An NMR self-diffusion study of the interactions between spermidine and oligonucleotides

Self-diffusion coefficients have been determined by pulsed field gradient nmr methods for spermidine in solutions of the oligonucleotides d(GC)₄ and d(GGAATTCC). The self-diffusion behavior of spermidine in solution of d(GC)₄ is very similar to that observed previously for methylspermidine (completely N-methylated spermidine). Moreover, the self-diffusion behaviors of spermidine in solutions of d(GC)₄ and d(GGAATTCC) are also quite similar, indicating that there is no significant influenceon on self-diffusion of oligonucleotide base composition. Furthermore, self-diffusion coefficients of the oligonucleotide d(GC)₈ show only a small dependence on oligonucleotide concentration, and no measurable dependence on sodium ion or magnesium ion concentration. © 1996 John Wiley & Sons, Inc.     

Molecular dynamics simulation of the reciprocal fused LiF–KBr mixture: local structure and self-diffusion coefficients

This paper describes the molecular dynamics simulation of the reciprocal fused LiF–KBr mixture, which is located above the critical mixing point, in the temperature range 1280–1450 K. The first coordination sphere is found to form as follows: a smaller ion is formed around a smaller counter-ion, and a larger ion is formed around a larger counter-ion. The calculated concentration dependence of the self-diffusion coefficients and the radial distribution functions of all ion pairs indicate that the degree of association of the Li–F pair increases as the lithium fluoride fraction in the mixture decreases.     

Concentration dependence of protein diffusion.

The concentration dependence of protein self-diffusion constants is described by a free volume diffusion theory which accounts for the effects of local protein concentration fluctuations.     

Tracer diffusion in F-actin and Ficoll mixtures. Toward a model for cytoplasm.

We have previously reported that self-diffusion of inert tracer particles in the cytoplasm of living Swiss 3T3 cells is hindered in a size-dependent manner (Luby-Phelps, K., D.L. Taylor, and F. Lanni. 1986. J. Cell Biol. 102:2015-2022; Luby-Phelps, K., P.E. Castle, D.L. Taylor, and F. Lanni. 1987. Proc Natl. Acad. Sci. USA. 84:4910-4913). Lacking a theory that completely explains our data, we are attempting to understand the molecular architecture responsible for this phenomenon by studying tracer diffusion in simple, reconstituted model systems. This report contains our findings on tracer diffusion in concentrated solutions of Ficoll 70 or Ficoll 400, in solutions of entangled F-actin filaments, and in solutions of entangled F-actin containing a background of concentrated Ficoll particles or concentrated bovine serum albumin (BSA). A series of size-fractionated fluorescein-Ficolls were used as tracer particles. By fluorescence recovery after photobleaching (FRAP), we obtained the mean diffusion coefficients in a dilute, aqueous reference phase (Do), the mean diffusion coefficients in the model matrices (D), and the mean hydrodynamic radii (RH) for selected tracer fractions. For each model matrix, the results were compared with similar data obtained from living cells. As in concentrated solutions of globular proteins (Luby-Phelps et al., 1987), D/Do was not significantly size-dependent in concentrated solutions of Ficoll 400 or Ficoll 70. In contrast, D/Do decreased monotonically with increasing RH in solutions of F-actin ranging in concentration from 1 to 12 mg/ml. This size dependence was most pronounced at higher F-actin concentrations. However, the shape of the curve and the extrapolated value of D/Do in the limit, RH----O did not closely resemble the cellular data for tracers in the same size range (3 less than RH less than 30 nm). In mixtures of F-actin and Ficoll or F-actin and BSA, D/Do was well approximated by D/Do for the same concentration of F-actin alone multiplied by D/Do for the same concentrations of Ficoll or BSA alone. Based on these results, it is possible to model the submicroscopic architecture of cytoplasm in living cells as a densely entangled filament network (perhaps made up of F-actin and other filamentous structures) interpenetrated by a fluid phase crowded with globular macromolecules, which in cytoplasm would be primarily proteins.     

Calculation of self-diffusion coefficients of the [BMIM][TFSA]/water system by molecular dynamics simulation

We performed a molecular dynamics simulation to calculate the self-diffusion coefficients of 1-Butyl-3-methylimidazolium bis(trifluoromethanesulfonyl)imide and water in a water–ionic liquid mixture. We then compared the simulated self-diffusion coefficients of cation, anion and water molecules with experimental data and with simulated data from the literature. Although the simulation overestimated the self-diffusion coefficients of ions, the simulated results qualitatively reproduced the enhancement of the self-diffusion coefficients of water as the water molar fraction increased. We also calculated the radial distribution functions to investigate the solution structure, i.e. the clustering of water molecules. The clustering of water in ionic liquid was found to play an important role in the enhancement of the diffusion of water molecules in the ionic liquid.     

1H-nmr study of water dynamics in hydrated collagen: transverse relaxation-time and diffusion analysis

Water proton transverse relaxation times (T2) and self-diffusion coefficients (D) were measured in randomly oriented hydrated collagen fibers. Three T2 relaxation times were discerned indicating the presence of at least three water fractions in the collagen sample. The D values associated with each water fraction were determined. The diffusion time dependence of D suggests water motion is restricted by macromolecular structure. The experimental results are discussed with reference to the structural properties of hydrated collagen fibers.     

Brownian dynamics simulations of probe and self-diffusion in concentrated protein and DNA solutions.

We have developed a Brownian dynamics algorithm for simulating probe and self-diffusion in concentrated solutions of DNA and protein. In these simulations, proteins are represented as spheres with radii given by their hydrodynamic radii, while DNA is modeled as a wormlike chain of hydrodynamically equivalent spherical frictional elements. The molecular interaction potentials employed by the program allow for intramolecular stretching and bending motions of the DNA chains, short-range Lennard-Jones interactions, and long-range electrostatic interactions. To test the program, we have carried out simulations of bovine serum albumin (BSA) probe diffusion and DNA self-diffusion in solutions of short-chain DNA as a function of both DNA concentration and solution ionic strength. In addition, we report on simulations of BSA self-diffusion as a function of BSA concentration and ionic strength. Based on a comparison to available experimental data, we find that our simulations accurately predict these transport properties under conditions of physiological salt concentration and predict the stronger concentration dependence observed at lower salt concentrations. These results are discussed in light of the nature of the intermolecular interactions in such systems and the approximations and limitations of the simulation algorithm.     

Sampling of protein dynamics in nanosecond time scale by 15N NMR relaxation and self-diffusion measurements.

This paper presents a procedure for detection of intermediate nanosecond internal dynamics in globular proteins. The procedure uses 1H-15N relaxation measurements at several spectrometer frequencies and hydrodynamic calculations based on experimental self-diffusion coefficients. New heteronuclear experiments, using pulse field gradients, are introduced for the measurement of translation diffusion coefficients of 15N labeled proteins. An advanced interpretation of recently published (Luginbühl et al., Biochemistry, 36, 7305-7312 (1997)) backbone amide 15N relaxation data, measured at two spectrometers (400 and 750 MHz for 1H) for N-terminal DNA-binding domain (1-63) of 434 repressor, is presented. Non-applicability of commonly used fast (picosecond) dynamics model (FD) was justified by (i) poor fit of relaxation data by the FD model-free spectral density function both for isotropic and anisotropic models of the overall molecular tumbling; (ii) specific dependence of the overall rotation correlation times calculated from T1/T2 ratio on the spectrometer frequency; (iii) mismatch of the ratio of longitudinal 15N relaxation times T1, measured at different spectrometer frequencies, in comparison with that anticipated for the FD model; (iv) significantly underestimated overall rotation correlation time provided by the FD model (5.50+/-0.15 and 5.80+/-0.15 ns for 750 and 400 MHz spectrometer frequency respectively) in comparison with correlation time obtained from hydrodynamics. On the other hand, all relaxation and hydrodynamics data are in good correspondence with the model of intermediate (nanoseconds) dynamics. Overall rotation correlation time of 7.5+/-0.7 ns was calculated from experimental translation self-diffusion rate using hydrodynamics formalism (Garcia de la Torre, J. and Bloomfield, V.A. Quart. Rev. Biophys., 14, 81-139 (1981)). The statistical analysis of 15N relaxation data along with the hydrodynamic consideration clearly revealed that most of the residues in 434(1-63) repressor are involved in the nanosecond internal dynamics characterized by the the mean order parameters of 0.59+/-0.06 and the correlation times of ca. 5 ns.     

Physicochemical characterization of generation 5 polyamidoamine dendrimers

The dispersity, size, and self-interaction of generation 5 polyamidoamine dendrimeric polymers with different terminal groups (surfaces) were characterized using several physicochemical techniques. Amino-surface dendrimers form oligomeric aggregates in aqueous solution, even in the presence of high salt concentrations (0.6M sodium phosphate). In contrast, the hydroxyl-surface polymer G5-OH behaves as a single homogeneous (or paucidisperse) species at low concentration. Measurements of density increment and the sedimentation and diffusion coefficients of G5-OH suggest a more swollen, porous structure than a globular protein of comparable mass. Measurements of the concentration dependence of sedimentation equilibrium of G5-OH in pH 7.2 phosphate buffer indicate the presence of significant electrostatic repulsion overlaid on weakly attractive interactions, leading to the formation of nonspecific aggregates at sufficiently high dendrimer concentration.     

Water self-diffusion behavior in yeast cells studied by pulsed field gradient NMR

The water self-diffusion behavior in yeast cell water suspension was investigated by pulsed field gradient NMR techniques. Three types of water were detected, which differ according to the self-diffusion coefficients: bulk water, extracellular and intracellular water. Intracellular and extracellular water self-diffusion was restricted; the sizes of restriction regions were approximately 3 and 15-20 microm, respectively. The smallest restriction size was determined as inner cell size. This size and also cell permeability varied with the growth phase of yeast cell. Cell size increased, but permeability decreased with increasing growth time. The values of cell permeabilities P(1)(d) obtained from time dependence of water self-diffusion coefficient were in good agreement with the permeabilities obtained from the exchange rate constants P(1)(eff). The values of P(1)(eff) were 7 x 10(-6), 1.2 x 10(-6) and 1.6 x 10(-6) m/s, and P(1)(d) were 6.3 x 10(-6), 8.4 x 10(-7), 1.5 x 10(-6) m/s for yeast cells incubated for 9 h (exponential growth phase), 24 h (end of exponential growth phase), and 48 h (stationary growth phase), respectively.     

Self-diffusion of polymers in cartilage as studied by pulsed field gradient NMR

Pulsed field gradient (PFG) nuclear magnetic resonance (NMR) was used to investigate the self-diffusion behaviour of polymers in cartilage. Polyethylene glycol and dextran with different molecular weights and in different concentrations were used as model compounds to mimic the diffusion behaviour of metabolites of cartilage. The polymer self-diffusion depends extremely on the observation time: The short-time self-diffusion coefficients (diffusion time Delta approximately 15 ms) are subjected to a rather non-specific obstruction effect that depends mainly on the molecular weights of the applied polymers as well as on the water content of the cartilage. The observed self-diffusion coefficients decrease with increasing molecular weights of the polymers and with a decreasing water content of the cartilage. In contrast, the long-time self-diffusion coefficients of the polymers in cartilage (diffusion time Delta approximately 600 ms) reflect the structural properties of the tissue. Measurements at different water contents, different molecular weights of the polymers and varying observation times suggest that primarily the collagenous network of cartilage but also the entanglements of the polymer chains themselves are responsible for the observed restricted diffusion. Additionally, anomalous restricted diffusion was shown to occur already in concentrated polymer solutions.     

Cold unfolding of β-hairpins: a molecular-level rationalization

Isolated β-hairpins in water have a temperature dependence of their conformational stability qualitatively resembling that of globular proteins, showing both cold and hot unfolding transitions. It is shown that a molecular-level rationalization of this cold unfolding can be provided extending the approach devised for globular proteins (Graziano G. Phys Chem Chem Phys 2010; 12:14245-14252). The decrease in the solvent-excluded volume upon folding, measured by the decrease in the solvent accessible surface area, produces a gain in configurational/translational entropy of water molecules that is the main stabilizing contribution of the folded conformation. This always stabilizing Gibbs energy contribution has a parabolic-like temperature dependence in water and is exactly counterbalanced at two temperatures (i.e., the cold and hot unfolding temperatures) by the always destabilizing Gibbs energy contribution due to the loss in conformational degrees of freedom of the peptide chain.     

Anomalous diffusion of proteins due to molecular crowding

We have studied the diffusion of tracer proteins in highly concentrated random-coil polymer and globular protein solutions imitating the crowded conditions encountered in cellular environments. Using fluorescence correlation spectroscopy, we measured the anomalous diffusion exponent alpha characterizing the dependence of the mean-square displacement of the tracer proteins on time, r(2)(t) approximately t(alpha). We observed that the diffusion of proteins in dextran solutions with concentrations up to 400 g/l is subdiffusive (alpha < 1) even at low obstacle concentration. The anomalous diffusion exponent alpha decreases continuously with increasing obstacle concentration and molecular weight, but does not depend on buffer ionic strength, and neither does it depend strongly on solution temperature. At very high random-coil polymer concentrations, alpha reaches a limit value of alpha(l) approximately 3/4, which we take to be the signature of a coupling between the motions of the tracer proteins and the segments of the dextran chains. A similar, although less pronounced, subdiffusive behavior is observed for the diffusion of streptavidin in concentrated globular protein solutions. These observations indicate that protein diffusion in the cell cytoplasm and nucleus should be anomalous as well, with consequences for measurements of solute diffusion coefficients in cells and for the modeling of cellular processes relying on diffusion.     

Evolution of cross-diffusion and self-diffusion

This article is concerned with the evolution of certain types of density-dependent dispersal strategy in the context of two competing species with identical population dynamics and same random dispersal rates. Such density-dependent movement, often referred to as cross-diffusion and self-diffusion, assumes that the movement rate of each species depends on the density of both species and that the transition probability from one place to its neighbourhood depends solely on the arrival spot (independent of the departure spot). Our results suggest that for a one-dimensional homogeneous habitat, if the gradients of two cross- and self-diffusion coefficients have the same direction, the species with the smaller gradient will win, i.e. the dispersal strategy with the smaller gradient of cross- and self-diffusion coefficient will evolve. In particular, it suggests that the species with constant cross- and self-diffusion coefficients may have competitive advantage over species with non-constant cross- and self-diffusion coefficients. However, if the two gradients have opposite directions, neither of the two dispersal strategies wins as these two species can coexist.     

Temperature dependence of water self-diffusion through lipid bilayers assessed by NMR

The temperature dependence of the coefficient of water self-diffusion across plane-parallel multib-ilayers of dioleoylphosphatidylcholine oriented on a glass support was studied in the 20–60°C range by pulsed field gradient NMR. The coefficient for transbilayer diffusion of water proved almost four orders of magnitude smaller than for bulk water, and 10 times smaller than that for lateral diffusion of lipid under the same conditions. The temperature dependence obeyed the Arrhenius law with apparent activation energy of 41 kJ/mol, much higher than that for bulk water (18 kJ/mol). The experimental data were analyzed using the “dissolution-diffusion” model, by simulating water passage through membrane channels, and by examining water exchange in states with different modes of translational mobility, including pore channels and bilayer defects. Each approach could take into account the role of bilayer permeability and assess the apparent activation energy for water diffusion in the hydrophobic part of the bilayer, which proved close to the value for bulk water. Estimates were obtained for water diffusion coefficients in the system, coefficients of bilayer permeability for water, and the influence of bilayer defects on the lateral and transverse diffusion coefficients.     

Interactions of spermidine and methylspermidine with DNA studied by nuclear magnetic resonance self-diffusion measurements.

The NMR pulsed field gradient self-diffusion method has been used to study the self-diffusion of the polyamine spermidine and the polyamine analog methylspermidine (completely N-methylated spermidine). The self-diffusion coefficient, D, was measured in solutions of calf thymus DNA prepared from nucleosome core particles (with an average length of 120 base pairs) as a function of the concentration ratio of polyamine to DNA phosphate. A study of the self-diffusion quotient, D/Do (where Do is the diffusion coefficient for free polyamine, not associated with DNA), in additions of spermidine and methyl-spermidine to solutions of NaDNA/NaCl, gave almost identical results with complete association of polyamine to DNA in the initial part of the titrations, indicating similar affinities for DNA. A large influence on the measured self-diffusion coefficients was detected for methylspermidine in NaDNA solutions with different concentrations of NaCl, which shows a considerable salt effect on the polyamine-DNA association. No notable differences in D/Do for methylspermidine were observed in competitive titrations of solutions of Li- and NaDNA, indicating that sodium and lithium ions behave similarly in their interactions with DNA. In titration experiments of methylspermidine into MgDNA solution, the results showed that the polyamine association is less effective than in the case of NaDNA, because of competition from magnesium binding to DNA. Comparisons with calculations based on the electrostatic Poisson-Boltzmann cell model were performed. It is suggested that the interaction is primarily of electrostatic nature, with no binding to specific sites on the DNA molecule.     

Evolution of cross-diffusion and self-diffusion

This article is concerned with the evolution of certain types of density-dependent dispersal strategy in the context of two competing species with identical population dynamics and same random dispersal rates. Such density-dependent movement, often referred to as cross-diffusion and self-diffusion, assumes that the movement rate of each species depends on the density of both species and that the transition probability from one place to its neighbourhood depends solely on the arrival spot (independent of the departure spot). Our results suggest that for a one-dimensional homogeneous habitat, if the gradients of two cross- and self-diffusion coefficients have the same direction, the species with the smaller gradient will win, i.e. the dispersal strategy with the smaller gradient of cross- and self-diffusion coefficient will evolve. In particular, it suggests that the species with constant cross- and self-diffusion coefficients may have competitive advantage over species with non-constant cross- and self-diffusion coefficients. However, if the two gradients have opposite directions, neither of the two dispersal strategies wins as these two species can coexist.     

PFG-NMR measurements of the self-diffusion coefficients of water in equilibrium poly(HEMA-co-THFMA) hydrogels

The self-diffusion coefficients for water in a series of copolymers of 2-hydroxyethyl methacrylate, HEMA, and tetrahydrofurfuryl methacrylate, THFMA, swollen with water to their equilibrium states have been studied at 310 K using PFG-NMR. The self-diffusion coefficients calculated from the Stejskal-Tanner equation, D(obs), for all of the hydrated polymers were found to be dependent on the NMR storage time, as a result of spin exchange between the proton reservoirs of the water and the polymers, reaching an equilibrium plateau value at long storage times. The true values of the diffusion coefficients were calculated from the values of D(obs) in the plateau regions by applying a correction for the fraction of water protons present, obtained from the equilibrium water contents of the gels. The true self-diffusion coefficient for water in polyHEMA obtained at 310 K by this method was 5.5 x 10(-10) m(2)s-1. For the copolymers containing 20% HEMA or more a single value of the self-diffusion coefficient was found, which was somewhat larger than the corresponding values obtained for the macroscopic diffusion coefficient from sorption measurements. For polyTHFMA and copolymers containing less than 20% HEMA, the PFG-NMR stimulated echo attenuation decay curves and the log-attenuation plots were characteristic of the presence of two diffusing water species. The self-diffusion coefficients of water in the equilibrium-hydrated copolymers were found to be dependent on the copolymer composition, decreasing with increasing THFMA content.     

Thermodynamics, kinetics, and salt dependence of folding of YopM, a large leucine-rich repeat protein

Small globular proteins have many contacts between residues that are distant in primary sequence. These contacts create a complex network between sequence-distant segments of secondary structure, which may be expected to promote the cooperative folding of globular proteins. Although repeat proteins, which are composed of tandem modular units, lack sequence-distant contacts, several of considerable length have been shown to undergo cooperative two-state folding. To explore the limits of cooperativity in repeat proteins, we have studied the unfolding of YopM, a leucine-rich repeat (LRR) protein of over 400 residues. Despite its large size and modular architecture (15 repeats), YopM equilibrium unfolding is highly cooperative, and shows a very strong dependence on the concentration of urea. In contrast, kinetic studies of YopM folding indicate a mechanism that includes one or more transient intermediates. The urea dependence of the folding and unfolding rates suggests a relatively small transition state ensemble. As with the urea dependence, we have found an extreme dependence of the free energy of unfolding on the concentration of salt. This salt dependence likely results from general screening of a large number of unfavorable columbic interactions in the folded state, rather than from specific cation binding.