Myelin is an insulating sheath forming around axons. Its biological function in neural systems and the growing mechanism have attracted increasing attention in the field of neuroscience (Lemke, 1988; Colognato and Franklin, 2004; Dutta et al., 2018; Stadelmann et al., 2019; Fields and Bukalo, 2020; Liu et al., 2021a). Previous studies reported a series of experimental observations about the micro-structures of myelin. For example, (1) The spiraling directions of neighboring myelin sheaths has a certain pattern. That is, the neighboring myelin sheaths on the same axon have the opposite spiraling direction (Richards et al., 1983), while the neighboring myelin sheaths on the adjacent axons have the same spiraling directions (Uzman and Nogueira-Graf, 1957; Bunge et al., 1989; Armati and Mathey, 2013); (2) For oligodendrocytes (OLs), the inner and outer tongues tend to be located within the same radial quadrant (Peters, 1961, 1964; Hildebrand, 1971; Webster, 1971; Fraher, 1972); (3) The axons of varying calibers tend to have myelin sheaths of the same thickness, resulting in the g-ratio phenomenon (FitzGibbon and Nestorovski, 2013; Stikov et al., 2015; Andersson et al., 2020); (4) Only the axon with sufficient caliber can be myelinated, resulting in the radial sorting phenomenon (Feltri et al., 2016; Harty et al., 2019; Ommer et al., 2019); and (5) For Schwann cells (SCs), one SC can only myelinate one axon. If the SC forms the remak bundle, it can never form the myelination, even if a large axon is ensheathed (Harty et al., 2019). These experimental observations indicate a multifaceted mechanism underlying myelin growth. For example, (1) the non-random spiraling phenomenon suggests that myelin growth can be influenced by the interaction between spatially closed myelin sheaths. (2) The same quadrant phenomenon indicates that myelin growth can be influenced by the relationship between the inner and outer tongues. (3) The g-ratio phenomenon indicates a possible correlation between inner tongue growth and the number of myelin lamellae. (4) The radial sorting phenomenon indicates a possible correlation between the myelin growth and the curvature of axons. (5) The characteristic SC properties in myelination and the remak bundle indicate the effect of the surrounding environment in formulating the growth of the inner tongue. Previous studies about mechanisms underlying myelin growth mainly focused on studying contributions from different molecules or proteins (Höke et al., 2003; Colognato and Franklin, 2004; Zheng et al., 2008; Orita et al., 2013; Hines et al., 2015; Feltri et al., 2016; Harty and Monk, 2017; Harty et al., 2019) without providing reasonable explanations for these phenomena. All these phenomena indicate an action at a distance, which is a kind of physical field, is dominating the formation of myelin growth. Thus, a study from a physical perspective can provide a substantial body of new knowledge yet to be discovered. In our previous study, the non-random spiraling phenomenon and the same quadrant phenomenon were explained from the perspective of the electromagnetic field (Wang et al., 2021) and electric field (Liu et al., 2021a). The former reveals the function of cytoplasmic channels in myelin sheath as a coil inductor and the role of the magnetic field in the neural signal. The latter reveals that the electric field modulates the growth of myelin. In this study, we further extend the hypothesis in our previous work, named as Hypothesis-E, to conduct in silico investigations of the physical origins of the unexplained myelin observations mentioned above. We name it Hypothesis-E, “E” refers to “electric.” In Hypothesis-E, an external negative E-field promotes myelin growth, while an external positive E-field inhibits myelin growth (Figure 1A). This study proposed three new hypotheses based on Hypothesis-E to further explain the physical origins of a series of morphological characteristics (Figures 1B–D) of the myelin.

FIGURE 1

Figure 1. A series of morphological characteristics of myelin explained a mathematical and physical perspective. (A) Hypothesis-E: The effect of E-field on myelin growth; (B,C) phenomena explained by Hypothesis-E: (B) g-ratio: The thickness of myelin sheath has a specific relationship with the diameter of the axon. (C) Radial Sorting: Myelin selectively myelinated axon based on axonal diameter; (D) SC of remak bundle cannot form myelin even when a large axon is ensheathed.

The myelin g-ratio, defined as the ratio between the inner and the outer diameter of the myelin sheath, has been reported in many experimental studies (FitzGibbon and Nestorovski, 2013; Stikov et al., 2015; Andersson et al., 2020). This precise relationship between axonal diameter and myelin sheath thickness has been reported is one of the most enigmatic questions: how is the myelinating glial cell instructed to make precisely the correct number of wraps? Transplantation of oligodendrocytes into nerve tracts containing axons of different sizes demonstrates that the number of wraps is determined by the axon but not by the glial cell because the transplanted glial cells elaborate myelin sheaths appropriate for their new location (Fanarraga et al., 1998). A key axonal signal for regulating myelin sheath thickness, the growth factor neuregulin (Ngr1), is now identified by Zuckerkandl and Pauling (1965). However, the detailed mechanisms of controlling the myelin wrapping by the axonal signal remain unclear.

The cross-section of a myelinated axon in the resting state (no action potential is activated) is shown in Figure 2A. The intracellular potential is more negative than the extracellular potential, resulting in a negative E-field on the inner tongue. This negative E-field is the driven force making the inner tongue grow and wrap around the axon to form myelination. Then the Hypothesis-EN (“N” refers to “negative”) is described as follows:

FIGURE 2

Figure 2. The model to explain g-ratio. (A) The cross-section of a myelinated axon in the static condition, the resting potential is equivalent to a voltage source; (B) a section of myelin cross-section with a radial angle of θ; (C) the equivalent circuit modeling the myelin cross-section.

The inner tongue of myelin is driven by a negative E-field from the axon in the resting state. The strength of the E-field on the inner tongue is proportional to its growth rate. When the E-field is lower than a threshold, the growth of the inner tongue terminates.

Figure 2B shows a mature myelinated axon with the number of myelin lamellae as N. The axonal radius is a, and the thickness of a single myelin lamella is b. Then the total myelin thickness, D, is b × N. We assume that the axonal cross-section is centrally symmetric. So we only simulate the local axon with a radial angle as θ, as shown in Figure 2B. The capacitance, C, of each layer is proportional to its area. Since the longitudinal length of each layer is identical, the capacitance of each layer is proportional to the arc length l:

C∝A⁢r⁢e⁢a∝l

Then for the nth layer, the capacitance, Cn, is proportional to its arc length ln:

Cn∝ln=θ×(a+(n-1)⁢b)

The voltage, Vn, on the nth layer is Vn=QnCn.

Here Qn is the charge on the capacitor. So the voltage, V1, on the first layer is V1=Q1C1.

Since all capacitors are connected in series, as shown in Figure 2C, the two boundary conditions are:

(1). The charge on each capacitor is the same, assigned with the value of Q:

Q=Q1=Q2=Q3=⋯=QN

(2). The resting potential, VR, is equivalent to a voltage source connected with these series-connected capacitors, as shown in Figure 2C, so VR is the sum of the voltage on all capacitors:

VR=∑n=1NVn=∑n=1NQnCn=Q×∑n=1N1Cn

The charge, Q, on each capacitor is:

Q=VR∑n=1N1Cn

The voltage, V1, on the first layer, which is the inner tongue, is as shown below:

V1=QC1=VRC1×∑n=1N1Cn=VRa×∑n=1N1(a+(n-1)⁢b)(1)

when the voltage potential, VR, and the thickness of a single myelin lamella, b are constants, the voltage on the inner tongue, V1, is only a function of the number of layers N, axonal radius a, and monotonically decreases with the number of layers, N. Here the threshold E-field proposed in Hypothesis-EN is defined as VN–T (“N” refers to “negative” and “T” refers to “threshold”).

And the ratio between VN–T and VR is defined as ηN–T:

ηN-T=VN-TVR(2)

Then the criteria for the max number of myelin lamellae Nmax is:

,,,]},,,]},,,]},,,,,]}],"socialLinks":[,"type":"Link","color":"Grey","icon":"Facebook","size":"Medium","hiddenText":true},,"type":"Link","color":"Grey","icon":"Twitter","size":"Medium","hiddenText":true},,"type":"Link","color":"Grey","icon":"LinkedIn","size":"Medium","hiddenText":true},,"type":"Link","color":"Grey","icon":"Instagram","size":"Medium","hiddenText":true}],"copyright":"Frontiers Media S.A. All rights reserved","termsAndConditionsUrl":"https://www.frontiersin.org/legal/terms-and-conditions","privacyPolicyUrl":"https://www.frontiersin.org/legal/privacy-policy"}'>