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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 kBT (-8.0 ± 0.2 kcal mol-1) and -13.1 ± 0.5 kBT (-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 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.

ACS nano 15(5), 8836 - 8847 (2021). doi:10.1021/acsnano.1c01374, 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., Published by Soc., Washington, DC

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 about 0.1 sec) of tubulin rings and oligomers upon dilution or addition of guanosine triphosphate. A slower disassembly (half-life of about 38 sec) was observed following a temperature increase. Our analysis showed that the assembly and disassembly processes were consistent with an isodesmic mechanism, involving a sequence of reversible reactions at which dimers were rapidly added/removed one at a time, terminated by a two orders-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.

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.

Gold nanoparticles (AuNPs) have been the focus of many studies owing to their unique optical and electronic properties and versatile applications. However, synthesis of stable and homogeneous AuNPs...

ACS omega 3(11), 16246 - 16252 (2018). doi:10.1021/acsomega.8b01289, Exposure of a protein to cosolutes, like denaturants, changes its folding equilibrium. To determine the ensemble of protein conformations at equilibrium, in the presence of weakly interacting cosolutes, we present a two-stage analysis of solution X-ray scattering data. In the first stage, Guinier analysis and Kratky plot revealed information about the compactness and flexibility of the protein. In the second stage, elastic network contact model and coarse-grained normal mode analysis were used to generate an ensemble of conformations. The scattering curves of the conformations were computed and fitted to the measured scattering curves to get insights into the dominating folding states at equilibrium. Urea and guanidine hydrochloride (GuHCl) behaved as preferentially included weakly interacting cosolutes and induced denaturation of hen egg-white lysozyme, which served as our test case. The computed models adequately fit the data and gave ensembles of conformations that were consistent with our measurements. The analysis suggests that in the presence of urea, lysozyme retained its compactness and assumed molten globule characteristics, whereas in the presence of GuHCl lysozyme adopted random coiled conformations. Interestingly, no equilibrium intermediate states were observed in both urea and GuHCl., Published by ACS Publications, Washington, DC

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.

Tubulin dimers are flexible entities serving as building blocks for construction of cellular polymers essential for the cytoskeleton. The conformational state of the dimer dictates the exact formation of assembly and can be regulated by cellular factors including spermine. Using solution X-ray scattering and cryo-TEM measurements we studied the behavior of tubulin assembly in the presence of millimolar spermine concentrations. The results discovered novel structural architectures of tubulin polymers and revealing fascinating hierarchical self-associations based on unique tubulin conical-spiral (TCS) subunits. We followed the assembly pathways of tubulin dimers with different spermine concentrations, from milliseconds to days, and discovered multiple phase transitions with increasing spermine concentration. At 1 mM spermine, tubulin assembled into tubulin helical-pitch (THP) structures, resembling tubulin-rings. Above 1.5 mM spermine, tubulin assembled into TCS architectures. TCS is a unique tubulin assembly, serving as a new building block subunit. TCS assembled into different architectures . The predominant structure was TCS-tube (TCST) that further assembled in a remarkable antiparallel orientation which formed bundles with 2D-cubic and unique quasi-2D hexagonal lattices. Each TCST in the quasi-2D hexagonal lattice was surrounded by four antiparallel TCSTs and two parallel TCSTs. All the above assemblies have never been observed before. At higher spermine concentrations, tubulin assembled into twisted inverted tubulin tubules (ITTs). Here we also show for the first time, the hierarchical assembly pathways from tubulin dimer to each of the above structures, using time-resolved experiments with millisecond temporal resolution. We discovered that the structures that formed at low spermine concentrations were transient precursors of the structures formed at higher spermine concentrations. The results are based on high quality cryo-TEM images, cutting edge synchrotron solution X-ray scattering measurements and state-of-the-art data analysis, using our home developed groundbreaking analysis software, D+. The findings can be relevant to a broad research fields including studies which explore different arrangements of the cytoskeletal network, or studies exploring the attraction forces between proteins that dictate their mode of assembly and molecular designed self-assembly of natural and/or synthetic analogous.

Dipolar lipid membranes may adsorb multivalent ions. The binding constant depends on the type of lipid and ions. In this paper, we focus on the adsorption of calcium ions onto 1,2-dilauroylphosphatidylcholine (DLPC) membrane. Using small-angle-X-ray scattering we found that at ambient room temperature ca. 0.6 mM CaCl2 is a critical concentration at which calcium ions adsorbed to 30 mg/mL (ca. 48 mM) DLPC membrane. We then determined the structure of the lamellar phases formed at CaCl2 concentrations below and above the critical concentration and characterized the effect of temperature and incubation time on the adsorption process. Our findings suggest that calcium adsorption to DLPC membranes requires an initial nucleation phase.

Journal of applied crystallography 52(1), 219 - 242 (2019). doi:10.1107/S1600576718018046, Published by Wiley-Blackwell, [S.l.]

In this paper, we present our new computer program, D+, which uses the reciprocal-grid (RG) algorithm to efficiently compute X-ray scattering curves from solutions of complex structures at high-resolution. Structures are defined in hierarchical trees in which subunits can be represented by geometric or atomic models. Repeating subunits can be docked into their assembly symmetries, describing their locations and orientations in space. The scattering amplitude of the entire structure can be calculated by computing the amplitudes of the basic subunits on 3D reciprocal-space grids, moving up in the hierarchy, calculating the RGs of the larger structures, and by repeating this process for all the leaves and nodes of the tree. For very large structures, a Hybrid method can be used to avoid numerical artifacts. In the Hybrid method, only grids of smaller subunits are summed and used as subunits in a direct computation of the scattering amplitude. D+ can accurately analyze both small- and wide-angle solution X-ray scattering data. We present how D+ applies the RG algorithm, accounts for rotations and translations of subunits, processes atomic models, accounts for the contribution of the solvent as well as the solvation layer of complex structures in a scalable manner, writes and accesses RGs, interpolates between grid points, computes numerical integrals, enables the use of scripts to define complicated structures, applies fitting algorithms, accounts for several coexisting uncorrelated populations, and accelerates computations using GPUs. D+ may also account for different X-ray energies to analyze anomalous solution X-ray scattering data. An accessory tool that can identify repeating subunits in a protein data bank (PDB) file of a complex structure is provided. The tool can compute the orientation and translation of repeating subunits needed for exploiting the advantages of the RG algorithm in D+. In addition, a python wrapper is also available, enabling more advanced computations and integration of D+ with other computational tools. Finally, we present a large number of tests and compare the results of D+ with other programs when possible and demonstrate the use of D+ to analyze solution scattering data from dynamic microtubule structures with different protofilament number. D+ and its source code are freely available (https://scholars.huji.ac.il/uriraviv/software/d-software) for academic users and developers.

Cyanobacteria light-harvesting complexes can change their structure to cope with fluctuating environmental conditions. Studying in vivo structural changes is difficult owing to complexities imposed by the cellular environment. Mimicking this system in vitro is challenging, as well. The in vivo system is highly concentrated, and handling similar in vitro concentrated samples optically is difficult because of high absorption. In this research, we mapped the cyanobacteria antennas self-assembly pathways using highly concentrated solutions of phycocyanin (PC) that mimic the in vivo condition. PC was isolated from the thermophilic cyanobacterium Thermosynechococcus vulcanus and measured by several methods. PC has three oligomeric states: hexamer, trimer, and monomer. We showed that the oligomeric state was changed upon increase of PC solution concentration. This oligomerization mechanism may enable photosynthetic organisms to adapt their light-harvesting system to a wide range of environmental conditions.

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.