Recharging the brain’s batteries: a thermodynamic perspective on modeling brain energetics

In their lead article, Shichkova and colleagues report a remarkably detailed model of the metabolic dynamics underlying energy metabolism in the brain (Shichkova et al. 2024). By incorporating many metabolic pathways based on a broad range of earlier work, they have designed a useful tool for probing the dynamics of brain energetics. Comparing a young and an aged brain metabolic state, they identified key differences and tested how modifications of specific metabolic components in the aged state could restore the young state. For example, in one case it was sufficient to simply increase the activity of the sodium/potassium ATPase, the transporter of three Na + ions out of the cell and two K + ions into the cell coupled to the conversion of one adenosine triphosphate (ATP) molecule to one adenosine diphosphate (ADP) molecule. This so-called "sodium pump" is thought to be a key player in brain energetics, consuming most of the ATP required for neural function, particularly at excitatory synapses (Attwell andLaughlin, 2001, Yu et al., 2018).The goal of modeling brain energy metabolism is to incorporate all the features of the neurons, glia, and vascular elements functioning as the neurovascular unit. This would provide a framework for integrating a wide range of studies from genetics to neurophysiology to non-invasive functional neuroimaging to novel therapeutics. It is a sweeping goal, and challenging because we are still trying to understand key elements of the physiology. For example, many metabolic and neural factors affect cerebral blood flow (CBF) (Howarth et al., 2021) but it is not clear how all these potential mechanisms combine to create a smoothly functioning CBF response to neural activity. Expanding the model to include this ongoing work is an important direction for future work. Nevertheless, by including many aspects of brain energetics the model by Shichkova et al. is an important framework to build on.The central question in modeling brain energetics is: how do we know the rates of different processes? Shichkova and colleagues used RNA expression data to estimate enzyme concentrations and extrapolate to the associated enzyme kinetics. (They acknowledged the caveat that mRNA levels do not fully reflect protein levels and activities.) In addition, though, there are thermodynamic effects on reaction rates when the processes are not far from equilibrium-as the entropy change decreases the process slows, independent of the details of the enzyme kinetics. These are essentially physiological effects that are not predictable from RNA expression alone, and which instead depend on the dynamically changing concentrations of key ions and metabolites. This Viewpoint article considers the modeling of brain energetics from a thermodynamic perspective, clarifying the basic ideas and describing an important, and somewhat counterintuitive, physiological effect.Thermodynamic reasoning enables us to identify aspects of the dynamics that are independent of the specific mechanisms involved. For example, to model how a cup of hot coffee cools we could include the thermal conductivity of the coffee and the cup, possible convective motions within the coffee, and even convective air motions due to blowing gently on the surface. However, independent of the exact mechanisms, the thermodynamics alone predicts the endpoint of the cooling process: the temperatures of the coffee and the room will equalize, and the detailed mechanistic modeling must be consistent with this endpoint.Creating a model that conforms to thermodynamic constraints can be challenging if the rates of the different mechanisms are taken from empirical data far from equilibrium, and another step may be needed to bring in thermodynamic consistency (Pan et al., 2019).Thermodynamic effects on the rate of a process depend on the net entropy change (S) involved, including all the interacting components. An intuitive way to formulate the role of S on dynamics is in terms of the fluctuation theorem, a perspective borrowed from physics (Evans D.J., 2002). Essentially, the fluctuation theorem captures the statistical nature of the second law of thermodynamics by dealing with probabilities for the forward direction of change (P+, the direction for positive S) and the reverse direction of change (negative S) within a given time interval . The fluctuation theorem relates these probabilities:□□ + □□ - = □□ ∆□□/□□ [1]where k is Boltzmann's constant.The fluctuation theorem provides a way to move beyond equilibrium and treat the nonequilibrium dynamics of biological systems (Buxton, 2024). Defining R0 = P+/ as the forward rate of the process, the net rate R of a process is:□□ = □□ 0 (1 -□□ -∆□□/□□ ) [2]The net rate involves two terms: a kinetic rate constant R0 that depends on concentrations of the reactants, enzyme activity, membrane permeability, and other parameters usually included in modeling dynamics; and a thermodynamic term that depends on the net entropy change. When S = 0, the system is in equilibrium, and the net rate of the process is zero.When S is large, the thermodynamic term no longer has a significant effect, and the process is irreversible in a thermodynamic sense with a rate R0.In practice, we typically deal with a physiological system interacting with a thermal bath at temperature T. The net entropy change S is expressed as the change in the Gibbs function G, with G = -TS (positive S corresponds to negative G). In the usual units, expressed on a per mole basis, the exponent S/k in Eq [2] becomes -G/RT, with RT ~2.6 kJ/mole at human body temperature. If G = -12 kJ/mol the thermodynamic effect reduces the rate by only ~1%, and the process is essentially irreversible. The G for a process depends on the ratio  of reactant to product concentrations (Nicholls and Ferguson, 2002):∆□□ = -□□□□ log Φ Φ 0 [3]where  is the value of  at equilibrium. For the sodium gradient,  is the ratio of extracellular to intracellular concentrations, and 0 depends on the membrane potential.Figure 1 is a sketch of brain energy metabolism, focusing on the key components involving an entropy change and a few key mechanisms. For the entropy components, the dependence of  on key reactant and product concentrations is indicated for the forward direction of change when entropy increases. Ion fluxes involved in neural activity include calcium ion entry into both the pre-synaptic and post-synaptic neuron and ion currents due to opening Na + and K + channels (Na + influx, K + efflux). The result is that neural activity increases intracellular Na + and Ca 2+ concentrations and extracellular K + concentration. The energetics pathway indicated by the solid black arrows reverses these changes.The sodium gradient between the inside and outside of the cell is a focal point in brain energetics. It serves as an amplifier for neural signaling, providing a strong inward sodium current when sodium channels open. The Na + gradient also acts as a battery to power other thermodynamically uphill processes involving neurotransmitter recycling and ion transport across the cell membrane. For example, Figure 1 includes the sodium/calcium exchanger, coupling transport of three Na + into the cell, a process with negative G, to transport of one Ca 2+ out of the cell, with a positive G. The Na + gradient, in turn, is restored with the sodium pump by coupling uphill movement of Na + out of the cell (now positive G) to a stronger battery-the ATP system. The ATP battery is restored by coupling to an even stronger battery, the metabolism of glucose with production of ATP. We can think of this as a chain of batteries, each charged by the previous battery and in turn charging the next battery, with voltages analogous to the associated G.For neural activity, the rates of each process indicated by a black arrow in Figure 1 must be balanced to achieve a steady state, with equal rates of Na + efflux and influx, and ATP restoration and consumption. If this rate balance is maintained, it is tempting to say the system is working well. However, this is complicated by another effect related to the thermodynamic viewpoint (Buxton, 2024), hinging on downstream effects related to Eq [2].Essentially, voltage degradation in one of the batteries in Figure 1 can cascade-degrading voltage in the battery being recharged, even though the net rates remain balanced.For example, the net G for the sodium pump depends on the negative GATP from the ATPto-ADP conversion and the positive GNa from pumping sodium against its gradient. If the negative GATP degrades (e.g., by reduction of the ATP/ADP ratio), the net G will fall, and if it falls low enough the sodium pump will slow down by Eq [2]. The sodium gradient will fall, but this also lowers the positive GNa required to pump the sodium against its gradient.If GNa falls sufficiently to restore the original net G, despite the reduction of GATP, the rate of the sodium pump can be restored. The somewhat counterintuitive result is that the overall rate of the sodium pump is maintained, but at the cost of degrading the GNa available from the sodium gradient. This has a cascading effect on downstream processes that depend on the negative GNa available when a sodium ion moves down its gradient, i.e., when the sodium gradient is used as a battery. For example, for the Na + /Ca 2+ exchanger the net G has been estimated to be about -7 kJ/mol in cardiac myocytes (Baartscheer et al., 2011), a range in which thermodynamic effects are significant.Another physiological effect that becomes clearer from a thermodynamic perspective is the observation that increased neural activity creates a CBF increase two-to three-fold greater than the increase of cerebral oxygen metabolism (CMRO2)-the origin of the blood oxygenation-level dependent (BOLD) effect in functional magnetic resonance imaging (MRI)studies. Because the G associated with oxidative metabolism depends on the O2 concentration in mitochondria, it is not enough to simply think about delivery of O2 to the capillary bed: O2 must be delivered while maintaining a sufficient O2 concentration in tissue to avoid degrading the available G (Wilson, 2013, Buxton, 2024). Modeling shows that a large CBF increase is needed to prevent the partial pressure of O2 (PO2) in tissue from falling, in good quantitative agreement with studies of brain activation and hypoxia (Buxton, 2024).In this way, a thermodynamic perspective provides an explanation for the physiological function served by a large CBF change even though the mechanisms producing that CBF change are not yet fully understood.the metabolic rate is necessary but not sufficient-the healthy brain must keep its batteries charged as well. In practice, there is some buffer in the sense that G could be reduced without impairing the next stage. An important research question is to determine how large that buffer is for each of the systems in Figure 1.In conclusion, the detailed modeling of brain energetics by Shichkova and colleagues (Shichkova et al. 2025) is an important advance. As the field progresses, modifying and building on this framework, a thermodynamic viewpoint can provide a useful complementary angle for modeling and understanding the physiology.Author contribution