Energy budgets govern synaptic precision and its regulation during plasticity

Synaptic transmission must balance the need for reliable signalling against the metabolic cost of achieving that reliability. How energetic constraints shape synaptic precision and its regulation during plasticity remains unclear. Here we develop an energy–constrained framework in which synapses minimise postsynaptic response variance subject to a fixed mean and an effective energy budget. Combinations of candidate physiological costs are used to estimate an energy cost for synaptic transmission; this cost is then inferred from quantal statistics. Analysing five published pre- and post-plasticity datasets, we find that observed synaptic mean–variance pairs cluster near a minimal-energy boundary, indicating that precision is limited by energetic availability. Model comparison identifies a dominant calcium pump-like cost paired with a smaller vesicle turnover-like cost, yielding a separable precision–energy relationship, $σ^{-2} \propto E^5$. We further show that plasticity systematically updates synaptic energy budgets according to the scale-free magnitude of mean change, enabling accurate prediction of post-plasticity variance from energy allocation alone. These results provide direct experimental support for the hypothesis that synaptic precision is governed by energy budgets, establishing energy allocation as a fundamental principle linking metabolic constraints, synaptic reliability, and plasticity.

💡 Research Summary

Synaptic transmission is intrinsically stochastic, yet reliable signaling is essential for neural computation. Increasing reliability (i.e., reducing trial‑to‑trial variability) inevitably raises metabolic expenditure, creating a trade‑off between precision and energy use. In this study, Malkin, O’Donnell, and Houghton formalize this trade‑off with an energy‑constrained optimization framework. They start from the classic quantal model, where a synapse is characterized by three parameters: the number of release‑ready sites (N), the release probability (p), and the quantal size (q). These parameters determine the mean postsynaptic response μ = N p q and the variance σ² = N p (1 − p) q².

The authors introduce a latent variable, the effective energy budget E, which is expressed as a weighted sum of candidate physiological cost components: calcium‑pump cost (dependent on p), vesicle‑membrane maintenance, actin scaffolding, vesicle trafficking, and protein turnover. Each component is modeled with a scaling law that links metabolic cost to (N, p, q). The total cost is E = Σ wᵢ Cᵢ(N, p, q), where wᵢ are non‑negative weights that sum to one.

The central hypothesis is that a synapse minimizes variance while keeping the mean fixed, subject to a fixed energy budget. This is cast as minimizing the objective L = σ² + λ E, where λ > 0 balances the units of variance and energy. Under the constraint μ = μ* (the observed post‑plasticity mean), the problem reduces to selecting (N, p, q) that achieve the lowest possible σ² for a given E.

To test the theory, the authors collected five published datasets that report paired pre‑ and post‑plasticity mean and variance measurements from various preparations (STDP in visual cortex, LTP in hippocampus, short‑lived potentiation, etc.). For each synapse they inferred the baseline energy budget E₀ from the observed (μ₀, σ₀²) using different candidate cost models. Model comparison (Bayesian Information Criterion and cross‑validation) identified a two‑term model as the best descriptor: a steep calcium‑pump term proportional to p/(1‑p) · p¹⁄⁴ and a linear vesicle‑turnover term proportional to N. This combination yields a simple scaling law σ⁻² ∝ E⁵, indicating that a modest increase in energy leads to a large reduction in variability.

Plasticity is then modeled as a scale‑free update of the energy budget. The authors propose that the magnitude of the mean change |Δμ| determines the fractional change in energy: E₁ = E₀ ·