Coupled phosphatase and kinase switches produce the tristability required for long-term potentiation and long-term depression

Abstract

Studies of long-term potentiation (LTP) and long-term depression (LTD) strongly suggest that individual synapses can be bidirectionally modified. A central question is the biochemical mechanisms that make LTP and LTD persistent. Previous theoretical models have proposed that the autophosphorylation properties of CaMKII could underlie a bistable molecular switch that maintains LTP, and there is experimental support for this mechanism. In contrast, there has been comparatively little theoretical or experimental work regarding the mechanisms that maintain LTD. Several lines of evidence indicate that LTD is not simply a reversal of previous LTP but rather involves separate biochemical reactions. These findings indicate that a minimal model of the synapse must involve a tristable system. Here, we describe a phosphatase (PP2A) switch, which together with a kinase switch form a tristable system. PP2A can be activated by a Ca(2+)-dependent process but can also be phosphorylated and inactivated by CaMKII. When dephosphorylated, PP2A can dephosphorylate itself. We show that these properties can lead to a persistent increase in PP2A during LTD (as reported experimentally), thus forming a phosphatase switch. We show that the coupled PP2A and CaMKII switches lead to a tristable system in which the kinase activity is high in the LTP state; the PP2A activity is high in the LTD state, and neither activity is high in the basal state. Our results provide an explanation for the recent finding that inhibition of PP2A prevents LTD induction.

Figure 1.

Simplified model. A, Biochemical reactions of CaMKII. The kinase activity is turned on by Ca²⁺/calmodulin stimulation or autocatalytic phosphorylation. B, Biochemical reaction for phosphatase. The phosphatase activity is turned on by dephosphorylation, which is produced either by Ca²⁺ stimulation or autocatalytic dephosphorylation. K and P indicate kinase and phosphatase respectively; pK and pP are the phosphorylated forms of enzymes; * indicates active enzyme. C, Simplified reaction scheme. Gray shading represents spine structure. Pointed and circled arrows indicate the activation and the inhibition pathways, respectively. Ca²⁺ influx through NMDAR can activate CaMKII (K) and protein phosphatase (P) in a manner that depends on the concentration of Ca²⁺. CaMKII and phosphatase can self-activate themselves and inhibit each other. Active kinase and phosphatase control AMPAR insertion and removal, respectively.

Figure 2.

Coupled kinase and phosphatase switches can produce tristability. A, Simulation results for coupled switch model. The basal state undergoes LTP in response to high concentration (4 μm for 2 s) of Ca²⁺. The basal state goes to LTD state in response to moderate Ca²⁺ elevation (2.2 μm for 2 s). B, Enzyme activities during LTP and LTD. Left panel, Kinase and phosphatase activities during LTP. K* and P* denote the concentration of active kinase and phosphatase respectively. Before Ca²⁺ stimulation, both kinase and phosphatase are nearly inactive. During high level of Ca²⁺ application, kinase activity is dominant. After Ca²⁺ removal, active kinase represses the phosphatase activity below its initial level (see inset). Right panel, Kinase and phosphatase activities during LTD. Phosphatase is activated by Ca²⁺ pulse of 1 μm for 2 s and stays in the active state after Ca²⁺ is removed. During maintenance of LTD, active phosphatase represses kinase activity (see inset). C, Robustness of basal state to perturbation. Different levels of Ca²⁺ pulses (step size, 0.1 μm for 2 s) are applied on top of basal concentration (0.1 μm), and responses are traced. Basal state is robust to the Ca²⁺ concentration less than or equal to 0.5 μm. Concentrations >0.6 μm evoke LTD (red trace). D, Dependence of sign of synaptic modification on Ca²⁺ level during a pulse (note similarity to BCM curve). E, Reversals of LTP and LTD. The basal state which is robust to small perturbation (the first stimulation: 0.4 μm Ca²⁺ for 2 s) undergoes LTP by the second stimulation (4 μm for 2 s). The third stimulation (2.2 μm for 1.4 s) reverses the potentiated state back to basal level (depotentiation). The fourth (2.2 μm for 2 s) and the fifth (2.93 μm for 2 s) stimulations induce and reverse LTD, respectively (dedepression).

Figure 3.

The dynamics of the model in phase space. Left panel, Black and gray curves indicate nullclines for kinase and phosphatase respectively. The vector field is indicated by gray arrows. Nullclines at resting Ca²⁺ concentration (0.1 μm) create five steady-states. Open and filled circles denote unstable and stable steady-states, respectively. Gray open circle indicates the basal state. K* and P* denote the concentration of active kinase and phosphatase respectively. Insets, The areas where nullclines intersect are magnified. Middle panels, Nullclines during Ca²⁺ influx. Top, During LTP induction, the Ca²⁺ elevation (4 μm for 2 s) deforms nullclines to create one stable state. Bottom, During LTD induction, the moderate level of Ca²⁺ elevation (2.2 μm for 2 s) deforms nullclines to create one stable state. The basal state becomes unstable and moves to the closest stable state (gray trace). Right panels, Nullclines after Ca²⁺ removal. Nullclines form three stable states again in the resting Ca²⁺ concentration. The state moves to the closest stable state, LTP (gray trace, top) or LTD (gray trace, bottom).