Underlying Mechanisms of Cooperativity, Input Specificity, and Associativity of Long-Term Potentiation Through a Positive Feedback of Local Protein Synthesis

Abstract

Long-term potentiation (LTP) is a specific form of activity-dependent synaptic plasticity that is a leading mechanism of learning and memory in mammals. The properties of cooperativity, input specificity, and associativity are essential for LTP; however, the underlying mechanisms are unclear. Here, based on experimentally observed phenomena, we introduce a computational model of synaptic plasticity in a pyramidal cell to explore the mechanisms responsible for the cooperativity, input specificity, and associativity of LTP. The model is based on molecular processes involved in synaptic plasticity and integrates gene expression involved in the regulation of neuronal activity. In the model, we introduce a local positive feedback loop of protein synthesis at each synapse, which is essential for bimodal response and synapse specificity. Bifurcation analysis of the local positive feedback loop of brain-derived neurotrophic factor (BDNF) signaling illustrates the existence of bistability, which is the basis of LTP induction. The local bifurcation diagram provides guidance for the realization of LTP, and the projection of whole system trajectories onto the two-parameter bifurcation diagram confirms the predictions obtained from bifurcation analysis. Moreover, model analysis shows that pre- and postsynaptic components are required to achieve the three properties of LTP. This study provides insights into the mechanisms underlying the cooperativity, input specificity, and associativity of LTP, and the further construction of neural networks for learning and memory.

Keywords: associativity; cooperativity; input specificity; local positive feedback; long-term potentiation.

Figure 1

(A) The pyramidal cell model with n excitatory synapses. The synapses are divided into two type pathways, P1 (n₁ synapses) and P2 (n₂ synapses), which deliver different stimuli to induce LTP. (B) Detailed illustration of the biological processes in the model. Here, we showed the processes from the presynaptic side to the synaptic cleft and then to the postsynaptic side, taking synapse 1 as an example. The presynaptic stimulation causes the release of the neurotransmitter Glu (blue dots) from the presynaptic nerve terminal into the cleft. The neurotransmitter promotes the opening of postsynaptic AMPA and NMDA glutamate receptor channels and results in Na⁺ and Ca²⁺ influx. BDNF (pink circles) binds to the postsynaptic TrkB receptor (1), increases the conductance of the NMDA channel (2), increases the postsynaptic Ca²⁺ concentration (3), subsequently regulates AMPA channel conductance via phosphorylation of CaMKII (4), and activates CREB proteins to induce BDNF transcription (5). BDNF transcription can be accumulated and locally translated into proteins in dendrites (6), and proteins are secreted from dendritic spines (7). Binding of secreted BDNF to the postsynaptic TrkB receptor leads to endocytic uptake of BDNF-TrkB complexes (8). BDNF in the synaptic cleft can induce postsynaptic mTOR-dependent local translation of BDNF mRNAs (9), and the synthesized BDNF proteins in turn are secreted into the cleft to form a local positive feedback loop.

Figure 2

Four stimulus protocols. Stimulus protocol 1: synapse 1 in the P1 pathway receives a stimulus of 100 Hz for 1 s. Stimulus protocol 2: all synapses in the P1 pathway receive a stimulus of 100 Hz for 1 s. Stimulus protocol 3: all synapses in the P2 pathway receive a weak stimulus (5 Hz for 4 s). Stimulus protocol 4: all synapses in the P1 pathway receive a strong stimulus (100 Hz for 4 s) and all synapses in the P2 pathway receive a weak stimulus (5 Hz for 4 s) simultaneously.

Figure 3

Different postsynaptic responses induced by the four stimulus protocols. (a1–a4) Representative excitatory postsynaptic potential (EPSP) traces before stimulation (green dashed lines) and at 5 h after stimulation (blue or red solid lines). (b1–b4) Amplitudes of EPSP, normalized to the EPSP amplitude without stimulation, before (blue bars) and at 5 h after stimulation (brown bars). (c1–c4) Representative AMPA-mediated excitatory postsynaptic current (EPSC) traces before stimulation (green dashed lines) and at 5 h after stimulation (blue or red solid lines). (d1–d4) AMPA-mediated EPSC amplitudes, normalized to the AMPA-mediated EPSC amplitude without stimulation, before (blue bars) and at 5 h after stimulation (brown bars). In all figures, values of P1 are represented by that at synapse 1, and values of P2 are represented by that at synapse 21, respectively. In (a,c), x-axes are the time from a given time point (before stimulation or 5 h after stimulation), y-axes are EPSP or EPSC. Scales of the axes are given by insets in (a1 or c1), respectively.

Figure 4

Time courses of cleft BDNF concentrations [BDNF] (a1–a4), the postsynaptic Ca²⁺ concentrations (C_post) (b1–b4), AMPA channel maximal conductances (g_AMPA) (c1–c4), normalized AMPA-mediated EPSC amplitudes (d1–d4), and normalized EPSP amplitudes (e1–e4) in P1 and P2 before and after stimulation (four stimulus protocols). In all protocols, the stimulations are given at t = 0.

Figure 5

The positive feedback loop at each synapse of the model in Figure 1. Cleft BDNF promotes the translation of BDNF mRNA (m_BDNF) in dendritic spines by binding to TrkB receptors, and the synthesized postsynaptic BDNF (BDNF_post) proteins can be secreted into the synaptic cleft to form a positive feedback loop.

Figure 6

The transient increase in C_post induces a high level of [BDNF] according to Equations (1), (2). (A) The 2 s elevation of C_post to 0.02 mM. (B) The corresponding [BDNF] time course. The basal value of C_post is assumed to be 0.004 mM, and the parameter m_BDNF = 0.1681 μM. Other parameter values are presented in Table A1.

Figure 7

Bifurcation diagrams of the simple motif model. (A) Bifurcation diagram of [BDNF] vs. C_post, where m_BDNF = 0.1681 μM. Limit points (fold bifurcation points) are marked as LP1 and LP2. (B) Two-parameter bifurcation diagram in the (C_post, m_BDNF) plane. The magenta star and dot depict the positions of (C_post, m_BDNF) at the basal level of C_post and during the C_post elevation, respectively.

Figure 8

Projection of system trajectories onto the two-parameter bifurcation diagram of the local positive feedback loop model. (A) (C_{post, 1}, m_BDNF) lies in region I before and after stimulation (the protocol 1). (B) (C_{post, 1}, m_BDNF) lies in region I and region III before and after stimulation, respectively (the protocol 2). (C) (C_{post, 21}, m_BDNF) lies in region I before and after stimulation (the protocol 2). (D) (C_{post, 21}, m_BDNF) lies in region I before and after stimulation (the protocol 3). (E) (C_{post, 21}, m_BDNF) lies in region I and region III before and after stimulation (the protocol 4), respectively.

Figure 9

Times course of (a1–a4) the total glutamate concentration [G]_T and (b1–b4) the postsynaptic membrane potential V_s under the four stimulus protocols.

Figure 10

The induction of LTP requires presynaptic neurotransmitter release and postsynaptic action potentials. Figures show the time courses of the glutamate concentration in a cleft ([G]_j), postsynaptic membrane potential (V_pj), the conductance of the NMDA channels (ḡ_{NMDA, j}), postsynaptic calcium concentrations (C_{post, j}), and maximal conductance of AMPA receptor channels (g_{AMPA, j}) for synapse j, respectively: (a1–e1) synapse 1 under protocol 1; (a2–e2) synapse 1 under protocol 2; (a3–e3) synapse 21 under protocol 2; (a4–e4) synapse 21 under protocol 2; (a5–e5) synapse 21 under protocol 4. In all cases, the stimulations (four stimulus protocols) are given at t = 0.

Figure 11

Dependence of LTP induction on the number of active synapses in pathway P1. Time courses of (A) the normalized amplitudes of EPSP and (B) AMPA-mediated EPSC of synapse 1 after stimulation (the protocol 2) for different values of n₁. The stimulations are given at t = 0.

Figure 12

Dependence of LTP induction on the coupling conductance between the soma and the spine membrane potentials. Time courses of (A) the normalized amplitudes of EPSP and (B) AMPA-mediated EPSC of synapse 21 after stimulation (the protocol 4) for different values of g_c. The stimulations are given at t = 0.