Synaptic Tagging and Capture

• Synaptic Tagging-and-Capture is a mechanistic framework where transient synaptic tags enable the selective capture of dendritically synthesized plasticity-related proteins, stabilizing synaptic changes.
• Mathematical and computational models quantify the dynamics of tag setting and protein synthesis, predicting critical time windows that support long-term potentiation and depression.
• The framework highlights the role of feedback loops and timing in synaptic modifications, with neuromorphic hardware implementations validating its principles under realistic constraints.

Synaptic tagging-and-capture (STC) is a mechanistic framework describing the selective conversion of transient, protein synthesis-independent synaptic plasticity into lasting, protein synthesis-dependent changes at individual synapses. This model addresses how weakly stimulated synapses, incapable of independently inducing long-term potentiation (LTP) or depression (LTD), can achieve persistent functional changes if their activity coincides with the induction of plasticity-related proteins (PRPs) triggered elsewhere. STC provides a molecular synaptic selection mechanism, central to the encoding and consolidation of long-term memory, that reconciles the spatial specificity of synaptic change with the diffuse nature of PRP synthesis in the dendrite. Theoretical models and neuromorphic hardware implementations have formalized and validated this hypothesis across biophysical and system levels (Atoui et al., 2024, Smolen et al., 2012, Smolen et al., 2020).

1. Molecular and Dynamical Principles of STC

STC is governed by the interplay between transiently set synaptic “tags” and the dendritic production, diffusion, and capture of PRPs. Molecular tagging occurs when coincident activity at a synapse induces phosphorylation events and associated biochemical changes, marking that synapse as eligible (“tagged”) for the subsequent incorporation of available PRPs. PRP synthesis, often triggered by strong stimulation elsewhere, follows separate signaling cascades and is distributed throughout the dendrite. Only synapses that are tagged during the interval of elevated PRP can “capture” these proteins, stabilizing weight changes into late-phase LTP or LTD. Thus, the model predicts a critical time window for STC, defined by the overlap in tag and PRP lifetimes (Smolen et al., 2012, Smolen et al., 2020).

Mathematical models instantiate the tag as a dynamical variable, for example as a product of kinases' phosphorylation states, which decays on a time scale of 1–2 hours (typical parameters k_dₑₚₕ₁ = 0.008 min⁻¹, τ_tag ≃ 125 min). PRP availability is modeled as a pool with separate kinetics (e.g., k_d,PRP = 0.022 min⁻¹, τ_PRP ≃ 45 min). Synaptic tagging is often modularized as TLTP (for LTP), TLTD (for LTD), and their biophysical determinants (e.g., CaMKII, ERK, PKA) (Smolen et al., 2012, Smolen et al., 2020).

2. Mathematical and Computational Models

Biophysical and phenomenological models execute the STC hypothesis by explicitly coupling the kinetics of tag setting, PRP synthesis, and synaptic weight change across spatial compartments. In the Smolen et al. framework, core equations include:

• Tag formation and decay (TLTP, TLTD) as functions of kinase activity and first-order decay:

$$d\,\textrm{S}_{CK}/dt = k_{p1} \cdot \textrm{CaMKII}_s \cdot (1{-}\textrm{S}_{CK}) - k_{d1} \cdot \textrm{S}_{CK}~$$

$\textrm{TLTP} = (\textrm{S}_{CK})^2$

• PRP production in the dendrite driven by ERK activation:

$$d\,\textrm{PRP}/dt = k_{t,PRP} \cdot (pTrans_{ERK})^2 + V_{b,PRP} - k_{d,PRP}\,\textrm{PRP}$$

• Weight updates require simultaneous presence of synaptic tag and PRP:

$$dW/dt = k_{ltp}\cdot TAG \cdot [PRP]\cdot[\textrm{PKM}_{act}]\cdot Plim/(Plim+K_{lim}) + k_{ltp,bas} - W/\tau_{ltp}$$

• Positive feedback by persistent kinase activity (notably PKMζ) underpins bistable maintenance of synaptic weights and biochemical memory (Smolen et al., 2012, Smolen et al., 2020).

These models predict that the critical determinant of synapse-specific memory persistence is the overlap in time of tag and PRP, with both quantities following exponential-like decays after their respective induction events. Cross-capture and the maintenance of LTP/LTD emerge as model-predicted phenomena.

3. Implementation on Neuromorphic Hardware

The BrainScaleS-2 neuromorphic system implements a calcium-based plasticity rule closely aligned with the STC hypothesis. In the hardware instantiation (Atoui et al., 2024):

• Calcium transients following pre- and postsynaptic spikes are integrated using analog AdEx adaptation circuits, sampled at intervals Δt = 50 μs (hardware) corresponding to 50 ms biological time.
• Early-phase weights (h(t)) rapidly track calcium and are mapped to 8-bit variables.
• Tagging is implemented via Heaviside-thresholded deviations of h(t) from baseline (h₀), without a binary tag variable. Potentiation and depression tags (T₊, T₋) are computed each timestep to gate late-phase weight updates.
• PRP synthesis proceeds when $|h-h_0|$ exceeds a threshold, updating an internal p variable; weight consolidation (z(t) for late-phase) is stochastically updated only when both tag and PRP are present.
• Multi-timescale processes are accommodated: fast calcium dynamics (τ_c = 10–100 ms), intermediate h (τ_h), and slow PRP/p and late-phase weights z (τ_p, τ_z in minutes–hours bio).
• Strict hardware constraints (integer-only arithmetic, stochastic rounding, 8-bit range) successfully capture canonical STC kinetics across four standard induction protocols, with mean trajectories showing <5% deviation from full software references.

This demonstration confirms that the principal features of biophysical STC models are robust to quantization, hardware acceleration (1000× biological timescales), and analog circuit approximations, provided multi-timescale stochastic update logic is respected.

4. Mechanistic Variants and Maintenance of Memory

Modeling efforts delineate several routes for long-term memory maintenance beyond the canonical tag-capture formulation. Smolen et al. (Smolen et al., 2020) compare four model variants:

1. Autonomous PKMζ synthesis: PKMζ self-activation provides self-sustaining feedback; maintenance of LTP is achieved if PKMζ also sustains the synaptic tag.
2. Persistent CaMKII activation: CaMKII autoactivation maintains low-amplitude tags and drives PKMζ synthesis via feedforward mechanisms, yielding long-term weight maintenance.
3. Recurrent synaptic reactivation: Ongoing W-dependent reactivation events transiently reset kinases and tags, sustaining late-phase weight changes through repeated tag-PRP overlap.
4. Synergistic feedback: Weak PKMζ autoactivation and synaptic reactivation together produce robust maintenance; either alone is insufficient.

All variants adhere to a core STC mechanism: only synapses with a (possibly submaximal) tag and concurrent PRP can induce or maintain weight increases. Distinctions between them rest on their assumptions for feedback loops, tag maintenance, and susceptibility to manipulation (e.g., kinase inhibitor washout, activity block).

5. Timescales and Critical Windows

Quantitative analysis establishes that both the tag and the PRP pool exhibit finite lifetimes, setting a defined temporal window for effective STC:

• LTP tag (TLTP): τ_tag ≈ 167 min
• PRP: τ_PRP ≈ 45 min
• Effective window for tag-PRP overlap: model yields ≈ ±75 min, agreeing with empirical observations (Smolen et al., 2012).

The probability of successful STC (conversion of early-phase to late-phase LTP/LTD) is therefore sharply constrained by the degree of overlap, synapse-by-synapse, between the tag set by synaptic activity and dendritically available PRPs. Failure of coincidence results in decay to baseline.

Cross-capture, where a tag at one synapse coincides with a PRP wave elicited by activity at another, is predicted and recapitulated in simulations. The bistability induced by PKMζ positive feedback is robust to expected levels of molecular noise; loss of stability emerges only in very small spines (V < 0.05 μm³).

6. Experimental Predictions and Confirmation

STC models make a series of testable predictions (Smolen et al., 2012, Smolen et al., 2020):

• SLFS alone should diffuse PKM_d throughout dendrites without focal spine accumulation.
• Peptide CaMKII inhibition during LTP induction or cross-capture should block PKM synthesis if the synaptic kinase CK_d is CaMKII.
• FRET-based imaging can be used to detect persistent, though diminished, tagging at potentiated synapses over days, discriminating between models with continuous versus pulsatile tag maintenance.
• PKMζ inhibition should collapse maintained LTP within minutes to hours, supporting a causal role in late-phase plasticity; partial inhibition yields only transient depression.

Functional STC models recapitulate the requirement for persistent kinase activity or recurrent synaptic reactivation for the enduring maintenance of LTP and long-term memory traces. Hardware implementations confirm faithful emulation under realistic physical and architectural constraints.

7. Limitations and Future Directions

Several caveats apply to current models and hardware realizations (Atoui et al., 2024):

• Fixed time discretization (Δt) limits the ability to track the fastest molecular events, with biological accuracy reliant on sub-100 μs timestepping.
• Simplified circuit models omit conduction delays and explicit calcium noise, which may affect fidelity, especially at high firing rates or in larger networks.
• State variable quantization (8-bit in hardware) necessitates reliance on stochastic rounding to avoid bias and maintain accuracy, particularly for slow variables (PRP, late-phase weight).
• Present implementations are validated primarily in single-synapse or small-scale architectures; evaluation at the network scale with true dendritic compartmentalization is ongoing.
• The full molecular diversity of synaptic tags, PRPs, and their spatiotemporal coordination remains an open subject, as does the interplay of spine morphology, diffusion barriers, and local translation.

A plausible implication is that efforts to build large-scale, biophysically accurate neuromorphic substrates for memory and computation will need to preserve the cascade of multi-timescale signaling and feedback outlined by STC models, robust to intrinsic fluctuations, quantization, and circuit non-linearities. Model-based predictions regarding the manipulation of tag or PRP lifetimes, kinase feedbacks, or synaptic reactivation will continue to inform empirical studies, clarifying requirements for persistence and specificity in long-term synaptic plasticity.