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Here we propose myelinated axons as potential biophoton waveguides in the brain, and we support this hypothesis with detailed theoretical modeling.

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These axons are tightly wrapped by a lamellar structure called the myelin sheath, which has a higher refractive index 26 than both the inside of the axon and the interstitial fluid outside see Fig. This compact sheath could therefore also serve as a waveguide, in addition to increasing the propagation speed of an action potential via saltatory conduction based on its insulating property There is some indirect experimental evidence for light conduction by axons 12 , 28 , including the observation of increased transmission along the axes of the white matter tracts, which consist of myelinated axons Myelin is formed in the central nervous system CNS by a kind of glia cell called oligodendrocyte.

The inset depicts the cross section in the transverse plane. The compact myelin shown in red terminates in the paranodal region near the Node of Ranvier, with each closely apposed layer of myelin ending in a cytoplasm filled loop shown in light red. For clarity in the depiction of the direction of the field at different points, the arrow length is renormalised to the same value everywhere. The adjacent color bar depicts the actual field magnitude. An interesting feature of photonic communication channels is that they can transmit quantum information as well.

The potential role of quantum effects in biological systems is currently being investigated in several areas, including olfaction 32 , 33 , avian magnetoreception 34 , 35 , and photosynthesis 36 , There is also growing speculation about the role of fundamental quantum features such as superposition and entanglement in certain higher level brain functions 15 , 24 , 38 , 39 , The answer to this question might be provided by quantum entanglement 41 , where the whole is more than the sum of its parts in a well-defined physical and mathematical sense.

However, nuclear spins can have coherence times of tens of milliseconds in the brain 43 , 44 , and much longer times are imaginable Long-lived nuclear spin entanglement has also been demonstrated in other condensed-matter systems at room temperature In contrast, photons are well suited for transmitting quantum information over long distances, which is why currently envisioned man-made quantum networks rely on optical communication channels typically optical fibers between spins 46 , Efficient light guidance therefore seems necessary for both classical and quantum optical networks in the brain.

In an attempt to answer this question, we have developed a detailed theoretical model of light guidance in axons. We show in the next section that the answer seems to be in the affirmative. For the majority of our simulations, we take the refractive indices of the compact myelin sheath, the axon and the fluid outside to be 1. This index contrast allows guided modes of light inside the myelin sheath. Although there are many scatterers both inside the axon cell organelles, e.

The modes are primarily confined in a waveguide if its dimension is close to or larger than the wavelength of the light. Myelinated axons in the brain greatly differ in length and caliber.

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Their diameters range from 0. Biophotons have been observed in the wavelength range 0.

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Most proteins including the proteins in the myelin sheath strongly absorb at wavelengths close to 0. To avoid absorption, we shall consider the transmission of light with wavelengths above 0. For different axon calibers, we send in light at different wavelengths, ranging from 0. This ensures good confinement in the myelin sheath to limit interactions with the inhomogeneous medium inside and outside the axon see Supplementary Information. Figure 1b shows the magnitude of the electric field of a cylindrically symmetric eigenmode of this structure for the wavelength 0.

The electric field is azimuthally polarized see Fig. Azimuthal polarization would prevent modal dispersion in the birefringent myelin sheath, whose optic axes point in the radial direction There are hundreds of other guided modes for this thickness of myelin sheath. Photons generated by a realistic source in the axons could couple to all these modes, with various coupling coefficients.


However, for the sake of simplicity and lack of knowledge of realistic photon emission characteristics by potential sources , we pick a single mode and study its transmission. Next, we discuss transmission in the presence of several optical imperfections e. The theory of various imperfections in optical fibers is developed with long distance communication in mind, which requires very small imperfections, and focuses on the conventional fiber geometry. Since the myelin sheath based waveguide does not pertain to either of these conditions, we shall mostly deal with explicit examples.

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We simulate short axonal segments as the computational resource requirements for FDTD are very high, and extrapolate the results for the full length of an axon. The lamellae, whose fusion and apposition leads to the formation of the compact myelin, terminate near the nodes in the paranodal region such that each lamella ends in a loop filled with dense cytoplasm see Fig. Many of these cytoplasmic loops are attached to the axonal membrane.

For a thin myelin sheath, the paradonal region is almost ordered, with the innermost lamella terminating first, and so on, but for thicker sheaths, many cytoplasmic loops do not reach the axonal surface, but terminate on other loops. The length of the paranodal region should, however, depend roughly on the the number of myelin lamellae, and hence on the thickness of the myelin sheath.

Figure 2a shows our model for the region of the axon close to the node see Methods section for detailed discussion on the model , and Fig. We interpret the results in terms of beam divergence and scattering, which are the two primary sources of loss here. Shorter wavelengths diverge less, but scatter more. In general, the transmission drops for all the wavelengths as the p-ratio increases, although the trend is less clear for the longest permissible wavelength. The number of cytoplasmic loops, and the microtubules in the paranodal region are kept in proportion to the thickness of the myelin sheath, and the volume of the paranodal region respectively see Methods.

In Fig. In general, the greater the mode volume, the less is the divergence. So, a mode with a larger mode volume corresponds to thicker myelin sheath should diverge less for the same paranodal length. Still, in Fig. For a fixed axon caliber, the transmission does not depend on the paranodal length in a well-defined way. One possible explanation for this feature is the unconventional nature of the waveguide itself.

The long wavelengths mostly suffer loss because of divergence. However, in these waveguides, not all the light that diverges is lost. There is a possibility of a fraction of the light diverging into the axon to come back into the myelin sheath at the end of the paranodal region. This sometimes even increases the transmission in the myelin sheath for longer paranodal regions.

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Increase in myelin thickness leads to better confinement, and less divergence. However, for larger p — ratios , the trend almost reverses, and thicker axons perform worse than thin ones. In these cases, scattering becomes more relevant than divergence, and longer paranodal regions lead to greater scattering. Even with such a sudden discontinuity in the sheath, we find that transmission can still be fairly high. We verified that the transmission after multiple paranodal regions can be approximately predicted by exponentiating the transmission through one see Supplementary Information.

Optical power from the eigenmodes of a straight waveguide leaks out on encountering bends. Bends of constant curvature have eigenmodes which can propagate with minimal loss, but axons typically change their curvature along their length.

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These bent—modes eigenmodes for circular bends are more lossy than the straight—modes eigenmodes for straight structures for changing curvature. Therefore, an appropriate way to quantify the bend losses for an arbitrary axon path will be to incident the straight—mode in a waveguide with continuously varying curvature, and observe the transmission in the myelin sheath at the other end. We choose a sinusoidal waveguide since it has alternating regions of positive and negative curvatures, and can thus serve as a prototype for any arbitrary contour.

Figure 3a is an example for an axon with radius 0. Bending losses for conventional S bend waveguides half a cosine function depend most strongly on the change of curvature A shorter wavelength is better confined and therefore yields higher transmission. But the inner part of a bent axon has a larger curvature than the outer part at each point. The thickness of the myelin sheath is not uniform all along the length of the axon.

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The mean of the distribution is in close agreement with that predicted by the g-ratio , and the standard deviation s. Figure 4d—f compare the total power transmission up to a wavelength from the myelin sheath boundaries in axons of different calibers. Thinner axons can tolerate greater percentage-inhomogeneity, suggesting a closer dependence on the absolute value of the inhomogeneity. Extrapolation for transmission in a longer segment of the axon is straightforward.

Longer correlation lengths would yield better transmission for the same s. We did not find suitable images of thicker myelinated axons, and longer segments from which a more realistic estimate of this particular inhomogeneity could be extracted.

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Axons can have quite arbitrary transverse cross-sectional shapes, and the ensheathing myelin partly imbibes that shape We give an example in Fig. As expected, transmission drops for all wavelengths as the cross-section becomes more random. Images in ref. If the axon and myelin sheath do not change the cross-sectional shape substantially along their length, there will be almost no more loss, as coupling loss is the primary source of loss here rather than the propagation loss.

However, if the cross-section changes significantly, there will be propagation loss as well. In addition to the sources of loss discussed above, there can be several other imperfections, the most significant of which is the cross-talk between axons. Light in a myelinated axon would not leak out significantly, even if placed in direct contact with cells of lower refractive indices than the myelin sheath.

However, if two or more myelinated axons are placed very close to each other side by side , then light leaks out from one to the other see Supplementary Information.

Cross-talk can be interpreted both as a loss and a coupling mechanism between axons in a nerve fiber. In general, the axons should be a wavelength apart to prevent cross-talk, which seems realistic from some of the images in ref. The other imperfections that we considered do not affect the transmission significantly.

Possible existence of optical communication channels in the brain

The refractive indices of the axon, the myelin sheath, and the outside medium, were taken to be constants for the simulations so far. Moreover, there can be astrocytes and other glia cells in the nodal region close to the axon. As light crosses this region from one internode to the other, it will pass through these cells. We modeled them as spheres with radii varying from 0. It is worth noting that in some regions of the internode apart from the paranodes , the myelin sheath might be unusually inhomogeneous for instance, by decompaction of the lamellae leading to additional scattering losses.

In biological tissues, and more so in the brain, scattering of light, rather than absorption, is the main source of attenuation of optical signals To our knowledge, the absorption coefficient of the myelin sheath has not been measured experimentally. We can only infer it indirectly with limited accuracy. But myelin can not be responsible for the majority of the absorption since grey matter almost devoid of myelin has comparable absorption coefficients It is likely that light sensitive structures e. Mammalian fat shows an absorption coefficient less than 0.

Water has similar absorption coefficients. Most proteins have a strong resonance peak close to 0. Only a direct measurement could tell us more. We discuss a few examples to estimate the attainable overall transmission. The internodal length is typically equal to — times the axonal diameter 51 , The predominant loss for these examples is in the paranodal regions. Sources and receivers would need to be located close to the ends of the myelinated sections of the axon to reduce coupling losses.

Let us note that photons could travel either way from the axon terminal up to the axon hillock or the other way round in an axon. One potential challenge for the use of biophotons for inter-neuron communication is the fact that biophoton emission rates per neuron seem to be quite low.