Structure, Assembly, and Disassembly of Tubulin Single Rings

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

Structure and Energetics of GTP- and GDP-Tubulin Isodesmic Self-Association

Tubulin self-association is a critical process inmicrotubule dynamics. The early intermediate structures, energetics,and their regulation by fluxes of chemical energy, associatedwith guanosine triphosphate (GTP) hydrolysis, are poorlyunderstood. 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) andbelow the critical concentration for the microtubule assembly, weanalyzed in-line size-exclusion chromatography−small-angle X-rayscattering (SEC-SAXS) chromatograms of GTP- and GDP-tubulinsolutions. Both solutions rapidly attained steady state. The SEC-SAXS data were consistent with an isodesmic thermodynamic modelof longitudinal tubulin self-association into 1D oligomers, terminated by the formation of tubulin single rings. The analysis showedthat free dimers coexisted with tetramers and hexamers. Tubulin monomers and lateral association between dimers were notdetected. The dimer−dimer longitudinal self-association standard Helmholtz free energies were −14.2 ± 0.4 k$_B$T (−8.0 ± 0.2 kcalmol$^{−1}$) 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 massfractions of dimers, tetramers, and hexamers as a function of the total tubulin concentration. A small fraction of stable tubulin singlerings, with a radius of 19.2 ± 0.2 nm, was detected in the GDP-tubulin solution. In the GTP-tubulin solution, this fraction wassignificantly lower. Cryo-TEM images and SEC-multiangle light-scattering analysis corroborated these findings. Our analyses providean accurate structure−stability description of cold tubulin solutions

Mechanism of Tubulin Oligomers and Single-Ring Disassembly Catastrophe

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

Mechanism of Tubulin Oligomers and Single-Rings Disassembly Catastrophe

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

Standards rule? Regulations, literacies and algorithms in times of transition

In this panel we seek to reflect upon the theme "internet rules" by drawing on the notion of standards, developed in Science and Technology Studies. The work of Susan Leigh Star lays a foundation for considering the relationships between rules, standards and algorithms as forms of infrastructure. In the panel, we explore the production of standards as they become transparent infrastructures, heeding Star and Lampland's call to restore these standards' "historical development, their political consequences, and the smoke-filled rooms always attached to decisions made about them" (2009:13). Standards – and algorithms – are rarely queried, as they promise and embody efficiency and order. Indeed, modernity may be described as a concentrated, relentless effort to contain the accidental, the arbitrary, the residual; to categorize, order, and routinize the unexpected; and to preclude the exceptional and unpredictable (Bauman, 1991) – in a word: to standardize. As Larkin writes, it is difficult to separate an analysis of infrastructures such as standards from the modernist belief that by promoting order, "infrastructures bring about change, and through change they enact progress, and through progress we gain freedom" (2013:332). It is ironic, then, that standards are distributed unevenly across the sociocultural landscape, that they are increasingly linked and integrated with one another, and that they codify, embody or prescribe social values that often carry great consequences for individuals and groups (Star and Lampland, 2009:5). In this context, the four papers and the moderator of this panel explore the meaning of contemporary standardization practices in such diverse fields as memory applications, crowd funding, biometric identification and national archiving, and internet literacy – viewing them as empirically distinct yet theoretically interrelated attempts to impose order in times of growing uncertainly. Together, they address two tensions that inform contemporary standardization efforts, regarding standards as an encounter between analogue and digital objects and practices; and as dialectic of invisibility and transparency, a pragmatic and symbolic endeavor

Mechanism of the Initial Tubulin Nucleation Phase

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

Reciprocal Grids: A Hierarchical Algorithm for Computing Solution X‑ray Scattering Curves from Supramolecular Complexes at High Resolution

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 3<i>D</i> 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

Structure of Dynamic, Taxol-Stabilized, and GMPPCP-Stabilized Microtubule

Microtubule (MT) is made of <i>αβ</i>-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