On 2017 Jan 14, Boris Barbour commented:

I have tried to clear up my confusion about the simulation conditions and more specifically the boundary conditions, which must often represent the physical context of the sphere. The Perspective seems to offer several versions, none of which is entirely satisfactory.

1) The images in Fig. 3 might be taken to suggest that the spheres are surrounded by nothing. In consequence, my calculation in the previous comment assumed a vacuum. However, one should of course read the equations and not put one's faith in Nature illustrations. I apologise to the authors and readers for initially jumping to this probably wrong conclusion.

2) Box 1 states that there is "no flux of the electric field" at the spine boundary. I think this would imply no net charge within and no net charge outside the spine, which would appear to be inconsistent with the case where the spine contains ions. (There are other logical possibilities: a grounded boundary or some exotic distributions with very specific inside-outside symmetries. But these are implausible in the present context). I therefore believe this statement refers to some special case or is an error. Or maybe it represents that well known and remarkably accurate approximation of strict electroneutrality?

3) Box 2 equation 5 gives a different boundary condition, this time with a non-zero electric field

E = Q/(4 * pi * er * e0)

However, I believe this contains an error. If the denominator also included a factor of R² , the equation would be dimensionally correct and also compatible with an infinite aqueous medium. The physical model would then be water everywhere, with a thin, "electrically invisible" barrier enclosing the ions. There would be no ions outside the spine. (It should be understood that we are dealing with "idealised" water that contains no ions, not even from the spontaneous dissociation of water molecules that occurs in reality.)

The corrected option 3) and therefore the infinite aqueous milieu seems the most plausible to me. In this case the arguments in the previous comment about the large potentials required in the "vacuum" case are still relevant, except that the values would be attenuated 80-fold by the relative permittivity of water. Voltages would range from about 20mV for 1000 ions to about 20V for 1000000. Figs. 3b and 3c would still require clearly unphysiological voltages.

In Fig. 4, the authors argue that the model spine has a "logarithmic capacitance" (i.e. V is proportional to log(Q)). However, they define V as the voltage difference between the centre and the rim of the spine. I see two problems with this definition.

1) A minor issue is that, in the model, most ions added to the spine distribute to radii other than zero (the centre), attaining a different potential in the process. An alternative might be the potential averaged over all charges.

2) A more significant issue is that the reference voltage is taken at the rim of the spine, which is well within the potential field of the spine, thereby excluding some if not most of that potential. All practical measurements and most neuronal current loops involve much larger distances outside the spine, and for these a reference at infinity is a reasonable approximation. This alternative of an external reference would require inclusion of the large voltages mentioned above. These are proportional to the charge and are likely to dominate the small intra-spine nonlinearities highlighted by the authors.

In the end, however, spines exist neither in a vacuum nor even in distilled water. As discussed in my earlier comments, most if not all of the electrical behaviour in insulators (dielectrics) described by the authors is likely a poor guide for what happens in conductors. The phenomena could thus be radically altered by the inclusion of a conducting external solution, ions of opposite charges at realistic (near equal) concentrations and a membrane.

On 2017 Jan 07, Boris Barbour commented:

[This comment has been edited as a result of uncertainty about the exact conditions for the simulations. Follow up in next comment.]

A simple calculation shows how unrealistic assumptions of significant deviations from electroneutrality are.

Imagine the sphere is in a vacuum, such that there is no external solution and the membrane capacitance is therefore absent. Then from Gauss' Law and symmetry it can be shown that the potential at the rim of the sphere with respect to infinity (i.e. a distant reference) will be:

V = Q/(4 * pi * e_0 * r),

where V is the potential, Q the charge, r the radius of the sphere and e_0 the vacuum permittivity. (This is equivalent to the classical isolated spherical conductor.)

Taking e_0 = 8.85E-12F/m, r = 0.5E-6m and an electronic charge of 1.6E-19C, we can calculate that just a single ion produces a potential of about 2.8mV. The 1000 ions in the simulation of Fig. 3a will therefore create a voltage of 2.8V (in my slightly smaller sphere), while the 1E6 charges of Fig. 3c would generate a whopping 2.8kV. Thus, the largest physiological potential could not generate a deviation from electroneutrality greater than the equivalent of a few tens of ions in the spine.

In practice a few thousand ions of the same sign can be accumulated (calculated in my first comment), but this is only possible because the charge-compensating mechanisms of the membrane capacitance and polarisation of the medium are present, which largely preserve electroneutrality.

On 2016 Dec 26, Boris Barbour commented:

Despite this article appearing in a journal dedicated to reviews, I appreciate it is tagged as a "Perspective", which presumably indicates that it contains some speculation. However, I still think it is worth pointing out to readers that electrostatic screening has in effect been omitted from the modelling, which could have an extremely strong influence on the phenomena illustrated, particularly as this is not made clear in the article.

This problem will only be addressed by analytical or numerical approaches that include at least two oppositely charged species at approximately physiological concentrations. I insist on this point because the cited preprint (like this Perspective) models the charge alone, which means only a single charged species is considered. Additional manuscripts treating this non-biological situation do not help address the biologically relevant questions. The standard approach to simulating the two-species system would be to include distinct electrodiffusion equations for the concentrations of cations and anions, whose difference yields the net charge distribution.

In the spirit of not jumping to conclusions or trusting to intuition in a complex situation, I would equally encourage readers (and the authors) to exercise due care before extrapolating from simulations with low concentrations of a single charged species to the situation with high concentrations of oppositely charged species.

EDIT: The effective omission of the membrane capacitance should also be rectified in any realistic modelling. This is because most if not all of the net charge in the spine will accumulate below the membrane, where it is quasi-neutralised by a symmetrical accumulation of opposite net charge the other side of the membrane. Without this mechanism, the actual capacitance of the spine/membrane will presumably be lower than observed in situ. In other words, biologically relevant voltages could not drive many charges into a spine without a membrane capacitance. The present modelling ignores the membrane capacitance because there is no extracellular saline in which an oppositely charged accumulation of ions can occur.

On 2016 Dec 26, Rafael Yuste commented:

We appreciate the concerns of Dr. Barbour and thank him for his frankness. But we alert the reader that this publication is not a proper experimental study but an opinion piece with a very limited set of data, which were added strictly to illustrate the point, and did not represent a comprehensive analysis of electrodiffusion in spines. Our review should be viewed precisely as what it is, a "Perspective", highlighting new and potentially controversial topics. The role of electrodiffusion in nanophysiology has been traditionally ignored by cable theory because of the difficulty to analytically solve the corresponding joint equations. Moreover, the interaction between electric fields and diffusion and geometry are not easy to dissect because they are highly nonlinear and sometimes counter intuitive and consequently difficult to discuss without adequate computational simulations. We, and others, are exploring this potentially important phenomenon with simulations and theoretical studies, some of which have already been published (https://arxiv.org/pdf/1612.07941.pdf), and which will hopefully address all the concerns of Dr. Barbour. We encourage the reader not to jump to quick dismissive conclusions but to be patient and wait for further work.

On 2016 Dec 26, Boris Barbour commented:

In this "perspective", the authors build up the importance of using full electrodiffusion simulations without an electroneutrality constraint to describe current flow and ion distributions within dendritic spines, rather than treating the cytoplasm as an Ohmic conductor. Although an electrodiffusion model is in principle more accurate and may in some cases be necessary, the authors do little to make their case here, because their illustrative model in Fig. 3 is quite divorced from physiological conditions.

They illustrate the equilibrium spatial distribution of ions within a small and isolated sphere of water, a situation loosely representing the head of a dendritic spine. When electrical interactions between the ions are considered at high concentrations, a highly nonuniform spatial distribution emerges. However, there are both trivial and fundamental problems with this apparently dramatic illustration.

It is worth fixing some numbers. Empirical measurements of membrane capacitance typically yield values of ~1microF/cm^2. So the capacitance of a typical spine head with diameter 0.5 microns will be about 10fF. Charging this capacitance to the most extreme membrane potentials observed in neurones (of the order of 100mV) will therefore require about 1fC, a charge that represents about 5000 ions. The volume of such a spine head would be about 70aL (attoLitres) and, assuming a 150mM saline of monovalents, would contain about 600000 each of cations and anions. The authors use a rather oversized spine head compared to this, but the numerical differences will be unimportant to what follows.

The authors simulate 1000, 100000 and 1000000 charges, but already the second number exceeds the largest net concentration of charges that will occur physiologically.

The concentrations they report are numerically incorrect at least in Fig. 3b (where the mean concentration should be 40 microM) and in Fig. 3c (where the mean concentration should be 400 microM).

A true representation of these gradients would include the existing 150mM saline. Thus, for Fig. 3a, the ~100nM gradient would be superimposed upon 150mM, about one part in a million, which may not be that significant.

Another important problem arises from the fact that the authors only include charges of one sign in their model, while physiological saline contains both cations and anions, in roughly if not exactly equivalent concentrations (we calculated above that the net charge represents of the order of 1% of ions present, and even this number is only made possible by the membrane capacitance). This unrealistic situation is likely to have a very strong influence on the behaviour illustrated, because the existence of ions of the opposite sign would allow electrostatic screening, which the authors have in effect banished from their model by only including a single ionic species.

The ionic gradients illustrated by the authors arise from collective mutual Coulombic repulsion (note that the submembrane ionic concentration shown is unrelated to the concentrations of charges normally occurring on either side of the membrane capacitance, because the external saline is absent in this model). Such Coulombic forces are usually annihilated over all but the shortest distances and times by electrostatic screening. The habitual approximation considers electrostatic shielding to cause an exponential attenuation of Coulombic interactions with a length constant of the Debye length. In 150mM monovalent saline the Debye length is about 0.6nm (using an approximate formula given on wikipedia), so, even over a fraction of a micron, Coulombic interactions should be attenuated to a cosmic degree and the forces generating the interesting concentration gradients of Fig. 3 are unlikely to operate.

In conclusion, although I'm not in a position to describe exactly the distribution of net charges in the spine head under physiological conditions in the absence of strict electroneutrality, neither are the authors. However, ignoring electrostatic screening seems to be an extremely unrealistic approximation.

On 2016 Dec 26, Boris Barbour commented:

In this "perspective", the authors build up the importance of using full electrodiffusion simulations without an electroneutrality constraint to describe current flow and ion distributions within dendritic spines, rather than treating the cytoplasm as an Ohmic conductor. Although an electrodiffusion model is in principle more accurate and may in some cases be necessary, the authors do little to make their case here, because their illustrative model in Fig. 3 is quite divorced from physiological conditions.

They illustrate the equilibrium spatial distribution of ions within a small and isolated sphere of water, a situation loosely representing the head of a dendritic spine. When electrical interactions between the ions are considered at high concentrations, a highly nonuniform spatial distribution emerges. However, there are both trivial and fundamental problems with this apparently dramatic illustration.

It is worth fixing some numbers. Empirical measurements of membrane capacitance typically yield values of ~1microF/cm^2. So the capacitance of a typical spine head with diameter 0.5 microns will be about 10fF. Charging this capacitance to the most extreme membrane potentials observed in neurones (of the order of 100mV) will therefore require about 1fC, a charge that represents about 5000 ions. The volume of such a spine head would be about 70aL (attoLitres) and, assuming a 150mM saline of monovalents, would contain about 600000 each of cations and anions. The authors use a rather oversized spine head compared to this, but the numerical differences will be unimportant to what follows.

The authors simulate 1000, 100000 and 1000000 charges, but already the second number exceeds the largest net concentration of charges that will occur physiologically.

The concentrations they report are numerically incorrect at least in Fig. 3b (where the mean concentration should be 40 microM) and in Fig. 3c (where the mean concentration should be 400 microM).

A true representation of these gradients would include the existing 150mM saline. Thus, for Fig. 3a, the ~100nM gradient would be superimposed upon 150mM, about one part in a million, which may not be that significant.

Another important problem arises from the fact that the authors only include charges of one sign in their model, while physiological saline contains both cations and anions, in roughly if not exactly equivalent concentrations (we calculated above that the net charge represents of the order of 1% of ions present, and even this number is only made possible by the membrane capacitance). This unrealistic situation is likely to have a very strong influence on the behaviour illustrated, because the existence of ions of the opposite sign would allow electrostatic screening, which the authors have in effect banished from their model by only including a single ionic species.

The ionic gradients illustrated by the authors arise from collective mutual Coulombic repulsion (note that the submembrane ionic concentration shown is unrelated to the concentrations of charges normally occurring on either side of the membrane capacitance, because the external saline is absent in this model). Such Coulombic forces are usually annihilated over all but the shortest distances and times by electrostatic screening. The habitual approximation considers electrostatic shielding to cause an exponential attenuation of Coulombic interactions with a length constant of the Debye length. In 150mM monovalent saline the Debye length is about 0.6nm (using an approximate formula given on wikipedia), so, even over a fraction of a micron, Coulombic interactions should be attenuated to a cosmic degree and the forces generating the interesting concentration gradients of Fig. 3 are unlikely to operate.

In conclusion, although I'm not in a position to describe exactly the distribution of net charges in the spine head under physiological conditions in the absence of strict electroneutrality, neither are the authors. However, ignoring electrostatic screening seems to be an extremely unrealistic approximation.