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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 - PowerPoint PPT Presentation
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Kim “Avrama” Blackwell
George Mason University
Modelling Calcium Concentration
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
Feedback Loops of Calcium DynamicsCalcium
Ca2+
Kinases
SK, BK
channelsMembrane
Potential
+
+
+
+
+
_
_
_
_
_
Potassium,
Sodium channels
Synaptic channels,
Calcium channels
Fast
Slow
Control of Calcium Dynamics
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)
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
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
CaL1.2
-10
-8
-6
-4
-2
0
0 5 10 15 20
Time
Cu
rren
t (n
A) 0
-20
20
CaT
-0.8
-0.6
-0.4
-0.2
0
0.00 5.00 10.00 15.00 20.00
Time (ms)
Cu
rren
t (n
A)
0
-20
20
VmVm
Calcium Currents
00.10.20.30.40.50.60.70.80.9
1
-80 -30 20
Membrane Potential (mV)
Ste
ady
Sta
te
CaR
CaL1.2
CaT
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
•Flux has units of moles per unit time, converted to concentration
using rxnpool, Ca_concen, diffshell, or pool object
Calcium Release through Receptor
Channels
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
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
IP3 Receptor
8 state model of DeYoung and Keizer, 1992
Figure from Li and Rinzel, 1994
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
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
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
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
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
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
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
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.
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
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
Radial and Axial Diffusion
Methods in Neuronal Modeling, Koch and SegevChapter 6 by DeSchutter and Smolen
Derivation of Diffusion Equation
• Diffusion in a cylinder
– Derive equation by looking at fluxes in and out of a slice of width x
Boundary Value
Problems, Powers
Derivation of Diffusion Equation
• Flux into left side of slice is q(x,t)
• Flux out of right side is q(x+x,t)
– Fluxes may be negative if flow is in direction opposite to arrows
• Area for diffusional flux is A
Boundary Value
Problems, Powers
Control of Calcium Dynamics
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
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
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)
Chemesis Calcium Objects
Calcium buffers implemented using rxnpool conservepool Reaction
Kinetikit: Pools reac
Morphology of Model Cell
Calcium Dynamics in Model Cell
Ca2+
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
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
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
Chemesis Calcium Objects
• CICR implements calcium release states using Markov kinetic channel formalism
States
Forward
rate
constants
Chemesis Calcium Objects
• CICR implements calcium release states using Markov kinetic channel formalism
One element for each state, Rxx
One of the elements may be conserved
• Parameters (Fields) 'Forward' rate constants,
State vector, e.g. 001 for 1 Ca++ and 0 IP3
bound
Fraction of receptors in this state (calculated)
Whether this element is conserved
Chemesis Calcium Objects• CICR (cont.)
• Messages (Inputs) required:
• IP3 concentration
• Cytosolic Ca++ concentration
• fraction of molecules in states that can transition to this state
• rate constant governing transition from other states to this state
• Calculates
• Fraction of molecules in the state
Chemesis Calcium Objects• CICRFLUX implements calcium release
• Messages (inputs) required:
• Calcium concentration of ER
• Calcium concentration of Cytosol
• Fraction of channels in open state, X
• Parameters (Fields)
• Permeability, P
• Units: 1 for moles, 1e-3 for mmoles, etc
• Number of independent subunits, q
• Calculates Ca flux = P*Xq (CaER-CaCyt)
Calcium Release
Cal3.g Illustrates how to set up calcium
release using cicr object Requires ER compartment with calcium
and buffers Calcium concentration increases, and
then stays elevated due to lack of pumps
Chemesis Calcium objects MMPUMP2 used for SERCA or PMCA
Pump Fields
Affinity (half _conc) Power (exponent) Maximum rate Units (1 for moles, 1e-3 for mmoles, etc)
Messages (inputs) Concentration
Calculates flux due to pump Different than the mmpump in genesis
Genesis mmpump has no hill coefficient
Chemesis Calcium objects NCX (not in any tutorial)
Fields Affinity (kmhill), and hill coefficient (hill) Stoichiometry (ratio of sodium to calcium) Vunits (1 for volts, 1e-3 for mv) Gbar (maximal conductance) Gamma (partition coefficient) T (temp)
Messages (inputs) Concentration of Na, Ca, both inside and
outside Vm
Calculates current due to pump
Chemesis Calcium Objects
• Leak implemented using CICRFLUX
• Messages (inputs) required: Calcium of cytosol
Calcium of ER or EC space
Value of 1.0 instead of open state
• Parameters (Fields)
Maximal Permeability (PL)
Hill coefficient (should be 1.0)
Calcium Release and SERCA
Cal4.g Implements IICR from Cal4.g Adds SERCA pump to remove calcium
from cytosol
Integrating Calcium Mechanisms
• RXNPOOL takes flux messages from various calcium sources VDCC sends message CURRENT, with fields
current and charge
Diffusion and calcium release send message RXN2MOLES or RXN2, with fields difflux1 and difflux2, or fluxconc1 and fluxconc2, respectively
Mmpump sends message RXN0MOLES with field moles_out (to cytosol) or moles_in
Voltage Dependent Calcium Channels
Cal7.g, Cal8.g Two concentration compartments, but
no calcium release channels Requires two voltage compartments Uses the Goldman-Hodgkin-Katz
formulation for driving potential Depolarizes the cell with current
injection to activate calcium channel
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