Energy budgets govern synaptic precision and its regulation during plasticity

TL;DR

The paper proposes that synaptic precision is governed by an effective energy budget and tests this by mapping mean-variance data from five pre-/post-plasticity datasets to an energy-cost framework based on quantal parameters $n$, $p$, and $q$. It identifies a dominant calcium-pump-like cost paired with a secondary vesicle turnover cost, yielding a separable precision–energy relation $\sigma^{2*} \propto E^{ -5}$ and a budget–precision power law. Plasticity updates the synaptic energy budget via a scale-free rule $\Delta E^{5/2} \approx m\,|\Delta\mu|^{2}/\mu_0 + c$, allowing energy reallocation to predict post-plasticity variance from energy allocation alone. The results demonstrate that synapses tend to operate near a minimum-energy boundary and that energy budgeting provides a mechanistic, quantitative bridge between metabolic constraints, synaptic reliability, and plasticity. Overall, energy allocation emerges as a fundamental organizing principle for how metabolic constraints shape synaptic reliability and learning dynamics.

Abstract

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.

Figures (8)

• Figure 3: Plasticity-induced changes in synaptic mean and variance. Each arrow shows the transition for a single synapse from baseline $(\mu_0,\sigma_0^2)$ to post-plasticity $(\mu_1,\sigma_1^2)$ across five datasets. Top row: log--log coordinates; bottom row: linear coordinates.
• Figure 4: Tradeoff between noise cost and energy cost for synaptic plasticity. Heat maps of (i) the noise term $\sigma^2$ (normalised by $\mu^{*2}$), (ii) the energy term $E$, and (iii) the combined objective over $(n,p)$ for the calcium pump$+$turnover model. Darker shades indicate higher values. The black cross marks the optimum for $\gamma=0.25$, $\mu^*=0.5$, and $\beta_p=0.7$.
• Figure 5: Impact of energy cost multiplier and scale factors on synapse expression.a) Heatmaps of optimal $(p^*,n^*,\sigma^{2*},E^*,\sigma^{2*}/E^*)$ across tradeoff parameterisations. Darker shades of green indicate higher solutions. b) Dependence of $p^*,n^*,\sigma^{2*},E^*$ on $\gamma$, illustrating how energetic pressure shapes synaptic precision and investment.
• Figure 6: Energy budget-dependent predictions for quantal parameters. With $\beta_p=0.95$ and $\mu^*=1$ fixed, panels show how a prescribed energy budget $E^*$ determines the optimal synaptic parameters $(n^*,p^*,\sigma^{2*})$ and the implied trade-off multiplier $\gamma$. The monotone trends reflect Eq. \ref{['eq:proportions_rewrite']}.
• Figure 7: Fitting budget updates.a)$E_1$ versus $E_0$ (dashed: identity). Most points lie above the line, indicating budget increases after plasticity. b) Linear relation between $\Delta E^{5/2}$ and the baseline-adjusted squared mean change $|\Delta\mu|^{2}/\mu_0$. c) Out-of-sample prediction of $E_1$ using $E_1^{\text{pred}}=(E_0^{5/2}+\Delta E_{\text{pred}}^{5/2})^{2/5}$ (dashed: identity). d) Exponent sweep for the energy coordinate $E^{\rho}$. Mean squared log error (MSLE) of held-out $E_{1}^{\text{state}}$ under leave-one-out cross-validation across all datasets (white curve = mean; green shaded band = $\pm$ SEM). The minimum clusters near $\rho\!\approx\!5/2$. Note: the empirically selected exponent coincides with the pump$+$turnover precision--energy law (Eq. \ref{['eq:power_law_rewrite']}), aligning the update coordinate with the natural reliability coordinate.