A model of bidirectional synaptic plasticity: from signaling network to channel conductance

Abstract

In many regions of the brain, including the mammalian cortex, the strength of synaptic transmission can be bidirectionally regulated by cortical activity (synaptic plasticity). One line of evidence indicates that long-term synaptic potentiation (LTP) and long-term synaptic depression (LTD), correlate with the phosphorylation/dephosphorylation of sites on the alpha-Amino-3-hydroxy-5-methyl-4-isoxazolepropionic acid (AMPA) receptor subunit protein GluR1. Bidirectional synaptic plasticity can be induced by different frequencies of presynaptic stimulation, but there is considerable evidence indicating that the key variable is calcium influx through postsynaptic N-methyl-d-aspartate (NMDA) receptors. Here, we present a biophysical model of bidirectional synaptic plasticity based on [Ca2+]-dependent phospho/dephosphorylation of the GluR1 subunit of the AMPA receptor. The primary assumption of the model, for which there is wide experimental support, is that the postsynaptic calcium concentration, and consequent activation of calcium-dependent protein kinases and phosphatases, is the trigger for phosphorylation/dephosphorylation at GluR1 and consequent induction of LTP/LTD. We explore several different mathematical approaches, all of them based on mass-action assumptions. First, we use a first order approach, in which transition rates are functions of an activator, in this case calcium. Second, we adopt the Michaelis-Menten approach with different assumptions about the signal transduction cascades, ranging from abstract to more detailed and biologically plausible models. Despite the different assumptions made in each model, in each case, LTD is induced by a moderate increase in postsynaptic calcium and LTP is induced by high Ca2+ concentration.

Figure 1.

A schematic of an excitatory glutamatergic synapse. Action potentials traveling down the presynaptic axon trigger the calcium-dependent release of glutamate. Glutamate binds to two types of postsynaptic ionotropic receptors, NMDARs and AMPARs. The postsynaptic terminal contains a set of enzymes (PP1, PP2b, PKA, CaMKII) that transduce the influx of Ca²⁺ through the NMDARs into changes in the phosphorylation state of GluR1, thereby regulating AMPAR conductance.

Figure 2.

General model of the phosphorylation/dephosphorylation cycle of the GluR1 subunit of the AMPAR. There are two phosphorylation sites on the GluR1 subunit of the AMPAR, serine 845 (S845) and Serine 831 (S831). GluR1 can be dephosphorylated at both sites (A), phosphorylated at S845 (A^p2), phosphorylated at S831 (A_p1), or phosphorylated at both S845 and S831 (). We assume two pairs of enzymes, the enzyme kinase 1 (K1)/enzyme phosphatase 1 (P1) pair phosphorylate and dephosphorylate site 1 (S831), whereas the enzyme kinase 2 (K2)/enzyme phosphatase 2 (P2) pair phosphorylate and dephosporylate site 2 (S845). High-frequency stimulation of the synapses (HFS) activates protein kinases, resulting in phosphorylation. Low-frequency stimulation of the synapse (LFS) activates protein phosphatases, resulting in phosphorylation.

Figure 3.

Kinase/phosphatase activation functions. (A) The calcium dependence of the activity of each of the four postsynaptic enzymes represented by a sigmoidal Hill function that takes into account the cooperative binding of calcium. (B) The calcium dependence of the activity of each of the four postsynaptic enzymes represented by a Michaelis-Menten function. Calcium concentration in arbitrary units.

Figure 4.

Levels of the double phosphorylated () state of AMPAR as a function of postsynaptic calcium concentration. Each graph represents an equilibrium solution obtained by the mass-action approach (equation 2). Low levels of imply LTD and high levels imply LTP. (A) Levels of state of AMPAR when the calcium dependence of each of the phosphorylation/dephosphorylation reactions is represented by a sigmoidal Hill function. (B) Levels of () state of AMPAR when the calcium dependence of each of the phosphorylation/dephosphorylation reactions is represented by a hyperbolic Michaelis-Menten function. Calcium concentration in arbitrary units.

Figure 5.

Levels of the () using the Michaelis-Menten approach. Each graph depicts equilibrium solutions obtained by numerical integration (equation 15) with two Kinases and two Phosphatases. (A) Levels of the () state of AMPAR when the calcium dependence of each of the phosphorylation/dephosphorylation reactions is represented by a sigmoidal Hill function (as in Fig. 3A). (B) Levels of () state of AMPAR when the calcium dependence of each of the phosphorylation/dephosphorylation reactions is represented by a hyperbolic Michaelis-Menten function (as in Fig. 3B). Calcium concentration in arbitrary units.

Figure 6.

Calcium-dependent activity of the kinase/phosphatase network. (Left) Introduction of specific activity-dependent protein kinases and protein phosphatases into the schematic representation of bidirectional phosphorylation/dephosphorylation of the GluR1 subunit of the AMPAR. A schematic description of the calcium-dependent signal transduction cascades that regulate AMPA receptor phosphorylation. An increase in postsynaptic calcium concentration results in an increase in postsynaptic calcium–calmodulin (Ca–CaM) concentration. Low levels of Ca–CaM stimulate PP2b activity directly, while higher levels of Ca–CaM stimulate CaMKII activity. PKA and PP1 are indirectly regulated by calcium. PKA is activated by camp, which can be generated by calcium-dependent adenylyl cyclase (AC) and degraded by phosphodiesterase (PDE). PP1 activity level is inhibited by the protein inhibitor 1/DARPP32 (I₁). The inhibition is released by dephosphorylation of inhibitor 1/DARPP32 via the activity of PP2b. (Modified from Lisman 1989). (Right) There are two phosphorylation sites on the GluR1 subunit of the AMPAR, serine 845 (S845) and serine 831 (S831). S845 is phosphorylated by protein kinase A (PKA) and dephosphorylated by protein phosphatase 1 (PP1); S831 is phosphorylated by calcium–calmodulin-dependent protein kinase II (CaMKII) and dephosphorylated by protein phosphatase 1 (PP1). High-frequency stimulation of the synapses (HFS) results in a large increase in postsynaptic calcium, and a resultant activation of the calcium–calmodulin-dependent protein kinases. Low-frequency stimulation of the synapse (LFS) results in a modest increase in postsynaptic calcium and a resultant activation of the calcium–calmodulin-dependent protein phosphatases. Modified from Kameyama et. al (1998).

Figure 7.

Levels of enzyme activity, GluR1 phosphorylation and AMPAR conductance as a function of postsynaptic calcium concentration. (A,B,C) Calculated from biochemical data with fixed calmodulin concentrations and varied calcium concentrations. (D,E,F) Calculated from data with fixed levels of calcium and varied levels of calmodulin. (A,D) Enzymatic activity (mol/min) as a function of postsynaptic calcium concentration. In both cases, the activation of PP1 is achieved at low concentrations, and the activation of PKA and CaMKII is achieved at higher concentrations. In A, the range of postsynaptic calcium concentrations that activate PP1 is very narrow, whereas in B there is a wider range of postsynaptic calcium concentrations that results in activation of PP1. Intermediate concentrations result in activation of PKA and high concentrations result in activation of CaMKII. (B,E) The resulting phosphorylation state (expressed as percentage of the total) of the GluR1 subunit of the AMPAR as a function of postsynaptic calcium concentration. The shape of the four curves in each graph is qualitatively similar. The most significant difference is that the range over which A is dominant is broader in the Ca–Calmodulin-based case. (C,F) Translating changes in AMPAR phosphorylation to AMPAR conductance (in arbitrary unit) gives qualitatively similar results when considering the dependence on . AMPAR conductance is lower than baseline levels at low concentrations of intracellular Ca or Ca–CaM, and reaches a maximal plateau level at ∼1 uM. The interesting differences are in the shapes of the curves, with a gradual increase in conductance when considering only the Ca dependence and a less gradual increase when considering Ca–CaM.