Fig 1.
Tubulin life cycle and lattice compaction upon GTP hydrolysis.
(A), Cartoon representation of structural intermediates in MT assembly and disassembly. Individual dimers are composed of α-tubulins (gray circles) and β-tubulins (orange circles when GTP-bound or cyan circles when GDP-bound). Lattice cross-sections (bottom) indicate the location of the seam interface. (B), Local conformational changes proposed to accompany GTP hydrolysis are shown schematically (viewed from within the lumen). Each monomer is illustrated as two domains: intermediate or I and nucleotide-binding or N (C-terminal domains are not shown for simplicity). Rearrangements in α-tubulin around the nucleotide-binding pocket at the inter-dimer interface result in a ∼0.2-nm lattice compaction. The PFs are aligned with respect to monomer βi (marked with a circle). Other more subtle changes (e.g., PF twisting) or intermediate nucleotide states (e.g., GDP-Pi) are not shown for simplicity.
Fig 2.
Elastic properties of isolated ‘infinite’ PFs.
(A), Simulation setup for the single-PF system. α-tubulin (gray) and β-tubulin (cyan) are shown in surface representation. Potassium and chloride ions are shown as orange and cyan spheres, respectively. Water molecules are hidden for clarity. Periodic box with the axial dimension Lz is marked by a black rectangle. (B), Equilibrium probability distributions of the dimer rise in the PFs obtained from stress-free simulations of the system in (A). Shaded areas show statistical uncertanties of the distributions estimated with umbrella sampling. Dashed lines indicate the dimer rise values observed in the cryo-EM densities of GMPCPP- and GDP-MTs. (C), Stress-strain curves calculated for the system in (A) in both GTP- (orange) and GDP-state (cyan). Strain is computed relative to the equilibrium dimer length of GDP-PF, and negative (positive) stresses correspond to PF compression (extension). Only separate fits to the positive and negative stress ranges are shown. (D), Bending stiffness parameters of GTP- and GDP-MTs calculated using the elastic moduli in (B) (all stress values) and for varying PF numbers (orange and cyan dots, respectively). Experimental values (dashed lines with shaded areas) represent inverse-variance weighted means and standard deviations that combine multiple independent thermal fluctuation measurements summarized in [29] and recently updated in [30].
Fig 3.
Lateral coupling and nucleotide state affect PF dynamics.
(A), Simulation setup for the double-PF system mimicking a standard (homotypic) lateral interface. Color coding as in Fig 2A. Water molecules are hidden for clarity. Periodic box is marked by a black rectangle. Individual PFs are labeled as (1) and (2). (B) and (C), Free energy surfaces of the system in (A) as a function of dimer rise and nucleotide state obtained by umbrella sampling. The surfaces are color-coded by free energy values with an increment of 1 kBT (dark red to gray). Black solid lines additionally show isoenergetic contours. Orange and cyan circles indicate the dimer rise values observed in the cryo-EM densities of GMPCPP- and GDP-MTs, respectively. Cartooned dimers in (B) schematically show the extreme conformations of the double-PF system in which both are similarly expanded or compacted (along the diagonal) or in conflicting conformations (along the anti-diagonal). The relative shift of 0.19 nm between the minima of the free energy sufraces in (B) and (C) is additionaly indicated.
Fig 4.
Relative thermodynamic stability of the lateral bond in the double-PF system.
(A), Thermodynamic cycle demonstrating the idea behind estimating the effect of unequal PF conformations on the association free energy between the PFs. While simulating the horizontal transitions (PF association) is computationally more expensive, the free energy changes linked to the vertical transitions (PF compaction) have already been obtained (Figs 2 and 3). (B) and (C), Distributions of the relative stability of the double-PF systems with respect to their equilibrium conformations marked with orange and cyan circles for GTP- and GDP-state, respectively, as a function of dimer rise and nucleotide state. White circles denote conformations with the strongest observed dimer rise mismatch. Free energy color coding is adjusted such that red (blue) areas correspond to conformations of the double-PF system in which the lateral bond is destabilized (stabilized) relative to equilibrium. White areas correspond to no change in the lateral bond stability.
Fig 5.
Lateral coupling induces long-range correlations between distant PFs.
(A) and (B), Side and top views of the simulation setup for the three-PF system mimicking a larger segment of the MT lattice. Color coding as in Figs 2A and 3A. Water molecules are hidden for clarity. Individual PFs are labeled as (1), (2) and (3). (C) and (D), Free energy energy landscapes of the system in (A) as a function of dimer rise and nucleotide state. The 3D landscapes were pairwise projected onto planes corresponding to 2D free energy landscapes of adjacent (α(1)β(1) − α(2)β(2) and α(2)β(2) − α(3)β(3), left and right, respectively) and non-adjacent PFs (α(1)β(1) − α(3)β(3), center). Orange and cyan circles indicate the dimer rise values observed in the cryo-EM densities of GMPCPP- and GDP-MTs, respectively. Note the shift between the GTP and GDP distributions by ∼0.2 nm along both reaction coordinates, consistent with the other simulations in Figs 2 and 3.