Fluctuation in the microtubule sliding movement driven by kinesin in vitro.

We studied the fluctuation in the translational sliding movement of microtubules driven by kinesin in a motility assay in vitro. By calculating the mean-square displacement deviation from the average as a function of time, we obtained motional diffusion coefficients for microtubules and analyzed the dependence of the coefficients on microtubule length. Our analyses suggest that 1) the motional diffusion coefficient consists of the sum of two terms, one that is proportional to the inverse of the microtubule length (as the longitudinal diffusion coefficient of a filament in Brownian movement is) and another that is independent of the length, and 2) the length-dependent term decreases with increasing kinesin concentration. This latter term almost vanishes within the length range we studied at high kinesin concentrations. From the length-dependence relationship, we evaluated the friction coefficient for sliding microtubules. This value is much larger than the solvent friction and thus consistent with protein friction. The length independence of the motional diffusion coefficient observed at sufficiently high kinesin concentrations indicates the presence of correlation in the sliding movement fluctuation. This places significant constraint on the possible mechanisms of the sliding movement generation by kinesin motors in vitro.     

Dynamic light scattering by kappa- and lambda-carrageenan solutions

The intensity correlation functions of kappa- and lambda-carrageenan in various salt solutions and at different concentrations have been determined with the help of dynamic light scattering. From the first cumulant of these correlation functions the values of the translational diffusion coefficients D have been derived. They increase with macromolecular concentration. The extrapolated values to infinite dilution of the diffusion coefficients increase with increasing salt concentration as expected from the salt concentration dependence of the r.m.s. radii of gyration determined previously by static light scattering. The translational diffusion coefficient of lambda-carrageenan in 0.1 M NaCl is smaller than the corresponding value for the kappa species. This is consistent with the difference in contour length and linear charge density of the two samples used. No satisfactory interpretation for the concentration dependence of the diffusion coefficient seems to be possible at present. Although current theories for the macromolecular and salt concentration dependence of D, taking into account charge effects, seem to be applicable, they do not allow for a consistent interpretation of the data. No specific difference between the solution behaviour of kappa- and lambda-carrageenan has been detected.     

A rotational diffusion coefficient of the 70S ribosome determined by depolarized laser light scattering

We have obtained a rotational diffusion coefficient of the 70S ribosome isolated from Escherichia-coli (MRE-600), from the depolarized light scattering spectrum measured by photon correlation spectroscopy. The intensity correlation function of depolarized scattered light contains contributions due to multiple scattered and anisotropy scattered light from the ribosomal particle. We discuss extensively the subtraction procedure used to obtain the rotational correlation time from the experimental correlation function. We have also obtained the translational diffusion coefficient from the same sample by determining the polarized correlation function. The hydrodynamic radius determined from the rotational diffusion coefficient is only slightly larger than the radius obtained from the translational diffusion coefficient. Therefore the ribosomal particle has a non-spherical shape. This conclusion, however, could be impaired by the effect of free draining of the ribosome.     

A rotational diffusion coefficient of the 70S ribosome determined by depolarized laser light scattering.

We have obtained a rotational diffusion coefficient of the 70S ribosome isolated from Escherichia-coli (MRE-600), from the depolarized light scattering spectrum measured by photon correlation spectroscopy. The intensity correlation function of depolarized scattered light contains contributions due to multiple scattered and anisotropy scattered light from the ribosomal particle. We discuss extensively the subtraction procedure used to obtain the rotational correlation from the time from the experimental correlation function. We have also obtained the translational diffusion coefficient from the same sample by determining the polarized correlation function. The hydrodynamic radius determined from the rotational diffusion coefficient is only slightly larger than the radius obtained from the translational diffusion coefficient. Therefore the ribosomal particle has a non-spherical shape. This conclusion, however, could be impaired by the effect of free draining of the ribosome.     

Length dependence of displacement fluctuations and velocity in microtubule sliding movement driven by sea urchin sperm outer arm beta dynein in vitro

We have studied the dependence on microtubule length of sliding velocity and positional fluctuation from recorded trajectories of microtubules sliding over sea urchin sperm outer arm beta dynein in a motility assay in vitro. The positional fluctuation was quantified by calculating the mean-square displacement deviation from the average, the calculation of which yields an effective diffusion coefficient. We have found that (1) the sliding velocity depends hyperbolically on the microtubule length, and (2) the effective diffusion coefficients do not depend on the length for sufficiently long microtubules. The length dependence of the sliding velocity indicates that the duty ratio, defined as the force producing period over the total cycle time of beta dynein interaction with microtubule, is very small. The length independence of the effective diffusion coefficient indicates that there is a correlation in the sliding movement fluctuation of microtubules.     

Structure and mobility of actin filaments as measured by quasielastic light scattering, viscometry, and electron microscopy

Actin filaments of different lengths were prepared by polymerizing actin in the presence of various concentrations of gelsolin, a protein which accelerates actin polymerization by stabilizing nuclei from which filaments grow and which binds to their fast growing ends. The lengths of the actin filaments following polymerization were measured by electron microscopy and showed that the number-average filament length agreed with the predicted length if each gelsolin molecule acted as a seed for the growth of an actin filament. The distribution of lengths was independent of the actin:gelsolin ratio and was similar to that of actin filaments polymerized in the absence of gelsolin (Lw/Ln = 1.8). The mobility of these filaments in solution was studied by quasielastic light scattering and by viscometry. The translational diffusion constant determined by quasielastic light scattering was in agreement with the infinite dilution values calculated from the dimensions and the distribution of lengths determined by electron microscopy for relatively short filament lengths. Under conditions where overlap of the rotational domains of the filaments would be expected to occur, the measured diffusion rates deviated from their predicted dilute solution values and the solution viscosity increased abruptly. The dependence of the diffusion constant and the solution viscosity on the length of the actin filaments can be explained in terms of a theory that describes the restraints on diffusion of independent rigid rods in semi-dilute solution. The results suggest that the rheology of actin filaments can be accounted for by steric restraints. The length of cytoplasmic actin filaments in some cell types is such that these steric constraints are significant and could produce large changes in physical properties with small changes in filament length.     

Quasi-elastic light scattering of Artemia ribosomes sedimented in a CsCl density gradient

It is impossible to measure the diffusion coefficient of macromolecules directly and accurately by quasi—elastic light scattering, when aggregates cannot be eliminated from the solutions to be investigated. Nevertheless, a simple method can be applied to overcome this problem in many cases. Aggregates are separated from the monomeric macromolecules by rate-zonal sedimentation in a CsCl density gradient in a transparent centrifugation tube; the monomers are then located by laser light scattering intensity measurements; photon correlation spectroscopy of the scattered light finally yields their diffusion coefficient. The viscosity of aqueous CsCl solutions at different temperatures and concentrations allows a good separation by centrifugation and a low uncertainty in the reduction of the measured diffusion coefficient to standard conditions.The application of the method to eukaryotic large ribosomal subunits is described as an example.     

How molecular motors are arranged on a cargo is important for vesicular transport

The spatial organization of the cell depends upon intracellular trafficking of cargos hauled along microtubules and actin filaments by the molecular motor proteins kinesin, dynein, and myosin. Although much is known about how single motors function, there is significant evidence that cargos in vivo are carried by multiple motors. While some aspects of multiple motor function have received attention, how the cargo itself--and motor organization on the cargo--affects transport has not been considered. To address this, we have developed a three-dimensional Monte Carlo simulation of motors transporting a spherical cargo, subject to thermal fluctuations that produce both rotational and translational diffusion. We found that these fluctuations could exert a load on the motor(s), significantly decreasing the mean travel distance and velocity of large cargos, especially at large viscosities. In addition, the presence of the cargo could dramatically help the motor to bind productively to the microtubule: the relatively slow translational and rotational diffusion of moderately sized cargos gave the motors ample opportunity to bind to a microtubule before the motor/cargo ensemble diffuses out of range of that microtubule. For rapidly diffusing cargos, the probability of their binding to a microtubule was high if there were nearby microtubules that they could easily reach by translational diffusion. Our simulations found that one reason why motors may be approximately 100 nm long is to improve their 'on' rates when attached to comparably sized cargos. Finally, our results suggested that to efficiently regulate the number of active motors, motors should be clustered together rather than spread randomly over the surface of the cargo. While our simulation uses the specific parameters for kinesin, these effects result from generic properties of the motors, cargos, and filaments, so they should apply to other motors as well.     

Comparison of molecular weight determination of sodium alginate by sedimentation-diffusion and light scattering

The weight average molecular weight, M̄_w, of sodium alginates were determined by the sedimentation-diffusion technique using photon correlation spectroscopy rather than boundary spreading in the analytical ultracentrifuge to determine the translational diffusion coefficients. This enables the diffusion coefficients to be determined easily and accurately. Excellent correlation is found between the observed zero concentration translational diffusion coefficient, D_O and the M̄_W values in a emphirical power law. The M̄_W obtained by sedimentation-diffusion and laser light scattering compare very favourably. The concentration dependence of the photon correlation spectroscopy data allowed determination of the coil overlap concentration, c*. The inverse proportionality of c* to both M̄_W and [η] is demonstrated.     

Mechanism of bovine liver glutamate dehydrogenase self-assembly: III. Characterization of the association-dissociation stoichiometry with quasi-elastic light scattering

The homodyne light-scattering autocorrelation function originating in translational diffusion has been simulated for a polymerization model proposed for a number of self-associating systems: the sequential addition of identical monomer units to a growing aggregate, with identical equilibrium constants for each step. Both spherical and rigid rod structures have been considered. When applied to quasi-elastic light scattering data on glutamate dehydrogenase self-assembly, the simulation results indicate the formation of elongated polymers having equivalent and identical association sites. The weak response of translational diffusion coefficients to solution non-ideality leads to a valuable test of the unique equilibrium constant assumption. On the other hand, it is shown that successful exploitation of quasi-elastic light scattering data on aggregating systems of this type relies heavily on independent information.     

Fibrinogen and the early stages of polymerization to fibrin as studied by dynamic laser light scattering

Human fibrinogen and the polymerization of fibrin after activation by the enzymes, thrombin and Batroxobin, were studied by means of dynamic laser light scattering (DLS). The apparent diffusion constant, D, for fibrinogen was measured and has a value of (1.80 +/- 0.42) X 10(-7) cm2 X s-1. D was found to contain contributions from the translational diffusion constant (Dt) as well as from the rotational diffusion constant (Dr). A comparison between experimental and calculated values of Dr and Dt suggests that fibrinogen in the absence of added Ca2+ expresses a certain degree of flexibility, while it is straightened in the presence of added Ca2+. The time dependence of D showed periodic oscillations, while the average D values decreased with time. Thrombin and Batroxobin caused similar behaviour of D. The period length was related to the enzyme concentration, clotting time (Ct) and the rate of release of fibrinopeptide A (FPA). No periodic oscillations were observed in experiments where the enzyme was replaced by saline, or in experiments using a dysfunctional fibrinogen (fibrinogen Aarhus) which displayed slow rates of FPA-release and polymerization. We propose that the periodic oscillations in a system far from equilibrium may be explained by conformational changes occurring in the fibrinogen molecule during enzyme activation and polymerization.     

The hydrodynamic characterization of waxy maize amylopectin in 90% dimethyl sulfoxide–water by analytical ultracentrifugation, dynamic, and static light scattering

Static light scattering of high amylopectin waxy maize starch gently dispersed in 90% dimethyl sulfoxide–water yielded a weight average molecular weight M_w and radius of gyration R_g of 560×10⁶ g/mol and 342 nm, respectively. To obtain an independent hydrodynamic characterization of these solutions, we measured the sedimentation coefficient for the main component in an analytical ultracentrifuge. The value of s⁰, the infinite dilution sedimentation coefficient, was 199 S. The translational diffusion coefficient D⁰ in very dilute solutions was measured by dynamic light scattering at 90° and found to be 2.33×10⁻⁹ cm²/s. An effective hydrodynamic radius R_h was calculated from this diffusion constant using the Stokes–Einstein equation and found to be 348 nm. The structure-related parameter ρ=R_g/R_h was calculated to be 0.98. The weight average molecular weight calculated from the Svedberg equation using the values measured for s⁰ and D⁰ was 593×10⁶ g/mol. This result is in reasonable agreement with the light scattering results. As light scattering results are subject to experimental errors due to the possibility of dust contamination, the presence of microgel or aggregates, and the questionable applicability of light scattering theory to interpret results for macromolecular sizes approaching the wave length of light used as a source for scattering, it is advisable to have corroborating hydrodynamic data when possible to further validate light scattering results in this very high molecular weight range.     

Structural intermediates in the assembly of taxoid-induced microtubules and GDP-tubulin double rings: time-resolved X-ray scattering.

We have studied the self-association reactions of purified GDP-liganded tubulin into double rings and taxoid-induced microtubules, employing synchrotron time-resolved x-ray solution scattering. The experimental scattering profiles have been interpreted by reference to the known scattering profiles to 3 nm resolution and to the low-resolution structures of the tubulin dimer, tubulin double rings, and microtubules, and by comparison with oligomer models and model mixtures. The time courses of the scattering bands corresponding to the different structural features were monitored during the assembly reactions under varying biochemical conditions. GDP-tubulin essentially stays as a dimer at low Mg(2+) ion activity, in either the absence or presence of taxoid. Upon addition of the divalent cations, it associates into either double-ring aggregates or taxoid-induced microtubules by different pathways. Both processes have the formation of small linear (short protofilament-like) tubulin oligomers in common. Tubulin double-ring aggregate formation, which is shown by x-ray scattering to be favored in the GDP- versus the GTP-liganded protein, can actually block microtubule assembly. The tubulin self-association leading to double rings, as determined by sedimentation velocity, is endothermic. The formation of the double-ring aggregates from oligomers, which involves additional intermolecular contacts, is exothermic, as shown by x-ray and light scattering. Microtubule assembly can be initiated from GDP-tubulin dimers or oligomers. Under fast polymerization conditions, after a short lag time, open taxoid-induced microtubular sheets have been clearly detected (monitored by the central scattering and the maximum corresponding to the J(n) Bessel function), which slowly close into microtubules (monitored by the appearance of their characteristic J(0), J(3), and J (n) - (3) Bessel function maxima). This provides direct evidence for the bidimensional assembly of taxoid-induced microtubule polymers in solution and argues against helical growth. The rate of microtubule formation was increased by the same factors known to enhance taxoid-induced microtubule stability. The results suggest that taxoids induce the accretion of the existing Mg(2+)-induced GDP-tubulin oligomers, thus forming small bidimensional polymers that are necessary to nucleate the microtubular sheets, possibly by binding to or modifying the lateral interaction sites between tubulin dimers.     

Physical properties of type i collagen in solution: Structure of α-Chains and β- and γ-components and two-component mixtures

The structure of thermally denatured Type I collagen has been studied using laser light scattering. The results indicate that the diffusion coefficients of α-chains and β- and γ-components are 1.550 ± 0.08 × 10^?7, 1.000 ± 0.05 × 10^?7, and 0.835 ± 0.04 × 10^?7 cm²/sec, respectively, at temperatures between 20 and 40°C. It is concluded from diffusion data that these species have hydrodynamic radii of about 13.8 nm (α-chain), 21.5 nm (β-component), and 25.7 nm (γ-component), consistent with previous studies of thermal denaturation by light scattering. It is also concluded, based on volume calculations, that a large volume increase occurs when the triple helix unfolds. Homodyne correlation functions for two component mixtures of α-chains and β-and γ-components appeared to decay exponentially. In all but one case discussed the correlation function could be fitted with a single component having a translational diffusion coefficient which was an intensity weighted average of the diffusion coefficient of each component present.     

Effects of dynein on microtubule mechanics and centrosome positioning

To determine forces on intracellular microtubules, we measured shape changes of individual microtubules following laser severing in bovine capillary endothelial cells. Surprisingly, regions near newly created minus ends increased in curvature following severing, whereas regions near new microtubule plus ends depolymerized without any observable change in shape. With dynein inhibited, regions near severed minus ends straightened rapidly following severing. These observations suggest that dynein exerts a pulling force on the microtubule that buckles the newly created minus end. Moreover, the lack of any observable straightening suggests that dynein prevents lateral motion of microtubules. To explain these results, we developed a model for intracellular microtubule mechanics that predicts the enhanced buckling at the minus end of a severed microtubule. Our results show that microtubule shapes reflect a dynamic force balance in which dynein motor and friction forces dominate elastic forces arising from bending moments. A centrosomal array of microtubules subjected to dynein pulling forces and resisted by dynein friction is predicted to center on the experimentally observed time scale, with or without the pushing forces derived from microtubule buckling at the cell periphery.     

Tau Protein Diffuses along the Microtubule Lattice

Current models for the intracellular transport of Tau protein suggest motor protein-dependent co-transport with microtubule fragments and diffusion of Tau in the cytoplasm, whereas Tau is believed to be stationary while bound to microtubules and in equilibrium with free diffusion in the cytosol. Observations that members of the microtubule-dependent kinesin family show Brownian motion along microtubules led us to hypothesize that diffusion along microtubules could also be relevant in the case of Tau. We used single-molecule total internal reflection fluorescence microscopy to probe for diffusion of individual fluorescently labeled Tau molecules along microtubules. This allowed us to avoid the problem that microtubule-dependent diffusion could be masked by excess of labeled Tau in solution that might occur in in vivo overexpression experiments. We found that approximately half of the individually detected Tau molecules moved bidirectionally along microtubules over distances up to several micrometers. Diffusion parameters such as diffusion coefficient, interaction time, and scanned microtubule length did not change with Tau concentration. Tau binding and diffusion along the microtubule lattice, however, were sensitive to ionic strength and pH and drastically reduced upon enzymatic removal of the negatively charged C termini of tubulin. We propose one-dimensional Tau diffusion guided by the microtubule lattice as one possible additional mechanism for Tau distribution. By such one-dimensional microtubule lattice diffusion, Tau could be guided to both microtubule ends, i.e. the sites where Tau is needed during microtubule polymerization, independently of directed motor-dependent transport. This could be important in conditions where active transport along microtubules might be compromised.     

Characterization of aggregate structure in mercerized cellulose/LiCl.DMAc solution using light scattering and rheological measurements

The structure of a semidilute solution of mercerized cellulose (CC1m) in 8% (w/w) LiCl.DMAc, which contained some aggregates, was investigated using static and dynamic light scattering measurements. The static scattering function of the polymer solution containing a small amount of aggregates can be separated into fast- and slow-mode components by combining static and dynamic light scattering measurements. The osmotic modulus was identical for the fast-mode component of the CC1m solutions and the native cellulose (CC1) solutions, in which cellulose is dispersed molecularly. This indicates that the molecularly dispersed component of the CC1m solutions has an identical conformation with the cellulose molecules in the CC1 solutions. The correlation length was also identical for the fast-mode components of CC1m solutions and the CC1 solutions, indicating that these solutions have the same mesh size of the polymer entanglement. These observations for the fast-mode components are consistent with the concentration dependence of the zero shear rate viscosity and the plateau modulus estimated in the rheological measurements. The slow-mode component, on the other hand, gave information on the aggregate structure in the CC1m solution. The radius of gyration of the aggregate structure estimated from the slow-mode component was about 70 nm, which is independent of the concentration of the solution. The plots for particle scattering factor of the slow-mode component lay between the theoretical curve of a sphere and a Gaussian chain, implying that the structure of the aggregate in the CC1m solution is like a multiarm polymer. A characteristic time of the slow-mode component calculated with the translational diffusion coefficient and the radius of gyration were almost identical with the relaxation time of the long-time relaxation observed in the rheological measurements. This indicates that the long-time relaxation of CC1m solutions originates in the translational diffusion of the aggregate structure in the solution.     

Microtubule elongation and guanosine 5'-triphosphate hydrolysis. Role of guanine nucleotides in microtubule dynamics

The tubulin concentration dependence of the rates of microtubule elongation and accompanying GTP hydrolysis has been studied over a large range of tubulin concentration. GTP hydrolysis followed the elongation process closely at low tubulin concentration and became gradually uncoupled at higher concentrations, reaching a limiting rate of 35-40 s-1. The kinetic parameters for microtubule growth were different at low and high tubulin concentrations. Elongation of microtubules has also been studied in solutions containing GDP and GTP in variable proportions. Only traces of GTP present in GDP were necessary to confer a high stability (low critical concentration) to microtubules. Pure GDP-tubulin was found unable to elongate microtubules in the absence of GTP but blocked microtubule ends with an equilibrium dissociation constant of 5-6 microM. These data were accounted for by a model within which, in the presence of GTP-tubulin at high concentration, microtubules grow at a fast rate with a large GTP cap; the GTP cap may be quite short in the region of the critical concentration; microtubule stability is linked to the strong interaction between GTP and GDP subunits at the elongating site; dimeric GDP-tubulin does not have the appropriate conformation to undergo reversible polymerization. These results are discussed with regard to possible role of GDP and GTP and of GTP hydrolysis in microtubule dynamics.     

Translational and Rotational Diffusion Constants of Tobacco Mosaic Virus from Rayleigh Linewidths

The translational and rotational diffusion constants of tobacco mosaic virus (TMV) have been determined from homodyne and heterodyne measurements of the spectrum of laser light scattered from dilute aqueous solutions of TMV. Our results for the translational and rotational constants respectively, reduced to 20 degrees C, are: D(T) = 0.280 +/- 0.006 x 10(-7) cm(2)/sec, and D(R) = 320 +/- 18 sec(-1). We include a theoretical derivation of the spectrum of light scattered from rod-shaped molecules which reproduces results obtained previously by Pecora, but which is specialized at the outset to the problem of dilute solutions so that simple single-particle correlation functions may be utilized. An analysis of the photocurrent spectrum for both the homodyne and heterodyne detection schemes is given. Various data reduction schemes utilized in the analysis of our spectra are described in some detail, and our results are compared with values of the diffusion constants obtained from other experiments.