All in One: The false dichotomy of electrical vs mechanical nature of action potentials

The article summarises our approach to the physics of action potential at a fundamental level and addresses some of the criticism and misconception related to its application to nerves, such as how it addresses the dissipation and temperature dependence of action potentials.

Figure A membrane pulse represented as a propagating perturbation in a thermodynamic manifold.

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​Recently, Scientific American and Spektrum magazines highlighted our alternative perspective on how signals in neurons propagate physically. Our approach has been presented as a mechanical one as opposed to an electrical one, which I believe creates a false dichotomy that needs to be addressed. For this blog entry, I didn’t want to list the limitations of the Hodgkin and Huxley based equations, vis a vis acoustic theory and address them one by one. There are many other research articles, blogs, and forums for that including the recent articles in Scientific American. Here I want to go beyond that and touch upon, in simple language, why the Hodgkin and Huxley model is unsatisfying at a deeper, more fundamental, and philosophical level. The ultimate objective of the acoustic theory, as envisioned by Konrad Kaufman, is the unification of the physics of the nerve pulse phenomenon leading to a fundamental understanding of the brain itself. This is why the mechanical vs electrical dichotomy, which might be good for an initial introduction to the debate, does a great disservice to the cause.
So the question we really want to answer is what would be the most general description of a wave phenomenon in a complex system? Also, what theoretical framework even allows dealing with all of its aspects (electrical, mechanical, optical, thermal, chemical, etc.) at once. This requires some understanding of thermodynamics beyond just conservation of energy and heat flow. Let me try to provide the most simple version of it in the next two paragraphs.
In a system, no matter how complex, things evolve towards equilibrium or maximum entropy. Entropy is not just an extensive quantity related to heat, but it’s a unique function of extensive observables that completely defines the physical state of the system. Thus entropy is an analytic function of the form S(x), where x‘s are variables that can be measured in an experiment such as volume, energy, charge, concentrations of various ion species etc. It is at this level that any phenomenon observed in the evolving system is unified. For example, the first derivative of S with respect to volume is related to pressure, with respect to energy is related to temperature, and with respect to charge is related to the electric field, etc. The system only cares about maximizing entropy and not about which arbitrarily defined quantity (volume, charge, etc.) needs to be altered to achieve the maximum entropy. Furthermore, the maximization might need to be done under certain constraints such as conservation of mass, momentum, and energy.
A two-dimensional description of an entropy potentialWhen we perturb a system from its resting state, the second law tries to restore the equilibrium. This is the origin of elasticity in a material and is given by the second derivative of the entropy function. In a viscoelastic material, if the perturbation is too fast for the relaxed entropy to be dissipated as heat, conservation of mass momentum and energy results in propagation. It should now be possible to see why it would be wrong to assume that any perturbation of the system will, in general, only be electrical or mechanical etc.
This unique approach to entropy and thermodynamics was instrumental in how Einstein successfully derived various thermodynamic results related to Brownian motion, blackbody radiation, specific heats of solids and critical opalescence. It is the second derivative of the state function that resulted in the original expression for wave-particle dualism. I.e. when the mean energy is high, light propagates as a wave, while when its small, we only observe particle like quantized energy fluctuations. Therefore, it won’t be a coincidence if we one day establish a similar dualism between quantized ion channel fluctuations and macroscopic action potentials as originally envisioned by Konrad Kaufmann.
To take these set of ideas and apply to a phenomenon like nerve impulse is obviously not trivial by any means. But that should not deter us from finding a description of the phenomenon in the image of the most fundamental laws known to us, which will go far beyond a circuit theory of resistors and capacitors. So what are the main challenges of applying these ideas to nerve membranes? I think the biggest challenge is at the philosophical level, as in what do we consider to be a true explanation. Thermodynamics describes a phenomenon in terms of macroscopic properties, i.e. specific heat, compressibility, dielectric etc. and in this way is intrinsically an emergent or top-down approach as opposed to a reductionist or bottom-up approach. One can find many mainstream articles from well-known authors on the philosophical dilemma of reductionism vs emergence in biology, which apply to this debate as well. The approach, therefore, requires a completely new set of tools and methods, that can measure the macroscopic state of the proper system to provide a quantitative description of the process. So for example, if we measure the compressibility of the membrane using a pipette puller, it is not obvious if we are measuring the proper compressibility relevant for propagation. Also, the effects of drugs and toxins will then need to be evaluated in terms of how they change the state and not how they lock into a hole that is 6 orders of magnitude smaller than the wavelength of an action potential.
The second challenge is that the various aspects of thermodynamics and acoustic that are invoked to describe the phenomenon of the action potential are extremely rare and poorly understood in the corresponding core fields themselves. Observations like all-or-none and annihilation upon collision will surprise many seasoned experts in nonlinear acoustics. I have shown that these action potential like properties actually result from a propagating phase transition, a rarely observed phenomenon otherwise. Such propagating transitions constitute the limiting behavior according to various principles of shock physics. Furthermore, the complete description will require unifying the statistical (channels) as well as the mean (action potential) aspect of the propagating field, again not your average fluid dynamics problem. Similarly, how acoustics and chemistry interact, a field known as sonochemistry, is another aspect of the problem that is poorly understood. Thus solving the problem of nerve pulse propagation in a thermodynamic framework actually amounts to solving major challenges in several fields simultaneously.
Coming to the soliton model, it is the simplest (first order nonlinearity and dispersion) description that was provided by Prof. Heimburg and Prof. Jackson in 2005 that tries to capture most but not all of the essential features of a propagating phase transition in a membrane. They had to step down from the high pedestal of the second law to make the first attempt at a quantitative description of the phenomenon based on thermodynamics and that is what the soliton model tries to do. Clearly, the simplification doesn’t capture the annihilation phenomenon as it requires incorporating higher order terms. That doesn’t mean the thermodynamic basis is wrong, which clearly allows annihilation as discussed above. Similarly, several other criticisms around reversibility and temperature specificity of phase transition simply result from a misunderstanding of these concepts.
The heating and cooling of the nerve fiber during an action potential, in sync with the electrical and mechanical signal, is reminiscent of gas compressing and expanding quickly in a cylinder. To first order, the process is usually assumed to be adiabatic, and an adiabatic process can still be dissipative. However, that is not even the point. It is not important if the heat rise and fall are exactly equal or not, rather the point is if the origin of heat is irreversible (dissipative) or reversible (temperature is a function of state). If the origin is reversibility, the temperature will fall in sync with pressure (state) just as observed during an action potential. Some dissipation is natural but that doesn’t form the basis of the phenomenon, which is the change in state. This is unlike the Hodgkin and Huxley model where the basis of the phenomenon, i.e. current flow along a potential gradient is irreversible, which causes only heating.
Similarly, a phase transition occurs at a fixed temperature only if all other variables are fixed. During an action potential membrane pressure and temperature both change and the phase transition is represented by a line (and not a point) in the PT diagram of state. Thus even at different temperature phase transition can occur at different values of pressure inside the pulse. In fact, this is related to how the amplitude and threshold of an action potential vary with temperature. I have previously given a detailed description of the physics behind how action potentials can still occur at different temperature if they require a phase transition.
There is no doubt that there are many open questions that need to be answered but the thermodynamic foundation of these ideas lays down a clear direction for the future research. Apart from explaining previous observations, the thermodynamic theory also makes clear predictions for new observations that will contradict the Hodgkin and Huxley based description. For example, a proper relation between membrane compressibility and conduction speed is beyond the scope of Hodgkin and Huxley model. Similarly, the release of energy during the collision of action potentials is another prediction that will announce complete departure from the Hodgkin and Huxley model. Like any good theory, apart from providing a satisfying description of the phenomenon at a deeper level, the thermodynamic approach also opens many new exciting possibilities for biological and biomedical research. Ultimately, it presents an opportunity for unifying the physics of the brain.

​Note: The article was previously published via my medium and linked in account as well.