Definition
A deterministic reaction-diffusion simulator is a software designed to approximate the dynamics of a system governed by the diffusion and interaction of species within or across domains in a deterministic fashion.
Detailed Description
In a neural tissue, much physiological activity is governed or moderated by diffusion and interaction of many types of molecules and ions. Intracellularly, signaling molecules and ions such as cAMP, G-proteins, and calcium diffuse and moderate the activity of ion channels and other proteins. They also interact with receptors on organelles, as seen with calcium-induced calcium release. Extracellularly, bulk diffusion of glutamate, calcium, sodium, and potassium has both pathological and physiological effects. In addition to diffusion through the aqueous media of intracellular and extracellular space, there is also diffusion of signaling molecules and of ion-channel-forming proteins within the membrane. Modeling and simulating such complex...
References
Blackwell KT, Kotaleski JH (2003) Modeling the dynamics of second messenger pathways. In: Kötter R (ed) Neuroscience databases: a practical guide. Springer US, Boston, pp 63–79. https://doi.org/10.1007/978-1-4615-1079-6_5
Bower JM, Cornelis H, Beeman D (2013) GENESIS, the GEneral NEural SImulation System. In: Jaeger D, Jung R (eds) Encyclopedia of computational neuroscience. Springer New York, New York, pp 1–8. https://doi.org/10.1007/978-1-4614-7320-6_255-1
Carnevale N, Hines M (2006) The NEURON book. Cambridge University Press, Cambridge
Crank J, Nicolson P (1996) A practical method for numerical evaluation of solutions of partial differential equations of the heat-conduction type. Adv Comput Math 6:207–226. https://doi.org/10.1007/BF02127704
Douglas J, Gunn JE (1964) A general formulation of alternating direction methods. Numer Math 6:428–453. https://doi.org/10.1007/BF01386093
Fife P (1979) Mathematical aspects of reacting and diffusing systems. Springer, Berlin
Hepburn I, Chen W, Wils S, De Schutter E (2012) STEPS: efficient simulation of stochastic reaction–diffusion models in realistic morphologies. BMC Syst Biol 6:36. https://doi.org/10.1186/1752-0509-6-36
Hindmarsh AC, Petzold LR (2005) LSODAR, ordinary differential equation solver for stiff or non-stiff system with root-finding. NEA 41:31
Hindmarsh AC, Brown PN, Grant KE, Lee SL, Serban R, Shumaker DE, Woodward CS (2005) SUNDIALS: suite of nonlinear and differential/algebraic equation solvers. ACM Trans Math Softw 31:363–396. https://doi.org/10.1145/1089014.1089020
Hoops S, Sahle S, Gauges R, Lee C, Pahle J, Simus N, Singhal M, Xu L, Mendes P, Kummer U (2006) COPASI – a COmplex PAthway SImulator. Bioinformatics 22:3067–3074. https://doi.org/10.1093/bioinformatics/btl485
Kerr RA, Bartol TM, Kaminsky B, Dittrich M, Chang J-CJ, Baden SB, Sejnowski TJ, Stiles JR (2008) Fast Monte Carlo simulation methods for biological reaction-diffusion systems in solution and on surfaces. SIAM J Sci Comput 30:3126–3149. https://doi.org/10.1137/070692017
Kotelenez P (1986) Law of large numbers and central limit theorem for linear chemical reactions with diffusion. Ann Probab 14:173–193
Langtangen HP, Logg A (2016) Solving PDEs in Python. Springer International Publishing, Cham. https://doi.org/10.1007/978-3-319-52462-7
Loew LM, Schaff JC (2001) The Virtual Cell: a software environment for computational cell biology. Trends Biotechnol 19:401–406. https://doi.org/10.1016/S0167-7799(01)01740-1
McDougal RA, Hines ML, Lytton WW (2013) Reaction-diffusion in the NEURON simulator. Front Neuroinform 7:28. https://doi.org/10.3389/fninf.2013.00028
Newton AJH, McDougal RA, Hines ML, Lytton WW (2018) Using NEURON for reaction-diffusion modeling of extracellular dynamics. Front Neuroinform 12:41. https://doi.org/10.3389/fninf.2018.00041
Rathinam M, Petzold LR, Cao Y, Gillespie DT (2003) Stiffness in stochastic chemically reacting systems: the implicit tau-leaping method. J Chem Phys 119: 12784–12794. https://doi.org/10.1063/1.1627296
Ray S, Bhalla US (2008) PyMOOSE: interoperable scripting in Python for MOOSE. Front Neuroinform 2. https://doi.org/10.3389/neuro.11.006.2008
Starruß J, de Back W, Brusch L, Deutsch A (2014) Morpheus: a user-friendly modeling environment for multiscale and multicellular systems biology. Bioinformatics 30:1331–1332. https://doi.org/10.1093/bioinformatics/btt772
Vayttaden SJ, Bhalla US (2004) Developing complex signaling models using GENESIS/Kinetikit. Sci STKE 2004:pl4. https://doi.org/10.1126/stke.2192004pl4
Acknowledgments
This work was partially supported by NIMH-R01MH086638, NIDCD-R01DC012947-06A1, and ARO-W911NF-19-1-0402.
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Anwar, H., Lytton, W.W., McDougal, R.A. (2022). Deterministic Reaction-Diffusion Simulators. In: Jaeger, D., Jung, R. (eds) Encyclopedia of Computational Neuroscience. Springer, New York, NY. https://doi.org/10.1007/978-1-0716-1006-0_185
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