Minireview - Microtubule and Tubulin Oligomers: Shape Transitions and Assembly by Intrinsically Disordered Protein Tau and Cationic Biomolecules

Abstract

In this mini-review, which is part of a special issue in honor of Jacob N. Israelachvili’s remarkable research career on intermolecular forces and interfacial science, we present studies of structures, phase behavior, and forces in reaction mixtures of microtubules (MTs) and tubulin oligomers, with either intrinsically disordered protein (IDP) Tau, cationic vesicles, or the polyamine spermine (4+). Bare MTs consist of thirteen protofilaments (PFs) on average where each PF is made of a linear stack of αβ-tubulin dimers (i.e. tubulin oligomers). We begin with a series of experiments, which demonstrate the flexibility of PFs towards shape changes in response to local environmental cues. First, studies show that MT-associated protein (MAP) Tau controls the diameter of microtubules upon binding to the outer surface implying a shape change in the cross-sectional area of PFs forming the MT perimeter. The diameter of a MT may also be controlled by the charge density of a lipid bilayer membrane that coats the outer surface. We further describe an experimental study where it is unexpectedly found that the biologically relevant polyamine spermine (+4e) is able to depolymerize taxol-stabilized microtubules with efficiency that increases with decreasing temperature. This MT destabilization drives a dynamical structural transition where inside-out curving of PFs, during the depolymerization peeling process, is followed by re-assembly of ring-like curved PF building blocks into an array of helical inverted tubulin tubules. We finally turn to a very recent study on pressure-distance measurements in bundles of MTs employing the small-angle X-ray scattering (SAXS)-osmotic pressure technique, which complements the Surface-Forces Apparatus technique developed by Jacob N. Israelachvili. These latter studies are among the very few, which are beginning to shed light on the precise nature of the interactions between MTs mediated by MAP Tau in 37°C reaction mixtures containing GTP and lacking taxol.

Graphical Abstract

INTRODUCTION

One of the many objectives in biophysics is to elucidate the nature of interactions between biological macromolecules including, for example, proteins, nucleic acids, lipids, which are responsible for the assembly of these building blocks on length scales from nanometers to microns of the order the cell size. This is because the various assembled structures and, in particular, the exposed surface shapes are often important to distinct cell functions. For example, during the cell cycle, extensive remodeling of cytoskeletal protein assemblies enables the complex process of cell division.¹ This mini-review is, in part, focused on the long-term goal to develop a comprehensive understanding of structures and forces between reconstituted cytoskeletal filamentous microtubules (MTs) and associated proteins, in particular, those derived or purified from neurons. We expect that such an understanding will address the key question of how the physical properties of cytoskeletal assemblies impact neuronal cell functions.^2,3

To begin our discussion of the cytoskeleton of neurons we show in Fig. 1A a drawing of a neuron where key subcellular components of the axon, cell body, and dendrites are depicted.⁴ This cartoon is accompanied by high-resolution quick-freeze and deep-etched electron micrographs by Nobutaka Hirokawa and collaborators displaying the highly distinct cytoskeletons of the axon and dendrite of vertebrate neurons with a large fraction of the intracellular space occupied by MTs and neurofilaments (NFs) (Fig. 1 (B,C)).^5,6 Microtubules are the dominant filaments in dendrites and are normally distributed throughout the cytoskeleton as single filaments (see Fig. 1B where one of the MTs is labeled with a yellow star). Neurofilaments (NFs, Fig. 1B, white arrow points to one NF) are either singly dispersed between MTs or appear in small bundles (Fig. 1B, labeled by a red star).^3,5 In contrast, in axons, NFs, which are oriented parallel to the axon, constitute the major cytoskeletal filaments (Fig.1C, red stars show the extensive NF-network). NFs, the intermediate filaments of neurons, consist of a core cylindrical body (≈ 10 nm diameter, Fig. 1C, white arrow) with protruding charged sidearms (Fig. 1C, yellow arrow) cross-linking neighboring filaments into a network.^3,6 When NF networks are reconstituted from purified NF-subunits they consist of liquid crystalline hydrogels under physiological pH and salt conditions.^7–10 MTs, which are immersed within the extended NF-network in axons, are primarily found to be isolated along the long axon. The exception to this is in the axon initial-segment (Fig.1A) where MTs are found to form small linear bundles commonly referred to as MT fascicles (Fig. 1C, blue star).¹¹ Interestingly, linear MT fascicles are also found to form spontaneously outside cells in reaction mixtures of tubulin and MAP Tau at 37°C in the presence of buffer containing GTP and 1mM of Mg²⁺.¹²

Figure. 1.

(A) Cartoon of a neuron showing elements of subcellular organization within the axon, cell body, and dendrites. Of interest to this mini-review are the heterogeneous cytoskeletal structures in distinct compartments consisting of microtubules (MTs), neurofilaments (NFs), and associated proteins. (B, C) Quick-freeze, deep-etch electron micrographs showing dendrite (B) and axon (C) cytoskeletons in spinal cord vertebrate neurons. In dendrites (B), MTs (one labeled by yellow star) are uniformly dispersed and NFs are either singly observed (white arrow) or in small bundles (red star). Cross-bridges between MTs and NFs are evident (microtubule-associated protein 2, MAP2, blue arrows). In axons (C), NFs (red stars) are the majority component and form oriented arrays surrounding MT bundles (blue star) or single MTs. White arrow points to NF core. Cross-bridges between NFs (NF-sidearm, yellow arrow), MTs (a microtubule-associate protein, red arrow) and MT and NF-sidearms (blue arrow) are evident. Bar = 100 nm. (A) Adapted with permission from reference 4. (B) and (C) Adapted with permission from references 5 and 6, respectively.

In non-dividing mature neurons, members of microtubule-associated proteins (MAPs) bind to and stabilize MTs against depolymerization. MAP Tau and MAP2 stabilize MTs in axons and dendrites, respectively.^13–19 EM studies show that MAPs may cross-bridge MTs into bundles in axons (Fig. 1C, red arrow).^5,6 Furthermore, NF-sidearms have been implicated in cross-linking NFs to MTs in axons (Fig. 1C, blue arrow). The electron micrographs of Fig. 1, depicting co-existence of MTs and NFs, highlight the formation of the distinct cytoskeletal structures present in axons and dendrites.

MAP Tau is an intrinsically disordered protein (IDP) and a biological polyampholyte (i.e. a charged polymer containing both positive and negative charged groups, see Fig. 2). Similarly, the C-terminal sidearms of NFs are intrinsically disordered polyampholytes projecting radially away form the NF cylindrical core.^7–10 While complementary protein shapes mediate induced-fit lock-and-key interactions in folded proteins,¹ IDPs play an important, yet poorly understood role, in mediating non-specific interactions.^20–22

Figure. 2.

(A) Cartoon showing Tau bound to a microtubule (MT) through its MTBR (yellow) segments, with the projection domain (green/purple, the main part of the N-terminal tail) having low MT affinity. (B) The top depicts the charge of 4RL Tau as a function of amino acid residues. The bottom shows that alternative splicing of exons 2 (red rectangle), 3 (orange), and 10 (blue) may result in the five other wild type isoforms. Wild type Tau consists of the amino-terminal tail (NTT), which includes the projection domain (PD, green/purple background) and proline-rich region (PRR, gray), the microtubule-binding region (MTBR, yellow) and carboxyl-terminal tail (CTT). Adapted from reference 12 with permission from the Nature Publishing Group.

The review is organized as follows. We first describe experiments on mixtures of taxol-stabilized MTs and MAP Tau isoforms as a function of increasing Tau/tubulin dimer molar ratio (i.e. increases in the coverage of the MT surface with Tau).²³ Here, we find that MAP Tau modifies the average number of PFs in MTs thus modifying the MT diameter. Remarkably, experiments also show that the MT diameter may also be varied by changes in the charge density of an adhering cationic lipid bilayer coating the outer surface of the MT.^24,25 The two studies demonstrate how attractive electrostatic interactions, whether it is between microtubules and Tau’s cationic microtubule binding regions or cationic liposomes, alter the cross-sectional area of PFs forming the perimeter of MTs. We next turn to a brief review of recent studies of the effect of polyamine spermine (4+), a multivalent counterion to anionic MTs, on the assembly structure of MTs.²⁶ At short times, spermine induces MT bundling.²⁷ However, with increasing time, spermine has a destabilizing effect on MTs by rupturing ionic bonds between PFs that make up the curved surface of MTs. The depolymerization of MTs via peeling of PFs leads to PF ring formation, which, in turn, leads to the stacking of PF-rings into helical inverted tubulin tubules. The tubules are referred to as inverted because the outer surface corresponds to the inner surface of MTs. These cell-free studies, which showed how multivalent spermine influences the overall stability of MT bundles are highly significant in elucidating how biologically related small biomolecules may play a fundamental role in modulating and remodeling the cytoskeleton in vivo, an emerging field of very high current interest in biological physics.

In the last part of the review we turn to recent studies, which demonstrate how the synchrotron SAXS-osmotic pressure technique allows one to obtain pressure-interfilament distance curves in dissipative reaction mixtures of tubulin and Tau at 37° C in the presence of the fuel molecule GTP required to maintain the dynamical bundled structure.²⁸ The technique was introduced in the biophysics community by Adrian Parsegian and collaborators over many years,²⁹ It complements the surface-forces-apparatus (SFA) methodology developed by Jacob Israelachvili for measuring forces between surfaces coated with a wide variety of macromolecules.^30. This more recent study also shows how forces between microtubules are fundamentally altered when comparisons are made between taxol-stabilized microtubules, described in the first part of the review, and microtubules undergoing dynamic instability with cycles of growth and shortening due to GTP hydrolysis.

MICROTUBULE-ASSOCIATED PROTEIN TAU REGULATES THE NUMBER OF PROTOFILAMENTS IN MICROTUBULES

Microtubules (MTs) are hollow cylinders with outer and inner diameters of about 25 nm and 15 nm, respectively (Fig. 2A).^31–35 Their building blocks are αβ-tubulin heterodimers (red/blue spheres in Fig. 2A), which stack to form linear protofilaments (PFs). During tubulin assembly, lateral interactions between tubulin oligomers (PFs of various lengths) leads to the curved MT wall. MTs are inherently dynamical and exhibit alternating periods of growth (tubulin polymerization) and shrinkage (depolymerization events or catastrophes) referred to as dynamic instability.^31,32 MTs and their dynamical assemblies are utilized by cells, typically in combination with MAPs, for a variety of activities, including, intracellular trafficking and chromosome segregation.^33,34

Human MAP Tau consists of six isoforms (Fig. 2B), those containing four C-terminal imperfect repeats, constituting the cationic MT binding domains R1–R4 and labeled 4R-Tau (see cartoon of Tau bound to MT in Fig. 2A), and those with three repeats (3R-Tau, R1–R3). Each family contains three distinct alternatively spliced isoforms, yielding N-terminal short (S), medium (M), and long (L) projection domains. The six Tau isoforms are labeled: 4RS, 4RM, 4RL, 3RS, 3RM, and 3RL, respectively. The N-terminal tail (NTT) consists of an anionic/cationic dipolar projection domain (PD) that projects off the MT surface, followed by a cationic proline rich domain with some MT affinity (Fig. 2B). The carboxyl-terminal tail (CTT) has low MT affinity.

The binding of different isoforms of Tau through the cationic binding domains (labeled MTBR, Fig. 2B) to MTs that are overall negative with charge density ≈ −0.66e/nm², stabilizes MTs against dynamic instability.^36–40 Aberrant behavior in Tau is responsible for neurodegenerative diseases including Alzheimer’s disease, Fronto-Temporal Dementia with Parkinsonism linked to chromosome-17, and Chronic Traumatic Encephalopathy in athletes.^41–43

In a recent study by Choi et al.²³ the cancer chemotherapy drug paclitaxel, which is referred to as taxol in the tubulin community, was used to fix microtubules against dynamic instability.^44–49 Synchrotron small-angle X-ray scattering (SAXS) was used to probe the structure of taxol-stabilized MTs in the presence of the human MAP Tau isoforms. The study revealed that Tau isoforms regulate the average size of the diameter of MTs at the ångstrom scale.²³ An example of the SAXS scattering profile for the 4RS-Tau isoform is shown in Figure 3A. The data corresponds to the form factor of MTs that was modeled as a hollow cylinder with the inner radius <R_in^MT> being the fitting parameter at constant wall thickness δ_w = 49 Å consistent with high resolution electron microscopy models of MTs with 13 protofilaments.⁴⁹

Figure. 3.

SAXS data showing that MAP Tau regulates the mean radius of MTs, or equivalently, the average protofilament number <N_pf>. (A) Synchrotron SAXS results of MTs with bound 4RS tau as a function of Tau to tubulin-dimer molar ratio in the reaction mixture (Φ). With increasing Tau, the SAXS profiles shift to lower q implying an increase in the MT radius. Colored lines are results of fits of the data to a model consisting of a hollow MT nanotube with the inner radius <R_in> being the sole fitting parameter. (B) The average inner radius <R_in> for two Tau isoforms (4RS and 3RS) plotted versus ϕ, the tau/tubulin-dimer molar ratio for the Tau fraction bound to the MT surface. The radial size of MTs increases as a function of increasing tau. (C) Schematic cross-sections of two MTs showing that with increasing Tau binding the distribution of protofilaments in MTs shifts towards MTs with larger <N_pf>, which leads to increases in <R_in>. A change in the diameter of MTs necessitates a change in the shape of tubulin dimers making up the protofilaments. Reprinted with permission from reference 23. Copyright 2009, Biophysical Society.

Most notably, the form factor SAXS data provide strong evidence that MAP Tau regulates the distribution of protofilament numbers in MTs. This is seen in the shift of the first minimum in SAXS, which is inversely proportional to the diameter of MTs, to lower q values as Φ (the tau to tubulin-dimer molar ratio in the reaction mixture) increases. Figure 3B is a plot depicting the increase of the average inner wall radius <R_in> of MTs and, equivalently, the corresponding average number of PFs per MT, <N_pf>, with increasing ϕ (the tau to tubulin-dimer molar ratio for the fraction of Tau bound to the MT surface). Significantly, <R_in> was observed to increase for 0 < ϕ < 0.2 and saturate for ϕ between 0.2 and 0.5. Thus, the data show that a local shape distortion of the tubulin dimer upon tau binding, is spread collectively over many dimers along the length of protofilament. The findings imply that MAP Tau mediates changes in the cross-sectional area of PFs forming the perimeter of MTs. This change in PF shape will result in changes in the number of PFs in MTs and thus the MT diameter.

Our findings imply that MAP Tau regulates the shape of individual protofilaments because it binds to only one side of the protofilament facing outwards away from the luminal surface of the MT. This will then change the spontaneous curvature of microtubules leading to changes in the measured curvature, which is inversely proportional to the MT radius. An important biological implication of these findings is a possible allosteric role for MAP Tau where the induced shape changes of the MT surface upon binding by tau may affect the MT binding activity of other MAPs present in neurons. Furthermore, the results, which provide insight on the regulation of the elastic properties of MTs by MAP Tau, due to changes in the MT diameter, may also have relevance to the mechanical properties of the cell cytoskeleton.

Stepwise Nanometer-Scale Changes in the Diameter of Microtubules Driven by a Cationic Lipid Bilayer Coating.

In an earlier study Raviv et al. investigated the interactions between cationic lipid vesicles and Microtubules and discovered that the mixture results in the spontaneous formation of lipid protein nanotubules (LPNs) under the appropriate conditions (Fig. 4A,B).^24,25 The LPNs exhibit a remarkable architecture with the lipid bilayer sandwiched between the microtubule and an outer tubulin oligomer layer.

Figure 4.

(A and B) Two views of lipid protein nanotube (LPN, with cross section view in B) made of a microtubule (tubulin subunits shown as red-blue-yellow-green objects) coated by a lipid bilayer membrane containing a mixture of cationic and neutral lipids (yellow lipid tails, green cationic headgroups, and white neutral headgroups). The lipid bilayer is further coated by tubulin rings. (C) Plot of the average number of protofilaments (PFs) per microtubule (MT), <N_pf>, and the inner wall radius, <R_in>, of the MT within the LPN complex as a function of x_CL, the mole fraction of cationic lipids in the lipid bilayer, or the membrane charge density (σ). The symbols in the inset correspond to different charged lipid to tubulin molar ratios R_CL/T. Solid symbols, for which R_CL/T = 160 ∙ x_CL, correspond to a series of data points at which the total number of lipids per tubulin is kept constant and is exactly enough to coat each MT with a bilayer. The arrow indicates the <N_pf> value of pure MTs, <N_pf>_MT =13.3, as obtained from the fit to the MT form factor. The three solid lines indicate the mean values of <N_pf> at each step. The broken lines indicate the upper and lower limits of <N_pf> at each step. Thus, the average number of protofilaments, or equivalently, the inner radius of the microtubule, changes in a step-wise fashion as the membrane charge density is changed. Reprinted with permission from reference 25. Copyright 2007, Biophysical Society.

The degree of overcharging of the lipid-protein nanotube enables the switching between two states of the LPN with either closed ends with lipid caps (when the LPN is positively overcharged) or open ends seen in Fig. 4A, when the LPN is negatively overcharged. This would form the basis for controlled chemical encapsulation and release.²⁴ Raviv et al. further discovered that the average number of protofilaments in MTs may be controlled by changes in the membrane charge density of the lipid bilayer coating the MT.²⁵ Figure 4C shows that as the membrane charge density, proportional to the molar fraction of cationic lipid x_CL, increases, the average number of protofilaments per microtubule (<N_pf>) and thus the inner radius <R_in>, decreases. What is surprising is that the change occurs in a step-wise fashion. Thus, the inner and outer diameters of the lipid-protein nanotube - a key parameter in chemical encapsulation and templating applications - may be controlled and varied by changes in the membrane charge density of the enveloping cylindrical lipid bilayer.

TRANSFORMATION OF TAXOL-STABILIZED MICROTUBULES INTO INVERTED TUBULIN TUBULES TRIGGERED BY A TUBULIN CONFORMATION SWITCH

A recent study by Ojeda-Lopez et al. employed the shape changing property of protofilaments, resulting from the enzymatic properties of the αβ-tubulin heterodimers, to study the impact on new self assembling structures.²⁶ The study took advantage of the well known property of PFs to exist in either a straight or curved conformation with the transition between these two states controlled by GTP hydrolysis.^31–35 The distinct conformations of PFs underlie the broad range of cellular activities of tubulin and polymerized tubulin (i.e. microtubules), which include imparting cell shape, as tracks for organelle transport, and as building blocks of dynamical spindles.¹ The work by Ojeda-Lopez et al. led to the remarkable discovery that tetravalent spermine (4+) controls the straight to curved transition rate even in taxol-stabilized tubulin.^26,50 This led to the creation of microtubule bundles in the presence of spermine on short time scales (Fig. 5B), which at longer times, undergo a dynamical transformation involving an inside-out curving of tubulin oligomers during the depolymerization peeling process (Fig. 5C) and concurrent re-assembly of curved tubulin building blocks into an array of inverted tubulin tubules (Fig. 5D). This new phase of tubulin assembly has been defined as a phase of bundles of inverted tubulin tubules (B_ITT). Thus, the study²⁶ led to a revision of the dogma in the MT field⁵⁰ that taxol-stabilized MTs were stable over extended periods of order months.

Figure. 5.

Schematic of a spermine (4+)-induced inversion process from bundles of taxol-stabilized microtubules (B_MT) to bundles of inverted tubulin tubules (B_ITT). (A and B) Taxol-stabilized microtubules (MTs, A) may be induced to form MT bundles above a critical concentration of spermine (4+) counterions (B_MT, B). The bundles result from the nonspecific electrostatic attraction between spermine coated MTs. (C and D) For concentrations several times larger than the critical bundling concentration a specific spermine-triggered straight-to-curved conformation transition in protofilaments, leads to MT disassembly into curved protofilaments (c-PFs) within the bundles (C). Concurrent to MT disassembly spermine counterions induce non-specific assembly of c-PFs into the B_ITT phase (D). Both phases are hierarchically ordered, liquid crystalline nanotubes, but the tubes are inverted: the tubulin surface, which is on the inside of the tubes in the B_MT phase is on the outside in the B_ITT phase. Adapted from reference 26 with permission from the Nature Publishing Group.

INTERFILAMENT FORCES IN MICROTUBULES BUNDLED BY TAU BY THE SAXS-OSMOTIC PRESSURE TECHNIQUE

The forces between filamentous MTs may be measured by using the SAXS-osmotic pressure technique, which involves performing in situ SAXS measurements of samples under osmotic pressure induced by a water soluble polymer depletant; for example, poly(ethylene oxide, PEO).^28,29,51,52 Synchrotron SAXS and TEM by Chung et al. show that dynamical MT bundles form spontaneously in reaction mixtures of Tau, tubulin, and GTP at 37°C (i.e. under dissipative conditions similar to the intracellular environment).¹² TEM of such bundles are depicted in Fig. 6A and synchrotron SAXS measurements reveal a wide wall-to-wall spacings (D_w–w) similar to that of MT bundles found in the axon initial-segment (see Fig. 1A,C). For example, for the 3RS Tau isoform, D_w–w ≈ 27 nm (Fig. 6B, at zero osmotic pressure).

Figure 6.

Force measurements, by Synchrotron SAXS-Osmotic Pressure studies of microtubule/Tau bundles, reveal two distinct bundle states. (A) Plastic embedded TEM side view of microtubules (MTs) assembled with Tau (3RM-Tau, 1/20 Tau/tubulin dimer molar ratio) show finite size MT/Tau bundles. (B): Osmotic pressure (P) - distance (D_w-w) curves for MT/3RS-Tau bundles using either 102K-PEO (magenta) or 20K-PEO (green). For 100K-PEO with diameter ≈ 40 nm the depletant cannot penetrate the bundles and with increasing P, measurements of the MT wall-to-wall spacing (D_w-w) shows a sudden transition to a collapsed MT bundle state (≈ 5 nm decrease) at P > P_c ≈ 300 Pa. This is indicative of a secondary energy minimum for MT bundles (magenta squares). With 20K-PEO as the polymer depletant, the transition to the collapsed bundle state is observed at higher P ≈ 5000 Pa (green squares). The discrepancy arises because the 20K-PEO depletant (diameter ≈ 15.6 nm) is smaller than the MT wall-to-wall spacing and partially penetrates the bundles giving rise to an “apparent pressure” larger than the actual applied pressure (the apparent pressure assumes the depletant does not penetrate the interior of the bundles). Above the transition the 20K-PEO depletant is expelled from the collapsed bundle and, as expected, the data for 100K-PEO and 20K-PEO overlap. (C and D) Cartoon of the osmotic pressure (P) induced transition from widely- spaced MT/Tau bundles (C) to a collapsed bundle state above a critical pressure (D). In the widely-spaced bundle state (C), weakly penetrating extended Tau projection domains (PDs) mediate transient charge-charge attractions between the cationic residues (purple/gray) and the anionic residues (green) of apposing PDs. The pressure induced transition to a collapsed state depicted in (D) (i.e. a secondary energy minimum at smaller spacings compared to widely-spaced bundles) corresponds to anti-parallel dimerization (i.e. ≈ full overlap) of Tau PDs occurring between the anionic section of the PD (green) and the cationic part of the PD (purple). (A, C, D) Adapted from reference 12 with permission from the Nature Publishing Group. (B) Adapted with permission from reference 28. Copyright 2018 American Chemical Society.

Figure 6B (magenta colored squares) displays the osmotic-pressure versus MT wall-to-wall spacing (P-D_w-w) curve for the 3RS-Tau isoform at a Tau/tubulin dimer molar ratio of 1/20 where D_w-w is obtained by synchrotron SAXS of MT/Tau bundles as a function of increasing wt% 102K-PEO (M_W = 100kDa).²⁸ The 102K-PEO is expected to have a diameter d100K-PEO = 4R_G/π^1/2 ≈ 40 nm.⁵² Here, R_G = 0.215MW^0.583 Å.⁵³ The relatively large size of 102K-PEO does not penetrate the interior region of the MT bundles and exerts an osmotic pressure on the bundle, which is a function of the concentration of the water soluble polymer.^28,51,53 Figure 6B shows that as a function of increasing wt% of 102K-PEO, the P-D_w-w curve exhibits a sharp rise between 40 Pa and ≈ 300 Pa and D_w-w decreases about 2 nm to 3 nm. The repulsive barrier is from Tau’s projection domain resisting osmotic compression (see Fig. 2). Above a critical pressure P > P_c ≈ 300 Pa, there is a rapid decrease in D_w-w from about 21.5 nm to 16.5 nm signaling a collapse of the bundle.

The large MT wall-to-wall spacing D_w-w ≈ 27 nm measured by SAXS for MTs bundled by 4RS Tau at P = 0 results from an extended state for Tau’s projection domain (PD). In this state the MT/Tau bundles are stabilized by attractions between oppositely charged residues of weakly penetrating apposing PDs between neighboring MT (Fig. 6C). The sudden transition above P_c indicates the onset of attraction between interpenetrating Tau chains on opposing MT surfaces, which would result in the decrease in D_w-w from ≈ 21.5 nm to ≈ 16.5 nm consistent with anti-parallel dimerization of Tau’s PDs (Fig. 6D) (i.e. due to the dipolar charge distribution of the PD, Fig. 2C). MTs bundled by PD dimers are in a second local energy minimum with a smaller wall-to-wall spacing distinct from the minimum in widely-spaced bundles at P = 0.

Figure 6B also plots the PD curve with 20K-PEO (green squares), which is the most widely used depletant in SAXS-osmotic pressure studies.^29,51 The abrupt decrease in D_w-w with 20K-PEO is now observed at higher pressures ≈ 5000 Pa by about an order of magnitude. This is because 20K-PEO is able to partially penetrate the MT bundle region due to its smaller diameter d20K-PEO (= 4R_G/π^1/2) ≈ 15.6 nm less than D_w-w ≈ 27 nm. This leads to a gradient in concentration of 20K-PEO between the outside and inside of the bundle effectively lowering the actual applied osmotic pressure. The “apparent pressure” plotted in Fig. 6B (green squares), which assumes all 20K-PEO is outside the bundle, is larger than the applied pressure (i.e. due to the difference in 20K-PEO concentration between outside and inside of the bundle) and so the transition to the collapsed MT bundle state is seen to occur at a higher “apparent pressure”. As expected we see that once the transition to the collapsed bundle state occurs the data for measurements with 20K-PEO and 100K-PEO are in agreement. This is because at the smaller spacings ≈ 5.0–6.0 nm, less than the diameter of 20K-PEO, 15.6 nm, the polymer is expelled from the bundle interior.

SUMMARY

We have presented an overview of recent work on the structural transitions related to shape changes in protofilaments, which make up the wall of microtubules, in the presence of intrinsically disordered protein Tau and separately cationic vesicles. In addition, we reviewed a study, which revealed how tetravalent spermine (4+), a biologically relevant polyamine with multiple distinct functions in cells,⁵⁴ may direct an evolution in the structure of taxol-stabilized microtubules. While at short times spermine bundles microtubules, at longer times, it leads to depolymerization of taxol-stabilized microtubules and stacking of stable tubulin rings in a helical manner creating an inverted tubulin tubule. MT disassembly and tubulin re-assembly is also notable because the surface that is on the inside of the microtubules is switched to the outside on the new array of inverted tubulin tubules; thus, stably exposing the “inner lumen” of microtubules. This provides a unique platform for experiments addressing interactions of biomolecules, in particular, MT-associated proteins, with the inner surface of MTs.

The SAXS-osmotic pressure technique, which was used to measure interfilament forces between Tau-coated MTs is nearly unique among force measuring techniques in enabling quantitative force measurements between filaments in suitable buffer conditions (pH, salt concentrations) with minimal disturbance to the bulk hydrogel containing the cytoskeletal filaments. This technique yields similar information obtainable from the surface-forces-apparatus (SFA) invented by Jacob N. Israelachvili. Our demonstration that the SAXS-osmotic pressure technique may access both repulsive and attractive regimes, and, measure the mechanical stability of MT/Tau bundles, suggests the feasibility of this type of force measurements in future studies in co-assembling mixtures of MTs and neurofilaments. For example, such measurements would allow one to obtain, for the first time, direct information on interfilament forces in interacting mixtures of MT and neurofilament hydrogels mimicking the cytoskeleton of different neuronal compartments (axons, cell body, and dendrites) (see Fig. 1), and should be transformative in yielding fundamentally new insights connecting forces to heterogeneously assembled structures.