neuronal-murburn-thermodynamic-electricity

name	neuronal-murburn-thermodynamic-electricity
description	Murburn thermodynamic framework for neuronal electrical activity - unified reaction-transport-relaxation model explaining resting potential, excitability, and signal propagation. Activation triggers: murburn, neuronal electricity, electron holding potential, redox thermodynamics, nonlinear dynamics.

Neuronal Electricality via Murburn-Thermodynamic Principles

A chemically-grounded, non-circular alternative to ion-centric models of neuronal electrical activity using Electron Holding Potential (EHP) and unified reaction-transport-relaxation equations.

Metadata

• Source: arXiv:2604.24772
• Authors: Kelath Murali Manoj, Nagamani Sukumar
• Published: 2026-04-15
• Categories: Neurons and Cognition (q-bio.NC), Subcellular Processes (q-bio.SC)

Core Methodology

Theoretical Foundation

The Murburn concept provides an umbrella framework for theorizing based on stochastic redox processes, offering novel models for:

• Metabolic processes
• Bioenergetic outcomes
• Electrophysiological phenomena

Key Innovation: Electron Holding Potential (EHP)

Electron Holding Potential (EHP) is a dimensionless field/state variable defined as:

EHP ∝ log(μₑ)  [logarithmically related to electron chemical potential]

This serves as the fundamental explanatory variable for neuronal activity, replacing traditional ion-centric models.

Unified Framework Components

The model integrates three key processes:

1. Local Redox Relaxation Dynamics

   • Stochastic redox processes at the molecular level
   • Local energy dissipation and redistribution

2. Spatial Transport

   • Driven by thermodynamic gradients
   • Non-equilibrium thermodynamic principles

3. Reaction-Transport-Relaxation Equation

∂EHP/∂t = D∇²EHP + f(EHP) - γ(EHP - EHP₀)

Where:
- D: spatial diffusion coefficient
- f(EHP): nonlinear local redox kinetics
- γ: relaxation rate
- EHP₀: resting potential reference

Emergent Phenomena

The nonlinear local redox kinetics naturally give rise to:

Phenomenon	Description
Threshold Behavior	All-or-none firing responses
Action Potential Waveforms	Stable spike generation
Signal Propagation	Axonal signal relay mechanisms
Resting Potential	Metabolic/redox state coupling

Implementation Guide

Mathematical Modeling

Step 1: Define EHP Field

import numpy as np

def ehp_field(x, t, EHP0, D, gamma, reaction_term):
    """
    EHP field evolution following reaction-transport-relaxation equation
    
    Args:
        x: spatial coordinate (axonal length)
        t: time
        EHP0: resting potential reference
        D: diffusion coefficient
        gamma: relaxation rate
        reaction_term: nonlinear redox function f(EHP)
    """
    # Spatial discretization
    dx = x[1] - x[0]
    dt = t[1] - t[0]
    
    # Initialize field
    EHP = np.ones((len(t), len(x))) * EHP0
    
    # Time evolution
    for i in range(1, len(t)):
        # Laplacian (diffusion)
        laplacian = np.gradient(np.gradient(EHP[i-1], dx), dx)
        
        # Update
        EHP[i] = EHP[i-1] + dt * (
            D * laplacian + 
            reaction_term(EHP[i-1]) - 
            gamma * (EHP[i-1] - EHP0)
        )
    
    return EHP

Step 2: Nonlinear Redox Kinetics

def redox_kinetics(EHP, k1, k2, k3, Ethreshold):
    """
    Nonlinear reaction term modeling redox processes
    
    Key features:
    - Threshold activation at Ethreshold
    - All-or-none response
    - Recovery dynamics
    """
    # Threshold-gated activation
    if EHP > Ethreshold:
        activation = k1 * (EHP - Ethreshold) ** k2
    else:
        activation = 0
    
    # Recovery term
    recovery = -k3 * EHP
    
    return activation + recovery

Step 3: Signal Propagation Simulation

def simulate_axonal_propagation(length, duration, dt, dx, stimulus_position):
    """
    Simulate action potential propagation along axon
    """
    nx = int(length / dx)
    nt = int(duration / dt)
    
    x = np.linspace(0, length, nx)
    t = np.linspace(0, duration, nt)
    
    # Parameters (example values, to be fitted)
    D = 1.0           # diffusion coefficient
    gamma = 0.1       # relaxation rate
    EHP0 = 0.0        # resting potential
    
    EHP = ehp_field(x, t, EHP0, D, gamma, 
                    lambda e: redox_kinetics(e, 10, 2, 0.5, 0.3))
    
    # Apply stimulus
    stimulus_time = int(0.1 * duration / dt)
    EHP[stimulus_time, stimulus_position] += 1.0
    
    return x, t, EHP

Experimental Validation Framework

Predictions for Testing

1. Metabolic-Activity Coupling

   • EHP should correlate with local redox state
   • Metabolic perturbations should alter electrical activity

2. Thermodynamic Consistency

   • Energy dissipation follows thermodynamic principles
   • No circular definitions (unlike ion-centric models)

3. Waveform Characteristics

   • Spike shape determined by nonlinear kinetics
   • Propagation speed depends on transport parameters

Applications

• Neuronal Dynamics Modeling: Unified framework for action potential generation and propagation
• Metabolic-Neural Coupling: Understanding how energy state affects neural function
• Neurodegenerative Disease: Investigating redox imbalance in pathological conditions
• Biophysical Education: Non-circular alternative to Hodgkin-Huxley formalism
• Cross-Scale Integration: Linking molecular redox to system-level electrical activity

Pitfalls

• Parameter Fitting: EHP parameters require careful calibration to experimental data
• Numerical Stability: Nonlinear kinetics may require adaptive time-stepping
• Validation Challenges: Direct EHP measurement not yet established experimentally
• Model Scope: Currently axon-focused; dendritic computation needs extension
• Comparison Bias: Traditional ion-centric models are deeply entrenched in literature

Related Skills

• neurocybernetic-large-scale-neuroscience: Large-scale neuroscience modeling
• brain-digital-twins-execution-semantics: Brain digital twin frameworks
• brain-network-controllability: Network control theory applications
• neural-dynamics-decision-making: Neural dynamics for decision processes

References

• Manoj, K. M., & Sukumar, N. (2026). Neuronal electricality founded in murburn-thermodynamic principles. arXiv:2604.24772.
• Murburn Concept: Stochastic redox processes as foundational mechanism