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

Action Potentials are all in one: The false dichotomy of electrical vs mechanical

Shamit Shrivastava
8 min readSep 16, 2018

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The article summarises our approach to the physics of action potential and addresses some of the criticism and misconception related to its application to nerves, in particular, how it addresses the dissipation and temperature dependence of action potentials.

Recently, Scientific American and Spektrum magazines highlighted our alternative and thermodynamic explanation for the phenomenon of nerve pulse propagation. Our approach has been presented as a mechanical one as opposed to the established electrical, which I believe creates a false dichotomy that needs to be addressed. The limitations of the Hodgkin and Huxley model, vis a vis thermodynamics has been discussed and debated extensively, and I believe the debate will continue in the foreseeable future. However, in this article, 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 thermodynamic theory is the unification of the physics of the nerve pulse phenomenon, in a framework that is scalable to entire populations of neurons, and ultimately, to the brain. This is why the mechanical vs electrical dichotomy, while convenient 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, like the excitable membrane of a neuron? 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 that goes beyond the basic textbook concepts of conservation of energy and accountancy of heat flow, that is, how a system when left to its devices, evolves towards equilibrium or the state of maximum entropy.

We see entropy not just as an extensive quantity related to heat, but as 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 extensive 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, respect to energy is related to temperature, and 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 typically happens under certain constraints such as constant volume, constant pressure, etc., or in the case of a propagating wave, conservation of mass, momentum, and energy.

When we perturb a system from its resting state, the second law acts* to restore the equilibrium. This is the origin of elasticity in a material and is given by the second derivative of the entropy function. The elasticity determines both; how big the response of a system to external perturbation and how fast it relaxes. In a viscoelastic material, in general, any perturbation will relax partly as heat dissipated away via direct (diffusive) transfer of heat and mass into the surrounding media and partly as sound propagated away into the surrounding via momentum transfer. The transfer of ions, as in action potential, belongs to the first category of mass transfer. But what about heat and momentum transfer? We believe that an understanding that is in line with the universal understanding of mass, momentum, and heat transfer in real media will represent a complete understanding of the nerve pulse phenomenon. In the 1980s, Konrad Kaufmann highlighted the need for such an approach and laid the way forward by combining two important principles from thermodynamics and interface sciences;

  1. That the proper system that represents the medium of nerve pulse propagation is a 2D interface. Interfaces and surfaces have their own entropy independent of the volume it encloses.
  2. The fate of a perturbation of this interface is then determined by the total derivative of it’s entropy potential as discussed above and as described in seminal works on thermodynamic fluctuations.

These principles were inspired by the unique approach to entropy and thermodynamics that was instrumental in 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 it's small, we only observe particle-like quantized energy fluctuations. A statistically similar relationship exists between the macroscopic action potentials or nerve impulse and the underlying current fluctuations or ion channels in the thermodynamic approach.

To take this set of ideas and apply them 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 the present status of 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 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 constructive or bottom-up approach. I have covered the dichotomy between a theory of principles (analytical) and a theory of synthesis in a previous blog. One can also find many mainstream articles on the philosophical dilemma of reductionism vs emergence in biology, which apply to this debate as well.

From a more practical standpoint, the emergent nature of the approach requires a different set of tools and methods, that can measure the macroscopic state of the proper system to provide a quantitative description of the nerve impulse phenomenon. 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, i.e. length and time scales over which the compressibility is measured, need to match the nerve impulse. 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 physics that are invoked to describe the phenomenon of the action potential are rare and poorly understood in the corresponding core fields as well. Our experimental observations of nonlinear solitary waves in a pure lipid membrane that show remarkable action potential like properties, like all-or-none excitation and annihilation upon collision, surprise and excite many seasoned experts in nonlinear acoustics. We have shown that these action potential-like properties actually result from a propagating phase transition, a rarely observed phenomenon in an average material. Such propagating transitions constitute the limiting behavior in shock physics, where a general textbook description of shock waves does not apply anymore. Furthermore, the complete description will require unifying the statistical (channels) as well as the mean (action potential) aspect of the impulse, again not an average fluid dynamics problem. Similarly, how acoustics and chemistry interact, a field known also 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 of nerve impulses, which is usually the first point of entry for many into this debate, it is the simplest (first order nonlinearity and dispersion) description that was provided by Prof. Heimburg and Prof. Jackson in 2005. The model captures many but not all of the essential features of a propagating phase transition in membranes. It was the first attempt at a quantitative description of the phenomenon based on the principles of thermodynamics discussed above. The model is by no means complete and took a semi-empirical approach to derive the wave equation. Clearly, the simplification doesn’t capture the annihilation phenomenon as it requires incorporating higher order terms. That doesn’t mean the thermodynamic theory is wrong, which clearly allows annihilation as discussed above. Since then Prof. Roland Netz's group has derived the wave equation for propagation of waves at compressible interfaces from first principles, i.e. by defining and solving the corresponding Navier-Stokes problem and they continue to progress rapidly.

I still prefer the analytical approach to the problem motivated by classical shock and detonation physics. The approach finally allowed me to derive a phenomenological description of the phenomenon, in general, and for the first time its outstanding characteristics, like annihilation upon collision, in particular.

Several other criticisms around reversibility and temperature specificity of phase transition result from a simple misunderstanding of these concepts. For example, 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 reversible, 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, the requirement of phase transitions for all-or-none excitation has been criticized, because it is perceived as contradicting the fact that action potentials exist over a wide range of temperatures, whereas phase transitions occur at a well-defined temperature. Here is the problem with the above criticism, 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 pressure-temperature (PT) diagram of state. Thus even at different temperature phase transitions 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 temperatures if they require a phase transition. The predictions were later proven experimentally.

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 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 the Hodgkin and Huxley model. Similarly, the release of energy during the collision of action potentials is another prediction that will announce a 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.

* anthropomorphizations throughout the article are for the sake of simplicity while emphasizing the top-down causality employed in these arguments.

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Shamit Shrivastava

Biophysics of sound in membranes and its applications. Post Doctoral Researcher, Engineering Sciences, University of Oxford, UK www.shamits.org