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The current challenges of structural biophysics include determining the structure of large self-assembled complexes, resolving the structure of ensembles of complex structures and their mass fraction, and unraveling the dynamic pathways and mechanisms leading to the formation of complex structures from their subunits. Modern synchrotron solution X-ray scattering data enable simultaneous high-spatial and high-temporal structural data required to address the current challenges of structural biophysics. These data are complementary to crystallography, NMR, and cryo-TEM data. However, the analysis of solution scattering data is challenging; hence many different analysis tools, listed in the SAS Portal (http://smallangle.org/), were developed. In this review, we start by briefly summarizing classical X-ray scattering analyses providing insight into fundamental structural and interaction parameters. We then describe recent developments, integrating simulations, theory, and advanced X-ray scattering modeling, providing unique insights into the structure, energetics, and dynamics of self-assembled complexes. The structural information is essential for understanding the underlying physical chemistry principles leading to self-assembled supramolecular architectures and computational structural refinement., Competing Interests: Declaration of Competing Interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper., (Copyright © 2023 Elsevier Inc. All rights reserved.)

We investigated how the self-association of isolated tubulin dimers affects the rate of GTP hydrolysis and the equilibrium of nucleotide exchange. Both reactions are relevant for microtubule (MT) dynamics. We used HPLC to determine the concentrations of GDP and GTP and thereby the GTPase activity of SEC-eluted tubulin dimers in assembly buffer solution, free of glycerol and tubulin aggregates. When GTP hydrolysis was negligible, the nucleotide exchange mechanism was studied by determining the concentrations of tubulin-free and tubulin-bound GTP and GDP. We observed no GTP hydrolysis below the critical conditions for MT assembly (either below the critical tubulin concentration and/or at low temperature), despite the assembly of tubulin 1D curved oligomers and single-rings, showing that their assembly did not involve GTP hydrolysis. Under conditions enabling spontaneous slow MT assembly, a slow pseudo-first-order GTP hydrolysis kinetics was detected, limited by the rate of MT assembly. Cryo-TEM images showed that GTP-tubulin 1D oligomers were curved also at 36 °C. Nucleotide exchange depended on the total tubulin concentration and the molar ratio between tubulin-free GDP and GTP. We used a thermodynamic model of isodesmic tubulin self-association, terminated by the formation of tubulin single-rings to determine the molar fractions of dimers with exposed and buried nucleotide exchangeable sites (E-sites). Our analysis shows that the GDP to GTP exchange reaction equilibrium constant was an order-of-magnitude larger for tubulin dimers with exposed E-sites than for assembled dimers with buried E-sites. This conclusion may have implications on the dynamics at the tip of the MT plus end., Competing Interests: Declaration of Competing Interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper., (Copyright © 2022 Elsevier B.V. All rights reserved.)

Tubulin nucleation is a highly frequent event in microtubule (MT) dynamics but is poorly understood. In this work, we characterized the structural changes during the initial nucleation phase of dynamic tubulin. Using size-exclusion chromatography-eluted tubulin dimers in an assembly buffer solution free of glycerol and tubulin aggregates enabled us to start from a well-defined initial thermodynamic ensemble of isolated dynamic tubulin dimers and short oligomers. Following a temperature increase, time-resolved X-ray scattering and cryo-transmission electron microscopy during the initial nucleation phase revealed an isodesmic assembly mechanism of one-dimensional (1D) tubulin oligomers (where dimers were added and/or removed one at a time), leading to sufficiently stable two-dimensional (2D) dynamic nanostructures, required for MT assembly. A substantial amount of tubulin octamers accumulated before two-dimensional lattices appeared. Under subcritical assembly conditions, we observed a slower isodesmic assembly mechanism, but the concentration of 1D oligomers was insufficient to form the multistranded 2D nucleus required for MT formation.

Cold tubulin dimers coexist with tubulin oligomers and single rings. These structures are involved in microtubule assembly; however, their dynamics are poorly understood. Using state-of-the-art solution synchrotron time-resolved small-angle X-ray scattering, we discovered a disassembly catastrophe (half-life of ∼0.1 s) of tubulin rings and oligomers upon dilution or addition of guanosine triphosphate. A slower disassembly (half-life of ∼38 s) was observed following an increase in temperature. Our analysis showed that the assembly and disassembly processes were consistent with an isodesmic mechanism, involving a sequence of reversible reactions in which dimers were rapidly added or removed one at a time, terminated by a 2 order-of-magnitude slower ring-closing/opening step. We revealed how assembly conditions varied the mass fraction of tubulin in each of the coexisting structures, the rate constants, and the standard Helmholtz free energies for closing a ring and for longitudinal dimer-dimer associations.

Tubulin self-association is a critical process in microtubule dynamics. The early intermediate structures, energetics, and their regulation by fluxes of chemical energy, associated with guanosine triphosphate (GTP) hydrolysis, are poorly understood. We reconstituted an in vitro minimal model system, mimicking the key elements of the nontemplated tubulin assembly. To resolve the distribution of GTP- and guanosine diphosphate (GDP)-tubulin structures, at low temperatures (∼10 °C) and below the critical concentration for the microtubule assembly, we analyzed in-line size-exclusion chromatography-small-angle X-ray scattering (SEC-SAXS) chromatograms of GTP- and GDP-tubulin solutions. Both solutions rapidly attained steady state. The SEC-SAXS data were consistent with an isodesmic thermodynamic model of longitudinal tubulin self-association into 1D oligomers, terminated by the formation of tubulin single rings. The analysis showed that free dimers coexisted with tetramers and hexamers. Tubulin monomers and lateral association between dimers were not detected. The dimer-dimer longitudinal self-association standard Helmholtz free energies were -14.2 ± 0.4 k B T (-8.0 ± 0.2 kcal mol -1 ) and -13.1 ± 0.5 k B T (-7.4 ± 0.3 kcal mol -1 ) for GDP- and GTP-tubulin, respectively. We then determined the mass fractions of dimers, tetramers, and hexamers as a function of the total tubulin concentration. A small fraction of stable tubulin single rings, with a radius of 19.2 ± 0.2 nm, was detected in the GDP-tubulin solution. In the GTP-tubulin solution, this fraction was significantly lower. Cryo-TEM images and SEC-multiangle light-scattering analysis corroborated these findings. Our analyses provide an accurate structure-stability description of cold tubulin solutions.

Tubulin, an essential cytoskeletal protein, assembles into various morphologies by interacting with an array of cellular factors. One of these factors is the endogenous polyamine spermine, which may promote and stabilize tubulin assemblies. Nevertheless, the assembled structures and their formation pathways are poorly known. Here we show that spermine induced the in vitro assembly of tubulin into several hierarchical architectures based on a tubulin conical-spiral subunit. Using solution X-ray scattering and cryo-TEM, we found that with progressive increase of spermine concentration tubulin dimers assembled into conical-frustum-spirals of increasing length, containing up to three helical turns. The subunits with three helical turns were then assembled into tubules through base-to-top packing and formed antiparallel bundles of tubulin conical-spiral tubules in a distorted hexagonal symmetry. Further increase of the spermine concentration led to inverted tubulin tubules assembled in hexagonal bundles. Time-resolved experiments revealed that tubulin assemblies formed at higher spermine concentrations assembled from intermediates, similar to those formed at low spermine concentrations. These results are distinct from the classical transition between twisted ribbons, helical, and tubular assemblies, and provide insight into the versatile morphologies that tubulin can form. Furthermore, they may contribute to our understanding of the interactions that control the composition and construction of protein-based biomaterials.

Single and double tubulin rings were studied under a range of conditions and during microtubule (MT) assembly and disassembly. Here, tubulin was purified from porcine brain and used without any further modifications or additives that promote ring assembly. The structure of single GDP-rich tubulin rings was determined by cryo-transmission electron microscopy and synchrotron solution X-ray scattering. The scattering curves were fitted to atomic models, using our state-of-the-art analysis software, D+ . We found that there is a critical concentration for ring formation, which increased with GTP concentration with temperature. MT assembly or disassembly, induced by changes in temperature, was analyzed by time-resolved small-angle X-ray scattering. During MT assembly, the fraction of rings and unassembled dimers simultaneously decreased. During MT disassembly, the mass fraction of dimers increased. The increase in the concentration of rings was delayed until the fraction of dimers was sufficiently high. We verified that pure dimers, eluted via size-exclusion chromatography, could also form rings. Interestingly, X-ray radiation triggered tubulin ring disassembly. The concentration of disassembled rings versus exposure time followed a first-order kinetics. The disassembly rate constant and initial concentration were determined. X-ray radiation-triggered disassembly was used to determine the concentration of rings. We confirmed that following a temperature jump, the mass fraction of rings decreased and then stabilized at a constant value during the first stage of the MT assembly kinetics. This study sheds light on the most basic assembly and disassembly conditions for in vitro single GDP-rich tubulin rings and their relation to MT kinetics.

Microtubule (MT) is made of αβ-tubulin heterodimers that dynamically assemble into a hollow nanotube composed of straight protofilaments. MT dynamics is facilitated by hydrolysis of guanosine-5'-triphosphate (GTP) and can be inhibited by either anticancer agents like taxol or the nonhydrolyzable GTP analogues like GMPPCP. Using high-resolution synchrotron X-ray scattering, we have measured and analyzed the scattering curves from solutions of dynamic MT (in other words, in the presence of excess GTP and free of dynamic-inhibiting agents) and examined the effect of two MT stabilizers: taxol and GMPPCP. Previously, we have analyzed the structure of dynamic MT by docking the atomic model of tubulin dimer onto a 3-start left handed helical lattice, derived from the PDB ID 3J6F . 3J6F corresponds to a MT with 14 protofilaments. In this paper, we took into account the possibility of having MT structures containing between 12 and 15 protofilaments. MTs with 12 protofilaments were never observed. We determined the radii, the pitch, and the distribution of protofilament number that best fit the scattering data from dynamic MT or stabilized MT by taxol or GMPPCP. We found that the protofilament number distribution shifted when the MT was stabilized. Taxol increased the mass fraction of MT with 13 protofilaments and decreased the mass fraction of MT with 14 protofilaments. GMPPCP reduced the mass fraction of MT with 15 protofilaments and increased the mass fraction of MT with 14 protofilaments. The pitch, however, remained unchanged regardless of whether the MT was dynamic or stabilized. Higher tubulin concentrations increased the fraction of dynamic MT with 14 protofilaments.

In many biochemical processes large biomolecular assemblies play important roles. X-ray scattering is a label-free bulk method that can probe the structure of large self-assembled complexes in solution. As we demonstrate in this paper, solution X-ray scattering can measure complex supramolecular assemblies at high sensitivity and resolution. At high resolution, however, data analysis of larger complexes is computationally demanding. We present an efficient method to compute the scattering curves from complex structures over a wide range of scattering angles. In our computational method, structures are defined as hierarchical trees in which repeating subunits are docked into their assembly symmetries, describing the manner subunits repeat in the structure (in other words, the locations and orientations of the repeating subunits). The amplitude of the assembly is calculated by computing the amplitudes of the basic subunits on 3D reciprocal-space grids, moving up in the hierarchy, calculating the grids of larger structures, and repeating this process for all the leaves and nodes of the tree. For very large structures, we developed a hybrid method that sums grids of smaller subunits in order to avoid numerical artifacts. We developed protocols for obtaining high-resolution solution X-ray scattering data from taxol-free microtubules at a wide range of scattering angles. We then validated our method by adequately modeling these high-resolution data. The higher speed and accuracy of our method, over existing methods, is demonstrated for smaller structures: short microtubule and tobacco mosaic virus. Our algorithm may be integrated into various structure prediction computational tools, simulations, and theoretical models, and provide means for testing their predicted structural model, by calculating the expected X-ray scattering curve and comparing with experimental data.