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Ion Permeability of Microtubule in Neuron Environment Chun Shen, and Wanlin Guo J. Phys. Chem. Lett., Just Accepted Manuscript • DOI: 10.1021/acs.jpclett.8b00324 • Publication Date (Web): 04 Apr 2018 Downloaded from http://pubs.acs.org on April 4, 2018

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The Journal of Physical Chemistry Letters

Ion Permeability of Microtubule in Neuron Environment Chun Shen, Wanlin Guo* State Key Laboratory of Mechanics and Control of Mechanical Structure and Key Laboratory for Intelligent Nano Materials and Devices of the Ministry of Education, and Institute of Nanoscience, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China

Email: [email protected] Phone: +86 25 84891896. Fax: +86 25 84895827

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Abstract Microtubules, constituted by end-to-end negatively charged α- and β-tubulin dimers, are long hollow pseudo-helical cylinders with internal and external diameters of about 16 and 26 nm, respectively, and widely exist in cell cytoplasm, neuron axons and dendrites. Although their structural functions in physiological processes, such as cell mitosis, cell motility and motor protein transport have been widely accepted, their role play in neuron activity remains attractively elusive. Here we show a new function of microtubules that they can generate instant response to a calcium pulse due to their specific permeability for ions. Our comprehensive simulations from all-atom molecular dynamics to potential of mean force and continuum modeling reveal that K+ and Na+ ions can permeate through the nanopores in the microtubule wall easily, while Ca2+ ions are blocked by the wall with a much higher free energy barrier. These cations are adsorbed to the surfaces of the wall with affinity decreasing in sequence for Ca2+, Na+, K+. As a result, when the concentration of Ca2+ ions increases outside the microtubule during neuronal excitation, K+ and Na+ ions will be driven into the microtubule, triggering subsequent axial ion redistribution within the microtubule. The results shed light on the possibility of the ion permeable microtubules involving in neural signal processing.

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Microtubules, found throughout the cytoplasm of eukaryotic cells as well as neurons, are not only the important component of the cytoskeleton1 serving as tracks for the transportation of biomolecules, but also involved in cell mitosis and cell motility.2 Microtubules are hollow protein cylinders and mainly composed of α- and β-tubulin dimers, which consist of amino acid residues with a net negative charge about 20-30 electrons per tubulin. The negative charges are mainly distributed on the surfaces of the microtubule wall.3-4 In neurons, microtubules are parallel to the axon with the positive ends always in the direction of the axon elongation,5 surrounding by mainly cations such as K+, Na+ and Ca2+ ions and anion mainly of Cl- ions in neuron cytoplasm. The distribution of these ions along the axon is widely recognized to play pivotal roles in the generation and transmission of neural signals as both the triggering and conduction of action potential have been found to largely depend on the local distribution of ions.6 Furthermore, it is expected that the charged microtubules must exert Coulomb force on ions nearby as microtubules can affect charged particles up to 5 nm from the microtubule surface.7 Therefore, it is important to explore the role of microtubules in neural activity. It has been shown experimentally that an isolated microtubule in ionic solutions can significantly amplify the ion current along the direction of microtubule in applied electric fields.8 The amplification of the current was reported to depend on the cation concentration.9 During neuronal excitation, significant changes in local concentration of ions can generate electrical potential in neuron cytoplasm.6 Microtubules always tend to grow along the externally applied electric field as shown experimentally.10-12 In addition, microtubules have been speculated to have effect on the ion propagation along their external surfaces by theoretical analysis based on the charge distribution on microtubule surfaces.3, 13-14 However, the ion permeability of the microtubule wall and the role of microtubules in the propagation of neural electric signal have seldom been investigated. Here we find by molecular dynamics (MD) simulations and coupled electrostatic field and diffusion dynamics analyses that K+, Na+ and Cl- ions can permeate through the nanopores in the microtubule wall, while Ca2+ ions are blocked by the wall with high affinity of attaching on the microtubule surface. The distributions of K+ and Na+ ions inside and outside the microtubule change remarkably when the Ca2+ ions are added to the solution. A local Ca2+ pulse raised around the

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microtubule can drive the K+ and Na+ ions into the microtubule, triggering ions redistribution along the microtubule lumen. We carried out a series of MD simulations on microtubule systems, containing different ions in the solution. The charge distribution in the microtubule as well as the ion distribution and permeation across the microtubule were analyzed. The ion redistribution along the microtubule lumen was calculated using the continuum theory incorporated in the COMSOL package. Detailed methods are described in Supporting Information. The basic building block of the microtubule is α- and β-tubulin dimer.15 The linear strands of longitudinally arranged α- and β-tubulin dimers assemble into protofilaments. The number of protofilaments is in the range 8–20 as observed in vitro and in vivo, and the most common architecture is 3-start helix with 13 protofilaments.16 In this work, we just focus on the case of the common 13-3 microtubule. As shown in Figure 1a, the microtubule contains 13 protofilaments that are arranged in a left-hand 3 start helix. Because of this arrangement, there are four types of nanopores in the microtubule wall as marked in Figure 1a. These nanopores have been demonstrated in many electron micrograph studies17-19 and reported for providing binding sites for tubulin-binding compounds such as taxanes and other microtubule-stabilizing agents20, which are about 10 Å in diameter.21 In all the simulations, distance from the central axis of the microtubule is denoted R. The average location of the microtubule wall is from R = 8 nm to R = 13 nm. The microtubule is solvated in the ionic solution, which is divided into the inside, surrounding and outside areas by the position relative to the microtubule wall, as shown in the z-view section in Figure 1a. Each α- and β-tubulin dimer carries 37 electronics and the microtubule within the simulation water box carries 481 electronics in total. The negative charges are mainly distributed on the microtubule surfaces as shown by the blue part in the 2D charge density map (Figure 1b). The average charge density of the external surface is about 0.19 e-/nm3, approximately four times as much as that of the internal surface. The most negatively charged part with a density of 1.0 e-/nm3, is located at R = 13 nm as shown in the bottom panel of Figure 1b.

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Structure and charge distribution of the microtubule. (a) The microtubule is displayed

periodically along z axis with α- and β-tubulins colored in green and magenta, respectively. The simulation water box is shown partially transparent. The upper right panel is a z-view section of the microtubule with the corresponding section radiuses marked. There are four types of nanopores in the microtubule wall formed by different patterns of the α- and β-tubulins as marked with grey circles and schematically shown in the bottom panel. (b) Top panel is a 2D charge density map in the xy-plane of the microtubule. The coordinate origin is at the center of the simulation system. The shaded parts on the coordinate axis denote the position of the cross section of microtubule. Bottom panel shows the charge distribution along the radial orientation of the microtubule. Distributions of ions around the microtubule The ions were initially added to simulation systems at random. In a simulation system with only K+ and Cl- ions in the solution, the initial concentrations of K+ and Cl- ions were 162 mM and 59 mM respectively, forming a neutralized system. During the simulation, the K+ ions gathered on the microtubule surfaces in a quite short period of time, less than 5 ns (Figure 2a), and then the distribution of K+ ions reached balance with sustained internal and external exchange through the nanopores. After the equilibrium of the ion distribution, the concentrations of K+ ions inside, surrounding and outside the microtubule were 68 mM, 216 mM and 100 mM, respectively (Figure 5



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2a). Figure 2b displays the 2D density map of K+ ions and the average normalized number densities of K+ and Cl- ions along the radial direction of the microtubule. It is found that K+ ions enrich around the microtubule surfaces and the area with highest concentration, up to 700 mM, is located between adjacent protofilaments. The concentration of K+ ions decreased with increasing distance from the microtubule surfaces to 90 mM in the bulk. Besides, the concentration of K+ ions near the outer surface of the microtubule (R = 13 nm) was 2.5 times as much as that near the inner surface (R = 8 nm). For comparison purposes, we calculated the Poison-Boltzmann (PB) distribution of K+ ions near the microtubule surface. The charge densities of the inner and outer surfaces were set to -0.02 C/m2 and -0.07 C/m2. The results are shown by the red curve in Figure S1, which is consistent with the ion distribution in our MD simulation. During the simulation, there was less exchange of the inside and outside Cl- ions (Figure S2a). Those initially near the microtubule run away from the negatively charged surfaces. As a result, the concentration of Cl- ions increased with increasing distance from the microtubule surfaces. Considering there are other cations in the cytoplasm, a new simulation was carried out with K+ and Na+ ions of the same concentration of 54 mM. Cl- ions were added to the solution to neutralize the simulation system. During the simulation, the cations adsorbed on the microtubule wall within several nanoseconds (Figure S3). In the surrounding area, the concentrations of K+ and Na+ ions were 82 mM and 85 mM respectively, indicating a stronger affinity of Na+ ions for the microtubule surfaces. To further investigate the influence of the change of ion concentration on the distribution of K+ ions, a test simulation was carried out. The initial configuration was constructed by adding another 50 K+ and 50 Cl- ions to the interior of the microtubule based on the configuration at 30 ns of the equilibrium system mentioned above (Figure S4). After equilibrium, 25 K+ ions diffused from the internal to the external of the microtubule. The ion concentrations of K+ ions inside, surrounding and outside the microtubule became 85 mM, 220 mM and 120 mM respectively.

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Distribution of K+ ions around the microtubule. (a) Averaged concentration of K+ ions

inside, surrounding and outside the microtubule. Inset shows the cross section of the simulation system with only cations labeled. (b) Averaged 2D density map of K+ ions in the xy-plane and normalized ion densities of K+ and Cl- ions along the dashed line, averaged over 5-50 ns. Permeability of the microtubule for ions The permeation of ions through the microtubule nanopores was observed from the MD trajectory. To investigate the ion permeability of the microtubule wall, further simulations were carried out with K+, Na+, Ca2+ and Cl- ions added to the solution. Considering the relatively low Ca2+ concentration in cytoplasm at neuron resting state, about 100 nM, and much higher value at neuron firing state,22 about 10 µM,23 a simulation system was constructed with all the Ca2+ ions added outside the microtubule (Figure 3a) based on the initial configuration of the simulation with only cations of K+ 7



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and Na+ ions. The initial concentration of Ca2+ ions in the outside area was 50 mM. After equilibrium, the concentration of Ca2+ ions in the bulk solution was about 170 µM. Although it is much higher than the experimental value due to the limited water box, the observation is not highly sensitive to the ion concentration. During the simulation, Ca2+ ions gathered on the outer surface of the microtubule and none of them entered the microtubule interior (Figure 3b). Compared with the system containing only K+ and Na+ cations, the concentrations of K+ and Na+ ions in the area near the outer surface of the microtubule were much lower in this system (Figure 3c). The enrichment of Ca2+ ions on the outer surface drives K+ and Na+ ions into the microtubule and more cations attached to the inner surface of the microtubule. For comparison, we change Ca2+ ions to Mg2+ ions and find that the Mg2+ ions cannot enter into the inside area either (Figure S5). As the microtubule is highly negatively charged, the divalent ions have high affinity to the microtubule surface, and the energy barrier is high for them to get into the nanopores. However, here we mainly focus on Ca2+ ions for the case of divalent ions, due to the vital role of Ca2+ ions in the neural signal process. Besides, as the parameters for the ions will affect the ion binding affinity to biomolecules, we also tested this simulation with hydrated Ca2+ model24 as comparison. Similarly, the concentration hydrated Ca2+ ions gathered in the surrounding area, although the concentration increased more slowly in the surrounding area and ended in a lower value compared with the result mentioned above (Figure S6a). However, there are several hydrated Ca2+ ions leaking into the inside area through the nanopores. This slight inconformity in ion passage may be in part due to the fact that the hydrated model does not allow water molecules in ion’s hydration shell to exchange with outer waters, different from the setting in the classical NBFIX model. To further test the permeability of the microtubule for the Ca2+ ions, another system was constructed with the same concentration of K+, Na+ and Ca2+ ions for 54 mM. The ions were uniformly distributed in the whole system at the initial state. In the simulation, both K+ and Na+ ions showed internal and external exchange as expected, while Ca2+ ions were completely separated by the microtubule wall. Likewise, Ca2+ ions showed extremely strong adsorption on the microtubule surfaces with the concentration of Ca2+ ions (dotted line in Figure 3c) much higher than that of Na+ and K+ ions in the surrounding area. As the charge distribution of the microtubule is relatively fixed,

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the microtubule can attract certain number of positive charges. The adsorption of Ca2+ ions on the microtubule surfaces makes K+ and Na+ ions leave the microtubule surfaces. As the microtubule is 3-start helices, there are four types of nanopores in the microtubule wall. The number ratio of the four types of nanopores is 12 : 12 : 1 : 1, corresponding to pore1, pore2, pore3 and pore4, as listed in Figure 1a. The detailed morphology of these pores is shown in Figure S7a. The average radius at the narrowest site of the pore is approximately 4.0 Å for pore1 and 3 Å for the other three types of nanopores (Figure S7b). According to the analysis above and the examination of the MD trajectory, the two main nanopores, namely pore1 and pore2, provide the main pathways for ions with different permeability (Figure 3d). As shown by the number of ions permeating through the nanopores per nanosecond, K+ ions are most likely to permeate through the microtubule wall, Na+ ions can also exchange through the nanopores with less permeation amount. However, no Ca2+ ion is observed to permeate through these nanopores during the MD simulations. Additionally, the potential of mean force (PMF) was calculated to investigate the free energy of ions in the two main nanopores. The results in Figure S7c show that a ~2 kcal/mol free energy barrier impedes the permeation of a K+ ion through pore1 or pore2, the barrier for a Na+ ion is ~7 mol/L, while the free energy barriers for a Ca2+ ion to permeate through pore1 and pore2 are 16 kcal/mol and 12 kcal/mol respectively, indicating the impermeability of the microtubule for Ca2+ ions. In all the simulations, the concentration of Cl- ions was low in the surrounding area and increased with increasing distance from the microtubule surfaces. For the case with less Cl- ions in the simulation system, there was no exchange of Cl- ions across the microtubule wall. When the concentration of Cl- ions became relatively high, more internal and external exchange of Cl- ions was observed through the MD trajectory. Detailed results for the distributions of Cl- ions in these simulations are shown in Supporting Information (Figure S2).

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section of the simulation system with only cations labeled. (b) Concentrations of K+，Na+ and Ca2+ ions inside, surrounding and outside the microtubule. (c) Normalized ion density of K+, Na+ and Ca2+ ions along the radical orientation of the microtubule. Inset shows equilibrated distribution of K+ (green), Na+ (blue) and Ca2+ (red) ions. The radius of the black circle is 10 nm. Dash line is the distribution of Ca2+ ions in a system with Ca2+ ions initially added inside and outside the microtubule. (d) Number of K+ and Na+ ions permeating through the four types of nanopores per nanosecond. Ion redistribution along microtubule lumen triggered by a Ca2+ pulse around the microtubule During neuron firing, the concentration of Ca2+ ions was reported to increase significantly outside the microtubule 23. To investigate the change in the distribution of ions around the microtubule at the neuron firing state, Ca2+ ions were added outside the microtubule at an initial concentration of 20 mM (Figure 4a), based on the configuration at 30 ns of the system shown in Figure 2, where there were only K+ and Cl- ions in the solution. During the simulation, the concentration of K+ ions 10


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decreased in the surrounding area and increases both inside and outside the microtubule within 10 ns, induced by the adsorption of Ca2+ ions to the microtubule outer surface. After 60 ns equilibration simulation, 85% Ca2+ ions were crowded in the surrounding area, as schematized in Figure 4c. Compared with the distribution of K+ ions in Figure 2, the average concentration of K+ ions in the inside area increases from 65 mM to 85 mM as certain K+ ions were driven into the microtubule (Figure 4a). To polish our result, we also tested this simulation with hydrated Ca2+ model, the K+ concentration also increased in the inside area, although the increment was small. Therefore, we conclude that a local pulse of Ca2+ ions outside the microtubule will create an increased concentration of K+ ions inside locally. To investigate how the locally increased K+ concentration leads to the change of K+ distribution along the microtubule lumen, a schematic finite element model was constructed in the frame of continuum mechanics.25 The α- and β-tubulins in this model were simplified as spheres with radius of 2 nm (Figure 4c), and they carried evenly distributed negative charges at densities of 0.26 e-/nm3 and 0.17 e-/nm3 respectively. The length of the tube was 85 nm and the internal and external diameters were 16 nm and 24 nm respectively. The tube was embedded in a much larger cylinder with a diameter of 100 nm, simulating the ionic solution. The initial ion concentration of K+ and Clions in the cylinder was 65 mM. After electrostatic equilibrium, the distribution of K+ ions around the microtubule was plotted in Figure S1, comparable with the PB distribution and the results from MD simulations. The diffusion coefficients of the K+ and Cl- ions were set according to the diffusion coefficient curves shown in Figure 4b, obtained from MD simulations mentioned above. An inflow boundary with concentration of 100 mM for K+ ions, was set at one end of the tube lumen. The calculation was carried out based on the coupled electrical field and sparse material transfer field. As shown in the inset of Figure 4d, the concentration of K+ ions was high at one end of the tube, forming a concentration gradient along the lumen. Subsequently, the concentration of K+ ions in the system increased. Time evolution of the averaged K+ density at R = 0 and 6 nm was shown in Figure 4d. The increased concentration of K+ ions at one end resulted in changes of electrostatic potential along the tube, driving the diffusion and redistribution of K+ ions along the tube that the concentration of K+ ions in the tube lumen increased. The results show, at least, qualitatively that if

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there is a concentration gradient along the microtubule lumen, the K+ ions will redistribute along the microtubule.

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lumen induced by a Ca2+ pulse. (a) Time evolution of K+ concentration inside the microtubule (R < 10 nm) without (left panel) and with (right panel) Ca2+ ions outside the microtubule. Insets show the K+ density along the radial orientation of the microtubule in the two cases with cations labeled. (b) Diffusion coefficients of K+ and Cl- ions (Dc) along the radial orientation. (c) A schematic of the adsorption of Ca2+ ions on the microtubule outer surface and the resulting distribution of K+ ions (yellow line). (d) Time evolution of K+ density at R = 0 (the central axis of the tube) and 6 nm (the circle near the inner surface of the tube) averaged over 20 nm in the middle part of the tube lumen. The insets show the longitudinal section views of the distribution of K+ ions at 10 ns and 100 ns calculated using COMSOL package. 12


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It has been widely recognized that a neuron mainly transports signals along its axon, in which microtubules always grow along the axon and serve as cytoskeleton and tracks for motor proteins.2, 5 According to the classical neural model, the action potential, triggered by typical stimulates,26 is propagated along the axon by sequentially activating the ion channels in the unmyelinated membrane, along with the changes of local ion concentration.27 It was also assumed that consciousness in the brain might originate from a quantum physics process called objective reduction orchestrated by microtubules.28 Here, according to the MD simulations and the calculation of continuum field model, we find that K+ and Na+ ions can permeate through nanopores in the microtubule wall with relatively low free energy barriers in the neuron environment, while Ca2+ ions are blocked by the wall with a free energy barrier at least 5 times higher than that for K+ ions. During neuron firing, the adsorption of Ca2+ ions on the outer surface of microtubule can generate redistribution of K+ and Na+ ions around the microtubule. In the simulation resembling the neuron firing where the concentration of Ca2+ ions rises locally outside the microtubule, K+ ions are squeezed into the microtubule lumen, resulting in a concentration gradient of K+ ions in the lumen along the microtubule. To achieve ion distribution equilibrium in the simulated microtubule system within the time scale of nanoseconds, we choose a relatively high calcium concentration compared with physiological condition. However, the change of K+ distribution would still be measurable with a lower Ca2+ concentration, as Ca2+ ions show much stronger affinity than K+ ions, and the Ca2+ ions would ultimately gather around the microtubule with high concentration. The permeability of the microtubule wall for ions as well as the formation of ion concentration gradient induced by a Ca2+ pulse is sufficiently indicated by the MD simulations and continuum electrostatic calculations. Though, at this moment, it is not clear whether the microtubule could serve as an independent channel for neural signal processing, the reported ion redistribution and propagation clearly emphasize its role in the neural signaling, because change of local ion concentration is heavily involved in numerous neural processes such as action potential propagation,29 enzymatic reactions in brain cortex30 and actin assembly.31 A combination of the function of microtubules with the classical neural signal pathway might provide a better understanding of neural signaling. We performed systematic molecular dynamics simulations and finite element calculation on the distribution and diffusion of ions around the microtubule. Our results show that the cations densely 13



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gather near the microtubule surface, resulting in much higher concentrations on the surfaces than that in the bulk solution. Both K+ and Na+ ions have continuous internal and external exchange during our simulations, while Ca2+ ions cannot pass through the nanopores. The permeability of the microtubule for ions increases from Ca2+, Na+ to K+, while the affinity decreases from Ca2+, Na+ to K+. Ca2+ ions exhibit so strong affinity for the microtubule outer surface that the appearance of a peak value of the Ca2+ concentration in neuron cytoplasm would drive K+ ions to the microtubule interior through the four types of nanopores in the microtubule wall. The caused concentration gradient would induce the diffusion and redistribution of K+ ions along the microtubule lumen. Acknowledgements This work was supported by 973 program (2013CB932604), National Natural Science Foundation of China (51535005), the Funding of Jiangsu Innovation Program for Graduate Education (KYLX15_0249) (“the Fundamental Research Funds for the Central Universities”) and a Project Funded by the Priority Academic Program Development of Jiangsu Higher Education Institutions. The authors thank Dr. H. Qiu (NUAA) for his helpful suggestion on MD simulation and paper writing. Supporting Information Available: Methods and Figure S1-S8 are included. This material is available free of charge via the Internet at http://pubs.acs.org. References (1)

Mandelkow, E.; Mandelkow, E. M. Microtubules and microtubule-associated proteins. Curr. Opin. Cell. Biol. 1995, 7, 72-81.

(2) Jesús, A. Microtubule functions. Life. Sci. 1992, 50, 327-334. (3) Tuszyński, J. A.; Brown, J. A.; Crawford, E.; Carpenter, E. J.; Nip, M. L. A.; Dixon, J. M.; Satarić, M. V. Molecular dynamics simulations of tubulin structure and calculations of electrostatic properties of microtubules. Math. Comput. Model. 2005, 41, 1055-1070. (4) Sanabria, H.; Miller, J. H., Jr.; Mershin, A.; Luduena, R. F.; Kolomenski, A. A.; Schuessler, H. A.; Nanopoulos, D. V. Impedance spectroscopy of alpha-beta tubulin heterodimer suspensions. Biophys. J. 2006, 90, 4644-4650. (5) van Beuningen, S. F.; Hoogenraad, C. C. Neuronal polarity: remodeling microtubule organization. Curr. Opin. Neurobiol. 2016, 39, 1-7. 2+

(6) Parri, H. R.; Gould, T. M.; Crunelli, V. Spontaneous astrocytic Ca

oscillations in situ drive NMDAR-mediated

neuronal excitation. Nat. Neurosci. 2001, 4, 803-812.

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Ion Permeability of a Microtubule in Neuron ... - ACS Publications

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