Search: CaMKII[Title] AND activation[Title] AND dynamics[Title] AND independent[Title] AND holoenzyme[Title] AND structure[Title] AND infinite[Title] AND subunit[Title] AND holoenzyme[Title] AND approximation[Title]

^{1}Richard D Berlin Center for Cell Analysis and Modeling, University of Connecticut Health Center, Farmington, CT 06030, USA. michalski@uchc.edu

Abstract

The combinatorial explosion produced by the multi-state, multi-subunit character of CaMKII has made analysis and modeling of this key signaling protein a significant challenge. Using rule-based and particle-based approaches, we construct exact models of CaMKIIholoenzymedynamics and study these models as a function of the number of subunits per holoenzyme, N. Without phosphatases the dynamics of activation are independent of the holoenzymestructure unless phosphorylation significantly alters the kinase activity of a subunit. With phosphatases the model is independent of holoenzyme size for N > 6. We introduce an infinitesubunitholoenzymeapproximation (ISHA), which simplifies the modeling by eliminating the combinatorial complexities encountered in any finite holoenzyme model. The ISHA is an excellent approximation to the full system over a broad range of physiologically relevant parameters. Finally, we demonstrate that the ISHA reproduces the behavior of exact models during synaptic plasticity protocols, which justifies its use as a module in large models of synaptic plasticity.

(A) A schematic of the CaMKIIholoenzymestructure. For simplicity, the holoenzyme is shown with 6 subunits instead of 12. The subunit numbering is arbitrary. A, association domain. K, kinase domain. (B) Six of the physiologically relevant states of CaMKII considered here. D_{UU} - Autoinhibited. C_{U} - CaM-bound, unphosphorylated. C_{P} - CaM-bound, phosphorylated on T286. D_{PU} - Phosphorylated on T286. D_{PP}- Phosphorylated on T286, T305, and T306. D_{UP} - Phosphorylated on T305 and T306. States D_{UU} and D_{UP} are inactive; the other states have varying activity binding to CaM. CaM_{I} binds Ca^{2+} in a standard bimolecular levels. (C) Calcium reaction to become CaM_{I}_{+1}. (D) Reaction diagram describing conversion between the six states of CaMKII. Phosphatase-mediated dephosphorylations are not shown. See the text for details.

Time dependent autophosphorylation of CaMKII using the three state model

The fraction of phosphorylated subunits after a 1 second and 6 second autophosphorylation reaction is plotted as a function of CaM_{4} for a system without phosphatase. The inset shows an expanded view of the values for the 1 second reaction at 1 μM CaM_{4}. At this scale the minute difference between the dimer result and the other results is visible. The results from all other holoenzyme sizes remain indistinguishable.

Frequency dependent phosphorylation of CaMKII using the three state model

The fraction of phosphorylated CaMKII subunits is plotted as a function of the frequency of 2 μM CaM_{4} pulses, for pulse durations of 500 ms, 200 ms, and 80 ms. The total number of pulses was varied to keep the total time of CaM_{4} exposure constant at 6 seconds: 12 pulses for 500 ms, 30 pulses for 200 ms, and 75 pulses for 80 ms. The frequency was varied by changing the time between the pulses. This sets maximum frequencies of 2 s^{−1}, 5 s^{−1}, and 12.5 s^{−1} for the 500 ms, 200 ms, and 80 ms runs, respectively.

Time dependent autophosphorylation of CaMKII using the three state model with r_{2}

= 0. The fraction of phosphorylated CaMKII subunits after a 6 second autophosphorylation reaction is plotted as a function of CaM_{4} for the limiting case r_{2} = 0.

The effect of phosphatase on CaMKII autophosphorylation in the three state model

(A) Equilibrium fraction of phosphorylated CaMKII subunits as a function of CaM_{4} for three concentrations of phosphatase: 0.1 μM, 1.0 μM, and 10 μM. (B) The curve for 0.1 μM PP1 is replotted on a log-log scale to illustrate the dramatic differences in model results at low CaM_{4} and low PP1.

The CaMKII system is nearly independent of holoenzyme size

F_{P} (blue) and F_{C} (red) obtained using a stochastic, particle-based simulation are plotted as a function of holoenzyme size after a 6 second autophosphorylation reaction without phosphatases (A) or in equilibrium with phosphatases (B). Systems in (A) contained 0.1 μM CaM_{4}. Systems in (B) contained 0.01 μM CaM_{4} and 1.0 μM PP1. Error bars represent the standard deviation of 5 simulations (A) or the standard deviation over the last 200 seconds (once the system reached equilibrium) of a 1000 second simulation (B).

Comparison of the ISHA to the hexamer in a three state model

(A) F_{P} as a function of CaM_{4} for a 1 second (open symbols) and 6 second (closed symbols) autophosphorylation reaction. (B) Equilibrium value of F_{P} as a function of CaM_{4} for varying amounts of PP1.

Comparison of the ISHA to the trimer in a six state model

(A–B) Fraction of phospho-T286 subunits as a function of Ca^{2+} after a 10 second phosphorylation reaction without PP1 (A) or in equilibrium with PP1 (B). (C–D) Fraction of phospho-T305 subunits as a function of Ca^{2+} after a 10 second phosphorylation reaction without PP1 (C) or in equilibrium with PP1 (D). All simulations contained 0.005 μM total CaMKII and 1.0 μM total CaM. Simulations in (B) and (D) contained 1.0 μM PP1.

Comparing the ISHA to the trimer under proto-typical synaptic plasticity protocols

(A–B) LTP protocol: at 1 s the system is subjected to 10 μM Ca^{2+} pulses at 100 Hz for 0.5 seconds. The duration of each pulse was 50 ms. (A) The fraction of active CaMKII, defined as the sum of all active CaMKII species, is plotted as a function of time for the trimer (black) and the ISHA (red). (B) The fraction of phospho-T286 (solid lines) and the fraction of phospho-T305 (dashed lines) is plotted as a function of time for the trimer (black) and the ISHA (red). (C–D) LTD protocol: at 1 s the system is subjected to 3 μM Ca^{2+} pulses at 1 Hz for 300 seconds. The duration of each pulse was 300 ms. (C) The fraction of active CaMKII as a function of time for the trimer (black) and the ISHA (red). The inset shows an expanded view between 175 and 181 seconds, and shows the 1 Hz oscillation in activated CaMKII. (D) The fraction of phospho-T286 (solid lines) and phospho-T305 (dashed lines) as a function of time for the trimer (black) and the ISHA (red). Total protein concentrations were the same for both protocols: 50 μM total CaMKII, 5 μM total CaM, and 0.5 μM PP1.

CaMKII[Title] AND activation[Title] AND dynamics[Title] AND independent[Title] AND holoenzyme[Title] AND structure[Title] AND infinite[Title] AND subunit[Title] AND holoenzyme[Title] AND approximation[Title]

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