Effect of Nucleotide State on the Protofilament ... - ACS Publications

Article Cite This: J. Phys. Chem. B 2018, 122, 6164−6178

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Effect of Nucleotide State on the Protofilament Conformation of Tubulin Octamers Anjela Manandhar,†,‡ Myungshim Kang,† Kaushik Chakraborty,† and Sharon M. Loverde*,†,‡ †

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Department of Chemistry, College of Staten Island, City University of New York, 2800 Victory Boulevard, Staten Island, New York 10314, United States ‡ Ph.D. Program in Biochemistry, The Graduate Center of the City University of New York, 365 Fifth Avenue, New York, New York 10016, United States S Supporting Information *

ABSTRACT: At the molecular level, the dynamic instability (random growth and shrinkage) of the microtubule (MT) is driven by the nucleotide state (GTP vs GDP) in the β subunit of the tubulin dimers at the MT cap. Here, we use large-scale molecular dynamics (MD) simulations and normal-mode analysis (NMA) to characterize the effect of a single GTP cap layer on tubulin octamers composed of two neighboring protofilaments (PFs). We utilize recently reported high-resolution structures of dynamic MTs to simulate a GDP octamer both with and without a single GTP cap layer. We perform multiple replicas of long-time atomistic MD simulations (3 replicas, 0.3 μs for each replica, 0.9 μs for each octamer system, and 1.8 μs total) of both octamers. We observe that a single GTP cap layer induces structural differences in neighboring PFs, finding that one PF possesses a gradual curvature, compared to the second PF which possesses a kinked conformation. This results in either curling or splaying between these PFs. We suggest that this is due to asymmetric strengths of longitudinal contacts between the two PFs. Furthermore, using NMA, we calculate mechanical properties of these octamer systems and find that octamer system with a single GTP cap layer possesses a lower flexural rigidity.

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INTRODUCTION The microtubule (MT) is a classic example of directional filamentous self-assembly found in nature. Within the MT, monomeric proteins (αβ tubulin heterodimers) dynamically self-assemble into hollow supramolecular filaments. These filaments are very stiff, with a persistence length of 1−8 mm1−6 and contour length of 5−10 μm.7 Together with other filamentous proteins such as actin, MTs compose the cytoskeleton of the cell. These vital supramolecular components guide cellular morphology, cellular trafficking, and cell division.8−10 The self-assembly process of tubulin into MTs is governed by the interaction of αβ tubulin heterodimers and the nucleotide state (guanosine triphosphate (GTP) vs guanosine diphosphate (GDP)) at the β subunit. The α subunit’s nucleotide binding site, termed the nonexchangeable nucleotide binding site (N-site) always has GTP bound to it, whereas the β subunit’s nucleotide binding site, termed the exchangeable nucleotide binding site (E-site), can have either GTP or GDP.11 A nucleation template, termed the γ-tubulin ring complex (γTuRC), initiates the formation of MTs. The γ tubulins of the ring complex establish strong longitudinal contacts with the α subunits of the incoming αβ tubulin heterodimers and develop a template for the complete MT in vivo.12,13 After the formation of a stable nucleus, αβ tubulin heterodimers align longitudinally in a head-to-tail fashion to © 2018 American Chemical Society

form polar protofilaments (PFs). Thirteen PFs combine laterally to form a hollow, cylindrical MT structure with an inner diameter of 12 nm and an outer diameter of 25 nm.7,14,15 The structure is dynamic, with the plus end undergoing stochastic switching between the polymerization and depolymerization phases.16−18 Furthermore, the dynamic instability of the MT is dependent on the nucleotide state of the β subunit at the plus end. While GTP promotes MT assembly, hydrolysis of GTP to GDP promotes MT disassembly.19,20 The relative strength of interactions at the lateral/ longitudinal interfaces guiding MT assembly and disassembly is still under discussion. Previous computational studies with all-atomistic simulations have suggested that the GDP-bound tubulin possesses weaker lateral contacts between tubulin dimers, promoting MT disassembly.21 A recent computational study of building artificial MT’s from wedge-shaped monomers has suggested that lateral contacts should be slightly greater than the longitudinal contacts to form tubule structures.22,23 There have been multiple computational studies to investigate the importance of both the lateral and longitudinal contacts for the assembly of tubulin dimers, singular PFs, as well as tubulin Received: March 5, 2018 Revised: April 25, 2018 Published: May 16, 2018 6164

DOI: 10.1021/acs.jpcb.8b02193 J. Phys. Chem. B 2018, 122, 6164−6178

Article

The Journal of Physical Chemistry B

atom simulations of tubulin octamers, with multiple replicas. Previous computational studies have characterized the structure of various tubulin oligomers, ranging from the dimer to short protofilaments to small lattice patches. We note that with allatom molecular dynamics approaches the maximum simulation time formerly achieved is 250 ns.21,26,35,36 Each tubulin octamer contains four dimers (1, 2, 3, and 4) and two neighboring protofilaments (PF-A and PF-B) as shown schematically in Figure 1C. The three GTP cap replicas are termed GTP1, GTP2, and GTP3, and the three GDP replicas are termed GDP1, GDP2, and GDP3. The setup of each of these three replicas of the two octamers differs only by a single GTP cap layer and are otherwise identical. To begin with, we characterize the conformations of the octamers, in terms of the intra-dimer, inter-dimer, and individual protofilament bending angles, as well as the dihedral angle between PFs. Next, we calculate the strength of the lateral contacts between neighboring PFs and longitudinal contacts at the inter-dimer interface within PFs. We find structural differences between neighboring PFs due to the presence of a single GTP cap layer. In all GTP cap replicas we observe a consistent trend of gradual curvature and weaker longitudinal contacts in PF-As, compared to PF-Bs. Following, we characterize the global motions of these two octamer systems using normal-mode analysis (NMA). We determine the flexural rigidity (kf), persistence length (lp), and bending modulus (Yf) from the vibrational frequencies of the first bending mode of the octamers, finding that a single GTP cap layer induces a lower flexural rigidity in the octamer. Thus, within this work, we explore computationally the effect of a single GTP cap layer on the PF conformation within tubulin octamers, as well as the resulting shift in the mechanical properties of the octamers. Herein, we show the influence of a single GTP cap layer on both the lateral and longitudinal contacts of PFs in shortened MTs. The conformation of each PF in the GTP cap replicas suggests that the MT structure and stability is a combination of both the “lattice” and “allosteric” models. The MT maintains its straighter, stable lattice due to the combination of both the GTP cap, as well as contacts with adjacent PFs. Similarly, from NMA, we find that the GTP cap octamer is more flexible compared to the GDP octamer, which might assist in maintaining contacts in the MT lattice crucial for its stability.

patches in both the GTP and GDP states. For example, allatomistic tubulin dimers as well as coarse-grained simulations of short PFs have reported bent dimer conformations for both the GTP and GDP states.24−27 Additionally, free energy calculations have reported that the free tubulin dimer favors a bent conformation and possesses a lower free energy than straighter conformations.28 Recent high resolution cryo-EM structures of MTs in the GTP-like, GDP, and GDP-Taxol state have suggested that the lateral contacts are similar in all three models, but the microtubule stability is primarily governed by contacts at longitudinal interfaces.29 Thus, additional computational models of both the GTP and GDP states of MTs can further characterize the differing PF conformations, resulting mechanical properties of the PFs, as well as the relative stability of these states. There exist two models that explain the link between nucleotide state, tubulin conformation, and MT dynamic instabilitythe “lattice model” and the “allosteric model”. The “lattice model” states that the free tubulin dimer exists in a bent conformation independent of nucleotide state, suggesting that the structural switch from bent to straight is activated by the polymerization contacts in the MT.30 On the contrary, the “allosteric model” states that GTP straightens the tubulin dimer and activates it for polymerization. Furthermore, this model argues that GDP tubulin, having a curved conformation, is not able to easily make lateral contacts in growing PFs; thus, it is unable to polymerize.31 Besides being favorable for polymerization, GTP tubulin is required at the plus end to retain the stability and the growing phase of the MT. Once the GTPs of the cap layer are hydrolyzed to GDPs, the tubulin dimers bend outward and the MT enters the depolymerization phase.19,20 Some in vitro studies have reported the presence of 1−2 layers of GTP in the cap, whereas in vivo studies have reported up to 55 layers of GTP in the cap of growing MTs.32−34 The exact number of layers of GTP in the MT cap and the mechanism of how these layers maintain the straight conformation of the GDP tubulins preceding it remains an active area of discussion. To study the effect of the nucleotide state at the cap/end layer of MT, we have conducted large-scale molecular dynamics (MD) simulations (1.8 μs in total, 0.3 μs for each replica, 0.9 μs for octamer system) of three replicas each of two tubulin octamer systemsa GTP cap octamer and a GDP octameras shown in Figure 1A,B. Here we have conducted the longest all-

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METHODS Selected Systems. Our systems include three initial smaller simulation studies of tubulin dimers (with GTP, GDP, and GTP+Taxol) and three replicas each of two tubulin octamers (two PFs, each containing two tubulin dimers) as shown in Figure 1A and B. The longitudinal nucleotide state sequence of tubulin subunits from bottom to top in Figure 1B for the “GDP octamer” is GTP-GDP-GTP-GDP, whereas the sequence for the “GTP cap octamer” from bottom to top as shown in Figure 1A is GTP-GDP-GTP-GTP. Each octamer contains two neighboring PFs as schematically shown in Figure 1c, which we term PF-A (composed by dimers 1 and 2) and PF-B (composed by dimers 3 and 4). Structural Data. Coordinates for the tubulin dimers (GDP dimer, GTP dimer and GDP + Taxol dimer) were extracted from the Nogales high-resolution microtubule-based cryo-EM structures (PDB IDs 3J6E, 3J6F, and 3J6G).29 We modified the GTP analogue, GMPCPP, in the β subunit of the GTP-like dimer to build the GTP dimer. MODELER37 was used to model the missing segment of H1−B2 (residues 39−48) of the

Figure 1. Tubulin octamer models: (A) GTP cap octamer, (B) GDP octamer, (C) schematic representation showing protofilaments A and B. Here, GTP and GDP are colored green and yellow, respectively. The four tubulin dimers 1, 2, 3, and 4 in each octamer are colored as dark blue, red, magenta, and black, respectively. 6165


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The Journal of Physical Chemistry B α subunit of each dimer. Here, the corresponding segment of the β subunit was used as the template for α subunit. The loops were modeled for GDP and GTP dimers, and then these modeled loops were added to each α subunit in the GDP and GTP cap octamers, respectively. Similar to the dimers, the coordinates for the GDP and GTP cap octamers were extracted from the Nogales GDP and GTP-like (GMPCPP) structures.29 For the GTP cap octamer, GMPCCs of the β subunits were modified to GTPs, similar to the dimers. Then, to construct the GDP octamers, the Mg2+ ion and γ phosphate bound to each GTP of β subunits of lower tubulin dimers were removed. Each octamer is simulated in a water box and they are not forming lateral or longitudinal contacts across periodic boundaries. MD Simulation. MD simulations of the dimers and the octamers were performed using NAMD 2.538 with the CHARMM36 force field.39 The parameters for GTP and GDP were constructed, combining the CHARMM36 parameters of ATP and Guanine. The parameters for Taxol were obtained from the Sept lab.7 All systems were solvated with TIP3P40 water and the charge was neutralized with Na+ counterions (0.08 M). The bonded and nonbonded interactions were both calculated with a 2 fs time step. The electrostatic and van der Waals interactions were calculated with a 12 Å cutoff, with a smooth switching function at 10 Å, and a pair list distance of 13.5 Å. All systems were simulated with an NPT ensemble at a temperature of 310 K. The temperature of the system was controlled using the Langevin dynamics method with a friction constant of 1 ps−1 and the pressure was controlled using the Nose-Hoover Langevin piston method.41 All system sizes are summarized in Table 1. VMD42 was used for visualization and analysis.

position vector for each node, and / is the N × N Hessian matrix of the second derivatives of the overall potential. From / , 3N − 6 nonzero eigenvalues (λ) and eigenvectors are obtained which are the values of frequency and direction of the individual modes, respectively. The angular frequency, ωn, for the nth mode is directly related to the eigenvalue (λn) of each specific mode as ωn = γλn . The related frequency, f n, is then calculated as f n = ωn/2πt0, where t0 is equivalent to one unit of time, 4.8888 × 10−14 s (based on the definition of energy in kcal/mol, mass in g/mol, and distance in Å).46 Assuming the octamers behave as linear elastic filaments, their mechanical properties can then be calculated from the vibrational normal modes of the filament.45

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RESULTS To begin with, we calculate the intra-dimer bending angles (θIA) of three tubulin dimersa GDP dimer, a GTP dimer, and a GDP+Taxol dimer as shown in Figure S1. As shown in Figure 2A, θIA is calculated as the angle formed by the intersection of the axes between the H7 helices of the α and β subunits. The Cα’s of residues 227 and 238 of each helix are used to form the H7 helix axis. The H7 helix is the central helix which connects the nucleotide binding domain and the intermediate domain.47 Knossow et al.47 and Jacobson et al.28 have characterized the changes in straight vs bent tubulin dimers using H7 helices. Moreover, a mutational study with T238A at the H7 helix of the β subunit has shown suppressed GTP hydrolysis dependent conformational changes, slower shrinking, and decreased catastrophe in MTs.48 Thus, H7 is a crucial structural element of tubulin dimers. Jacobson et al.28 has used the same H7 helix orientations to calculate tubulin bending. Voth et al.25 determined tubulin bending by calculating the movement of α and β subunits with respect to one another using the center of mass of each subunit. However, Jacobson et al.28 has compared these methods and reported that although both methods are not identical, they exhibit a strong correlation. We calculate the angle as

Table 1. Simulation Systems water atoms

total atoms

simulation box, Å3

simulation time, ns

GTP

63,456

76,988

70

GDP +Taxol GDP

52,098

65,649

57,849

71,287

GTP cap replicas GDP replicas

211,536

265,296

210,549

264,293

82 × 84 × 128 76 × 82 × 122 82 × 82 × 122 134 × 100 × 218 134 × 102 × 216

systems Dimers

Octamers

70

⎯ ⎛ → A· B⃗ ⎞⎟⎛⎜ 180 ⎞⎟ θIA = cos−1⎜⎜ ⎟ ⎝ |A⃗ ||B⃗ | ⎠⎝ π ⎠

70 300 (× 3)

where A⃗ is the axis along the H7 helix of the α subunit and B⃗ is the axis along the H7 helix of the β subunit. The distribution of θIA sampled over the last 30 ns of dimer simulations is shown in Figure S2A. Taxol, a MT stabilizing drug, straightens the conformation of tubulin and facilitates MT polymerization.1,35,49 On the contrary, GDP tubulin dimers in solution and at the MT tip have a curved conformation.20 Our study is consistent with previously reported simulation studies.1 Indeed, θIA distributions for the three tubulin states are consistent with reported θIA values determined with MD simulation studies conducted by Natarajan et al.26 using the 1JFF crystal structure.50 Comparing the GTP dimer with the GDP dimer and the GDP+Taxol dimer, the GTP dimer has a peak θIA value between GDP and GDP+Taxol. This suggests that, at the dimer level, GTP has a comparable but weaker effect as compared with Taxol on the degree of intra-dimer bending. Figure S2B shows the potential of mean force (PMF) as a function of θIA, calculated from the probability distribution over 70 ns. The PMF is defined as51,52

300 (× 3)

Normal Mode Analysis of Tubulin Octamers. To study the normal modes of the tubulin octamers, the Protein Dynamics and Sequence Analysis (ProDy) program43 was used. An anisotropic elastic network model (ENM)44 was constructed, with a node at each Cα atom position. For any two nodes, i and j closer than the assigned cutoff distance rc of 12 Å, i and j are subject to a harmonic potential (Vij) defined as Vij = (1/2)γ(sij − sij0)2 = (1/2)γ [(Xi − Xj)2 + (Yi − Yj)2 + (Zi − Zj)2 ]1/2 − sij0

(

(2)

2

)

(1)

Here s0ij is the equilibrium separation, and sij is the instantaneous separation between i and j, and γ is the elastic constant of the springs, equal to 1 kcal/molÅ2.45 The total potential energy, 1 Vtotal, can then be represented as Vtotal = 2 Δr T /Δr where Δr is the 3N dimensional vector describing the fluctuations of the

G(rs , r ) = −kBT[lnP(rs , r ) − lnPmax ] 6166

(3)


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Figure 2. Intra-dimer bending angle (θIA). (A) θIA for each dimer is measured as the angle formed by intersection of axes through H7 helices (yellow) of α and β subunits. (B) 1-D potential of mean force (PMF) as a function of θIA. Comparative θIA in octamer systemsGTP cap octamers (left panel) and GDP octamers (right panel).

Table 2. Average Intra-Dimer Bending Angles (θIA) for Last 50 ns of Dimer 1, 2, 3, and 4 of GTP Cap and GDP Octamer Replicasa Protofilament - A Dimer1 - θIA GTP1 GTP2 GTP3 Average

11.66 17.62 9.16 12.81

± ± ± ±

Protofilament -B Dimer2 - θIA

2.64 2.85 2.67 4.47

5.66 12.27 14.94 10.96

± ± ± ±

2.31 2.47 2.45 4.58

Dimer3 - θIA 7.90 10.88 11.00 9.93

± ± ± ±

Protofilament - A Dimer1 - θIA GDP1 GDP2 GDP3 Average a

13.85 10.45 14.17 12.82

± ± ± ±

3.11 2.77 3.44 3.54

Dimer4 - θIA

3.15 2.38 2.57 3.07

13.85 19.69 14.57 16.04

± ± ± ±

2.41 2.17 2.77 3.58

Protofilament -B Dimer2 - θIA 13.83 12.42 6.96 11.07

± ± ± ±

2.53 2.43 2.31 3.83

Dimer3 - θIA 17.98 9.37 6.23 11.19

± ± ± ±

3.78 2.35 2.88 5.83

Dimer4 - θIA 21.40 10.23 17.94 16.52

± ± ± ±

2.37 2.41 2.65 5.29

Replicas are 300 ns each.

where P(rs, r) is the probability distribution and Pmax denotes the maximum probability. Compared to GDP+taxol, the GTP dimer has its minimum shifted ∼5° right, and the GDP dimer shifted ∼10° right. The same trend is observed for free energy minimums of the taxol bound dimer (1JFF),53 GMPCPP bound dimer (cryo-EM structure),31 and zampanolide and epothilone bound GDP dimers (4I4T, 4I50)54 as reported by Jacobson et al.28 In order to further characterize the subtle effect of GTP as compared with GDP on the conformation of tubulin, while including at least one neighboring PF, we next characterize the effect of a single GTP cap layer on the conformation of tubulin octamers as shown in Figure 1. We begin by characterizing the effect of this single GTP cap layer on (i) the intra-dimer bending angles of each dimer, (ii) the inter-dimer bending angle of each neighboring protofilament (PF-A and PF-B), (iii) the overall protofilament bending angles, and (iv) the dihedral angles between the neighboring protofilaments. First, we characterize the effect of a single GTP cap layer on the intra-dimer bending angles (θIA) of each tubulin octamer. The θIA of each dimer in each octamer is determined in the same way as previously described for the tubulin dimers as shown in eq 2 and as sketched in Figure 2A. Figure 2B shows

the 1D PMF as a function of intra-dimer bending angle for each dimer, calculated from the probability distribution over 300 ns. We observe dimers of both the GTP cap and GDP octamers exhibit minimum in the range of ∼8−22°. For the GTP cap replicas, dimer 4 has the minimum shifted toward the right compared to other dimers. However, in the GDP octamers we do not observe a consistent trend for the minimums. As compared with Jacobson et al.,28 we note that the range of minimum for both our dimers as reported in Figure S2B and also Figure 2B display minimums shifted away from the straight conformation of ∼0°, with an increased degree of bending. The θIA distributions, sampled over the last 50 ns of 300 ns trajectories, are shown in Figure 2C. The average θIA values of the last 50 ns of the 300 ns trajectories for each octamer system are shown in Table2. For the GTP1 and GTP2 octamers, we observe a similar trend with dimers 1 and 4 having a peak at a greater θIA value compared to dimers 2 and 3. However, in the GTP3 octamer, the bottom dimers 2 and 4 have a peak at a greater θIA value compared to the upper dimers 1 and 3. Thus, in all three replicas, dimer 4 has a peak at the greatest θIA value (GTP1−15°, GTP2−20°, and GTP3−18°). This holds true for the average θIA values. Dimer 4 always has the highest θIA value with an average 16.04° ± 3.58°. Next, we find that the average 6167


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Figure 3. Interdimer bending angle (θIE). (A) θIE for each PF is measured as the angle formed by intersection of axes through H7 helices (red) of upper and lower tubulin dimers. (B) 2-D potential of mean force (PMF) for θIE as a function of PF-A and PF-B. Scale bar is in kcal/mol. (C) θIE probability distribution for octamer systems (for last 50 ns out of 300 ns)GTP cap octamers (left panel) and GDP octamers (right panel).

Table 3. Average Inter-Dimer Bending Angles (θIE) for Last 50 ns of Protofilament A and B PF-A θIE GTP1 GTP2 GTP3 Average

20.63 25.51 16.07 20.74

± ± ± ±

2.96 1.43 2.20 4.48

PF-B θIE 16.26 9.38 16.73 14.12

± ± ± ±

PF-A θIE

2.30 1.41 1.71 3.83

GDP1 GDP2 GDP3 Average

18.96 4.10 11.40 11.49

± ± ± ±

1.78 1.44 2.49 6.37

PF-B θIE 18.74 5.14 18.48 14.12

± ± ± ±

1.98 1.51 2.68 6.69

GTP1 octamer, θIE of PF-A and PF-B only partially overlap with peak θIE value of ∼20° for PF-A and ∼17° for PF-B. For the GTP2 octamer, the distributions for θIE values of PF-A and PF-B are significantly different, with a peak θIE value of ∼26° for PF-A and ∼10° for PF-B. The time dependence of θIE in these GTP cap octamers is shown in Figure S3 where we see θIE converges at the end of 300 ns for the GTP1 and GTP3 octamers. As observed in Figure 3C and Figure S3, θIE diverges for the GTP2 octamer resulting in a bent PF-A and straighter PF-B. In comparison to the GTP cap octamers, Figure 3C shows the last 50 ns probability distribution of θIE values for the three GDP octamer replicas. For GDP1, both PFs are bent with a peak θIE value of ∼19°, whereas for GDP2, both PFs are straighter with a smaller peak θIE value of ∼4° for PF-A and ∼6° for PF-B. For GDP3, PF-A is straighter with a peak θIE value of ∼11° and PF-B is bent with a peak θIE value of ∼19°. The time dependence of θIE for GDP octamers is shown in Figure S3, further clarifying the differing trends of the θIE values in the three GDP octamer replicas. In summary, θIE values of both PFs converge during the later stages of simulations in two out of three GTP cap octamer replicas, and one of the three GTP cap octamer replica exhibits diverging θIE values of the PFs, whereas in the GDP octamers, θIE values of both PFs are very similar throughout the simulations in two out of three replicas, and one of the three GDP octamer replicas exhibits significantly different θIE values of its PFs. Interestingly, we observe a significant effect of the single layer GTP cap on θIE on PF-A compared to PF-B as shown in Table 3. We find the average θIE value for last 50 ns for PF-B in GDP octamers (14.12° ± 6.69°) is similar to GTP cap octamers (14.12° ± 3.83°), whereas the average θIE for PF-A of GDP octamers (11.49° ± 6.37°) is significantly lower compared to GTP cap octamers (20.74° ± 4.48°). The same trend is exhibited in 2-D PMF calculations.

θIA values of each dimer in the GTP cap octamer is similar to the average θIA values of the GDP octamer. Moreover, dimer 4 always has the highest θIA value with an average 16.52° ± 5.29°. To summarize, these results suggest that a single GTP cap layer does not have a significant effect on the bending behavior at the intra-dimer level. Furthermore, we observe that dimer 4 always maintains the highest θIA for octamer systems, independent of the nucleotide state of the cap. Studies have reported that in the presence of protective GTP cap layer/s, MTs are stable with straighter PFs and favor polymerization.7 To study the effect of the single GTP cap layer on the PF conformation of our octamers, we calculate interdimer bending angles (θIE). As shown in Figure 3A, θIE measures the angle between two vertically aligned dimers in each PFbetween dimer 1 and 2 in PF-A and dimer 3 and 4 in PF-B. It is calculated as the angle subtended by the axes through the center of masses (COMs) of H7’s of the lower dimers and upper dimers. Figure 3B shows the 2D PMF distribution as a function of both inter-dimer bending angles, PF-A and PF-B, calculated from the probability distribution over 300 ns. For the time period we ran our simulations (3 replicas each, 300 ns each replica, 900 ns for each octamer system), we observe that the GTP cap octamers explore more states compared to the GDP octamer replicas. However, all three GTP cap replicas exhibit a minimum in the PMF at ∼PFA θIE ∼ 20−25°. In comparison, the GDP replicas exhibit varying minimum, indicating that more sampling could be performed for the GDP replicas. However, two out of three PMFs for the GDP replicas appear to be shifted to the left, suggesting a lower θIE for PF-A compared to the GTP-cap octamers. Figure 3C (right panel) shows the last 50 ns probability distributions of θIE over the 300 ns trajectories for the GTP cap octamers. For the GTP3 octamer, the peak θIE values of PF-A and PF-B perfectly overlap at ∼17°. For the 6168


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The Journal of Physical Chemistry B Nogales et al.29,55 have reported that after GTP hydrolysis at the inter-dimer E-site (Figure 4A), the β-T3 and the β-T5 loops

whereas in PF-B, GDP stays bound to the E-site (Figure 4B). This corresponds with a decrease in the number of H-bonds between GDP and the β-T3 and β-T5 loops of the lower dimer and an increase in the number of H-bonds between GDP and the α-T7-H8 loop of the upper dimer of PF-A (Figure 4C). Furthermore, the GDP in PF-A breaks all H-bonds after ∼10 ns simulation with the lower dimer. However, in PF-B, the GDP maintains these H-bonds until the end of the simulation trajectory (Figure 4C). In particular, ASN-101 of the β-T3 loop of the lower dimer makes H-bonds with GDP during initial as well as final stages in both PF-A and PF-B as shown in Figure S4. We outline the major residues of each loop involved in forming H-bonds with GDP as shown in Table S1. Different residues of the β-T5 loop participate in H-bond formation with GDP for PF-A and PF-B, whereas for the β-T3 and α-T7-H8 loops at least one residue is common for both PFs. In agreement with Nogales et al.29 our results support the critical role of these 3 loops in stabilizing the hydrolyzed GTP in the Esite cavity. Furthermore, we suggest that the α-T7-H8, β-T3, and β-T5 loops, and their contact with GDP are critical in maintaining the inter-dimer bending angle. Next, we calculate the protofilament bending angles, θPF, to characterize the overall bending conformation along the PF from the bottom subunit to top subunit. The θPF for all H7 along the PF (i.e., β1-H7, α2-H7, and β2-H7) is calculated. The θPF values provide information on how much each H7 has deviated from its initial position. The θPF for each H7 is calculated as the angle formed by COMs of initial H7, initial α1-H7, and final H7 positions. The overall θPF is characterized by β2 − θPF of each PF. Figure 5A shows the last 50 ns probability distributions of θPF for the β1, α2, and β2 subunits of the GTP cap octamers. We observe that PF-A of GTP1 is bent with peak β2 − θPF value of ∼18°, and PF-B occupies two conformationsstraight with peak β2 − θPF value of ∼9° and bent with peak β2 − θPFvalue of ∼18°. Similarly, in the GTP2 octamer, PF-A is bent with peak β2 − θPF value of ∼24° compared to PF-B with peak β2 − θPF value of ∼16°. Whereas in the GTP3 octamer, PF-A is straighter with peak β2 − θPF value of ∼16° compared to PF-B with peak β2 − θPF value of

Figure 4. (A) Locations of β-T3 loop (magenta), and β-T5 loop (blue) of lower dimers, α-T7-H8 (red) of upper dimers, and E-site GDP (licorice representation) at the inter-dimer interface of GTP2 octamer replica. (B) Initial (i, iii) and final (ii, iv) locations of β-T3, βT5, α-T7-H8, and GDP at the inter-dimer interface PF-A and PF-B. (C) Number of H-bonds of the inter-dimer E-site GDP with β-T3 loop, and β-T5 loop of lower dimers, and α-T7-H8 of upper dimers in PF-A and PF-B of GTP2 octamer during 300 ns simulation.

of the lower dimer and α-T7-H8 loops of the upper dimer reorganize, creating longitudinal compaction at the inter-dimer E-site. The initial and final locations of the β-T3 loop (pink), βT5 loop (blue), α-T7-H8 loops (red), and GDP (licorice representation) of the GTP2 octamer is shown in Figure 4B. For PF-A, the GDP moves away from the inter-dimer E-site and repositions near the α-T7-T8 loop of the upper dimer,

Figure 5. Protofilament bending angles (θPF) in GTP cap octamers. (A) Comparative θPF’s for β1, α2, and β2 in PF-A (left panel) and PF-B (right panel) of GTP cap octamers for the last 50 ns. (B) Last snapshot of PF-A and PF-B of GTP cap octamers where each bead represents COM of H7s. 6169


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Table 4. Average Protofilament Bending Angles (θPF) for Last 50 ns of Protofilament A and B (PF-A and PF-B) of GTP Cap and GDP Octamer Replicas Protofilament - A β1 − θPF

α2 − θPF

± ± ± ±

12.13 ± 1.78 18.37 ± 1.53 11.74 ± 1.53 14.08 ± 3.44 Protofilament - A

GTP1 GTP2 GTP3 Average

4.62 12.23 4.96 7.27

GDP1 GDP2 GDP3 Average

13.20 12.34 16.15 13.90

1.76 1.37 1.59 3.85

β1 − θPF ± ± ± ±

Protofilament - B β2 − θPF 16.15 22.65 14.54 17.78

α2 − θPF

1.40 1.53 1.51 2.20

16.61 15.78 17.79 16.73

± ± ± ±

± ± ± ±

2.09 1.46 1.68 3.92

β2 − θPF

1.54 1.47 1.34 1.67

21.30 15.54 20.81 19.21

± ± ± ±

Protofilament - B

(α2 − β1) θPF (β2 − α2) θPF (α2 − β1) θPF GTP1 GTP2 GTP3 Average

7.51 6.14 6.78 6.81

± 1.57 4.03 ± ± 1.30 4.28 ± ± 1.02 2.80 ± ± 1.43 3.70 ± Protofilament - A

0.69 0.47 0.50 0.85

1.92 2.40 1.96 2.09

(α2 − β1) θPF (β2 − α2) θPF (α2 − β1) θPF GDP1 GDP2 GDP3 Average

3.41 3.44 1.64 2.83

± ± ± ±

0.99 0.54 0.99 1.21

4.69 0.48 3.01 2.73

± ± ± ±

0.55 0.35 0.58 1.80

2.20 1.16 4.60 2.65

(β2 − α2) θPF

± 1.28 4.77 ± ± 0.60 2.27 ± ± 0.90 1.98 ± ± 0.99 3.01 ± Protofilament - B ± ± ± ±

0.76 0.63 0.87 1.63

0.65 0.39 0.44 1.35

(β2 − α2) θPF 5.04 1.77 4.15 3.65

± ± ± ±

8.61 ± 3.91 13.33 ± 1.45 17.44 ± 2.11 13.13 ± 4.50 Protofilament - B

3.25 1.38 2.27 4.33

18.45 9.43 8.03 11.97

± ± ± ±

1.38 1.60 1.39 4.84

α2 − θPF 20.64 8.30 12.63 13.86

± ± ± ±

1.48 1.56 1.61 5.35

β2 − θPF 13.38 15.61 19.42 16.14

± ± ± ±

3.89 1.49 1.97 3.64

β2 − θPF 25.69 10.06 16.79 17.51

± ± ± ±

1.63 1.49 1.52 6.59

(Figure 6B). As shown by the time dependence (Figure S6) and probability distributions (Figure 6A) of θPF of GDP octamers, we do not observe a consistent trend for the PF bending. For the GDP octamers the average values of θPF for β1, α2, and β2 for PF-A and PF-B are not significantly different (Table 4). Thus, the average curvatures for PF-A and PF-B in the GDP octamers are not significantly different. Overall, in the GTP-cap octamers we observe a consistent gradual curvature in PF-A compared to a “kinked” conformation of PF-B. This gradual curvature of PF-A leads to curling and splaying between PFs of the GTP-cap octamers that is characterized by dihedral angles as discussed next. Following, we calculate the dihedral angle between PF-A and PF-B. As shown in Figure S7A, H7s of the top (β1, β3) and bottom (α2, α4) subunits of each PFs are used to calculate the bending angles and dihedral angles between PFs and explained further in the Supporting Information. As shown in Figure S7B, the dihedral angles are calculated in two waysonly positive magnitude (green) and positive and negative magnitude (black). If the angle between the two PFs is due to bending away from the plane connecting the bottom subunits, then their bending angle and the absolute magnitude of the dihedral angle will overlap as observed for the GTP1, GTP2, and all GDP octamers. If PF’s are bending away from each other in the plane connecting bottom subunits, then their bending angle and the magnitude of the dihedral angle will not overlap as observed for the GTP3 octamer. As discussed earlier, due to the gradual curvature along PF-A compared to PF-B of the GTP-cap octamers, at the end of 300 ns simulation time, we observe higher dihedral/bending angles in GTP1 (∼8°) and GTP2 (∼7°) characterizing “curling” of PFs, and a higher bending angle in GTP3 (∼7°) characterizing “splaying” between PFs. While the three GDP octamer replicas also exhibit some degree of “curling”, the average dihedral angle for all three GDP octamers at the end of 300 ns simulations (5.48° ± 1.11°) is lower than the average dihedral angle between PFs for the GTP-cap octamers (7.41° ± 0.32°). To summarize, we have studied the effect of a single GTP cap layer on the bending conformation of dimers within the PF (intra-dimer and inter-dimer), bending along the PFs, as well as the degree of bending between PFs in our overall octamer systems. At the dimer level, we do not find a significant effect of a single GTP cap layer on the intra-dimer bending angle, θIA, behavior. At the PF level, we find that the inter-dimer bending angle, θIE, at the interface of tubulin dimers converges for 2 out of 3 GTP cap octamer replicas. The divergence observed in the

Table 5. Average Difference in the Protofilament Bending Angles (θPF) for Last 50 ns between α2 and β1 Helices ((α2−β1) θPF) and β2 and α2 Helices ((β2−α2) θPF) of PFA and PF-B of GTP Cap and GDP Octamer Replicas Protofilament - A

α2 − θPF

± ± ± ±

6.69 10.94 15.48 11.03

β1 − θPF

1.61 1.51 1.39 3.02

∼20°. At the end of 300 ns simulation, we observe that PF-A is most bent in GTP2 and PF-B is most bent in GTP3 (Figure 5B). The time dependence of θPF of the GTP cap octamers (Figure S5) as well as θPF distributions for each H7 shows there is gradual curvature along PF-A as there is significant increase of θPF values as you move up from β1 to α2 to β2, whereas in PF-B there is a “kink” at β1 and the remaining PF is straighter. In PF-A of GTP cap octamers the average β1 − θPF value is 7.27° ± 3.85°, and as we move up, the average value of α2 − θPF increases by an average of 6.81° ± 1.43° to 14.08° ± 3.44° and that of β2 − θPF increases by an average of 3.70° ± 0.85° to 17.78° ± 3.92° (Tables 4 and 5), whereas in PF-B, the average

β1 − θPF

0.56 0.47 0.77 1.51

value of α2 − θPF is significantly greater (11.03° ± 4.33°) compared to PF-A. However, the average increase of θPF from β1 to α2 is only 2.09° ± 0.99° and the average increase of θPF from α2 to β2 is only 3.01° ± 1.35°. The differential bending values of θPF creates a more curved PF-A compared to “kinked” PF-B in GTP cap octamers. For the GDP octamers, we observe that PF-B of GDP1 is bent with peak β2 − θPF value of ∼27° compared to PF-A with peak β2 − θPF value of ∼22° (Figure 6A). The scenario is reversed for the GDP2 and GDP3 octamers. In GDP2 PF-A is bent with a peak β2 − θPF value of ∼16° compared to a straighter PF-B with a peak β2 − θPF value of ∼11°. In GDP3 octamer PF-A is bent with a peak β2 − θPF value of ∼22° compared to a straighter PF-B with a peak β2 − θPF value of ∼19°. At the end of 300 ns simulation we observe that both PF-A and PF-B are most bent in the GDP1 octamer 6170


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Figure 6. Protofilament bending angles (θPF) in GDP octamers. (A) Comparative θPF’s for β1, α2, and β2 in PF-A (left panel) and PF-B (right panel) of GDP octamers. (B) Last snapshot of PF-A and PF-B of GDP octamers where each bead represents COM of H7s.

Figure 7. Lateral Contacts. (A) Lateral contacts between PF-A and PF-B. M loop (red) of PF-B makes lateral contacts with H1-B2 loop (yellow) and H2-B3 loop (green) of PF-A. Fraction of lateral contacts (n1) for 300 ns between α2-α4 (black), β2-β4 (red), α1-α3 (green), and β1-β3 (dark blue) for octamer systems.

GTP2 octamer is due to the inter-dimer E-site GDP of PF-A losing H-bonds with lower β-T3 and β-T5 loops and gaining Hbonds with upper α-T7-H8 loop, and then moving away from the original cavity. As a result, PF-A has wider interfacial cavity in PF-A compared to PF-B, resulting in a greater θIE. Following, we characterize the protofilament-bending angle, θPF, which demonstrates that a single GTP cap layer introduces a gradual curvature along PF-A and a “kinked” conformation of PF-B for all GTP cap octamers. This gradual curvature is found to lead to the “curling” or “splaying” between PFs in the GTP cap octamers as shown by greater bending angles compared to the

GDP octamers. In comparison, we did not observe a clear trend for the GDP octamers in terms of θIE’s and θPF’s; however, we did find that the dihedral bending angle between the two PFs is consistently lower for the GDP octamers than for the GTP cap octamers. Therefore, a single GTP cap layer influences PF conformations at both the inter-dimer, as well as the PF level. This increased bending angle between the two neighboring PFs suggests that a single GTP cap layer can lead to tension between the neighboring PFs that results in “curling” or “splaying”. This is consistent with the recent model proposed by Nogales et al.29 that the hydrolysis of GTP to GDP in the 6171


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Figure 8. Longitudinal Contacts. (A) Longitudinal contacts between lower β and upper α subunits. α T7 loop (red), H8 (green), and H10 (yellow) makes longitudinal contacts with β T2-H2 loop (cyan), T3 loop (magenta), T5 loop (dark blue), H6 (orange), H1 (black), and H6-H7 loop (tan). (B) Fraction of native longitudinal contacts (n1) for 300 ns in PF-A (red) and PF-B (black) in GTP cap (left panel) and GDP (right panel) octamers.

replicas. For the last 50 ns simulation we find the average conserved native lateral contacts between the subunit pairs for GTP cap octamer replicas (0.151 ± 0.143) is not significantly different compared to the average of GDP octamer replicas (0.163 ± 0.091). We next determine the fraction of native longitudinal contacts conserved over time (Figure 8) at the inter-dimer interface between dimers 1 and 2, and dimers 3 and 4 along PFA and PF-B, respectively. Here, we consider the longitudinal contacts to be characterized by the interaction between the T7 loop, H8 and H10 of the α subunits of the upper dimers with the T2-H2 loop, T3 loop, T5 loop, H6, H1, and H6−H7 loop of the β subunits of lower dimers (Figure 8A). These contacts are suggested to form the overall longitudinal contacts by Voth et al.21 As shown in Figure 8B, we find that the PF-Bs of all GTP-cap octamers conserve more native longitudinal contacts over time as compared to the neighboring PF-A in all three replicas (GTP1, GTP2, and GTP3). For the last 50 ns simulation we find that the average fraction of conserved native longitudinal contacts of all GTP octamer replicas of PF-B (0.470 ± 0.033) to be significantly higher than the average for PF-A (0.238 ± 0.103). The same trend is not observed for GDP octamer replicas. In the GDP octamers, the GDP1 replica has similar longitudinal contacts for both PFs, in the GDP2 replica the strength of longitudinal contacts converges during the last ∼100 ns, and in the GDP3 replica PF-A has stronger longitudinal contacts compared to PF-B. For the last 50 ns simulation, the average conserved fraction of native longitudinal contacts of GDP octamers of PF-B (0.344 ± 0.141) is not significantly different compared to the average of PF-A (0.325 ± 0.047). These findings suggest that the overall lateral contacts in all GTP cap and GDP octamers are not significantly different. However, in the presence of a single GTP cap layer, PF-B conserves more longitudinal contacts over time along the

neighboring layer of the cap and the formation of a GTP-GDP dimer interface results in E-site compaction and subsequent strain between neighboring PFs that leads to catastrophe, unless bound by a stabilizing agent. The differential bending also suggests differing strengths of longitudinal contacts that will be examined in the next section. This effect may be mitigated by the multiple neighboring PFs in the full MT. Lateral and Longitudinal Contacts. Next, we characterize the strength of both lateral contacts between PFs and longitudinal contacts along PFs during the course of the simulation trajectories. We use MDAnalysis56,57 to calculate the fraction of native contacts, n1, present between the selected residues throughout the trajectory. The initial structure is used as the reference structure, and if the selected residues are within an 8 Å cutoff radius at a particular point in the trajectory relative to the initial structure, this is counted as a native contact. Throughout the simulation, depending on the number of residues still within the cutoff radius, the fraction of native contacts is calculated accordingly. Previous simulation of infinite tubulin lattices have suggested that longitudinal contacts are similar for both nucleotide states, whereas lateral contacts are weaker in the GDP state.21 We first determine the fraction of native lateral contacts, n1, over time, comparing the GTP-cap and GDP octamers. Here, we consider the lateral contacts to be characterized by the interaction between the Mloops of every subunit of PF-B with the H1−B2 and H2−B3 loops of the adjacent subunits of PF-A as shown in Figure 7A. Previous studies have reported these loops as the major participants of lateral contacts between adjacent dimers.21,36,50,54 As shown in Figure 7B, we compare the fraction of lateral contacts that are conserved over time between the β1-β3, α1-α3, β2-β4, and α2-α4 subunits in pairs of adjacent dimers (dimer1-dimer3 and dimer2-dimer4). We observe that the fraction of native lateral contacts for both GTP cap and GDP octamers tend to decrease over time for all three 6172


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Figure 9. (A) Fraction of selected longitudinal contacts between β-T3, T5, and α-T7-H8 segment in PF-A (red) and PF-B (black) of GTP-cap (left panel) and GDP (right panel) octamers. Average contact map between the residues of β-T3 (x-axis) and α-T7-H8 (y-axis) in PF-A and PF-B of (B) GTP cap octamers and (C) GDP octamers.

longitudinal contacts compared to PF-B. In the GDP3 replica, the average selected longitudinal contacts in PF-A (0.567 ± 0.024) is significantly higher compared to PF-B (0.171 ± 0.027). Contrary to the GTP2 replica, the inter-dimer E-site GDP still remains in the original cavity in the GDP3 replica. As shown in Figure S8A, the inter-dimer E-site GDP in PF-A is stabilized by its H-bonds with β-T3 and β-T5 loops of lower dimer and α-T7-H8 loop of upper dimer throughout the simulation. However, in PF-B (Figure S8B) after about ∼150 ns, GDP is stabilized in the cavity prominently by H-bonds with β-T5 loop of lower dimer. Taken together, in PF-B, the lower average of conserved selected longitudinal contacts and loss of H-bonds of inter-dimer GDP with the α-T7-H8 loop of the upper dimer suggests that the α-T7-H8 loop in the GDP3 replica has shifted away from the β-T3 and β-T5 loops of the lower dimers. Similar to θIE of PF-A in the GTP2 replica (Figure 3), in the GDP3 replica we observe a higher θIE for PFB (Figure 3) where the longitudinal contacts between β-T3 and β-T5 loops of lower dimer and α-T7-H8 loop of upper dimer is weaker than in PF-A. This further supports the critical role of interaction between inter-dimer GDP with the α-T7-T8, β-T3, and β-T5 loops in maintaining θIE. In the GDP3 replica, we also discover E-site GDPs at the cap layer leaving their binding cavity. As shown in Figure S9A, GDP from PF-B leaves first, comes back near the PF-A and PF-B interface between the top subunits and then GDP from PF-A leaves and finally both GDPs associate. We calculate the number of H-bonds of these GDPs with the T3 loop (magenta), T5 loop (blue), and T4 loop (green) which are close to these GDPs. As shown in Figure S9B, GDPs at the cap layer are dominantly stabilized by H-bonds with the T4 loop which is completely lost after ∼200 ns in PF-B and ∼250 ns in PF-A. In both PFs the H-bonds between GDP and ASN-101 of the T3 loop is the last H-bond to break before they leave the cavity. We outline the major residues of each loop involved in H-bond formation with GDP at the cap layer in the GDP3 replica as shown in Table S3. To summarize, in the GDP3 replica we observe that PF-B has a higher inter-dimer bending angle, θIE, weaker selected longitudinal contacts suggesting shifting away of the α-T7-H8 loop from the inter-dimer E-site. This phenomenon might be correlated with the GDPs of the cap layer leaving their binding cavities. Furthermore, we suggest

PF as compared with PF-A further suggesting that the GTP cap induces asymmetric longitudinal contacts in neighboring PFs. Following, we calculate the fraction of native selected longitudinal contacts that are conserved over time between βT3 and β-T5 of the lower dimer, and α-T7-T8 of the upper dimer. Nogales et al.29 and our H-bond analysis (Figure 4) have shown that these loops are crucial to stabilize the inter-dimer Esite GDP in the binding cavity and maintain PF conformation. As shown in Figure 9, the GTP cap octamers replicas GTP1 and GTP3 show similar conservation of these selected longitudinal contacts for both PF-A and PF-B over time as compared to the GTP2 octamer replica. For the GTP2 octamer replica, PF-B has a higher fraction of native selected longitudinal contacts that are conserved over time compared to PF-A. Table S2 shows the average conserved fraction of selected longitudinal contacts for last 50 ns between these loops for PF-A and PF-B for each octamer. We observe that GTP2 replica has significantly higher average conserved selected longitudinal contacts for PF-B (0.605 ± 0.020) compared to PF-A (0.281 ± 0.043). This phenomenon is further illustrated in Figure 9B, contact maps between the β-T3 loop (x-axis) and α-T7-H8 loops (y-axis) averaged over the 300 ns simulation trajectories for all three replicas. Since the contacts between βT5 and α-T7-H8 loops were not dominant, these contacts are not shown in the contact map. For the GTP2 replica, we observe a brighter contact map for PF-B compared to PF-A, indicating that the contacts between the lower β-T3 loop and the upper α-H7-H8 loop at the inter-dimer interface are more conserved for PF-B compared to PF-A. Here, the brighter contact map and stronger longitudinal contacts represent that the β-T3 loop of the lower dimer and the α-T7-H8 loop of upper dimer are closer in PF-B than PF-A. This agrees well with Nogales et al.29 where these loops come closer to create longitudinal compaction. This suggests that after GTP hydrolysis, if these loops do not reorganize to create compaction, the inter-dimer GDP can move away from its original binding site and reposition itself near the upper α-T7H8 loop and create a wider interfacial cavity. For the GDP octamers, as shown in Figure 9 both the GDP1 and GDP2 replicas possess a similar strength of selected longitudinal contacts between these three loops. However, for the GDP3 replica, PF-A has a higher fraction of conserved selected 6173


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average rmsd of dimers 1 (10.98 ± 1.98) and dimers 2 (9.00 ± 1.63) is very small. This shows that in the GTP cap octamers, free β M-loops at the cap layer (dimer 1) have higher fluctuation compared to β M-loops of other dimers. In GTP3, where PFs are splaying, dimer 3 loses lateral contacts with dimer 1 and its β M-loop is free. The rmsd of β M-loop of dimer 3 is similar to that of dimer 1 after PFs start splaying (after ∼100 ns). This suggests that the presence of a single GTP cap layer increases the fluctuation of free β M-loops of the cap layer, but significantly reduces the fluctuation and stabilizes the free β M-loops of lower dimers. Furthermore, our results suggest that GTP hydrolysis creates a structural intermediate, a GTP/GDP interface, that leads to differential longitudinal contacts between neighboring protofilaments which leads to strain/tension in the MT lattice. This tension could be relieved through bending in the form of “curling” or “splaying” during depolymerization. However, we note that the degree of tension/strain will depend entirely on the neighboring PFs. Normal Mode Analysis. Following, we characterize the effect of this single GTP cap layer on the tubulin octamer with normal model analysis (NMA) using the Protein Dynamics and Sequence Analysis (ProDy) Python package.43 NMA is a standard technique to study large-scale, global, functional motions of proteins in their native state. These large-scale fluctuations with lower frequency and higher amplitude are highly cooperative and involve large substructures, and are thus called global motions.64−66 We find four dominant normal modes of tubulin octamers as schematically sketched in Figure 10: (i) a “scissor-like” mode, (ii) a “bending/peeling” mode,

for tubulin octamers without a single GTP cap layer, GDP exchange at the cap layer might occur which could be correlated to the differential strength of selected longitudinal contacts at the inter-dimer interface in the PFs. Overall, we characterize structural differences observed in dimers and PFs in tubulin octamers, in the presence and absence of a single GTP cap layer. Requirement of the GTP cap layer in the growing MT end is well-established for the polymerization phase.18,19 MTs undergo a depolymerization phase once these GTP cap layer/s hydrolyze to GDPs.7,18 In our GDP octamer replicas, only 1 out of 3 octamers possesses two bent PFs, whereas 1 octamer has straight PFs and the remaining replica possesses both bent and straight PFs. These octamers also do not have a clear trend for PF curvature. These results indicate that GDP octamers may occur in several configurations. In the GDP3 replica where selected longitudinal contacts were weaker in PF-B compared to PF-A, E-site GDPs of the cap layer were found to be leaving the binding site. This phenomenon suggests nucleotide exchange can occur at the cap of GDP octamers. Previous experimental58,59 and computational60−62 studies have reported nucleotide exchange phenomenon at MT ends. Our results suggest nucleotide exchange can occur in smaller tubulin oligomers such as octamers. In the case of the GTP cap octamer replicas, we observe PF-A is more curved compared to PF-B. Moreover, PF-B has stronger longitudinal contacts at the interface compared to PF-A. These results show that a single GTP cap layer has asymmetric effects on PF curvature and the strength of inter-dimer longitudinal contacts, which could lead to tension at the GTP-cap layer interface between neighboring PFs. This interesting phenomenon suggests that a single GTP cap layer alone is not enough to keep octamers in a straighter conformation. Moreover, PF-B being straighter, possessing conserved lateral contacts between the M-loop and H1-B2 and H2-B3 loops, suggests that adjacent PFs might be the next requirement to maintain lateral contacts and support the straighter MT lattice. In both the GTP2 and GDP3 replicas, we observe greater inter-dimer bending angles for PFs which have weaker selected longitudinal contacts. In these replicas, GDP is stabilized by H-bonds with either the upper α-T7-H8 loop or the lower β-T5 loop instead of a combination of H-bonds with the lower β-T3 and β-T5 loops and the upper α-T7-H8 loop. These results parallel with the Nogales29 model which suggests that organization of these three loops and their contacts with the inter-dimer GDP is crucial to keep the GDP in the binding cavity and maintain the inter-dimer bending angle and conformation of PF. Previous studies have supported the model that MT depolymerization is initiated by GTP hydrolysis followed by the weakening of lateral contacts.7,18 Grafmueller et al.21 suggested that the hydrolysis of GTP facilitates distortion of Mloops, thus weakening the lateral contacts. Another study has reported that helical β M-loops in the stable microtubule lattice assist in stronger lateral contacts.63 Figure S10 shows the rootmean-square-displacements (rmsds) of β M-loops of dimer 1, 2, 3, and 4 for GTP cap and GDP octamers throughout the simulation. We observe β M-loops of dimer-1 of GTP cap octamers have higher rmsds compared to other dimers in the GTP cap octamer. As shown in Figure S10 and Table S4, in the GTP cap octamers the rmsd of dimer 2 is significantly lower compared to dimer 1. For the GTP cap octamers, the average rmsd for the last 50 ns simulation for dimers 1 (15.16 ± 3.46) is significantly higher compared to the average rmsd of dimers 2 (6.93 ± 0.93). Whereas for GDP octamers the difference in

Figure 10. Normal modes of tubulin octamers: (A) Scissor like motion; (B) Peeling motion; (C) Bending sideways motion; and (D) Sliding motion.

(iii) a “lateral bending” mode, and (iv) a “sliding” or shearing mode. In the “scissor-like” mode, the ends of each PF are moving in opposite directions and moving away from and close to the adjacent PF’s end. In the “bending/peeling” motion, there is longitudinal bending in the same direction as PF’s peel during the depolymerizing phase. In the “lateral bending” both PFs bend sideways. In the “sliding” or shearing mode each PF is vertically sliding up or down, and the motion of each PF is opposite to the adjacent PF. 6174


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kf−MT values are within the range of the reported kf values of MT. Next, we calculate persistence length of MT, lp−MT as explained in Supporting Information. We find lower lp−MT for the GTP cap MT (0.54 ± 0.05 mm) compared to the GDP MT (0.66 ± 0.05 mm). Experimentally, for longer MT’s, a wide range of lp (1−8 mm) is well-established.1−3,5,6,72 Recent studies have suggested a shorter lp for shorter MT lengths. A thermal fluctuation study of the paclitaxel-stabilized MT reported the decrease of lp from 5 to 0.11 mm when decreasing the MT length from 48 to 3 μm.3 Also, MT ends shorter than 1 μm were reported to have a lp value of 0.08 mm.72 Furthermore, simulation studies of the MT have shown a lp varying from 0.8 to 2 mm with increasing MT length,45 while simulation studies for tubulin hexamers reported a smaller lp of the paclitaxel-stabilized system (1.2 mm) compared to a nonstabilized system (6.9 mm).1 In the study by Sept et al.,1 the hexamers were coarse-grained to 6 beadsone bead per subunit and the calculations were done assuming an isotropic MT system utilizing the equipartition theorem and assuming harmonic dependence. Also, the lp for hexamers was calculated 2D from 2D Young’s modulus, Y2D s as lp = Ys I/kBT, where I is the second moment of area and the I value of the whole MT was used instead of their hexamer system. Our assumed MT has only 2 layers of tubulin dimers making it a very short MT (0.016 μm). Thus, calculated lp−MT values are in the range of experimentally reported lp values for the shorter MT lengths studied. Next, we calculate Young’s modulus of the MT, as explained in Supporting Information. Here, IMT is the second moment of area of the MT, 1 × 10−32 m4.45 We find a lower Yf−MT value for the GTP cap MT (0.23 ± 0.02 GPa) as compared with the GDP MT (0.28 ± 0.02 GPa). Simulation studies have shown the Yf−MT values of MT ranging from 0.3 to 1 GPa, increasing with the length of MT.45 Our Yf−MT values are slightly lower than the reported values, since our MTs have only 2 layers of tubulin dimers compared to hundreds of layers of tubulin dimers in physiological MT. Overall, we see significant differences in the values of the mechanical properties for the larger MT as compared with smaller tubulin systems. However, the trend for these values is conserved in both smaller tubulin systems as well as the full MT. In the MT, each PF has adjacent PFs on both sides, the overall rigidity of the MT due to numerous lateral and longitudinal contacts should be greater than our octamer systems where each PF has only one neighboring PF and the longitudinal contacts are at only one inter-dimer interface. Previously reported values for the kf for MTs (∼10−24 N m2)68−70 are also higher compared to tubulin hexamers (∼10−26 N m2).1 Overall, the calculated values of kf, lp, and Yf for the octamers and MTs indicate the presence of the GTP cap layer makes the octamer and MTs more stable, softer, and more flexible, facilitating stronger lateral and longitudinal contacts.

The last frames of all octamers are selected to determine the global motions from the first 10 modes and calculate their mechanical properties. For all the octamers, the “scissor-like” mode is always the dominant mode and has the lowest frequency in the range of 1.46 × 1011 to 2.06 × 1011 Hz, and the “sliding” mode always has the highest frequency in the range of 4.37 × 1011 to 5.45 × 1011 Hz. From the associated frequencies obtained from NMA, mechanical properties (the flexural rigidity (kf), persistence length (lp), and bending modulus (Yf)) of octamers as well as full MTs are calculated as explained below, and in further detail in the Supporting Information. Values of the mechanical properties are averaged for the three replicas of each octamer and MT. The summary of the calculated mechanical properties comparing the GTP cap and GDP octamers and their MTs are shown in Table S5 and S6. To begin with, using dispersion relations, the flexural rigidity, kf, is calculated from the vibrational frequency of the first bending mode as explained in Supporting Information. We find that kf for the GTP cap octamer (3.19 × 10−25 N m2 ± 2.91 × 10−26 N m2) is lower than the kf for the GDP octamer (3.87 × 10−25 Nm2 ± 2.19 × 10−26 Nm2). From the kf, we next calculate persistence length, lp. We find lower lp for the GTP cap octamer (0.07 ± 0.01 mm) compared to the GDP octamer (0.09 ± 0.01 mm). Then, we calculate the corresponding value of the bending modulus, Yf, using two approaches as detailed in Supporting Information. For the first approach, assuming the base of octamer to be a rectangular plane we find a lower Yf for the GTP cap octamer (4.43 ± 0.40 GPa) as compared with the GDP octamer (5.36 ± 0.40 GPa). For the second approach, considering each octamer as two attached solid cylinders we find Yf values similar to the values obtained from the first calculation: 3.96 ± 0.36 GPa for the GTP cap octamer and 54.80 ± 0.36 GPa for the GDP octamer. Following, assuming a MT as a bundle formed by the combination of 13 PFs, we calculate kf of the full MT (kf−MT) using Yf of the octamer as described by Matsudaira et al.67 and as detailed in the Supporting Information. We find that kf−MT of the GTP cap MT (2.32 × 10−24 N m2 ± 2.11 × 10−25 N m2) is lower than the kf−MT of the GDP MT (2.81 × 10−24 N m2 ± 2.11 × 10−25 N m2). This parallels with previous experimental studies on MTs that have reported lower kf values for paclitaxelstabilized MTs (1.9 × 10−24 to 4.7 × 10−24 N m2), compared to nonstabilized MTs (3.7 × 10−24 to 9.2 × 10−24 N m2).68−70 Moreover, simulation studies by Deriu et al.45 reported a length-dependent kf, with a range of 4 × 10−24 to 9 × 10−24 N m2, increasing with the length of the MT. Additional simulation studies of tubulin hexamers have also reported a lower kf for paclitaxel-stabilized systems (0.56 × 10−26 N m2) compared to nonstabilized systems (1.25 × 10−26 N m2).1 In comparison with simulation studies, experimental characterization has used four methodsbuckling force, relaxation, hydrodynamic flow, and thermal fluctuationsto measure kf of MTs.68−71 Although the methods utilize the same mechanical principles, the results vary depending on underlying assumptions regarding the system (static vs dynamic), or the characterization technique used (classical mechanics, statistical mechanics, or hydrodynamics). Still, the majority of results show that the paclitaxelstabilized MTs have a lower kf compared to nonstabilized MTs. Given that the GTP cap octamer is a more stable octamer compared to the GDP octamer, the kf values obtained for our octamers agree well with the trend of a lower kf value for a stabilized system than that for a nonstabilized system. Our

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DISCUSSION AND CONCLUSION We have characterized structural differences observed within and between PFs for tubulin octamers in the presence and absence of a single GTP cap layer using multiple replicas of long-time all-atomistic molecular dynamics simulations (3 replicas, 0.3 μs for each replica, 0.9 μs for each octamer system, and 1.8 μs total). We observe both θIA and θIE values compared to their initial state vary significantly during simulation over 300 ns. All dimers in each octamer possess 6175


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The Journal of Physical Chemistry B the same initial θIA values (GDP ∼ 3.6°, and GTP cap ∼ 1.9°) and both PFs in each octamer possess the same initial θIE values (GDP ∼ 0.5°, and GTP cap ∼ 0.2°). As discussed above, this trend is lost during 300 ns simulation of each replica. Particularly, we do not see a significant difference in the intra-dimer bending properties of our octamers. GTP cap octamers have a greater protofilament bending angle and lower conservation of longitudinal contacts for PF-A as compared to PF-B. Furthermore, in the GTP cap octamer replicas, PF-A has a gradual curvature and PF-B has a “kink” at the β1 monomer, then straightens toward the upper dimer. Furthermore, we observe “splaying” and “curling” between these PFs. Our results are consistent with the suggestions by Nogales et al.29 that MT stability is regulated by the longitudinal contacts rather than by the lateral contacts, and that upon hydrolysis a GTP-GDP intermediate structure forms that could lead to tension with the MT. We also find that the interaction between the inter-dimer GDP at the E-site with α-T7-H8, β-T3, and β-T5 loops is critical in maintaining the inter-dimer bending angle and keeping GDP in the E-site cavity. We also observe that, in the absence of the GTP cap layer, in one GDP octamer, the GDPs escape from the cap layer, suggesting the possibility of nucleotide exchange in tubulin oligomers (octamers). The calculated mechanical properties further support the effect of a single GTP cap layer on the flexibility of the octamers. The GTP cap octamer replicas are found to have higher flexibility compared to the GDP octamer replicas, which can facilitate the contacts within and between the PFs to stabilize the MT lattice. Therefore, we propose a model that is a combination of the previously described allosteric and lattice models, suggesting that lateral and longitudinal contacts between PFs, as well as differences in nucleotide state are necessary to locally change the curvature state of the MT. Based on these results, we suggest that both adjacent PFs as well as a protective GTP cap layer are required to keep the MT stable. Our octamers missing adjacent PFs are comparable to tapered MT ends where few PFs grow longer than other PFs.73,74 These PFs missing their adjacent PFs with fewer lateral contacts are suggested to be unstable and act as “hot spots” for GTP cap loss and undergo depolymerization.74 In order to better understand the competitive role of GTP cap layers and lateral contacts at these tapered ends, simulations of larger tubulin systems with three PFs with three dimers and different nucleotide states can be the next step. This will provide detailed insights into how an outer PF (missing lateral contacts) behaves compared to inner PF (with complete lateral contacts), and how their behavior is affected by different nucleotide states. Also, these octamers only represent short PFs of MTs where each tubulin dimer is experiencing different lateral and longitudinal contacts. To better characterize the behavior of dimers and PFs in a MT like environment, a much bigger system is vital. With the limitations of all-atom simulations, the next approach to take is coarse-grained (CG) MTs. Several studies have used CG MTs to study their dynamics.75−77 However, to accurately characterize the interaction of the nucleotides with their nearby loops and quantify the role of various residues in maintaining MT contacts, a hybrid all-atomistic and coarse-grained approach might be required. Here, one can model with lower resolution the core residues and with greater resolution peripheral residues that are involved in nucleotide and MT contacts. We have simulated our octamers in the presence of sodium chloride as our counterions. Several experimental studies have

reported interesting MT structural behavior in the presence of different cations. For example, tubulin polymerizes into sheets in the presence of Zn2+, and MT depolymerizes in the presence of Ca2+.50,78 A recent study by Bachand et al.79 has shown concentration dependent mechanical properties of MTs. However, these salt dependent effects are mediated via the highly negative C-terminal tails of tubulin dimers.79 Since these C-terminal tails are missing in our model the choice of salt should not have major impact on the conformations and mechanical properties of octamers. As our future work, we will be exploring the interaction of various salts with C-terminal tails and their impact on the conformations and mechanical properties of MTs. Several experimental studies have reported point mutations affecting MT dynamics and lattice contacts resulting in a varied binding nature with drugs and MAPs.80,81 Only a few simulation studies have characterized the effect of point mutations such as suppressed catastrophe48 and altered intra-dimer tubulin−tubulin binding strength.82 With advances in computational resources and higher resolution atomic structures of tubulin dimers in various states, one can exploit simulation tools to further characterize MT properties at the molecular level.

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ASSOCIATED CONTENT

* Supporting Information S

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jpcb.8b02193. Simulation details on dimer and octamer systems; supplementary figures reporting H-bond analysis at the N-site and E-site, dihedral angles between PFs, RMSDs, of β M-loops. Details on calculation of mechanical properties from NMA and supplementary figures on cross-correlation observed within octamer. (PDF)

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. ORCID

Myungshim Kang: 0000-0002-4778-8240 Sharon M. Loverde: 0000-0002-7643-6498 Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This research was supported, in part, by the NSF through TeraGrid resources under grant number TG-CHE130099 and a grant of computer time from the City University of New York High Performance Computing Center under NSF Grants CNS0855217, CNS-0958379 and ACI-1126113. S. M. L. acknowledges start-up funding received from College of Staten Island and City University of New York. A. M. also acknowledges partial support thanks to the Rosemary O’Halloran scholarship awarded to female chemists in the Chemistry department at College of Staten Island.

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ABBREVIATIONS MT, microtubule; GDP, guanosine diphosphate; GTP, guanosine triphosphate; PF, protofilament 6176


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Effect of Nucleotide State on the Protofilament ... - ACS Publications

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