MASON UNIVERSITY   (United States)

Author keywords

Calcium dynamics; Diffusion; Enzyme kinetics; Second messengers; Signaling pathways; Stochastic simulation

Indexed keywords

ADENYLATE CYCLASE; AMPA RECEPTOR; CALCIUM; CALCIUM ACTIVATED POTASSIUM CHANNEL; CALCIUM CHANNEL L TYPE; CYCLIC AMP DEPENDENT PROTEIN KINASE; CYCLIC AMP DEPENDENT PROTEIN KINASE ANCHORING PROTEIN; G PROTEIN COUPLED RECEPTOR; ION CHANNEL; PHOSPHATASE; PHOSPHOLIPASE A2; PROTEIN KINASE C;

ALGORITHM; CALCIUM TRANSPORT; CELL FRACTIONATION; CHEMICAL REACTION; DENDRITE; ELECTRIC ACTIVITY; ENZYME ACTIVATION; ENZYME MECHANISM; ENZYME SUBSTRATE COMPLEX; GENETIC TRANSCRIPTION; HIPPOCAMPAL CA1 REGION; NERVE CELL PLASTICITY; PHOTOTRANSDUCTION; POSITIVE FEEDBACK; PRIORITY JOURNAL; PROTEIN SYNTHESIS; PYRAMIDAL NERVE CELL; REVIEW; SIGNAL TRANSDUCTION; STOICHIOMETRY;

CALCIUM DYNAMICS; DIFFUSION; ENZYME KINETICS; SECOND MESSENGERS; SIGNALING PATHWAYS; STOCHASTIC SIMULATION;

ANIMALS; CALCIUM; HUMANS; MODELS, BIOLOGICAL; NEURONS; NONLINEAR DYNAMICS; SIGNAL TRANSDUCTION; STOCHASTIC PROCESSES;

EID: 84887617704     PISSN: 01650270     EISSN: 1872678X     Source Type: Journal    
DOI: 10.1016/j.jneumeth.2013.05.008     Document Type: Review

References (113)

1. Abel T., Nguyen P.V., Barad M., Deuel T.A., Kandel E.R., Bourtchouladze R. Genetic demonstration of a role for PKA in the late phase of LTP and in hippocampus-based long-term memory. Cell 1997, 88:615-626.
2. Ajay S.M., Bhalla U.S. A propagating ERKII switch forms zones of elevated dendritic activation correlated with plasticity. HFSP Journal 2007, 1:49-66.
3. Aksamitiene E., Achanta S., Kolch W., Kholodenko B.N., Hoek J.B., Kiyatkin A. Prolactin-stimulated activation of ERK1/2 mitogen-activated protein kinases is controlled by PI3-kinase/Rac/PAK signaling pathway in breast cancer cells. Cellular Signalling 2011, 23:1794-1805.
4. Allam S.L., Ghaderi V.S., Bouteiller J.M., Legendre A., Ambert N., Greget R., et al. A computational model to investigate astrocytic glutamate uptake influence on synaptic transmission and neuronal spiking. Frontiers in Computational Neuroscience 2012, 6:70.
5. Allbritton N.L., Meyer T., Stryer L. Range of messenger action of calcium ion and inositol 1,4,5-triphosphate. Science 1992, 258:1812-1815.
6. Andrews S.S., Addy N.J., Brent R., Arkin A.P. Detailed simulations of cell biology with Smoldyn 2.1. PLoS Computational Biology 2010, 6:e1000705.
7. Antunes G., De Schutter E. A stochastic signaling network mediates the probabilistic induction of cerebellar long-term depression. The Journal of Neuroscience: the Official Journal of the Society for Neuroscience 2012, 32:9288-9300.
8. Bardsley W.G., Leff P., Kavanagh J., Waight R.D. Deviations from Michaelis-Menten kinetics. The possibility of complicated curves for simple kinetic schemes and the computer fitting of experimental data for acetylcholinesterase, acid phosphatase, adenosine deaminase, arylsulphatase, benzylamine oxidase, chymotrypsin, fumarase, galactose dehydrogenase, beta-galactosidase, lactate dehydrogenase, peroxidase and xanthine oxidase. The Biochemical Journal 1980, 187:739-765.
9. Bartol T.M., Land B.R., Salpeter E.E., Salpeter M.M. Monte Carlo simulation of miniature endplate current generation in the vertebrate neuromuscular junction. Biophysical Journal 1991, 59:1290-1307.
10. Berkefeld H., Sailer C.A., Bildl W., Rohde V., Thumfart J.O., Eble S., et al. BKCa-Cav channel complexes mediate rapid and localized Ca2+-activated K+ signaling. Science 2006, 314:615-620.
11. Bhalla U.S. Mechanisms for temporal tuning and filtering by postsynaptic signaling pathways. Biophysical Journal 2002, 83:740-752.
12. Bhalla U.S. Multiscale interactions between chemical and electric signaling in LTP induction, LTP reversal and dendritic excitability. Neural Networks: the Official Journal of the International Neural Network Society 2011, 24:943-949.
13. Bhalla U.S., Iyengar R. Emergent properties of networks of biological signaling pathways. Science 1999, 283:381-387.
14. Bisegna P., Caruso G., Andreucci D., Shen L., Gurevich V.V., Hamm H.E., et al. Diffusion of the second messengers in the cytoplasm acts as a variability suppressor of the single photon response in vertebrate phototransduction. Biophysical Journal 2008, 94:3363-3383.
15. Blackwell K.T. Paired turbulence and light do not produce a supralinear calcium increase in Hermissenda. Journal of Computational Neuroscience 2004, 17:81-99.
16. Blackwell K.T. Calcium: the answer to life, the universe, and everything. 20 years of computational neuroscience 2013, Springer. J.M. Bower (Ed.).
17. Blackwell K.T., Hellgren-Kotaleski J. Modeling the dynamics of second messenger pathways. Neuroscience databases. A practical guide 2002, 63-80. Kluwer Academic Publishers, Boston. R. Kotter (Ed.).
18. Blaustein M.P., Juhaszova M., Golovina V.A., Church P.J., Stanley E.F. Na/Ca exchanger and PMCA localization in neurons and astrocytes: functional implications. Annals of the New York Academy of Sciences 2002, 976:356-366.
19. Bower J.M., Beeman D. The book of genesis: exploring realistic neural models with the general neural simulation system 1998, Springer-Verlag, New York. 2nd ed.
20. Brown S.A., Moraru I.I., Schaff J.C., Loew L.M. Virtual NEURON: a strategy for merged biochemical and electrophysiological modeling. Journal of Computational Neuroscience 2011, 31:385-400.
21. Brown S.A., Morgan F., Watras J., Loew L.M. Analysis of phosphatidylinositol-4,5-bisphosphate signaling in cerebellar Purkinje spines. Biophysical Journal 2008, 95:1795-1812.
22. Byrne M.J., Waxham M.N., Kubota Y. Cellular dynamic simulator: an event driven molecular simulation environment for cellular physiology. Neuroinformatics 2010, 8:63-82.
23. Byrne M.J., Waxham M.N., Kubota Y. The impacts of geometry and binding on CaMKII diffusion and retention in dendritic spines. Journal of Computational Neuroscience 2011, 31:1-12.
24. Chen W.W., Niepel M., Sorger P.K. Classic and contemporary approaches to modeling biochemical reactions. Genes & Development 2010, 24:1861-1875.
25. Chen X., Vinade L., Leapman R.D., Petersen J.D., Nakagawa T., Phillips T.M., et al. Mass of the postsynaptic density and enumeration of three key molecules. Proceedings of the National Academy of Sciences of the United States of America 2005, 102:11551-11556.
26. Costa-Mattioli M., Sossin W.S., Klann E., Sonenberg N. Translational control of long-lasting synaptic plasticity and memory. Neuron 2009, 61:10-26.
27. Cowan A.E., Moraru I.I., Schaff J.C., Slepchenko B.M., Loew L.M. Spatial modeling of cell signaling networks. Methods in Cell Biology 2012, 110:195-221.
28. Daoudal G., Debanne D. Long-term plasticity of intrinsic excitability: learning rules and mechanisms. Learning & Memory 2003, 10:456-465.
29. De Young G.W., Keizer J. A single-pool inositol 1,4,5-trisphosphate-receptor-based model for agonist-stimulated oscillations in Ca2+ concentration. Proceedings of the National Academy of Sciences of the United States of America 1992, 89:9895-9899.
30. Desdouits F., Cheetham J.J., Huang H.B., Kwon Y.G., da Cruz e Silva E.F., Denefle P., et al. Mechanism of inhibition of protein phosphatase 1 by DARPP-32: studies with recombinant DARPP-32 and synthetic peptides. Biochemical and Biophysical Research Communications 1995, 206:652-658.
31. Djurfeldt M., Hjorth J., Eppler J.M., Dudani N., Helias M., Potjans T.C., et al. Run-time interoperability between neuronal network simulators based on the MUSIC framework. Neuroinformatics 2010, 8:43-60.
32. Drawert B., Lawson M.J., Petzold L., Khammash M. The diffusive finite state projection algorithm for efficient simulation of the stochastic reaction-diffusion master equation. The Journal of Chemical Physics 2010, 132:074101.
33. 2+ release. Biophysical Journal 1994, 67:2191-2204.
34. Elf J., Ehrenberg M. Spontaneous separation of bi-stable biochemical systems into spatial domains of opposite phases. Systems Biology 2004, 1:230-236.
35. Faas G.C., Raghavachari S., Lisman J.E., Mody I. Calmodulin as a direct detector of Ca(2+) signals. Nature Neuroscience 2011, 14:301-304.
36. Fallahi-Sichani M., El-Kebir M., Marino S., Kirschner D.E., Linderman J.J. Multiscale computational modeling reveals a critical role for TNF-α receptor 1 dynamics in tuberculosis granuloma formation. Journal of Immunology 2011, 186:3472-3483.
37. Fey D., Croucher D.R., Kolch W., Kholodenko B.N. Crosstalk and signaling switches in mitogen-activated protein kinase cascades. Frontiers in Physiology 2012, 3:355.
38. Giepmans B.N., Adams S.R., Ellisman M.H., Tsien R.Y. The fluorescent toolbox for assessing protein location and function. Science 2006, 312:217-224.
39. Gillespie D.T. Exact stochastic simulation of coupled chemical reactions. The Journal of Physical Chemistry 1977, 81:2340-2361.
40. Gillespie D.T. Approximating accelerated stochastic simulation of chemically reacting systems. Journal of Chemical Physics 2001, 115:1716-1733.
41. Greer P.L., Greenberg M.E. From synapse to nucleus: calcium-dependent gene transcription in the control of synapse development and function. Neuron 2008, 59:846-860.
42. Haberman R. Elementary applied partial differential equations with fourier series and boundary value problems 1997, Prentice Hall. 3d ed.
43. Hamer R.D., Nicholas S.C., Tranchina D., Lamb T.D., Jarvinen J.L. Toward a unified model of vertebrate rod phototransduction. Visual Neuroscience 2005, 22:417-436.
44. Hartmann J., Konnerth A. Determinants of postsynaptic Ca2+ signaling in Purkinje neurons. Cell Calcium 2005, 37:459-466.
45. Harvey C.D., Yasuda R., Zhong H., Svoboda K. The spread of ras activity triggered by activation of a single dendritic spine. Science 2008, 321:136-140.
46. Hattne J., Fange D., Elf J. Stochastic reaction-diffusion simulation with MesoRD. Bioinformatics 2005, 21:2923-2924.
47. Hawk J.D., Abel T. The role of NR4A transcription factors in memory formation. Brain Research Bulletin 2011, 85:21-29.
48. Hemmings H.C., Greengard P. DARPP-32, a dopamine- and adenosine 3':5'-monophosphate-regulated phosphoprotein: regional, tissue, and phylogenetic distribution. The Journal of Neuroscience: the Official Journal of the Society for Neuroscience 1986, 6:1469-1481.
49. Herberg F.W., Maleszka A., Eide T., Vossebein L., Tasken K. Analysis of A-kinase anchoring protein (AKAP) interaction with protein kinase A (PKA) regulatory subunits: PKA isoform specificity in AKAP binding. Journal of Molecular Biology 2000, 298:329-339.
50. Hernjak N., Slepchenko B.M., Fernald K., Fink C.C., Fortin D., Moraru I.I., et al. Modeling and analysis of calcium signaling events leading to long-term depression in cerebellar Purkinje cells. Biophysical Journal 2005, 89:3790-3806.
51. Hirschberg B., Maylie J., Adelman J.P., Marrion N.V. Gating properties of single SK channels in hippocampal CA1 pyramidal neurons. Biophysical Journal 1999, 77:1905-1913.
52. Howard A.D., McAllister G., Feighner S.D., Liu Q., Nargund R.P., van der Ploeg L.H., et al. Orphan G-protein-coupled receptors and natural ligand discovery. Trends in Pharmacological Sciences 2001, 22:132-140.
53. Hulme J.T., Lin T.W., Westenbroek R.E., Scheuer T., Catterall W.A. Beta-adrenergic regulation requires direct anchoring of PKA to cardiac CaV1.2 channels via a leucine zipper interaction with A kinase-anchoring protein 15. Proceedings of the National Academy of Sciences of the United States of America 2003, 100:13093-13098.
54. Iyengar K.A., Harris L.A., Clancy P. Accurate implementation of leaping in space: the spatial partitioned-leaping algorithm. The Journal of Chemical Physics 2010, 132:094101.
55. Jafri M.S. Models of excitation-contraction coupling in cardiac ventricular myocytes. Methods in Molecular Biology 2012, 910:309-335.
56. Jahr C.E., Stevens C.F. Calcium permeability of the N-methyl-D-aspartate receptor channel in hippocampal neurons in culture. Proceedings of the National Academy of Sciences of the United States of America 1993, 90:11573-11577.
57. Jain P., Bhalla U.S. Signaling logic of activity-triggered dendritic protein synthesis: an mTOR gate but not a feedback switch. PLoS Computational Biology 2009, 5:e1000287.
58. Keller D.X., Franks K.M., Bartol T.M., Sejnowski T.J. Calmodulin activation by calcium transients in the postsynaptic density of dendritic spines. PLoS One 2008, 3:e2045.
59. Kerr R.A., Bartol T.M., Kaminsky B., Dittrich M., Chang J.C., Baden S.B., et al. Fast Monte Carlo simulation methods for biological reaction-diffusion systems in solution and on surfaces. SIAM Journal on Scientific Computing 2008, 30:3126.
60. Khan S., Reese T.S., Rajpoot N., Shabbir A. Spatiotemporal maps of CaMKII in dendritic spines. Journal of Computational Neuroscience 2012, 33:123-139.
61. Khan S., Zou Y., Amjad A., Gardezi A., Smith C.L., Winters C., et al. Sequestration of CaMKII in dendritic spines in silico. Journal of Computational Neuroscience 2011, 31:581-594.
62. Kim M., Park A.J., Havekes R., Chay A., Guercio L., Oliveira R.F., et al. Colocalization of PKA with adenylyl cyclase enhances PKA activity during L-LTP induction. PLoS Computational Biology 2011, 7:e1002085.
63. Kinney J.P., Spacek J., Bartol T.M., Bajaj C.L., Harris K.M., Sejnowski T.J. Extracellular sheets and tunnels modulate glutamate diffusion in hippocampal neuropil. The Journal of Comparative Neurology 2013, 521:448-464.
64. Koh W., Blackwell K.T. An accelerated algorithm for discrete stochastic simulation of reaction-diffusion systems using gradient-based diffusion and tau-leaping. The Journal of Chemical Physics 2011, 134:154103.
65. Korenbrot J.I. Speed adaptation, and stability of the response to light in cone photoreceptors: the functional role of Ca-dependent modulation of ligand sensitivity in cGMP-gated ion channels. The Journal of General Physiology 2012, 139:31-56.
66. Lamb T.D. Stochastic simulation of activation in the G-protein cascade of phototransduction. Biophysical Journal 1994, 67:1439-1454.
67. Lamb T.D., Pugh E.N. A quantitative account of the activation steps involved in phototransduction in amphibian photoreceptors. The Journal of Physiology 1992, 449:719-758.
68. Lee S.J., Escobedo-Lozoya Y., Szatmari E.M., Yasuda R. Activation of CaMKII in single dendritic spines during long-term potentiation. Nature 2009, 458:299-304.
69. Lipkow K., Andrews S.S., Bray D. Simulated diffusion of phosphorylated CheY through the cytoplasm of Escherichia coli. Journal of Bacteriology 2005, 187:45-53.
70. Lisman J., Schulman H., Cline H. The molecular basis of CaMKII function in synaptic and behavioural memory. Nature Reviews. Neuroscience 2002, 3:175-190.
71. Liu Z., Pu Y., Li F., Shaffer C.A., Hoops S., Tyson J.J., et al. Hybrid modeling and simulation of stochastic effects on progression through the eukaryotic cell cycle. The Journal of Chemical Physics 2012, 136:034105.
72. Maravall M., Mainen Z.F., Sabatini B.L., Svoboda K. Estimating intracellular calcium concentrations and buffering without wavelength ratioing. Biophysical Journal 2000, 78:2655-2667.
73. Marino S., Hogue I.B., Ray C.J., Kirschner D.E. A methodology for performing global uncertainty and sensitivity analysis in systems biology. Journal of Theoretical Biology 2008, 254:178-196.
74. Micheva K.D., Busse B., Weiler N.C., O'Rourke N., Smith S.J. Single-synapse analysis of a diverse synapse population: proteomic imaging methods and markers. Neuron 2010, 68:639-653.
75. Mironov S.L., Skorova E., Taschenberger G., Hartelt N., Nikolaev V.O., Lohse M.J., et al. Imaging cytoplasmic cAMP in mouse brainstem neurons. BMC Neuroscience 2009, 10:29.
76. Moraru I.I., Schaff J.C., Slepchenko B.M., Blinov M.L., Morgan F., Lakshminarayana A., et al. Virtual Cell modelling and simulation software environment. IET Systems Biology 2008, 2:352-362.
77. Neves S.R., Tsokas P., Sarkar A., Grace E.A., Rangamani P., Taubenfeld S.M., et al. Cell shape and negative links in regulatory motifs together control spatial information flow in signaling networks. Cell 2008, 133:666-680.
78. Nimchinsky E.A., Yasuda R., Oertner T.G., Svoboda K. The number of glutamate receptors opened by synaptic stimulation in single hippocampal spines. The Journal of Neuroscience: the Official Journal of the Society for Neuroscience 2004, 24:2054-2064.
79. Novak B., Tyson J.J., Gyorffy B., Csikasz-Nagy A. Irreversible cell-cycle transitions are due to systems-level feedback. Nature Cell Biology 2007, 9:724-728.
80. Oancea E., Meyer T. Protein kinase C as a molecular machine for decoding calcium and diacylglycerol signals. Cell 1998, 95:307-318.
81. Oliveira R.F., Kim M., Blackwell K.T. Subcellular location of PKA controls striatal plasticity: stochastic simulations in spiny dendrites. PLoS Computational Biology 2012, 8:e1002383.
82. Oliveira R.F., Terrin A., Di B.G., Cannon R.C., Koh W., Kim M., et al. The role of type 4 phosphodiesterases in generating microdomains of cAMP: large scale stochastic simulations. PLoS One 2010, 5:e11725.
83. Pierce K.L., Premont R.T., Lefkowitz R.J. Seven-transmembrane receptors. Nature Reviews. Molecular Cell Biology 2002, 3:639-650.
84. Premont R.T., Gainetdinov R.R. Physiological roles of G protein-coupled receptor kinases and arrestins. Annual Review of Physiology 2007, 69:511-534.
85. Putkey J.A., Kleerekoper Q., Gaertner T.R., Waxham M.N. A new role for IQ motif proteins in regulating calmodulin function. The Journal of Biological Chemistry 2003, 278:49667-49670.
86. Rankovic V., Landgraf P., Kanyshkova T., Ehling P., Meuth S.G., Kreutz M.R., et al. Modulation of calcium-dependent inactivation of L-type Ca2+ channels via beta-adrenergic signaling in thalamocortical relay neurons. PLoS One 2011, 6:e27474.
87. Rossinelli D., Bayati B., Koumoutsakos P. Accelerated stochastic and hybrid methods for spatial simulations of reaction-diffusion systems. Chemical Physics Letters 2008, 451:136-140.
88. Rothberg B.S., Magleby K.L. Gating kinetics of single large-conductance Ca2+-activated K+ channels in high Ca2+ suggest a two-tiered allosteric gating mechanism. The Journal of General Physiology 1999, 114:93-124.
89. Sahle S., Mendes P., Hoops S., Kummer U. A new strategy for assessing sensitivities in biochemical models. Philosophical Transactions. Series A, Mathematical, Physical, and Engineering Sciences 2008, 366:3619-3631.
90. Schmidt H., Arendt O., Eilers J. Diffusion and extrusion shape standing calcium gradients during ongoing parallel fiber activity in dendrites of Purkinje neurons. Cerebellum 2012, 11:694-705.
91. Schmidt H., Stiefel K.M., Racay P., Schwaller B., Eilers J. Mutational analysis of dendritic Ca2+ kinetics in rodent Purkinje cells: role of parvalbumin and calbindin D28k. The Journal of Physiology 2003, 551:13-32.
92. Shalin S.C., Hernandez C.M., Dougherty M.K., Morrison D.K., Sweatt J.D. Kinase suppressor of Ras1 compartmentalizes hippocampal signal transduction and subserves synaptic plasticity and memory formation. Neuron 2006, 50:765-779.
93. Singh P., Hockenberry A.J., Tiruvadi V.R., Meaney D.F. Computational investigation of the changing patterns of subtype specific NMDA receptor activation during physiological glutamatergic neurotransmission. PLoS Computational Biology 2011, 7:e1002106.
94. Sivakumaran S., Hariharaputran S., Mishra J., Bhalla U.S. The database of quantitative cellular signaling: management and analysis of chemical kinetic models of signaling networks. Bioinformatics 2003, 19:408-415.
95. Solovyova N., Verkhratsky A. Neuronal endoplasmic reticulum acts as a single functional Ca2+ store shared by ryanodine and inositol-1,4,5-trisphosphate receptors as revealed by intra-ER [Ca2+] recordings in single rat sensory neurones. Pflugers Archiv: European Journal of Physiology 2003, 446:447-454.
96. Stenesh J. Core topics in biochemistry 1993, 283. Cogno Press.
97. Takahashi K., Arjunan S.N., Tomita M. Space in systems biology of signaling pathways - towards intracellular molecular crowding in silico. FEBS Letters 2005, 579:1783-1788.
98. Tanaka K. Alteration of second messengers during acute cerebral ischemia - adenylate cyclase, cyclic AMP-dependent protein kinase, and cyclic AMP response element binding protein. Progress in Neurobiology 2001, 65:173-207.
99. Tang Y., Othmer H.G. A model of calcium dynamics in cardiac myocytes based on the kinetics of ryanodine-sensitive calcium channels. Biophysical Journal 1994, 67:2223-2235.
100. Tostevin F., ten Wolde P.R., Howard M. Fundamental limits to position determination by concentration gradients. PLoS Computational Biology 2007, 3:e78.
101. Tranchina D., Sneyd J., Cadenas I.D. Light adaptation in turtle cones. Testing and analysis of a model for phototransduction. Biophysical Journal 1991, 60:217-237.
102. Tuckwell H.C. Quantitative aspects of L-type Ca2+ currents. Progress in Neurobiology 2012, 96:1-31.
103. Tzafriri A.R., Edelman E.R. On the validity of the quasi-steady state approximation of bimolecular reactions in solution. Journal of Theoretical Biology 2005, 233:343-350.
104. Uchigashima M., Narushima M., Fukaya M., Katona I., Kano M., Watanabe M. Subcellular arrangement of molecules for 2-arachidonoyl-glycerol-mediated retrograde signaling and its physiological contribution to synaptic modulation in the striatum. The Journal of Neuroscience: the Official Journal of the Society for Neuroscience 2007, 27:3663-3676.
105. Vayttaden S.J., Bhalla U.S. Developing complex signaling models using GENESIS/Kinetikit. Science's STKE: Signal Transduction Knowledge Environment 2004, 2004:l4.
106. von Kriegsheim A., Baiocchi D., Birtwistle M., Sumpton D., Bienvenut W., Morrice N., et al. Cell fate decisions are specified by the dynamic ERK interactome. Nature Cell Biology 2009, 11:1458-1464.
107. Waas W.F., Rainey M.A., Szafranska A.E., Dalby K.N. Two rate-limiting steps in the kinetic mechanism of the serine/threonine specific protein kinase ERK2: a case of fast phosphorylation followed by fast product release. Biochemistry 2003, 42:12273-12286.
108. Wils S., De Schutter E. STEPS: modeling and simulating complex reaction-diffusion systems with python. Frontiers in Neuroinformatics 2009, 3:15.
109. Xia Z., Storm D.R. The role of calmodulin as a signal integrator for synaptic plasticity. Nature Reviews. Neuroscience 2005, 6:267-276.
110. Xie Z., Adamowicz W.O., Eldred W.D., Jakowski A.B., Kleiman R.J., Morton D.G., et al. Cellular and subcellular localization of PDE10A, a striatum-enriched phosphodiesterase. Neuroscience 2006, 139:597-607.
111. Young M.E., Carroad P.A., Bell R.L. Estimation of diffusion coefficients of proteins. Biotechnology and Bioengineering 1980, 22:947-955.
112. Zi Z. Sensitivity analysis approaches applied to systems biology models. IET Systems Biology 2011, 5:336.
113. Zi Z., Zheng Y., Rundell A.E., Klipp E. SBML-SAT: a systems biology markup language (SBML) based sensitivity analysis tool. BMC Bioinformatics 2008, 9:342.