Haueis and Colaço show that metabolic considerations function as explanatory constraints on cognitive models, demonstrating that ignoring them comes at a cost for cognitive modeling. But what is it that makes them explanatorily relevant, and what exactly do they explain? As we shall see, metabolic constraints on synaptic memory traces are explanatory since they identify dependency relations that account for the background conditions of memory formation.

Haueis and Colaço’s core evaluative case – the comparison of linear cascade models (Benna & Fusi, Reference Benna and Fusi2016) with cyclical models incorporating non-equilibrium steady states (Karbowski, Reference Karbowski2019) – is presented as demonstrating that metabolic considerations play “an evidential and constraining role” for synaptic memory models. Showing that a class of models is metabolically impossible is indeed an explanatory achievement but not one that bears directly on the phenomenon of memory formation itself. What Karbowski’s model shows is which architectures are biologically unrealistic, thereby delimiting the space of metabolically feasible synaptic models. A synapse at thermodynamic equilibrium is a dead synapse. Models that presuppose otherwise were never live options. What needs clarifying, at this stage, is what metabolic constraints are explanatory for. Constraints of this kind are commonly understood to account for which outcomes are possible and which are impossible, not for why a system produces one outcome rather than another (Lange, Reference Lange2016). These are genuinely different explananda. When metabolic constraints bear on synaptic memory, they are informative in a preliminary, eliminative sense. They tell us which models to bracket before the explanatory work begins. The evidential function of metabolic considerations here is thus to provide evidence about background conditions. Such evidence concerns the variables one holds fixed when evaluating models. The deficiency identified in linear cascade models is that these models fall outside the metabolically acceptable bounds that delineate the background conditions of memory formation.

Explanatory constraints are taken by Haueis and Colaço to do more than merely delimit. They argue that metabolic costs “guide and structure the outcome of synaptic consolidation” towards longer memory traces. Haueis and Colaço adopt this language from Ross (Reference Ross2023). The structuring function of constraints, according to Ross, usually operates through a form of channeling: vascular pathways spatially guide blood flow to specific regions, and molecular pathways direct a substrate through a specific sequence of enzymatic conversions. These are cases where the architecture of the constraining system determines the potential states the explanatory target will take on. In contrast, the synaptic architecture Karbowski’s model describes does not channel memory traces toward longer durations (where the relevant notion of duration is decay rate rather than persistence of a consolidated trace). The duration of a memory trace depends on the stimulation the synapse receives. That longer memories are relatively cheaper does not mean shorter ones are impossible. A synapse that receives weak and brief stimulation will produce a short-lived trace despite the architecture favoring longer traces. What is more, the sense in which the architecture favors longer memories is that you get more bang for your buck. In certain parameter regimes of the model, the cost landscape favors longer traces per unit of energy spent (Karbowski, Reference Karbowski2019, p. 1484). Unlike a vascular pathway, this is an efficiency gradient, not a dynamical bias of the system. Even so, an energetically favorable outcome is explanatorily irrelevant for a given phenomenon if it does not track the actual conditions under which that phenomenon obtains.

What dependency relation is there, then, between the structure of synaptic architecture and memory duration? At the moment of encoding, more energy would result in longer potential traces. Yet after encoding, memory duration decouples from energy expenditure (Karbowski, Reference Karbowski2019, pp. 1482–3). This means duration need not depend on energy expenditure. The cost of memories does not, pace Haueis and Colaço, constrain the outcome of “synaptic consolidation.” These dynamics are quite different from how the structuring function of constraints is supposed to work, where the constraining variable channels the process toward specific outcomes.

If metabolic constraints do not guide, where do they lead us? They delineate the background conditions of the target phenomenon (Craver, Reference Craver2007). Haueis and Colaço point in this direction when they characterize metabolic resources as causally unspecific enabling conditions in the case of mental effort. If metabolic constraints on synaptic memory are similarly enabling conditions, then what determines explanatory relevance is the invariance of a causal relationship across a domain-specific range of such conditions (Woodward, Reference Woodward2010). Previously, I argued that synaptic models of memory draw their explanatory power from the fact that their variables are causally invariant across a range of background conditions (Najenson, Reference Najenson2024). For instance, synaptic mechanisms can be demonstrated to support memory across a wide range of behavioral tasks (Morris et al., Reference Morris, Anderson, Lynch and Baudry1986; Nabavi et al., Reference Nabavi, Fox, Proulx, Lin, Tsien and Malinow2014; Rioult-Pedotti, Friedman, & Donoghue, Reference Rioult-Pedotti, Friedman and Donoghue2000). Interestingly, a non-equilibrium steady state is a highly stable but non-specific condition. It holds across all living synapses. It is an open empirical question, but memory traces may be largely invariant to metabolic fluctuations within a fixed range of non-equilibrium steady states. So, coming back to where I started, what makes metabolic constraints on synaptic models of memory explanatorily relevant is that they explain which synaptic models are biologically possible. Their explanatory relevance lies in determining the background on which we evaluate how specific and invariant synaptic mechanisms are.