Why a stronger synapse is a more expensive synapse
A synapse is the junction where one neuron passes a signal to another. Strengthening it, as happens during learning, means making that junction bigger or more numerous, and the hypothesis holds that this is not free. Larger and more numerous synapses imply higher energy costs for the cell [4]. The proposed burden is not only fuel: stronger synapses are described as raising energy consumption and increasing the demand for delivery of materials to the synapse, alongside greater cellular stress [2].
The framing matters because it turns a learning rule into a resource problem. If every waking hour added strength without limit, the hypothesis warns of unsustainable increases in cellular energy demands and a decline in signal quality [1]. Sleep, in this account, is the counterweight that keeps synaptic strength within a range the brain can afford to run [3].
How the energy side is actually measured
The most direct handle on the energy claim is brain metabolism itself. Synaptic activity is described as accounting for the large majority of the brain's energy metabolism, which is why changes in synaptic strength should show up as changes in metabolic rate [5]. In mouse studies, cerebral metabolic rates were found to fall after a period of sleep, a pattern treated as support for the hypothesis that sleep reduces the metabolic load built up during wakefulness [5].
That is an indirect test: it measures the cost at the level of the whole tissue rather than at a single synapse. It is consistent with stronger synapses being expensive, but on its own it does not prove that synapse size is what drives the metabolic change.
Looking at the synapses themselves
The structural side of the hypothesis is tested by ultrastructural studies, which use electron microscopy to measure synapse size and number directly [3]. These studies examine whether synaptic strength is maintained within limits that are sustainable both for energy consumption and for cellular stress, which is the outcome the hypothesis predicts [3].
Putting the two kinds of evidence together gives a coherent picture: metabolism measurements track the running cost of a strengthened brain, while structural measurements track whether the synapses themselves shrink back. Neither line alone settles the question, and the hypothesis is best supported where the two agree.
What the hypothesis leaves open
Several of the accounts here lay out the logic of the hypothesis rather than testing it. The proposal that sleep exists to offset the costs of plasticity is presented as a framework with implications for energy and cellular stress, not as a demonstrated mechanism [2]. The same is true of the broader claim that sleep is the price brains pay for plasticity, which is offered as an organizing idea [1].
The molecular and cellular account likewise explains the need for sleep in terms of the energy costs of larger and more numerous synapses without presenting new tests of those costs [4]. So the strongest empirical footing described here is the metabolic data from mice and the ultrastructural measurements of synapse size and number [5][3]; the rest is the hypothesis's explanatory scaffolding, which remains to be tested in detail.
Sources used in this answer
Phi and SHY: The Development, Application, and Testing of Integrated Information Theory and the Synaptic Homeostasis Hypothesis
The synaptic homeostasis hypothesis proposes that unchecked synaptic strengthening would cause unsustainable rises in cellular energy demands and reduced signal quality, and the paper discusses testing the hypothesis without detailing experiments in its abstract.
Sleep and the price of plasticity: from synaptic and cellular homeostasis to memory consolidation and integration
The hypothesis holds that sleep counteracts the energetic and cellular costs of waking synaptic strengthening, including higher energy consumption and greater demand for delivery of materials, though the paper does not provide experimental tests of these costs.
Sleep and synaptic down-selection
Ultrastructural studies provide experimental evidence bearing on the hypothesis by examining whether synaptic strength is kept sustainable in terms of energy consumption and cellular stress.
Molecular and cellular mechanisms of the restorative effects of sleep
Increases in the size and number of synapses imply increases in energy costs, which the hypothesis uses to explain the need for sleep, without presenting experimental tests of those costs.
Letter to the editor “Cerebral Metabolism and Sleep Homeostasis: A Comment on Vyazovskiy et al”
Mouse data show cerebral metabolic rates fall after sleep, and because synaptic activity accounts for most of the brain's energy metabolism, this is treated as support for the hypothesis.