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Kim “Avrama” Blackwell George Mason University

Modelling Calcium Concentration. Kim “Avrama” Blackwell George Mason University. Importance of Calcium. Calcium influences channel behaviour, and thereby spike dynamics Short term influences on calcium dependent potassium channels

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Kim “Avrama” Blackwell George Mason University

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  1. Modelling Calcium Concentration Kim “Avrama” BlackwellGeorge Mason University

  2. Importance of Calcium • Calcium influences channel behaviour, and thereby spike dynamics • Short term influences on calcium dependent potassium channels • Long term influences such as potentiation and depression via kinases • Electrical activity influences calcium concentration via ICa • Phosphorylation influences calcium concentration via kinetics of calcium permeable channels

  3. _ _ _ _ _ + + + + + Feedback Loops of Calcium Dynamics Calcium Slow Kinases Fast Ca2+ SK, BK channels Membrane Potential Potassium, Sodium channels Synaptic channels, Calcium channels

  4. Control of Calcium Dynamics

  5. Control of Calcium Dynamics • Calcium Sources • Calcium Currents • Multiple types of voltage dependence calcium channels (L, N, P, Q, R, T) • Calcium permeable synaptic channels (NMDA) • Release from Intracellular Stores (smooth endoplasmic reticulum) • IP3 Receptor Channel (IP3R) • Ryanodine Receptor Channel (RyR)

  6. Control of Calcium Dynamics • Calcium Sinks • Pumps • Smooth Endoplasmic Calcium ATPase (SERCA) • Plasma Membrane Calcium ATPase (PMCA) • Sodium-Calcium exchanger • Source or Sink • Buffers - bind calcium when concentration is high, releases calcium as concentration decreases • Calmodulin – active • Calbindin - inactive • Diffusion – moves calcium from high concentration to low concentration regions

  7. Calcium Currents • L type (CaL1.x) • High threshold, Long lasting, no voltage dependent inactivation • T type (CaL3.x) • Low threshold, Transient, prominent voltage dependent inactivation Vm Vm

  8. Calcium Currents N type (Cal2.x) High threshold (but lower than L type), moderate voltage dependent inactivation (Neither long lasting nor transient) P/Q type (Cal2.x) P type found in cerebellar Purkinje cells Properties similar to L type channel R type (Cal2.x) Used to be “Residual” current Now subunit identified

  9. •Flux has units of moles per unit time, converted to concentration using rxnpool, Ca_concen, diffshell, or pool object

  10. Calcium Release through Receptor Channels

  11. Calcium Release • Calcium Release Receptor Channels are modelled as multi-state molecules • One state is the conducting state • For IP3 receptor state transitions depend on calcium concentration and IP3 concentration • For Ryanodine receptor, state transitions depend on calcium concentration

  12. Dynamics of Release Channels • Both IP3R and RyR have two calcium binding sites: • Binding to one site is fast, causes fast channel opening • Binding to other site is slower, causes slow channel closing • IP3R has an additional binding site for IP3

  13. IP3 Receptor • 8 state model of DeYoung and Keizer, 1992 • Figure from Li and Rinzel, 1994

  14. Dynamics of Release Channels • Dynamics similar to sodium channel: • IP3 with low calcium produces small channel opening • Channel opening increases calcium concentration • Higher concentration causes larger channel opening • Positive feed back produces calcium spike

  15. Dynamics of Release Channels • High calcium causes slower channel closing • Slow negative feedback • Channel inactivates • Inactivation analogous to sodium channel inactivation • SERCA pumps calcium back into ER • Calcium concentration returns to basal level

  16. Calcium Extrusion Mechanisms • Plasma Membrane Calcium ATPase (PMCA) pump and sodium calcium exchanger (NCX) are the primary mechanism for re-equilibrating calcium in spines and thin dendrites (Scheuss et al. 2006) • These mechanisms depress with high activity or calcium concentration • Decay of calcium transient is slower • Positive feedback elevates calcium in small compartments

  17. Calcium ATPase Pumps • Plasma membrane (PMCA) • Extrudes calcium to extracellular space • Binds one calcium ion for each ATP • Affinity ~300 -600 nM • Smooth Endoplasmic Reticulum (SERCA) • Sequesters calcium in SER • Binds two calcium ions for each ATP • Affinity ~100 nM

  18. Sodium Calcium Exchange (NCX) • Stoichiometry • 3 sodium exchanged for 1 calcium • Charge transfer • Unequal => electrogenic • One proton flows in for each transport cycle • Small current produces small depolarization • Theoretical capacity ~50x greater than PMCA

  19. Sodium Calcium Exchange (NCX) • Depolarization may reverse pump direction • Ion concentration change may reverse direction • Increase in Naint or decrease in Naext • Increase in internal sodium may explain activity dependent depression • Increase in Caext or decrease in Caint

  20. Other formulations in Campbell et al. 1988 J Physiol., DiFrancesco and Noble 1985 Philos Trans R Soc Lond B, Weber et al. 2001 J Gen Physiol

  21. Calcium Buffers • Calmodulin is a major calcium binding protein • Binds 4 calcium ions per molecule • High affinity for target enzymes • Calcium-Calmodulin Dependent Protein Kinase (CaMKII, CaMKIV) • Phosphodiesterase (PDE) • Adenylyl Cyclase (AC) • Protein Phosphatase 2B (PP2B = calcineurin) • KD1 = 1.5 uM, KD2 = 10 uM, • Recent estimates in Faas, Raghavachari, Lisman, Mody (2011) Nat Neurosci.

  22. Calcium Buffers • Calbindin • Binds 4 calcium ions per molecule • Not physiologically active • 40 M in CA1 pyramidal neurons (Muller et al. 2006) • Diffusion coefficient = 20 m2/s • KD = 700 nM, kon = 2.7 x107 /M-sec • Parvalbumin • In fast spiking interneurons

  23. Diffusion • Calcium decay in spines exhibits fast and slow components (Majewska et al. 2000) • Fast component due to • Buffered diffusion of calcium from spine to dendrite, which depends on spine neck geometry • Pumps, which are independent of spine neck geometry • Slow component matches dendritic calcium decay • Solely controlled by calcium extrusion mechanisms in the dendrite

  24. Radial and Axial Diffusion Methods in Neuronal Modeling, Koch and Segev Chapter 6 by DeSchutter and Smolen

  25. Derivation of Diffusion Equation • Diffusion in a cylinder • Derive equation by looking at fluxes in and out of a slice of width Dx Boundary Value Problems, Powers

  26. Derivation of Diffusion Equation • Flux into left side of slice is q(x,t) • Flux out of right side is q(x+Dx,t) • Fluxes may be negative if flow is in direction opposite to arrows • Area for diffusional flux is A Boundary Value Problems, Powers

  27. Control of Calcium Dynamics

  28. Genesis Calcium Objects • Ca_concen • Simplest implementation of calcium • Fields • Time constant of decay • Minimum calcium • B = 1 / (z F vol): volume to produce 'reasonable' calcium concentration • Inputs • Calcium current

  29. Genesis Calcium Objects • Code of all the following is in src/concen • Concpool • Calcium concentration without diffusion • Fields: Shape and size • Inputs: • Buffer rate constants, bound and free • MMpump coefficients • Influx and outflux of stores

  30. Genesis Calcium Objects • difshell • concentration shell. Has ionic current flow, one-dimensional diffusion, first order buffering and pumps, store influx • Calculates volume and surface areas from diameter (dia), thick (length) and shape_mode (either slab or shell) • Combines rxnpool, reaction and diffusion into one object, thus must define kb, kf, diffusion constant • To store buffer concentrations, use • fixbuffer • Non-diffusible buffer (use with difshell) • difbuffer • Diffusible buffer (use with difshell)

  31. Chemesis Calcium Objects • Calcium buffers implemented using • rxnpool • conservepool • Reaction • Kinetikit: • Pools • reac

  32. Morphology of Model Cell

  33. Calcium Dynamics in Model Cell Ca2+

  34. Calcium Buffers • CalTut.txt explains all tutorials step-by-step • Cal1-SI.g • Creates pools of buffer, calcium and calcium bound buffer • Creates bimolecular reaction for buffering

  35. Chemesis Calcium Objects • Diffusion • Parameters (Fields) • Diffusion constant, D • Units: 1 for SI, 1e-3 for mMole, etc. • Dunits: 1 for meters, 1e-3 for mm, etc. • Messages (Inputs) • Length, concentration, surface area from two reaction pools • Calculates • Flux from one pool to another • D SA Conc / len

  36. Calcium Buffers and Diffusion • Cal2-SI.g • Two compartments: soma and dendrite • Calcium binding to buffer is implemented in function • Diffusion between soma and dendrite • Cal2difshell.g • Same system, using difshell and difbuffer • Computationally more efficient

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