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.
Synapses are intrinsically noisy-vesicle release is probabilistic, vesicle pools are finite, and postsynaptic responses fluctuate across trials even when pre-and postsynaptic activity are repeated (Larkman et al., 1992;Allen and Stevens, 1994;Huang and Stevens, 1997;van Rossum et al., 2003). If this variability is too large, transmission becomes unreliable and information processing degrades (Zador and Pearlmutter, 1996;Zador, 1998;Nolte et al., 2019); if it is too small, achieving and maintaining such precision may incur substantial metabolic cost (Levy and Baxter, 2002;Harris et al., 2015Harris et al., , 2019;;Malkin et al., 2024). Synapses must therefore regulate reliability under energetic constraint. How this regulation emerges, and whether synaptic precision reflects an underlying energetic principle, remains unclear.
A classical and experimentally grounded description of synaptic transmission is provided by the quantal model (Katz and Miledi, 1972), in which synaptic responses arise from the stochastic release of discrete neurotransmitter packets. In this framework, synaptic efficacy and variability are determined by three quantal parameters: the number of release-ready vesicles or release sites (𝑛), the release probability (𝑝), and the quantal size (𝑞), which together determine the mean and variance of postsynaptic responses (Del Castillo and Katz, 1954;Bliss and Collingridge, 1993;Scheuss et al., 2002;Brock et al., 2020). These parameters reflect identifiable biological processes, including vesicle availability, presynaptic release machinery, and postsynaptic receptor function (Malinow and Malenka, 2002;Körber and Kuner, 2016). Quantal statistics therefore provide a mechanistically interpretable description of synaptic transmission and an experimentally accessible link between physiological state and functional reliability.
Importantly, quantal parameters do not vary independently. Across diverse preparations, empirical studies show systematic co-variation between 𝑛, 𝑝, and 𝑞 during plasticity and across synapses (Costa et al., 2015(Costa et al., , 2017;;Biederer et al., 2017;Gou et al., 2022). This coordinated variation suggests that synaptic reliability is regulated subject to underlying constraints, rather than adjusted arbitrarily through independent molecular mechanisms. However, existing theories primarily describe how synaptic mean strength changes during plasticity (Malenka and Bear, 2004;Abbott and Regehr, 2004), and provide limited explanation for how synaptic variability is regulated or why synapses exhibit particular reliability levels.
Several lines of evidence suggest that reliability is constrained by energetic considerations. Increasing release probability requires elevated presynaptic Ca 2+ influx and ATP-dependent clearance; maintaining vesicle pools and release readiness requires continual vesicle cycling, membrane maintenance, and protein turnover. These processes impose substantial energetic costs Attwell and Laughlin (2001); Engl and Attwell (2015); Karbowski (2019)). Consistent with this view, theoretical work has shown that optimising reliability under energetic constraint produces heterogeneous synaptic noise levels consistent with Bayesian learning principles (Malkin et al., 2024;Rusakov et al., 2020;Aitchison et al., 2021). These results suggest that synaptic variability may reflect an optimal allocation of metabolic resources, rather than unavoidable biological imprecision.
Here we test the hypothesis that synaptic precision is constrained by an effective energy budget that limits attainable reliability. We propose that each synapse operates near a minimum-energy boundary determined by its mean strength and available metabolic resources. In this framework, energy is treated as a latent state variable inferred from experimentally measured synaptic statistics. The quantal parameters (𝑛, 𝑝, 𝑞) provide a physiological basis for constructing candidate energy cost models, enabling quantitative inference of effective synaptic energy budgets from observed mean and variance.
A key prediction of this framework is that synaptic precision obeys a strict relationship with energy availability: at fixed mean strength, increasing precision requires increasing energetic investment. Furthermore, if plasticity reallocates metabolic resources, changes in synaptic strength should be accompanied by predictable changes in energy budget and, consequently, synaptic variability.
In this study, we develop an energy-constrained framework that combines biophysically motivated cost models with experimental measurements of synaptic transmission. Using five published datasets reporting pre-and post-plasticity synaptic mean and variance, we infer effective synaptic energy budgets and test whether observed synapses operate near the predicted minimum-energy boundary. We then determine how synaptic energy budgets change during plasticity and test whether these budget changes predict post-plasticity v
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