A model for synaptic development regulated by NMDA receptor subunit expression

Abstract

Activation of NMDA receptors (NMDARs) is highly involved in the potentiation and depression of synaptic transmission. NMDARs comprise NR1 and NR2B subunits in the neonatal forebrain, while the expression of NR2A subunit is increased over time, leading to shortening of NMDAR-mediated synaptic currents. It has been suggested that the developmental switch in the NMDAR subunit composition regulates synaptic plasticity, but its physiological role remains unclear. In this study, we examine the effects of the NMDAR subunit switch on the spike-timing-dependent plasticity and the synaptic weight dynamics and demonstrate that the subunit switch contributes to inducing two consecutive processes—the potentiation of weak synapses and the induction of the competition between them—at an adequately rapid rate. Regulation of NMDAR subunit expression can be considered as a mechanism that promotes rapid and stable growth of immature synapses.

Appendix A: Derivation of Eqs. (13–15)

As shown in van Rossum et al. (2000), synaptic weight distribution P(w) obeys

$$\frac{1}{{f_{{{\text{pre}}}} }}\frac{{\partial P{\left( {w,t} \right)}}}{{\partial t}} = - \frac{\partial }{{\partial w}}{\left[ {r_{1} {\left( w \right)}P{\left( {w,t} \right)}} \right]} + \frac{1}{2}\frac{{\partial ^{2} }}{{\partial w^{2} }}{\left[ {r_{2} {\left( w \right)}P{\left( {w,t} \right)}} \right]},$$

(16)

$$r_{1} {\left( w \right)} = A_{ + } p_{p} - A_{ - } p_{d} ,$$

(17)

$$r_{2} {\left( w \right)} = A_{ + } ^{2} p_{p} + A_{ - } ^{2} p_{d} ,$$

(18)

where p _p and p _d denote the probability that LTP and LTD occur by the presynaptic event, respectively. By the same assumptions as van Rossum et al., we obtain the following relations: p _d  = f _post t ₋ and p _p  = p _d (t ₊/t ₋)(1 + w/W _tot). If we substitute these equations into Eqs. (17) and (18), and set A(w) = r ₁(w)/f _post and B(w) = r ₂(w)/f _post, then Eqs. (16–18) can be rewritten as Eqs. (13–15).