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Avrama Blackwell George Mason University

Modeling Calcium Concentration and Biochemical Reactions. Avrama Blackwell George Mason University. Objectives. Explain importance of and relation between biochemical reactions and calcium dynamics Present equations describing biochemical reactions and calcium dynamics

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Avrama Blackwell George Mason University

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  1. Modeling Calcium Concentration and Biochemical Reactions Avrama BlackwellGeorge Mason University

  2. Objectives • Explain importance of and relation between biochemical reactions and calcium dynamics • Present equations describing biochemical reactions and calcium dynamics • Describe mechanisms modulating calcium concentration • Demonstrate dynamics using small simulations

  3. Importance of Calcium • Calcium influences channel behavior, 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

  4. Importance of Biochemical Reactions • Some mechanisms of calcium dynamics are modeled as biochemical reactions • Second messengers, .e.g Dopamine, modulate channel behavior • Second messenger pathways are modeled as biochemical reactions

  5. Biochemical Reactions • Bimolecular Reactions • Stoichiometric interactions between substrate molecules to form product molecule • Formation of bond between the substrate molecules • Stoichiometric implies that the reaction specifies the number of each molecule required for reaction • Molecules are consumed in order to make product

  6. Biochemical Reactions • Bimolecular Reactions • Reaction order is the number of simultaneously interacting molecules • First order reaction: single substrate becomes product • Rate constants: rate (units of per sec) at which substrate becomes product • Ratio of rate constants gives concentration of substrates and products at equilibrium

  7. When to Model Biochemical Reactions • Metabotropic Receptors • Protein does not form channel • Protein is linked to GTP binding protein • Effect mediated by • Activated G protein subunits • Down stream second messengers

  8. Ionotropic vs Metabotropic From Nicholls et al. Sinauer

  9. Activation of GTP Binding Protein From Nicholls et al. Sinauer

  10. Direct Modulation of Channel via Active G Protein Subunits From Nicholls et al. Sinauer

  11. From Nicholls et al. Sinauer

  12. From Nicholls et al. Sinauer

  13. Importance of Calcium Dynamics

  14. Control of Calcium Dynamics • Calcium Current • Pumps • Smooth Endoplasmic Calcium ATPase (SERCA) • Plasma Membrane Calcium ATPase (PMCA) • Sodium-Calcium exchanger

  15. Control of Calcium Dynamics • Release from Intracellular Stores • IP3 Receptor Channel (IP3R) • Ryanodine Receptor Channel (RyR) • Buffers • Diffusion

  16. Calcium Current High Threshold, Persistent

  17. Derivation of Diffusion Equation • Diffusion in a cylinder • Derive equation by looking at fluxes in and out of a slice of width Dx

  18. 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

  19. Radial and Axial Diffusion From Koch and Segev, MIT Press Chapter 6 by DeSchutter and Smolen

  20. Calcium Release through IP3R Levitan and Kaczmark, Oxford Press

  21. Calcium Release • Receptors are modeled 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

  22. 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

  23. IP3 Receptor • 8 state model of DeYoung and Keizer • Figure from Li and Rinzel

  24. Flow of calcium ions through release channels Levitan and Kaczmark, Oxford Press

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

  26. 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

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