Motion of myosin fragments during actin-activated ATPase: fluorescence correlation spectroscopy study.

The rates of the translational motion of myosin fragments, heavy meromyosin (HMM), and heavy meromyosin subfragment-1 (HMM S-1) were measured during actin-activated ATPase reaction by the method of fluorescence correlation spectroscopy. This technique monitors the random fluctuations in the concentration of fluorescent molecules in an open volume which result from the translational diffusion of the molecular species under observation. The statistical behavior of the fluctuations is represented in the form of the autocorrelation function, which is related to the translational diffusion coefficient of the fluorescent molecules. The translational motion of fluorescently labeled myosin fragments was progressively slowed down after additions of increasing amounts of actin in the presence of excess MgATP. When these results are interpreted according to a simple binding scheme, the extent of the retardation can be used to obtain the apparent association constant for binding of S-1 and HMM to actin in the presence of MgATP. In 0.1M KCl and at 23°C, the apparent association constants were determined as K_app^HMM = 2.2 × 10⁴M^?1 and K_app^S-1 = 8.8 × 10³ for HMM and S-1, respectively.     

Quasielastic light scattering from solutions of filamentous viruses. II. Comparison between theories and experiments

We have compared four theoretical effects of rodlike macromolecules with the fast components, i.e., components other than translational diffusion, of our experimental data, which are presented as amplitude autocorrelation functions of electric field scattered from dilute solutions of monodisperse rodlike viruses with lengths from 3300 Å for tobacco mosaic virus to 20,000 Å for Pf1. The four effects are (1) the optic anisotropy treated by Aragón and Pecora, (2) coupled translational–rotational diffusion due to anisotropy in translational mobility recently reformulated by Gierke, (3) anisotropic rotational diffusion with respect to the direction of translational displacement first discussed by Berne and Pecora, and (4) the bending mode of a rod by Fujime and Maruyama. We show that both the first and second effects are required to explain the enhancement of amplitude of the translational diffusion at the expense of fast components. The experimental decay rates of the fast component exceed that of the rotational diffusions. In order to explain the excessive decay rate in the fast component, we need to include a minute amount (～1%) of bending mode of rodlike viruses, especially in longer viruses such as M13 and Pf1.     

Ionic strength effects on macroion diffusion and excess light-scattering intensities of short DNA rods

Quasielastic and static light-scattering measurements were made on DNA isolated from chicken erythrocyte mononucleosomes as a function of ionic strength between 6 × 10^?4 and 1.0M. A transition from single-exponential autocorrelation functions to markedly non-single-exponential decays was observed around 10^?2M ionic strength and was accompanied by a large decrease in the excess light-scattering intensity. Autocorrelation functions recorded below 10^?2M salt were well fit by the sum of two exponential relaxation which differed by as much as 100-fold in time constants. Apparent diffusion coefficients for the fast and slow processes plateaued around 10^?3M with numerical values approximately 10-fold and 1/10, respectively, of the translational diffusion coefficient for mononucleosome DNA at high ionic strength. This behavior is similar to that observed with poly(L -lysine), for which the slow decay has been associated with a transition to an extraordinary phase. The strong and complex salt dependence observed here illustrates potential difficulties in deriving structural information from scattering by polyions at low ionic strength.     

Rotational relaxation of macromolecules determined by dynamic light scattering. II. Temperature dependence for DNA

Correlation functions have been determined for the fluctuating intensity of the depolarized component of forward-scattered laser light from solutions of DNA. The molecular correlation function of calf thymus DNA (mol wt ～15 × 10⁶) appears to exhibit a longest relaxation time (τ_25,w, ～ 18 msec) close to what one would predict from the flowdichroism measurements of Callis and Davidson and, in addition, manifests a spectrum of faster times down to tenths of milliseconds. Furthermore, a major fraction of the amplitude of fluctuations in the angular distribution of segment axes is relaxed on a very much shorter time scale (of the order of 20 microseconds) that appears to be relatively insensitive to molecular weight of the DNA, or to near-melting temperatures. The temperature profile of the longest relaxation time has been obtained and found to exhibit a peculiar spike near T_m, which, together with the absence of a corresponding spike in the (high shear) viscosity, has been interpreted as indicative of an increase in the molecular weight of the DNA in a narrow temperature region near T_m. Correlation functions for polarized light scattered at finite angles were obtained in an attempt to determine the temperature dependence of the translational diffusion coefficient. Although the data contain an extremely slow component that does not admit a simple interpretation, there is some indication of a decrease in the translational diffusion coefficient near T_m, thus supporting the notion of an aggregation occurring near T_m. Finally, a “counterion escape” mechanisn is proposed for the apparent aggregation.     

Dynamic light scattering of aqueous solutions of linear aggregates induced by thermal denaturation of ovalbumin

Dynamic light scattering measurements were performed on dilute aqueous solutions of native ovalbumin (OA) and on those of linear OA aggregates induced by thermal denaturation at low ionic strength and neutral pH. The weight-average molecular weight M_w of four aggregates tested ranged from 1,700,000 to 5,500,000. The translational diffusion coefficient D₀ of native OA at infinite dilution was estimated as 8.70 × 10 ^?7 cm²/s, which gave 56.0 Å as the diameter of the rigid spherical particle. The intensity autocorrelation function of linear OA polymers was analyzed with the cumulant method to obtain the first cumulant Λ_e. The dependence of Λ_e on the scattering vector q at very low polymer concentration was found intermediate between those of a flexible chain and a rigid rod. The translational diffusion coefficient D_tr [≡ (T_e/q²)_{q → 0}] was in proportion to M, and the magnitude was in good agreement with a value calculated from the wormlike cylinder model with values of three parameters determined in an earlier study, M_L = 1600 Å^?1, d = 120 Å, and Q = 230 Å, where M_L, d, and Q are the molecular weight per unit length, diameter, and persistence length, respectively. Based on these results, a new model, to be called as the dimer model, was proposed to interpret the formation mechanism of linear OA polymers induced by thermal denaturation. © 1993 John Wiley & Sons, Inc.     

Quasielastic light-scattering study of polyadenylic acid solutions. II

Quasielastic light scattering is used to study saline solutions of polyadenylic acid with varying polymer concentrations and molecular masses. These experiments clearly show the existence of two relaxation times. For dilute solutions, when the chains are mutually independent, the fast mode is due to the free diffusion of the polymer chains. For concentrations above the overlap concentration C*, the fast mode is due to the propagation of collective excitations of the pseudolattice of polymer chains. The slow modes are observed when the polymer concentration is in the vicinity of the overlap concentration C*. A series of experiments shows that both their relaxation time and amplitude depend only on the polymer concentration and not on the polymer molecular mass. This result rules out any previous explanation based on individual chain motion. Furthermore, since the amplitudes depend on the time elapsed from the preparation of the solution, the slow modes are due to the diffusion of concentration inhomogeneities in the pseudolattice.     

Quasielastic light scattering from solutions of filamentous viruses. I. Experimental

Intensity fluctuations of laser light scattered from filamentous viruses Pf1 [length L (Å) × diameter d (Å) = 20,000 × 90], M13 (9000 × 90), potato virus X (5150 × 130), and tobacco mosaic virus (3000 × 180) in sucrose density gradients were measured with a photon correlation spectrometer over a range of scattering angles from 15° to 120°. The experimental data can be approximated by two exponential decays, “slow” and “fast.” The slow decay rate constant t corresponds to the translational diffusion D of the virus, i.e., t = K²D, where K is the magnitude of the scattering vector. The amplitude of the slow component, i.e., translational diffusion, remains greater than that of the fast component, even at high KL. The fast decay rate constant t is also proportional to K² for viruses such as Pf1, M13, and even potato virus X. In the companion paper, we shall attribute the amplitude enhancement of the translational diffusion to the coupling of its anisotropy to the rotational diffusion modes. In order to explain the excessive decay rates in the fast component, we need to consider the bending mode of rodlike viruses, especially in the longer viruses such as M13 and Pf1, in addition to the usually expected rotational diffusion modes.     

Internal dynamics of d(CGCAAATTTGCG)2: a comparison of NMR relaxation measurements with a molecular dynamics simulation

We report the analysis of a 250 ps molecular dynamics simulation of the dodecamer d(CGCAAATTT-GCG)₂ immersed in a rectangular box of 3469 water molecules with 22 Na⁺ counterions. The internal dynamics of the molecule were investigated by studying the relevant autocorrelation functions related to the ¹³C-NMR relaxation parameters of the C1′-H1′ bonds of the sugar rings. The calculated effective correlation times τ _e (∼13 ps) and the order parameter S² (∼0.82) of the Lipari and Szabo formalism (Lipari and Szabo 1982a, b) are in satisfactory agreement with those determined previously by NMR (Gaudin et al. 1995, 1996). ¹H-¹H NOE buildups have also been measured experimentally and agree with those computed from the simulation. These results validate the simulation, and a more detailed analysis of the internal dynamics of the dodecamer was undertaken. Analysis of the distributions and of the autocorrelation functions of the glycosidic angle flucuations χ shows that the rotational motion of the sugar rings about their glycosidic bond conforms to a restricted diffusion mechanism. The amplitude of the motions and the diffusion constant are 20° and 17.10⁹ rad²s^–1 respectively. These values are in good agreement with ¹³C NMR data. Furthermore the simulation allows us to rule out another model also consistent with the experiment, consisting of a two-state jump between a syn and an anti conformation. Received: 19 November 1996 / Accepted: 17 March 1997     

Intensity fluctuation spectroscopy and transfer RNA conformation. III. Influence of NaCl concentration on the size and shape of the initially salt-free tRNA in solution.

The influence of sodium ion concentration in solution on the initially salt-free conformation of bulk tRNA from baker's yeast has been investigated by means of photon correlation spectroscopy. From the measured values of translational (D^T) and rotational (D^R) diffusion coefficients, the semiaxes of an ellipsoid of revolution, which are hydrodynamically equivalent to the tRNA molecule, were calculated for tRNA solutions in pure H₂O as well as in 0.005, 0.1, 0.5M NaCl and 0.01M MgCl₂ solutions at pH 4.2 and 7.5. These data, combined with our previous studies, suggested a model which describes the formation of an ordered tRNA structure due to increasing NaCl concentrations. Furthermore, we have obtained information concerning intermolecular interactions between tRNA molecules in solution. In low-salt or salt-free tRNA solutions, we detected in the linewidth distribution function an extra-fast component which can be attributed as possibly due to charge fluctuations related to the reaction of ionization of organic bases. In our light-scattering linewidth measurements, we do not see fluctuations of charged and uncharged states directly as concentration fluctuations. Rather, we postulate a modulation of long-range intermolecular electrostatic interactions between the tRNA molecules due to such charge fluctuations. It is this modulation which is related to the fast component of the time correlation function at finite concentrations. A quantitative theory is needed to provide a more definitive explanation of the dynamical behavior of tRNA in salt-free or low-salt solutions.     

Dynamic viscoelastic properties of solutions of shear-degraded deoxyribonucleic acid

Calf thymus and salmon sperm deoxyribouncleie acid were degraded by high-shear stirring to molecular weights M in the range of 1.3–3.2 × 10⁶ and purified by chromatography on methylated bovine serum albumin. Dynamic viscoelastic properties of the fragmented products, in aqueous glycerol solutions in the concentration range of c = 0.003–0.01 g./ml., were investigated with the apparatus of Birnboim and Ferry. At values of the product cM higher than 4 × 10³, the frequency dependence of the components of the complex shear modulus, G′ and G″, displayed a plateau region in which G′ > G″ – ων₁η_S, similar to that observed in concentrated solutions of coiling polymers where it is attributed to an entanglement network (ω is radian frequency, ν₁ volume fraction of solvent, and η₈, solvent viscosity). The width of this plateau region on the logarithmic frequency scale is given by Δ = 3.8 (log cM – 3.56). At lower values of cM, the frequency dependence is intermediate between those predicted by the theory of Zimm for flexible coiled macromolecules and by the theory of Kirkwood and Auer for rods. Fitting to the Zimm theory gives highly discrepant values for molecular weights, while fitting the low-frequency end of the dispersion to the Kirkwood-Auer theory gives reasonable agreement for both molecular weight and rotary diffusion coefficient. It is concluded that the helical fragments appear as nearly rigid rods in their behavior at very low frequencies, but at higher frequencies reveal substantial bending flexibility.     

Fluorescence correlation spectroscopy with high count rate and low background: analysis of translational diffusion

An epi-illuminated microscope configuration for use in fluorescence correlation spectroscopy in bulk solutions has been analyzed. For determining the effective sample dimensions the spatial distribution of the molecule detection efficiency has been computed and conditions for achieving quasi-cylindrical sample shape have been derived. Model experiments on translational diffusion of rhodamine 6G have been carried out using strong focusing of the laser beam, small pinhole size and an avalanche photodiode in single photon counting mode as the detector. A considerable decrease in background light intensity and measurement time has been observed. The background light is 40 times weaker than the fluorescence signal from one molecule of Rh6G, and the correlation function with signal-to-noise ratio of 150 can be collected in 1 second. The effect of the shape of the sample volume on the autocorrelation function has been discussed. Correspondence to: R. Rigler     

Macromolecular crowding in biological systems: hydrodynamics and NMR methods

Most biologically relevant environments involve highly concentrated macromolecular solutions and most biological processes involve macromolecules that diffuse and interact with other macromolecules. Macromolecular crowding is a general phenomenon that strongly affects the transport properties of macromolecules (rotational and translational diffusion) as well as the position of their equilibria. NMR methods can provide information on molecular interactions, as well as on translational and rotational diffusion. In fact, rotational diffusion, through its determinant role in NMR relaxation, places a practical limit on the systems that can be studied by NMR. While in dilute solutions of non-aggregating macromolecules this limit is set by macromolecular size, in crowded solutions excluded volume effects can have a strong effect on the observed diffusion rates. Hydrodynamic theory offers some insight into the magnitude of crowding effects on NMR observable parameters.     

A theoretical model of the pinocytotic vesicular transport process in endothelial cells

A new theoretical model for vesicular transport in single endothelial cells is described using a kinetic molecular approach in which the vesicle diffusion process is coupled with the vesicle attachment/detachment process occurring at the cell plasmalemmal boundaries. Rate constants k^d_i, k_i characterizing a two stage reaction sequence in the attachment/detachment region and the vesicle diffusion coefficient D are obtained by comparison of the theory with the results of tracer studies. For the condition of rapid vesicle loading/discharge of macromolecules it is found that the permeability of endothelial cells to macromolecules tends to be controlled by the vesicular attachment/detachment process rather than the vesicle diffusion process. The rate limiting step in the vesicle attachment/detachment process tends to be the reaction process involving the rate at which a vesicle and the plasmalemmal membrane are brought into/separated from intimate contact rather than that involving the rate of formation/dissolution of the membrane diaphragm of an attached vesicle. Estimated relaxation times for processes occurring in the attachment/detachment region and in the diffusion region, the vesicle transit time in the diffusion region, and the viscosity of the cytoplasm in the diffusion region are deduced. Fair agreement is obtained between the predicted and the observed temperature dependence of the permeability.     

Intensity-fluctuation spectroscopy and tRNA conformation. II. Changes of size and shape of tRNA in the melting process

We have measured the translational (D^T) and rotational (D^R) diffusion coefficients of bulk tRNA from baker's yeast during the thermal unfolding process by means of photon-correlation spectroscopy. It should be noted that our estimate of the rotational diffusion coefficient represented, for the first time, measurements on a small macromolecule in solution by the photoelectron time-of-arrival technique with a delay-time resolution of 1 nsec. The melting curves expressed in terms of δD^T vs temperature were consistent with the literature data in revealing the melting steps and their dependence on NaCl concentration. Additionally, it was possible to prove the existence of an intermediate, more compact structure during the initial steps of the thermal unfolding process. We found that the temperature ranges over which this intermediate structure appears depend strongly on salt concentration. By utilizing both translational and rotational diffusion coefficients and Perrin's equations for ellipsoids of revolution, we have computed the values of the equivalent length and width of tRNA molecules in solution at four different temperatures for NaCl concentrations of 0.2, 0.5, and 1M. The approximate model of ellipsoids of revolution also permits us to obtain an estimate of the radius of gyration, which is in very good agreement with literature data measured by means of small-angle x-ray scattering. Furthermore, we have measured the shape and size changes of tRNA with varying NaCl concentrations at room temperatures (25°C). The molecule becomes smaller and more spherical when NaCl concentration increases. As a result of partial melting at 70°C, the macromolecule is surprisingly elongated with an approximate axial ratio of 8:1 and has dimensions of about 180/22Å. Such information on conformational changes by a simultaneous determination of rotational and translational diffusion coefficients illustrates the potential of this approach, not available by other methods.     

Histone-induced conformational changes in DNA as probed by quasi-elastic light scattering.

Quasi-elastic light scattering as measured by intensity fluctuation (self-beat) spectroscopy in the time domain can be profitably used to follow both the translational diffusion D and the dominant internal flexing mode τ_int of DNA and its complexes with various histones in aqueous salt solutions. Without histones, DNA is found to have D = 1.6 × 10^?8 cm²/sec and τ_int ? 5 × 10^?4 sec in 0.8 M NaCl, 2 M urea at 20°C. Total histone as well as fraction F2A induce supercoiling (D = 2.6 × 10^?8 cm²/sec, τ_int ? 2.8 × 10^?4 sec) whereas fraction F1 induces uncoiling (D = 1.0 × 10^?8 cm²/sec, τ_int ? 9.4 × 10^?4 sec). Upon increasing the salt concentration to 1.5 M the DNA–histone complex dissociates (D = 1.8 × 10^?8 cm²/sec). Upon decreasing the salt concentration to far below 0.8 M, the DNA–histone complex eventually precipitates as a chromatin gel.     

Prediction of a low-frequency mode in bovine pancreatic trypsin inhibitor molecule

One of the frontiers today in molecular biology is to measure, identify and go further to predict the low-frequency internal motion of biological macromolecules, which is crucially important for understanding the dynamic mechanism of various biological functions occurring in such molecules. Based on the theory of continuity model developed recently for dealing with the internal low-frequency motion of a biological macromolecule, it is predicted that the low-frequency phonons with wave number of about 23 cm^?1 might be excited in BPTI molecule.     

Band centrifugation of macromolecules in self-generating density gradients. III. Conditions for convection-free band sedimentation

The conditions for convection-free hand sedimentation are analyzed in terms of the negative density gradients associated with the leading edge of a band and the positive density gradients generated during the experiment. The amount of material necessary to perform a band-centrifugation experiment depends on the diffusion coefficient of the macromolecules, which determines the rate at which the concentration at band maximum decreases, and on the extinction coefficient at the wavelength of observation. The maximum negative gradients in bands of macromolecules with diffusion and extinction coefficients typical of proteins, nucleic acids, and viruses are calculated. Positive density gradients generated by diffusion of small molecules between the thin lamella and the bulk solution are calculated for bulk solutions such us 1M NaCl or 95% D₂O. These “diffusion gradients” are generally adequate to stabilize bands of the above macromolecules. Positive density gradients generated by sedimentation of salts within the bulk solution may be significant in providing stability near the bottom of the cell. The effects of inadequate stabilizing gradients are discussed, and are found to cause forward spreading of the band.     

Dynamic light scattering as a probe of superhelical DNA-intercalating agent interaction

Polarized dynamic light-scattering measurements on superhelical pBR322-plasmid DNA solutions in 0.2M NaCl, 2 mM NaPi, pH 7.0, 2 mM EDTA result in a translational diffusion coefficient D = (3.77 ± 0.10) × 10^?8 cm²/s for the native molecule. Modeling the DNA, in the simplest approximation, as a 10 × 440-nm effective hydrodynamic rigid rod yields a good fit to the apparent diffusion coefficient angular-dependence data up to 70°; the model fails at higher angles, probably due to the effects of flexibility or branching of the rod. Diffusion coefficient titration experiments with a platinum complex intercalating agent (PtTS) result in a titratable superhelix density of σ = ?0.079 ± 0.008 under our experimental conditions, corresponding to about 34 superhelical turns in the native DNA. The DNA contour length predicted by our two independent results, the rod dimensions and the number of superhelical turns, is in excellent agreement with the contour length calculated from the number of base pairs, supporting the hydrodynamic approximation of an effective rodlike structure for this small DNA molecule in solution.     

Laser light-scattering analysis of the dimerization of transfer ribonucleic acids with complementary anticodons

Photon-correlation spectroscopy is a powerful technique for measuring the translational diffusion coefficient of particles and macromolecules in solution. In the study described here, this technique was used to analyze a specific dimerization process involving the association of two tRNA molecules through complementary anticodons. The tRNAs used in the analysis were E. coli tRNA and yeast tRNA^Phe. The experimental data on the concentration dependence of the observed diffusion constants are shown to agree well with theoretical predictions. From these data, the equilibrium constant of the association reaction was determined for dimers formed over a wide range of temperatures and in several different solution conditions. In solutions of 0.1M ionic strength at 22°C, the equilibrium constants vary from 1 × 10⁵M^?1 in the absence of magnesium to 1.5 × 10⁶M^?1 in 10 mM Mg⁺². The enthalpy and entropy changes for dimer formation in the absence and presence, 5 and 10 mM, of magnesium have been obtained from the temperature dependence of the equilibrium constant. The results show that both ΔH and ΔS contribute to the free energy of binding and that their relative contributions are similar for each solution condition evaluated.     

Peptide self-association in aqueous trifluoroethanol monitored by pulsed field gradient NMR diffusion measurements

Defining the self-association state of a molecule in solution can be an important step in NMR-based structure determination. This is particularly true of peptides, where there can be a relatively small number of long-range interactions and misinterpretation of an intermolecular NOE as an intramolecular contact can have a dramatic influence on the final calculated structure. In this paper, we have investigated the use of translational self-diffusion coefficient measurements to detect self-association in aqueous trifluoroethanol of three peptides which are analogues of the C-terminal region of human neuropeptide Y. Experimentally measured diffusion coefficients were extrapolated to D⁰, the limiting value as the peptide concentration approaches zero, and then converted to D_20,w, the diffusion coefficient after correction for temperature and the viscosity of the solvent. A decrease in D_20,w of about 16% was found for all three peptides in aqueous TFE (30% by volume) compared with water, which is in reasonable agreement with the expected decrease upon dimerisation, the presence of which was indicated by sedimentation equilibrium measurements. Apparent molecular masses of these peptides in both solutions were also calculated from their diffusion coefficients and similar results were obtained. Several potential internal standards, including acetone, acetonitrile, dimethylsulfoxide and dioxane, were assessed as monitors of solution viscosity over a range of trifluoroethanol concentrations. Compared with independent measurements of viscosity, acetonitrile was the most accurate standard among these four. The practical limitations of a quantitative assessment of peptide self-association from translational diffusion coefficients measured by PFGNMR, including the calculation of apparent molecular mass, are also discussed.