The important consequences of the reversible heat production in nerves and the adiabaticity of the action potential

Abstract

It has long been known that there is no measurable heat production associated with the nerve pulse. Rather, one finds that heat production is biphasic, and a heat release during the first phase of the action potential is followed by the reabsorption of a similar amount of heat during the second phase. We review the long history the measurement of heat production in nerves and provide a new analysis of these findings focusing on the thermodynamics of adiabatic and isentropic processes. We begin by considering adiabatic oscillations in gases, waves in layers, oscillations of springs and the reversible (or irreversible) charging and discharging of capacitors. We then apply these ideas to the heat signature of nerve pulses. Finally, we compare the temperature changes expected from the Hodgkin-Huxley model and the soliton theory for nerves. We demonstrate that heat production in nerves cannot be explained as an irreversible charging and discharging of a membrane capacitor as it is proposed in the Hodgkin-Huxley model. Instead, we conclude that it is consistent with an adiabatic pulse. However, if the nerve pulse is adiabatic, completely different physics is required to explain its features. Membrane processes must then be reversible and resemble the oscillation of springs more than resembling “a burning fuse of gunpowder” (quote A. L. Hodgkin). Theories acknowledging the adiabatic nature of the nerve pulse have recently been discussed by various authors. It forms the central core of the soliton model, which considers the nerve pulse as a localized sound pulse.

Introduction

The nerve pulse is generally regarded as a purely electrical phenomenon (Johnston and Wu, 1995). However, one also finds measurable changes in nerve thickness, length and temperature. The latter changes are not well-known and, if they are recognized at all, are considered low-amplitude side-effects of the voltage pulse (El Hady and Machta, 2015). In the present paper we focus on the temperature changes and the remarkable fact that the magnitude of this signal displays a larger energy than that related to the voltage changes - i.e., it is not a small signal.

In 1845, Emil du Bois-Reymond was the first to measure electrical currents and voltage changes in stimulated muscles and nerves (du Bois-Reymond, 1848), which were found to be of similar magnitude. Hermann von Helmholtz, 1848 was familiar with du Bois-Reymond’s experiments. In 1852, he was the first to determine the velocity of the nervous impulse (von Helmholtz, 1852), which he found to be close to the velocity of sound. Besides having a degree in physiology, Helmholtz was also an exquisite physicist and later became a professor of physics in Berlin. In 1847, Helmholtz proposed the first law of thermodynamics (von Helmholtz, 1847). It states that the change of energy in a system is related to the absorption or release of heat and the work performed. Du Bois-Reymond’s nerve and muscle experiments combined with his own considerations made Helmholtz interested in the heat production of muscles and nerves. Considering the similarities of their currents, he expected that chemical reactions and heat generation in muscles and nerves would also be similar. When performing experiments on frog muscles, he could measure temperature changes after repetitive muscle contraction that were of the order of 0.035°C (von Helmholtz, 1848). With the same experimental setup he found that the temperature changes in the nerves leading to this muscle were unmeasurably small (i.e., smaller than 0.002°C, which was the sensitivity limit of his experiment). This finding indicated that the mechanisms of heat production in muscles and nerves must be very different. In particular, the lack of measurable heat production indicates that no metabolism took place during the nerve pulse and that the process under consideration might be of reversible physical nature. Helmholtz found this negative result interesting enough to dedicate a section of his paper to heat production in nerves (von Helmholtz, 1848).

Stimulated by von Helmholtz, 1848’ intriguing finding, similar experiments were performed in subsequent research while increasing the sensitivity of the experimental setup. In 1868, Heidenreich (Heidenhain, 1868) improved the sensitivity of the heat recordings by about a factor of 10 using a thermopile. Like Helmholtz, he did not find any heat liberation during the nervous impulse. In 1890, Rolleston (1890) came to a similar conclusion using a platinum resistance thermometer. In 1891, Stewart (1891) repeated the experiments on mammalian nerve using a similar setup. He also found no heat production. In 1897, Cremer (1897) also failed to find any heat production in olfactory nerves of pike, carp, and barbel. In 1912, Archibald Vivian Hill (1912) performed experiments on sciatic nerves of frogs (Rana temporaria) using a very sensitive thermopile consisting of 30 iron-constatan thermocouples in series. He summarized:

“By a thermo-electric method it is shown that tetanus, up to 25 secs., of a live nerve, does not cause a change of temperature (other than at the seat of excitation) of more than about ${10}^{-6\circ }$C. There is no evidence of any change at all, but the method does not allow conclusions beyond this limit. For every single propagated disturbance the change of temperature therefore cannot exceed about ${10}^{-8\circ }$C., a hundred million^th of a degree. This corresponds to an oxidative process, in which only one molecule of oxygen is used in a space of visible size, viz. a 3.7 μcube. This suggests very strongly, though of course it does not finally prove, that the propagated nervous impulse is not a wave of irreversible chemical breakdown, but a reversible change of a purely physical nature.”

Later in his life (Hill, 1959) he commented about this early phase of heat measurements:

“Why did people go on trying to measure the heat production of nerve, in spite of repeated failure? Chiefly, I suppose, in order to settle the question of whether the nerve impulse is the sort of physical wave in which the whole of the energy for transmission is impressed on the system at the start. ”

W. M. Bayliss (1915) summarized the situation in his textbook ‘Principles of general physiology’:

“The result makes it impossible to suppose that any chemical process resulting in an irreversible loss of energy can be involved in the transmission of a nerve impulse, and indicates that a reversible physicochemical one of some kind is to be looked for.”

Thus, the conclusion that had to be drawn from the experiments before the World War I was that in contrast to a contracting muscle, the nerve pulse generates no measurable heat. Therefore, it was considered most likely that the nerve pulse consisted of a reversible physical phenomenon similar to a mechanical wave. While Hill’s paper was very influential after its publication, it is nearly forgotten today.

In the following decades, Hill became the dominating authority in the measurement of heat production in muscles and nerves. In 1922, he was rewarded with the Nobel prize for physiology. The problem of the undetectable heat production of the nerve pulse continued to bother Hill. In the second half of the 1920s, he and his collaborators Downing and Gerard managed to improve the sensitivity of the temperature measurements (Downing et al., 1926). Between 1926 and 1935, he continued studying the problem of heat generation in nerves (Hill, 1929, 1932, 1933a, 1933b, 1934; Downing and Hill, 1929; Feng and Hill, 1933a, 1933b, 1933c). Since the heat production (if there should be any) was obviously very small, Hill and collaborators measured the heat production during a repetitive stimulus of the nerve. Stimulation frequencies around 70 Hz were used (Hill, 1929). A typical experiment on frog nerves is shown in Fig. 1. There is a continuous small increase in heat production during repetitive stimulation, and there is a decaying heat production after the stimulation ceases that lasts several seconds. This suggests that the heat production is not due to the propagating pulse itself but to metabolism in the background. To make a formal distinction between the two contributions, Hill called the heat production during the impulse itself the ‘initial heat’ and the production after the pulse (the background metabolism) the ‘recovery phase’. The initial heat is the heat of the propagating pulse. Since the heat data were recorded in 1 s blocks, it was not possible to resolve the heat production of the action potential itself. Hill nevertheless concluded that there is no indication for an initial heat (Hill, 1932):

“The heat production of nerve is believed to occur in two phases, ‘initial’ and ‘recovery’; the former is presumably an accompaniment of the physical and chemical changes which take place during the propagation of the impulse; the latter, of the processes by which those changes are reversed and the nerve restored to its initial state. It is not easy to separate the one from the other; indeed, during the earlier part of this research it was realised that in a strict sense, and on the evidence available, there might really be no “initial” heat at all.”

Thus, by the end of this period the heat production of the nerve pulse itself could still not be resolved and it was questionable whether it existed at all. There was, however, clear evidence of metabolism in the background related to repetitive stimulation on a time scale significantly longer than that of the nerve pulse.

In a seminal publication in 1958, Abbott, Hill and Howarth (Abbott et al., 1958) (see also (Hill and Howarth, 1958) first resolved the initial heat response during the action potential in nerves from the legs of spider crabs. They called their article “The positive and negative heat production associated with a nerve impulse”. It was found that, during the rising phase of the action potential, heat is released into the environment of the nerve. This heat is mostly reabsorbed (to at least 70%) in a second phase of the action potential. Some experiments from (Abbott et al., 1958) are shown in Fig. 2. The existence of a reabsorption of heat is clearly surprising.

At the time it was not clear whether the heat is completely reabsorbed, or whether some heat is dissipated. Further, there existed no satisfactory explanation for both the qualitative and quantitative behavior of the heat production.

Hodgkin (1964, p.70) acknowledged the problem arising from Abbott et al.’s result in his monograph from 1964

“In thinking about the physical basis of the action potential perhaps the most important thing to do at the present moment is to consider whether there are any unexplained observations which have been neglected in an attempt to make the experiments fit into a tidy pattern. … perhaps the most puzzling observation is one made by A. V. Hill and his collaborators Abbott and Howarth (1958). … On reinvestigating the initial heat of crab nerve with better time resolution, Hill and his colleagues found that it was diphasic and that an initial phase of heat liberation was followed by one of heat absorption. … a net cooling on open-circuit was totally unexpected and has so far received no satisfactory explanation.”

During the next 30 years, Hill’s studies were continued and were refined by close collaborators, in particular by Howarth, Abbott and Ritchie (Abbott et al., 1965; Howarth et al., 1968, 1979; Abbott and Howarth, 1973; Ritchie, 1973; Howarth, 1975; Howarth and Ritchie, 1979). Temperature changes were recorded by a series of many (i.e. 96 (Abbott et al., 1958)) thermocouples. The thermocouples were insulated from electrical contact by embedding them into a raisin. Since raisin has bad heat conduction features and the thermocouples have a heat capacity of their own, one has to consider the distortion of the recordings by the setup itself. In order to obtain the true heat change, the results of the measurement have to be deconvoluted using the response function of the instrument (Fig. 3). Therefore, all of these studies used a so-called heat block analysis (shown in Fig. 2), which is a kind of empirical deconvolution of the measured data and the response function of the instrumentation (Fig. 3, B). It is described in detail in (Howarth, 1975). Due to the long response time of the setup ($\ge 60$ ms), these experiments are limited to nerves with very long action potentials such as the rabbit vagus nerve or garfish olfactory nerve at low temperature with pulse widths of about 100–200 ms.

In all of the above papers the authors came to the conclusion that the charging and discharging of a membrane capacitor (expected in the electrical models for nerve conduction (Hodgkin and Huxley, 1952)) cannot explain the observed changes in heat. The authors propose that most of the reversible heat production is due to entropy changes within the membrane during the action potential (see section 4.1).

The essential findings of the heat experiments are summarized in a review by Ritchie & Keynes from 1985 (Ritchie and Keynes, 1985). They ruled out the possibility that the heat reabsorption phase of the action potential was due to heat diffusion into the bulk medium. The local heating of a nerve showed that heat diffusion away from the nerve is much slower than the reabsorption of heat that is measured during the action potential. This control experiment is shown in Fig. 3 (B) (Ritchie and Keynes, 1985). They also found that the action potential is exactly in phase and approximately proportional to the square of the transmembrane voltage (Fig. 4). Thus, the heat release is proportional to the energy of charging and discharging a capacitor. After some initial doubts in earlier papers on whether the heat reabsorption is complete, they also found that all heat is reabsorbed within experimental accuracy. In fact, they could show that, even for action potentials with a hyperpolarization phase, the total heat followed voltage (Fig. 4) (Ritchie and Keynes, 1985).

The above experiments were limited to long action potentials of 100–200 ms. However, most nerve impulses display a temporal length on the order of 1 ms, which is about 2 orders of magnitude faster. Measurement of the heat release in such nerves requires different methods. Tasaki and Iwasa managed to obtain a faster response time by using a heat-sensitive polyvinylidene fluoride film (Tasaki and Iwasa, 1981). They recorded an action potential of 25 ms length in lobster nerve and later in garfish olfactory nerve and myelinated nerve fibers from bullfrog on action potentials with a time scale of 10–20 ms (Tasaki et al., 1989). As in the earlier measurements by Abbott, Howarth and Ritchie, Tasaki and collaborators found that the integrated heat is very small and consistent with nearly complete reabsorption. Results are shown in Fig. 5. These authors concluded that the heat production is in phase with the nerve pulse but that the total heat is unlikely to be caused by charging and discharging the membrane capacitor. The time course of voltage and heat was not always identical (Fig. 5 left a and b). They proposed that the heat production might originate from ion exchange in the superficial layer of the axoplasm (Tasaki et al., 1989) which was an idea generally favored by Tasaki. He proposed that the nerve pulse is accompanied by a phase transition in the proteins on the surface of the nerve (Tasaki, 1999).

It should be noted that, in addition to the striking reabsorption of heat, various other experiments indicate that the nerve pulse is not a purely electrical phenomenon. It has been found that the membrane of the axon changes its thickness (Tasaki et al., 1989; Iwasa and Tasaki, 1980; Iwasa et al., 1980; Tasaki and Iwasa, 1982a, b; Gonzalez-Perez et al., 2016) and its length (Tasaki et al., 1980, 1989; Wilke and Atzler, 1912), i.e., a change in axon dimension. Further, it has been shown in birefringence, light scattering and fluorescence experiments that lipids in the membrane change orientation and order during the pulse (Cohen et al., 1968; Tasaki et al., 1968, 1969a, 1969b, 1971; Cohen and Keynes, 1971). This indicates that the physical reality in nerves is far richer than that assumed in a purely electrical picture.