Quantitative validation of the calcium-dependent GluR1 phosphorylation model of bidirectional synaptic plasticity in intact dendritic spines

The 2005 model of Castellani, Quinlan, Bersani, Cooper and Shouval derived steady-state predictions for bidirectional synaptic plasticity from a mass-action and Michaelis-Menten cascade linking postsynaptic calcium through four enzymes (two kinase/phosphatase pairs acting on serines 831 and 845 of the AMPA-receptor subunit GluR1) to receptor phosphorylation and single-channel conductance: moderate calcium favors dephosphorylation (LTD), high calcium favors phosphorylation (LTP). The authors stated five limitations that stand between this model class and a quantitatively validated description of real synapses: kinetic parameters and total enzyme concentrations cannot currently be extracted in intact spines; the well-mixed, population-averaged, deterministic formulation may fail at the small molecule counts and spatial compartmentalization of real spines; the phosphorylation-mediated conductance change excludes AMPA-receptor insertion/removal, presynaptic release-probability changes, and CaMKII-autophosphorylation-based maintenance, which the authors expect to modify, but not negate, the model's results (an open extension of the model rather than a condition of its own validation); direct-Ca versus Ca-CaM enzyme-activation variants make different quantitative predictions and need experimental discrimination; and the steady-state predictions for sustained calcium elevation are untested against physiological transient calcium signals and protocol-dependent plasticity magnitudes. The problem remains open.

Background

Long-term potentiation (LTP) and long-term depression (LTD) are persistent activity-dependent increases and decreases in the strength of excitatory synapses, studied widely as cellular substrates of learning and memory. Fast excitatory transmission in the mammalian brain is largely mediated by AMPA receptors (ionotropic glutamate receptors), tetrameric channels whose GluR1 (also called GluA1) subunit carries two functionally important phosphorylation sites on its intracellular tail: serine 831 (S831), phosphorylated by CaMKII (calcium/calmodulin-dependent protein kinase II) and protein kinase C (PKC), which increases the receptor single-channel conductance, and serine 845 (S845), phosphorylated by protein kinase A (PKA), which increases the channel mean open time. Dephosphorylation is mediated largely by protein phosphatase 1 (PP1), whose activity is inhibited when its binding protein inhibitor-1 is phosphorylated by PKA and restored when inhibitor-1 is dephosphorylated by the calcium-dependent phosphatase calcineurin. The induction signal for bidirectional plasticity is postsynaptic calcium (Ca) entering through NMDA (N-methyl-D-aspartate) receptors: moderate elevations favor phosphatase activation and LTD, large elevations favor kinase activation and LTP, an ordering that echoes the BCM (Bienenstock-Cooper-Munro) theory of visual-cortex plasticity, in which the sign of synaptic modification depends on postsynaptic activity relative to a sliding threshold. Building on the earlier molecular switch model of Lisman (1989) in which CaMKII autophosphorylation stores synaptic memory, Castellani, Quinlan, Bersani, Cooper and Shouval (Learning & Memory 12:423-432, 2005) constructed a biophysical model that starts from postsynaptic Ca and ends at AMPA-receptor single-channel conductance. Two enzyme pairs (a kinase and a phosphatase acting on each of S831 and S845, instantiated with CaMKII, PKC, PKA and PP1 regulated through inhibitor-1 and calcineurin) are described first by first-order mass-action kinetics (transition rates as functions of Ca) and then by Michaelis-Menten kinetics (the standard saturating-enzyme rate law), with each enzyme activation a sigmoidal Hill function of Ca reflecting cooperative binding of multiple Ca ions; a detailed variant derives enzyme activation from the concentration of calcium-bound calmodulin (Ca-CaM, the Ca sensor protein that activates CaMKII and calcineurin) instead of from Ca directly, using measured Ca-CaM relations. The model computes steady-state phosphorylation distributions and the corresponding AMPA-receptor conductance for a sustained Ca elevation, and in every variant moderate Ca yields net dephosphorylation (LTD) and high Ca net phosphorylation (LTP), consistent with experimental LTP/LTD curves and with the site-specific measurements of Lee et al. (2000). Companion work by the same collaboration (the calcium control hypothesis of Shouval, Bear and Cooper (2002) and Shouval et al. (2002)) had translated related biophysical models into dynamical synaptic-weight rules driven by transient Ca signals that reproduce rate- and spike-timing-based induction protocols. The 2005 paper is explicit that its quantitative predictions rest on experimentally unsupported ground. First, the maximal and basal enzyme activities ($V_{max}$, $V_{base}$) cannot be extracted from experimental data because they depend critically on total enzyme concentrations in vivo, and the remaining kinetic parameters ($k_{1/2}$, Hill coefficient $h$) are taken from heterogeneous literature sources. Second, the model treats the dendritic spine (the submicron biochemical compartment hosting the postsynaptic machinery, containing on the order of tens of AMPA receptors and enzyme molecules) as a well-mixed volume with population-averaged receptor counts, so stochastic fluctuations and spatial compartmentalization of enzymes could qualitatively change the phosphorylation steady states; Monte-Carlo reaction-diffusion simulations of single synapses (Franks, Bartol and Sejnowski 2002, using the MCell simulator) had begun to examine such assumptions, and whether these issues are fundamental remained undetermined. Third, only phosphorylation-mediated single-channel conductance change is modeled, although AMPA-receptor insertion and removal at the synapse, presynaptic release-probability changes, and CaMKII-autophosphorylation-based maintenance of potentiation (Malinow and Malenka 2002) are established expression and maintenance mechanisms; the paper states that such additional mechanisms will modify, but not negate, its results, and that it focuses on early postsynaptic signaling events involved in the induction of LTP/LTD. Fourth, the two activation conventions, enzymes activated by Ca directly versus by Ca-CaM, produce markedly different phosphorylation and conductance curves; the paper explicitly proposes examining basal S845 versus S831 phosphorylation (its assumption that PKA activity at basal calcium levels is greater than activity of PP1, PP2b or CaMKII) as an experimental test of the validity of its detailed model, and the variants' differing predicted Ca dependence of PP1 activation points to a further discriminating measurement that the paper does not explicitly propose. Fifth, all predictions are steady states for sustained Ca elevation; whether they extend to the transient Ca signals produced by physiological induction protocols, and whether the model can quantitatively predict protocol-dependent plasticity magnitudes, was left open.

Problem Statement

The question is whether the calcium-dependent GluR1 phosphorylation model of bidirectional synaptic plasticity can be turned from a qualitative, steady-state account into a quantitatively validated one. For the phosphorylation-to-conductance cascade of Castellani et al. (2005), the source states the limitations that currently stand between the model and quantitative validation: (1) the kinetic parameters ($V_{max}$, $V_{base}$, $k_{1/2}$, Hill coefficient $h$) and total enzyme concentrations of the postsynaptic enzymes in intact dendritic spines cannot currently be extracted from experimental data, so the model's quantitative predictions cannot yet be validated or falsified; (2) whether stochastic fluctuations arising from the small numbers of AMPA receptors and enzymes per spine, and spatial compartmentalization of enzymes within the spine, qualitatively alter the predicted steady-state phosphorylation distributions remains undetermined; (3) the model excludes the other established expression and maintenance mechanisms, namely AMPA-receptor insertion/removal, presynaptic release-probability changes, and CaMKII-autophosphorylation-mediated maintenance, which the authors expect to modify, but not negate, its results, so how the phosphorylation dynamics interact with them in shaping the induction and maintenance of bidirectional plasticity is an open extension of the model rather than a condition of its own validation; (4) which enzyme-activation convention (direct Ca versus Ca-CaM) is correct remains experimentally undecided, the paper itself proposing examination of basal S845 versus S831 phosphorylation under controlled conditions as a test of its detailed model; and (5) whether the steady-state-derived rules extend to physiological transient Ca signals, with the model quantitatively predicting the sign and magnitude of plasticity for defined induction protocols, was left open. These components share one scientific objective, validation or falsification of a specific quantitative mechanism for bidirectional plasticity. For the phosphorylation-to-conductance rules, the open questions are: (1) the extent to which the kinetic parameters and total enzyme concentrations are fixed by the available experimental data; (2) whether stochastic fluctuations and spatial compartmentalization qualitatively change the predicted steady-state phosphorylation distributions; (4) which activation convention the available measurements support, and what further measurement, if any, would discriminate them; and (5) whether the steady-state-derived rules extend to physiological transient Ca signals, together with the sign and, where the data permit, the magnitude of plasticity predicted for defined induction protocols.

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