Diffusion-activation model of CaMKII translocation waves in dendrites
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1 Diffusion-activation model of CaMKII translocation waves in dendrites Paul Bressloff Berton Earnshaw Department of Mathematics University of Utah June 2, 2009 Bressloff, Earnshaw (Utah) Diffusion-activation model of CaMKII waves June 2, / 21
2 The amazing brain Introduction Bressloff, Earnshaw (Utah) Diffusion-activation model of CaMKII waves June 2, / 21
3 Introduction Neurons communicate at synapses Neuronal communication Bressloff, Earnshaw (Utah) Diffusion-activation model of CaMKII waves June 2, / 21
4 Introduction Communication at a synapse Neuronal communication Kandel, Schwartz & Jessel (2000) Bressloff, Earnshaw (Utah) Diffusion-activation model of CaMKII waves June 2, / 21
5 Synaptic plasticity Introduction Synaptic plasticity Collingridge et al., Nat. Rev. Neurosci. (2004) Bressloff, Earnshaw (Utah) Diffusion-activation model of CaMKII waves June 2, / 21
6 Introduction Synaptic plasticity Excitatory synapses and dendritic spines Most excitatory synapses of CNS located in dendritic spines Matus, Science (2000) Bressloff, Earnshaw (Utah) Diffusion-activation model of CaMKII waves June 2, / 21
7 Heterosynaptic plasticity Introduction Synaptic plasticity V (mv) ms 5 mv test control - 50 µm Time (min) Engert & Bonhoeffer, Nature (1997) Bressloff, Earnshaw (Utah) Diffusion-activation model of CaMKII waves June 2, / 21
8 Introduction CaMKII holoenzyme Kolodziej et al., J Biol Chem (2000) family of 28 isoforms derived from four genes (α, β, γ, δ) holoenzyme formed from two hexameric rings targets substrates responsible for expression of LTP necessary and sufficient for LTP Bressloff, Earnshaw (Utah) Diffusion-activation model of CaMKII waves June 2, / 21
9 Kinetics of CaMKII subunit Introduction Lisman et al., Nat Rev Neurosci (2002) Bressloff, Earnshaw (Utah) Diffusion-activation model of CaMKII waves June 2, / 21
10 Activation states of CaMKII Introduction "Primed" Ca/CaM dependent "Activated" Ca/CaM independent via autophosphorylation Lisman et al., Nat Rev Neurosci (2002) Bressloff, Earnshaw (Utah) Diffusion-activation model of CaMKII waves June 2, / 21
11 Experiments Rose et al., Neuron (2009) Bressloff, Earnshaw (Utah) Diffusion-activation model of CaMKII waves June 2, / 21
12 Diffusion-activation model Diffusion-activation model of 30µm soma Ca 2+ spike dendrite x = 0 x = L translocation diffusion-activation primed CaMKII activated CaMKII Bressloff, Earnshaw (Utah) Diffusion-activation model of CaMKII waves June 2, / 21
13 Diffusion-activation model Equations for diffusion-activation model p t = D 2 p x 2 kap a t = D 2 a + kap ha x2 s t = ha p = concentration of primed CaMKII in shaft a = concentration of activated CaMKII in shaft s = concentration of activated CaMKII in spines k = activation rate h = translocation rate Bressloff, Earnshaw (Utah) Diffusion-activation model of CaMKII waves June 2, / 21
14 Simulation of model for CaMKIIα Diffusion-activation model CaMKII [norm. conc.] total in spines total in dendrite primed in dendrite activated in dendrite 10 sec 65 sec CaMKII [norm. conc.] sec x [µm] 348 sec x [µm] D = 1µm 2 /s, h = 0.03/s, k = 0.28/s c = 0.9µm/s Bressloff, Earnshaw (Utah) Diffusion-activation model of CaMKII waves June 2, / 21
15 Wave speed Fisher s equation in absence of translocation p t = D 2 p x 2 kap a t = D 2 a + kap ha x2 s t = ha When h = 0, p + a is constant (normalized to one). Bressloff, Earnshaw (Utah) Diffusion-activation model of CaMKII waves June 2, / 21
16 Wave speed Fisher s equation in absence of translocation p t = D 2 p x 2 kap a t = D 2 a + kap ha x2 s t = ha When h = 0, p + a is constant (normalized to one). Substituting p = 1 a into equation for a yields Fisher s equation a t = D 2 a + ka(1 a) x2 Bressloff, Earnshaw (Utah) Diffusion-activation model of CaMKII waves June 2, / 21
17 Wave speed Fisher s equation in absence of translocation p t = D 2 p x 2 kap a t = D 2 a + kap ha x2 s t = ha When h = 0, p + a is constant (normalized to one). Substituting p = 1 a into equation for a yields Fisher s equation a t = D 2 a + ka(1 a) x2 Fisher s equation supports traveling fronts with speed c = 2 Dk Bressloff, Earnshaw (Utah) Diffusion-activation model of CaMKII waves June 2, / 21
18 Wave speed Wave speed in presence of translocation When h 0, wave speed is c = 2 D(k h) a c/ (Dk) h/k b wave speed c [µm/s] CaMKIIα CaMKIIβ activation rate k [1/s] Bressloff, Earnshaw (Utah) Diffusion-activation model of CaMKII waves June 2, / 21
19 Wave speed Calculating wave speed c = 2 D(k h) Can verify wave speed analytically by 1 changing into traveling wave coordinates z = x ct c dp dz = D d2 p dz 2 kap c da dz = D d2 a + kap ha dz2 2 linearizing about the invaded state (p, a) = (1, 0) 3 calculating eigenvalues 0, c d, c ± c 2 4D(k h) 2D Bressloff, Earnshaw (Utah) Diffusion-activation model of CaMKII waves June 2, / 21
20 Wave speed Calculating wave speed c = 2 D(k h) Can verify wave speed analytically by 1 changing into traveling wave coordinates z = x ct c dp dz = D d2 p dz 2 kap c da dz = D d2 a + kap ha dz2 2 linearizing about the invaded state (p, a) = (1, 0) 3 calculating eigenvalues 0, c d, c ± c 2 4D(k h) 2D If last eigenvalues are complex, a oscillates about zero as z, so c 2 4D(k h) 0 c 2 D(k h) Bressloff, Earnshaw (Utah) Diffusion-activation model of CaMKII waves June 2, / 21
21 Wave speed Calculating wave speed c = 2 D(k h) Can verify wave speed analytically by 1 changing into traveling wave coordinates z = x ct c dp dz = D d2 p dz 2 kap c da dz = D d2 a + kap ha dz2 2 linearizing about the invaded state (p, a) = (1, 0) 3 calculating eigenvalues 0, c d, c ± c 2 4D(k h) 2D If last eigenvalues are complex, a oscillates about zero as z, so c 2 4D(k h) 0 c 2 D(k h) As with Fisher s equation, minimum wave speed is observed Bressloff, Earnshaw (Utah) Diffusion-activation model of CaMKII waves June 2, / 21
22 Wave propagation failure Wave speed Speed c = 2 D(k h) propagation failure when k < h CaMKII [norm. conc.] total in spines total in dendrite primed in dendrite activated in dendrite 10 sec 60 sec CaMKII [norm. conc.] sec x [µm] 240 sec x [µm] Bressloff, Earnshaw (Utah) Diffusion-activation model of CaMKII waves June 2, / 21
23 Summary Minimal diffusion-activation model with translocation supports Formula for wave speed c = 2 D(k h) Wave propagation failure when k < h Bressloff, Earnshaw (Utah) Diffusion-activation model of CaMKII waves June 2, / 21
24 Discussion and future directions Heterosynaptic plasticity and synaptic tagging Comparison to other diffusion-trapping models (e.g. AMPA receptor trafficking) Threshold for wave initiation (modeling Ca 2+ spike, stochastic effects) Physiological dendrites (branching, discrete spines, heterogeneities) Bressloff, Earnshaw (Utah) Diffusion-activation model of CaMKII waves June 2, / 21
25 Thank you! Thanks to Paul Bressloff (Utah, Oxford) NSF Bressloff, Earnshaw (Utah) Diffusion-activation model of CaMKII waves June 2, / 21
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