Reduced Gibbs free energy supply hinders brain information processing during mental fatigue

Abstract: Background: Brain information processing deteriorates as cortical neurons gradually transition from a rested state into fatigue. Subjectively, fatigue is experienced as a state of weariness, tiredness, or lack of energy that reduces the ability to work safely and effectively. Objective: In this theoretical paper, we pinpoint the physical origin of brain fatigue in the gradual deterioration of biochemical reaction quotients and transmembrane ion concentration gradients, which increase neuronal excitability and decrease the signal-to-noise ratio in the brain cortex. Methods: Brain performance in a rested state versus fatigue is examined by well-established, data-driven computer models for energy transport inside protein $α$-helices in the presence of thermal noise for different ATP energy states or for pyramidal neuron firing of action potentials under electric stimulation in a rested membrane state versus fatigue. Results: We found that reduced Gibbs free energy supply from ATP hydrolysis impairs the cooperative effect between amide I excitons propagating inside protein $α$-helices, with resulting decreased thermal stability of molecular solitons. Concurrent changes in Nernst reversal potentials for Na+ or K+ ions further led to neuronal hyperexcitability and a higher risk of neuronal depolarization block during mental fatigue. Conclusions: Detailed computational modeling showed that inefficient protein function due to diminished ATP energy status, alters the electrophysiological properties of individual neurons, thereby impairing their information processing capacity for the proper execution of cognitive tasks. Scheduling practices aimed at intermittent recovery of the rested brain state during intellectually challenging work could protect physical and mental wellbeing, prevent burnout, and enhance long-term productivity.

• The paper proposes that mental fatigue reduces ATP-hydrolysis free energy, moving neuronal biochemistry toward equilibrium and weakening the molecular and ionic processes required for reliable information processing.
• Computational simulations suggest that reducing protein excitation from three to two amide I quanta sharply shortens soliton propagation, while degraded sodium and potassium gradients increase hyperexcitability and depolarization-block risk in CA1 neurons.
• The framework predicts that local metabolic and ionic disruption may impair cognitive accuracy before noticeable subjective fatigue or macroscopic EEG changes, supporting testable research on recovery breaks and energy-aware brain monitoring.

Thermodynamic Mechanisms of Cognitive Impairment During Mental Fatigue

Central thesis

“Reduced Gibbs free energy supply hinders brain information processing during mental fatigue” presents a thermodynamic account of mental fatigue as a reversible decline in neuronal computational capacity caused by reduced biochemical free-energy availability (2608.10211). The paper argues that fatigue is not merely a subjective state or an undifferentiated reduction in metabolic activity. Rather, it emerges from progressive displacement of intracellular biochemical reactions and transmembrane ionic distributions toward thermodynamic equilibrium. This displacement reduces the Gibbs free energy available from ATP hydrolysis, compromises energy-dependent protein function, weakens ionic concentration gradients, increases neuronal excitability, and ultimately degrades the signal-to-noise ratio of cortical information processing.

The analysis spans three physical scales. At the molecular scale, the paper models ATP-dependent energy transport through protein $\alpha$-helices using thermally perturbed Davydov solitons. At the cellular scale, it evaluates the effect of diminished sodium and potassium reversal potentials on action-potential generation in a morphologically detailed CA1 pyramidal neuron. At the systems level, it relates these cellular alterations to cognitive errors, hyperexcitability, glutamatergic accumulation, delayed fatigue detection, and the potential value of intermittent recovery periods.

The paper is theoretical and computational rather than experimental. Its principal contribution is therefore a mechanistic synthesis: it links metabolite concentrations, nonequilibrium thermodynamics, molecular energy transport, membrane electrophysiology, and behavioral impairment within a single causal framework.

ATP hydrolysis as a variable free-energy source

A foundational distinction in the paper is between ATP consumption and the free energy actually released by ATP hydrolysis. ATP is often described as the cellular “energy currency,” but the usable energy is not fixed by ATP concentration alone. It depends on the reaction quotient,

$$Q = \frac{[\mathrm{ADP}][\mathrm{P_i}]}{[\mathrm{ATP}]},$$

and on the intracellular concentrations of ATP, ADP, and inorganic phosphate. The relevant thermodynamic quantity is therefore

$$\Delta G = \Delta G^\circ + \frac{k_{\mathrm B}T}{q_{\mathrm e}}\ln Q,$$

with the magnitude of $-\Delta G$ determining the free energy available for biological work.

Using reported metabolite concentrations, the paper estimates ATP-hydrolysis free energies of approximately $0.57~\mathrm{eV}$ in liver, $0.62~\mathrm{eV}$ in brain, and $0.68~\mathrm{eV}$ in heart. These values exceed the standard free energy of ATP hydrolysis because metabolically active organs maintain reaction quotients substantially displaced from equilibrium. The brain consequently operates with a high phosphorylation potential despite its limited capacity to store energy locally.

The manuscript estimates that the brain consumes approximately $25.6$ mol of ATP per day, corresponding to roughly $13$ kg of ATP hydrolyzed daily. This estimate illustrates the extraordinary turnover of ATP, although the authors correctly emphasize that ATP mass turnover is not equivalent to useful thermodynamic work. A modest change in the ATP/ADP/phosphate balance can reduce $|\Delta G_{\mathrm{ATP}}|$ without necessarily producing a proportional reduction in total ATP concentration.

Figure 1: ATP utilization in neuronal morphology and voltage-gated sodium-channel physiology, emphasizing the dependence of electrical signaling on ATP-maintained ionic gradients.

The proposed fatigue mechanism begins when neuronal activity increases the concentrations of reaction products and dissipates ionic gradients faster than metabolic and pump systems can restore them. The resulting increase in $$Q = \frac{[\mathrm{ADP}][\mathrm{P_i}]}{[\mathrm{ATP}]},$$0 reduces the magnitude of ATP-hydrolysis free energy. In the paper’s formulation, fatigue is thus a progressive reduction in the thermodynamic distance from equilibrium rather than an abrupt failure of ATP production.

Molecular energy transport and the soliton threshold

To connect ATP free energy with protein function, the paper uses a stochastic three-spine Davydov model of amide I excitons propagating along a protein $$Q = \frac{[\mathrm{ADP}][\mathrm{P_i}]}{[\mathrm{ATP}]},$$1-helix. The model includes nearest-neighbor excitonic coupling, nonlinear exciton-lattice interaction, elastic coupling between peptide groups, damping, and thermal noise satisfying the fluctuation-dissipation theorem at $$Q = \frac{[\mathrm{ADP}][\mathrm{P_i}]}{[\mathrm{ATP}]},$$2.

Protein $$Q = \frac{[\mathrm{ADP}][\mathrm{P_i}]}{[\mathrm{ATP}]},$$3-helices are treated as three coupled hydrogen-bonded spines. The amide I excitation is associated primarily with the carbonyl component of the peptide group. In the model, nonlinear coupling between vibrational excitation and lattice displacement can produce a localized traveling excitation, or molecular soliton, capable of transporting energy without immediate dispersive loss.

Figure 2: Poly-alanine $$Q = \frac{[\mathrm{ADP}][\mathrm{P_i}]}{[\mathrm{ATP}]},$$4-helix architecture showing the three hydrogen-bonded spines that support coupled amide I excitations.

The paper compares solitons containing $$Q = \frac{[\mathrm{ADP}][\mathrm{P_i}]}{[\mathrm{ATP}]},$$5 and $$Q = \frac{[\mathrm{ADP}][\mathrm{P_i}]}{[\mathrm{ATP}]},$$6 amide I exciton quanta. With an approximate energy of $$Q = \frac{[\mathrm{ADP}][\mathrm{P_i}]}{[\mathrm{ATP}]},$$7 per quantum, these correspond to total excitation energies of $$Q = \frac{[\mathrm{ADP}][\mathrm{P_i}]}{[\mathrm{ATP}]},$$8 and $$Q = \frac{[\mathrm{ADP}][\mathrm{P_i}]}{[\mathrm{ATP}]},$$9, respectively. Under identical realizations of thermal noise, the three-quantum soliton survives for at least $$\Delta G = \Delta G^\circ + \frac{k_{\mathrm B}T}{q_{\mathrm e}}\ln Q,$$0 ps and can transport energy up to approximately $$\Delta G = \Delta G^\circ + \frac{k_{\mathrm B}T}{q_{\mathrm e}}\ln Q,$$1 nm. The two-quantum soliton persists for only about $$\Delta G = \Delta G^\circ + \frac{k_{\mathrm B}T}{q_{\mathrm e}}\ln Q,$$2 ps and travels less than $$\Delta G = \Delta G^\circ + \frac{k_{\mathrm B}T}{q_{\mathrm e}}\ln Q,$$3 nm before thermal dispersion.

Figure 3: Thermal-noise simulations comparing the substantially greater lifetime and propagation distance of three-quantum versus two-quantum protein solitons.

The numerical contrast is strong: reducing the excitation from three to two quanta decreases the reported reliable propagation range to less than $$\Delta G = \Delta G^\circ + \frac{k_{\mathrm B}T}{q_{\mathrm e}}\ln Q,$$4 of the rested-state range. The paper interprets this as a discrete energetic threshold. At approximately $$\Delta G = \Delta G^\circ + \frac{k_{\mathrm B}T}{q_{\mathrm e}}\ln Q,$$5, brain ATP hydrolysis can support three excitons, whereas a reduction below approximately $$\Delta G = \Delta G^\circ + \frac{k_{\mathrm B}T}{q_{\mathrm e}}\ln Q,$$6 permits at most two. The claimed consequence is a sharp deterioration in molecular energy-transfer reliability despite a relatively small change in available free energy.

The paper also reports a nominal molecular energy-conversion efficiency exceeding $$\Delta G = \Delta G^\circ + \frac{k_{\mathrm B}T}{q_{\mathrm e}}\ln Q,$$7, with less than $$\Delta G = \Delta G^\circ + \frac{k_{\mathrm B}T}{q_{\mathrm e}}\ln Q,$$8 not incorporated into useful soliton excitation. This result is accompanied by an important qualification: the high efficiency leaves a safety margin of less than $$\Delta G = \Delta G^\circ + \frac{k_{\mathrm B}T}{q_{\mathrm e}}\ln Q,$$9. Consequently, the proposed system is efficient but energetically fragile.

This molecular argument is conceptually important but also constitutes one of the paper’s most model-dependent claims. Davydov solitons remain a contested description of biologically relevant energy transport, and the mapping from ATP-hydrolysis free energy to an integer number of amide I quanta is not established as a general mechanism in neuronal proteins. The simulations demonstrate behavior within the specified model; they do not independently establish that ATP energy is transferred through this pathway in intact neurons. The numerical threshold should therefore be interpreted as a prediction of the model rather than a directly measured biochemical discontinuity.

Ionic gradients and neuronal hyperexcitability

The second computational component uses a morphologically complete CA1 pyramidal neuron implemented in NEURON. The model includes transient and persistent sodium currents, several potassium currents, multiple calcium currents, calcium-dependent potassium currents, and the hyperpolarization-activated mixed cation current. The authors alter the sodium and potassium Nernst reversal potentials to represent rested and fatigued ionic conditions.

In the rested condition, the model uses

$-\Delta G$0

In the fatigue condition, the reversal potentials are shifted toward equilibrium:

$-\Delta G$1

These shifts represent partial dissipation of the sodium and potassium gradients caused by repetitive activity and insufficient restoration by the $-\Delta G$2 pump. The paper notes that more than $-\Delta G$3 of the neuronal ATP budget may be consumed by this pump, making ionic homeostasis a major energetic constraint on information processing.

Figure 4: CA1 pyramidal-neuron simulations showing how degraded sodium and potassium reversal potentials alter spike trains, firing-frequency responses, and susceptibility to depolarization block.

The model predicts that the fatigued ionic condition increases excitability and makes the neuron more vulnerable to depolarization block. In the rested state, the neuron tolerates injected somatic currents up to approximately $-\Delta G$4 nA while maintaining physiological firing below $-\Delta G$5 Hz. Under degraded ionic gradients, the same external drive produces higher excitability and a greater tendency toward sustained depolarization and cessation of regular spiking.

The paper’s interpretation is deliberately nontrivial: neuronal fatigue is not initially characterized by reduced excitability, but by excessive and poorly controlled excitability. As ionic gradients diminish, the membrane becomes less capable of discriminating relevant synaptic inputs from stochastic or background fluctuations. Spontaneous firing, erratic responses, and reduced sensory selectivity can therefore precede complete firing failure. At sufficiently severe gradient dissipation, however, hyperexcitability transitions into depolarization block, producing a near-total loss of reliable spike coding.

This prediction is consistent with the general principle that neuronal information capacity depends not simply on firing rate but on the stability, selectivity, and dynamic range of spike responses. A neuron that fires more readily can nevertheless encode less information if its baseline activity and response variability increase. The paper accordingly frames mental fatigue as a degradation of signal-to-noise ratio rather than only a reduction in the number of action potentials.

From subcellular depletion to cognitive impairment

The proposed causal sequence is summarized by four linked processes:

1. accumulation of ATP-hydrolysis products and dissipation of ionic gradients;
2. increased reaction quotients and movement toward thermodynamic equilibrium;
3. reduced Gibbs free energy available for molecular and pump-mediated work;
4. impaired neuronal information processing through protein dysfunction and altered excitability.

The paper emphasizes that energetic failure is spatially heterogeneous. ATP, ADP, phosphate, creatine phosphate, and ionic concentrations are compartmentalized across somata, dendrites, axons, and dendritic spines. Mitochondria can be recruited near active synapses, while creatine kinase provides a local phosphocreatine buffer. These mechanisms imply that fatigue may begin in microscopic compartments before becoming detectable at the whole-neuron or macroscopic network scale.

This multiscale interpretation explains why EEG and fMRI may detect fatigue relatively late or indirectly. Standard EEG has limited spatial resolution, and measurable changes may require alterations across approximately $-\Delta G$6--$-\Delta G$7 cortical neurons. fMRI measures hemodynamic consequences rather than neuronal free-energy availability directly. The paper therefore predicts a latent interval in which synaptic and neuronal computation is already degraded, while conventional macroscopic neurophysiological measures remain relatively insensitive.

A particularly bold claim is that cognitive performance can deteriorate before the individual experiences a clear subjective feeling of tiredness. The authors distinguish metabolic energy deficit from subjective fatigue and propose that subtle errors, slowed decisions, and impaired filtering may appear before conscious fatigue awareness. This has practical significance for safety-critical occupations, in which subjective alertness cannot be treated as a sufficient indicator of cognitive reliability.

The discussion also incorporates glutamatergic homeostasis. Prolonged activity may increase extracellular glutamate when astroglial uptake and glutamate–glutamine cycling become less effective. Elevated glutamate would further promote neuronal hyperexcitability and potentially excitotoxic stress. In the proposed framework, glutamate accumulation is not the primary thermodynamic cause of fatigue but a downstream amplifier of impaired ionic and metabolic regulation.

Methodological strengths and limitations

The principal strength of the paper is its explicit mechanistic integration. Rather than treating fatigue as a purely psychological construct or as a generic correlate of reduced glucose utilization, it identifies specific physical variables: $-\Delta G$8, $-\Delta G$9, $0.57~\mathrm{eV}$0, Nernst potentials, channel currents, firing-frequency curves, soliton lifetime, and propagation distance. The use of a full morphological CA1 model is also preferable to a point-neuron abstraction for evaluating how altered ionic driving forces interact with realistic cellular geometry.

The matched-noise comparison in the soliton simulations is methodologically appropriate because it isolates the effect of exciton number from differences in thermal-noise realization. Similarly, the electrophysiological comparison keeps the channel and morphology model fixed while changing reversal potentials, providing a direct estimate of the effect of ionic-gradient degradation.

Several limitations constrain the strength of the conclusions. First, the estimated brain ATP-hydrolysis free energy is based on metabolite concentrations drawn from heterogeneous literature sources and treated as representative of broad physiological states. Real neuronal energetics are compartment-specific, dynamic, and coupled to oxygen delivery, mitochondrial redox state, astrocytic metabolism, and vascular regulation.

Second, the transition from reduced ATP free energy to exactly two rather than three amide I excitons assumes a particular quantized coupling between biochemical free energy and protein vibrational modes. This assumption is not validated in the paper through direct measurements of neuronal protein energy transport. The resulting soliton lifetimes and distances are therefore conditional on the Davydov model, parameterization, and initial conditions.

Third, the fatigue neuron simulation represents a complex metabolic process by changing only $0.57~\mathrm{eV}$1 and $0.57~\mathrm{eV}$2. This is useful for isolating ionic-gradient effects, but real fatigue may also modify channel kinetics, conductance densities, calcium handling, synaptic release probability, mitochondrial ATP production, astrocytic buffering, neuromodulation, and network connectivity. The model consequently demonstrates plausibility rather than a complete physiological simulation of mental fatigue.

Fourth, the paper extrapolates from an individual CA1 pyramidal neuron to cortical cognitive performance. CA1 neurons are relevant to hippocampal computation but are not interchangeable with neocortical pyramidal neurons, prefrontal microcircuits, or distributed cortical networks. Network-level compensation, inhibitory interneuron recruitment, synaptic scaling, and neuromodulatory control could either amplify or attenuate the cellular effects.

Practical and theoretical implications

The practical implication is a scheduling hypothesis: frequent, relatively short recovery intervals may be more effective than infrequent long breaks because the underlying molecular and ionic systems may cross nonlinear energetic thresholds. If three-quantum soliton stability and ionic-gradient integrity both deteriorate progressively, early restoration could prevent a larger downstream loss of computational reliability.

This recommendation should not be treated as a clinical protocol on the basis of the simulations alone. It is instead a testable prediction. Future studies could compare break schedules while simultaneously measuring reaction metabolites, phosphocreatine, extracellular potassium, glutamate, EEG microstates, pupil dynamics, reaction-time variability, and decision accuracy. The strongest validation would require spatially resolved measures of ATP/ADP/phosphate ratios and ionic gradients in behaving animals or human-compatible metabolic imaging.

The theoretical implications extend beyond fatigue. The paper presents neuronal information processing as a nonequilibrium function that depends on maintaining biochemical and electrochemical gradients. This perspective provides a unified language for studying fatigue, sleep pressure, hypoxia, aging-related hyperexcitability, seizure susceptibility, neuroinflammation, and neuropsychiatric disorders. It also suggests that the relevant variable for brain performance may be phosphorylation potential and local free-energy availability rather than bulk ATP concentration.

For future AI research, the framework may motivate energy-aware computational architectures in which reliability depends on local energetic budgets, adaptive duty cycles, and controlled reduction of processing intensity. Neuromorphic systems could implement analogues of ionic-gradient depletion, recovery, and depolarization block to study graceful degradation under resource constraints. More immediately, AI systems deployed in safety-critical settings could benefit from monitoring operator cognitive-load proxies and enforcing recovery schedules, although such applications require empirical validation rather than direct transfer of the paper’s molecular model.

Conclusion

“Reduced Gibbs free energy supply hinders brain information processing during mental fatigue” proposes that mental fatigue is a reversible nonequilibrium thermodynamic state in which ATP-hydrolysis free energy becomes insufficient to preserve both efficient molecular energy transport and stable neuronal ionic gradients (2608.10211). Its simulations report a sharp loss of protein-soliton stability when excitation decreases from three to two amide I quanta, together with increased neuronal hyperexcitability and vulnerability to depolarization block when sodium and potassium reversal potentials move from rested to fatigued values.

The paper’s strongest contribution is the integration of biochemical thermodynamics with molecular and electrophysiological computation. Its strongest limitation is that the molecular soliton mechanism and the simplified mapping from metabolic fatigue to reversal-potential changes remain model-dependent. The central hypothesis is nevertheless experimentally tractable: local reductions in phosphorylation potential and ionic-gradient integrity should precede or accompany declines in cognitive reliability, potentially before subjective fatigue or macroscopic EEG abnormalities become evident.