The polymer mat: Arrested rebound of a compressed polymer layer

Compression of an adsorbed polymer layer distorts its relaxed structure. Surface force measurements from different laboratories show that the return to this relaxed structure after the compression is released can be slowed to the scale of tens of minutes and that the recovery time grows rapidly with molecular weight. We argue that the arrested state of the free layer before relaxation can be described as a Guiselin brush structure1, in which the surface excess lies at heights of the order of the layer thickness, unlike an adsorbed layer. This brush structure predicts an exponential falloff of the force at large distance with a decay length that varies as the initial compression distance to the 6/5 power. This exponential falloff is consistent with surface force measurements. We propose a relaxation mechanism that accounts for the increase in relaxation time with chain length.Comment: 24 pages, 5 figre

Structure and Intermolecular Interactions between L-Type Straight Flagellar Filaments.

Bacterial mobility is powered by rotation of helical flagellar filaments driven by rotary motors. Flagellin isolated from the Salmonella Typhimurium SJW1660 strain, which differs by a point mutation from the wild-type strain, assembles into straight filaments in which flagellin monomers are arranged in a left-handed helix. Using small-angle x-ray scattering and osmotic stress methods, we investigated the structure of SJW1660 flagellar filaments as well as the intermolecular forces that govern their assembly into dense hexagonal bundles. The scattering data were fitted to models, which took into account the atomic structure of the flagellin subunits. The analysis revealed the exact helical arrangement and the super-helical twist of the flagellin subunits within the filaments. Under osmotic stress, the filaments formed two-dimensional hexagonal bundles. Monte Carlo simulations and continuum theories were used to analyze the scattering data from hexagonal arrays, revealing how the bundle bulk modulus and the deflection length of filaments in the bundles depend on the applied osmotic stress. Scattering data from aligned flagellar bundles confirmed the theoretically predicated structure-factor scattering peak line shape. Quantitative analysis of the measured equation of state of the bundles revealed the contributions of electrostatic, hydration, and elastic interactions to the intermolecular forces associated with bundling of straight semi-flexible flagellar filaments

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

Effect of Tubulin Self-Association on GTP Hydrolysis and Nucleotide Exchange Reactions

Tubulin nucleation, microtubule (MT) assembly, stability, and dynamics depend on GTP hydrolysis and nucleotide exchange reactions. We investigated how the self-association of isolated tubulin dimers affects the rate of GTP hydrolysis and the equilibrium of nucleotide exchange. 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 using HPLC for determining the concentrations of tubulin-free and tubulin-bound GTP and GDP and by SAXS and cryo-TEM. We observed no GTP hydrolysis below the critical conditions for MT assembly, despite the assembly of tubulin 1D curved oligomers and single rings, showing that their assembly did not involve GTP hydrolysis under our conditions. Under conditions enabling spontaneous slow MT assembly, a slow pseudo-first-order GTP hydrolysis kinetics was detected, limited by the rate of MT assembly. 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 calculate, at each tubulin concentration, the distributions of single rings, 1D oligomers, and free dimers, and thereby 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

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

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