Anomalies in sedimentation. II. Testing the entanglement hypothesis

Zones of T2 DNA were sedimented through uniform solutions of T7 DNA to determine if the smaller DNA molecules would become entangled in the larger. No entanglement could be demonstrated even at high DNA concentrations. It is suggested that molecular entanglement is not responsible for the sudden loss of DNA from solution which occurs in high centrifugal fields. This communication also includes observations on the effects of rotor speed on the sedimentation behavior of DNA in high centrifugal fields, distortion of zone shape at high concentrations, and hydrodynamic interactions between DNA and MS2 bacteriophage particles.     

Effects of static magnetic fields on diffusion in solutions

Static magnetic fields affect the diffusion of biological particles in solutions through the Lorentz force and Maxwell stress. These effects were analyzed theoretically to estimate the threshold field strength for these effects. Our results show that the Lorentz force suppresses the diffusion of charged particles such as Na+, K+, Ca2+, Cl-, and plasma proteins. However, the threshold is so high, i.e., more than 10(4) T, that the Lorentz force does not affect the ion diffusion at typical field strengths (a few Tesla at most). Since the threshold of gradient fields for producing a change in ion diffusion through the Maxwell stress is more than 10(5) T2/m for paramagnetic molecules (FeCl3, O2) and plasma proteins, their diffusion would be unaffected by typical gradient fields (100 T2/m at most) and even by high gradient fields (less than 10(5) T2/m) used in magnetic separation techniques. In contrast, movement of deoxygenated erythrocytes and FeCl3 colloids (more than 10(3) molecules) is influenced by the usual gradient fields due to a volume effect.     

The biophysics of DNA hybridization with immobilized oligonucleotide probes.

A mathematical model based on receptor-ligand interactions at a cell surface has been modified and further developed to represent heterogeneous DNA-DNA hybridization on a solid surface. The immobilized DNA molecules with known sequences are called probes, and the DNA molecules in solution with unknown sequences are called targets in this model. Capture of the perfectly complementary target is modeled as a combined reaction-diffusion limited irreversible reaction. In the model, there are two different mechanisms by which targets can hybridize with the complementary probes: direct hybridization from the solution and hybridization by molecules that adsorb nonspecifically and then surface diffuse to the probe. The results indicate that nonspecific adsorption of single-stranded DNA on the surface and subsequent two-dimensional diffusion can significantly enhance the overall reaction rate. Heterogeneous hybridization depends strongly on the rate constants for DNA adsorption/desorption in the non-probe-covered regions of the surface, the two-dimensional (2D) diffusion coefficient, and the size of probes and targets. The model shows that the overall kinetics of DNA hybridization to DNA on a solid support may be an extremely efficient process for physically realistic 2D diffusion coefficients, target concentrations, and surface probe densities. The implication for design and operation of a DNA hybridization surface is that there is an optimal surface probe density when 2D diffusion occurs; values above that optimum do not increase the capture rate. Our model predicts capture rates in agreement with those from recent experimental literature. The results of our analysis predict that several things can be done to improve heterogeneous hybridization: 1) the solution phase target molecules should be about 100 bases or less in size to speed solution-phase and surface diffusion; 2) conditions should be created such that reversible adsorption and two-dimensional diffusion occur in the surface regions between DNA probe molecules; 3) provided that 2) is satisfied, one can achieve results with a sparse probe coverage that are equal to or better than those obtained with a surface totally covered with DNA probes.     

Variable-Field Analytical Ultracentrifugation: I. Time-Optimized Sedimentation Equilibrium

Sedimentation equilibrium (SE) analytical ultracentrifugation (AUC) is a gold standard for the rigorous determination of macromolecular buoyant molar masses and the thermodynamic study of reversible interactions in solution. A significant experimental drawback is the long time required to attain SE, which is usually on the order of days. We have developed a method for time-optimized SE (toSE) with defined time-varying centrifugal fields that allow SE to be attained in a significantly (up to 10-fold) shorter time than is usually required. To achieve this, numerical Lamm equation solutions for sedimentation in time-varying fields are computed based on initial estimates of macromolecular transport properties. A parameterized rotor-speed schedule is optimized with the goal of achieving a minimal time to equilibrium while limiting transient sample preconcentration at the base of the solution column. The resulting rotor-speed schedule may include multiple over- and underspeeding phases, balancing the formation of gradients from strong sedimentation fluxes with periods of high diffusional transport. The computation is carried out in a new software program called TOSE, which also facilitates convenient experimental implementation. Further, we extend AUC data analysis to sedimentation processes in such time-varying centrifugal fields. Due to the initially high centrifugal fields in toSE and the resulting strong migration, it is possible to extract sedimentation coefficient distributions from the early data. This can provide better estimates of the size of macromolecular complexes and report on sample homogeneity early on, which may be used to further refine the prediction of the rotor-speed schedule. In this manner, the toSE experiment can be adapted in real time to the system under study, maximizing both the information content and the time efficiency of SE experiments.     

Sedimentation analysis of noninteracting and self-associating solutes using numerical solutions to the Lamm equation.

The potential of using the Lamm equation in the analysis of hydrodynamic shape and gross conformation of proteins and reversibly formed protein complexes from analytical ultracentrifugation data was investigated. An efficient numerical solution of the Lamm equation for noninteracting and rapidly self-associating proteins by using combined finite-element and moving grid techniques is described. It has been implemented for noninteracting solutes and monomer-dimer and monomer-trimer equilibria. To predict its utility, the error surface of a nonlinear regression of simulated sedimentation profiles was explored. Error contour maps were calculated for conventional independent and global analyses of experiments with noninteracting solutes and with monomer-dimer systems at different solution column heights, loading concentrations, and centrifugal fields. It was found that the rotor speed is the major determinant for the shape of the error surface, and that global analysis of different experiments can allow substantially improved characterization of the solutes. We suggest that the global analysis of the approach to equilibrium in a short-column sedimentation equilibrium experiment followed by a high-speed short-column sedimentation velocity experiment can result in sedimentation and diffusion coefficients of very high statistical accuracy. In addition, in the case of a protein in rapid monomer-dimer equilibrium, this configuration was found to reveal the most precise estimate of the association constant.     

Effects of excluded surface area and adsorbate clustering on surface adsorption of proteins. II. Kinetic models

Models for equilibrium surface adsorption of proteins have been recently proposed (Minton, A. P., 2000. Biophys. Chem. 86:239-247) in which negative cooperativity due to area exclusion by adsorbate molecules is compensated to a variable extent by the formation of a heterogeneous population of monolayer surface clusters of adsorbed protein molecules. In the present work this concept is extended to treat the kinetics of protein adsorption. It is postulated that clusters may grow via two distinct kinetic pathways. The first pathway is the diffusion of adsorbed monomer to the edge of a preexisting cluster and subsequent accretion. The second pathway consists of direct deposition of a monomer in solution onto the upper (solution-facing) surface of a preexisting cluster ("piggyback" deposition) and subsequent incorporation into the cluster. Results of calculations of the time course of adsorption, carried out for two different limiting models of cluster structure and energetics, show that in the absence of piggyback deposition, enhancement of the tendency of adsorbate to cluster can reduce, but not eliminate, the negative kinetic cooperativity due to surface area exclusion by adsorbate. Apparently noncooperative (Langmuir-like) and positively cooperative adsorption progress curves, qualitatively similar to those reported in several published experimental studies, require a significant fraction of total adsorption flux through the piggyback deposition pathway. According to the model developed here and in the above-mentioned reference, the formation of surface clusters should be a common concomitant of non-site-specific surface adsorption of proteins, and may provide an important mechanism for assembly of organized "protein machines" in vivo.     

The dynamics of protein hydration water: a quantitative comparison of molecular dynamics simulations and neutron-scattering experiments

We present results from an extensive molecular dynamics simulation study of water hydrating the protein Ribonuclease A, at a series of temperatures in cluster, crystal, and powder environments. The dynamics of protein hydration water appear to be very similar in crystal and powder environments at moderate to high hydration levels. Thus, we contend that experiments performed on powder samples are appropriate for discussing hydration water dynamics in native protein environments. Our analysis reveals that simulations performed on cluster models consisting of proteins surrounded by a finite water shell with free boundaries are not appropriate for the study of the solvent dynamics. Detailed comparison to available x-ray diffraction and inelastic neutron-scattering data shows that current generation force fields are capable of accurately reproducing the structural and dynamical observables. On the time scale of tens of picoseconds, at room temperature and high hydration, significant water translational diffusion and rotational motion occur. At low hydration, the water molecules are translationally confined but display appreciable rotational motion. Below the protein dynamical transition temperature, both translational and rotational motions of the water molecules are essentially arrested. Taken together, these results suggest that water translational motion is necessary for the structural relaxation that permits anharmonic and diffusive motions in proteins. Furthermore, it appears that the exchange of protein-water hydrogen bonds by water rotational/librational motion is not sufficient to permit protein structural relaxation. Rather, the complete exchange of protein-bound water molecules by translational displacement seems to be required.     

Application of pulsed-gradient Fourier transform nuclear magnetic resonance to the study of self-diffusion of phospholipid vesicles.

A pulsed-gradient Fourier transform nuclear magnetic resonance (NMR) technique was appplied to the study of diffusion of phospholipid vesicles. The diffusion coefficient of dimyristoyllecithin vesicles (DML) in a D2O-phospahte buffer at 37 degrees is D = 1.9 TIMES 10(-6) cm2/sec. In a solution made viscous by DNA addition, the diffusion coefficient of DML vesicles was 3.5 times 10(-7) cm2/sec. These values compare favorably with the diffusion rate for liposomes as determined by ultracentrifugation and by Stokes law calculation. The data suggest that DML diffusion is controlled primarily by whole liposome migration as opposed to movement of individual molecules within the liposome, liposome rotation, or fast exchange between lecithin molecules in solution and in vesicles.     

A theory for the displacement of proteins and viruses with polyethylene glycol.

The displacement action of polyethylene glycol of different molecular weights may be linked to the ability of the polymers to form coiled particles in solution. From conclusions drawn from their sedimentating properties in centrifugal fields the polyethylene glycols of low molecular weights, as expected, are less randomly coiled than those of higher molecular weight. It is suggested that protein molecules have the ability to diffuse into the coils of the polyethylene glycol from which they are excluded when the random coiling increases with increasing polymer concentration. From considerations based on the interaction of the polymer filament with the displaced particle the distribution of the substance between the coils and the intermolecular spaces may be predicted semi-quantitatively.     

Restricted diffusion of molecules in porous affinity chromatography adsorbents.

A restricted diffusion model is constructed and solved in order to study the permeability of large adsorbate molecules in the pores of affinity chromatography media, when the adsorbate molecules are adsorbed onto immobilized ligands. The combined effects of steric hindrance at the entrance to the pores and frictional resistance within the pores, as well as the effects of pore size distribution, pore connectivity of the adsorbent, molecular size of adsorbate and ligand, and the fractional saturation of adsorption sites (ligands), are considered. Affinity adsorbents with dilute and high ligand concentrations are examined, and the permeability of the adsorbate in porous networks of connectivity nT is studied by means of effective medium approximation (EMA) numerical solutions. As expected, the permeability of the adsorbate decreases as the size of the adsorbate and/or ligand molecule increases. The permeability also decreases when the fractional saturation of the ligands increases, as well as when the pore connectivity of the network decreases. The dependence of the permeability on the pore connectivity tends to be less marked in adsorbents with concentrated ligand than in porous media with dilute ligand concentration. The conditions are also presented for which the percolation threshold is attained in a number of different systems. The restricted diffusion model and results of this work may be of importance in studies involving the modeling, prediction of the dynamic behavior, design, and control of affinity chromatography (biospecific adsorption) systems employing porous adsorbents. The theoretical results may also have important implications in the selection of a ligand as well as in the selection and construction of an affinity porous matrix, so that the adsorbate of interest can be efficiently separated from a given solution. Furthermore, with appropriate modifications this restricted diffusion model may be used in studies involving the immobilization of ligands or enzymes in porous solids.     

The measurement of the rotational diffusion coefficient of bovine plasma fibronectin by electric birefringence technique

Although the conformation of fibronectin has been widely investigated by various techniques, there has not yet been any determination of its rotational diffusion coefficient. We report here this determination by the transient electric birefringence study of solutions of bovine plasma fibronectin at physiological ionic strength. The solutions showed a positive birefringence. A linear relationship was observed between the intensity of the birefringence at equilibrium and the square of the electric field within the range of fields applied (up to 12.5 kV.cm-1). The field-independent decay of the induced birefringence was described by a single exponential with a relaxation time of 0.76 (+/- 0.08) microsecond at 23 degrees C. This establishes fibronectin in solution as a globally rigid structure with a rotational diffusion coefficient, at 20 degrees C, of 202,000 s-1. This result allows the first rigorous determination of the low-resolution structure of fibronectin. It is important to notice that the analysis combines only results obtained in physiological conditions on native molecules and follows a strict hydrodynamic interpretation. The conclusion of this work is that a hollow sphere of about 20 nm external diameter can be proposed as a model for the three-dimensional structure of the fibronectin molecule in solution. This new model suggests the fibronectin could have the structure of a carrier protein.     

Correlations between internal mobility and stability of globular proteins.

The recent work is surveyed which leads to the suggestions that the conformation of globular proteins in solution corresponds to a dynamic ensemble of rapidly interconverting spatial structures, that clusters of hydrophobic amino acid side chains have an important role in the architecture of protein molecules, and that mechanistic aspects of protein denaturation can be correlated with internal mobility seen in the native conformation. These conclusions resulted originally from high resolution 1H nuclear magnetic resonance (NMR) studies of aromatic ring mobility, exchange of interior amide protons and thermal denaturation of the basic pancreatic trypsin inhibitor and a group of related proteins. Various new approaches to further characterize proteins in solution have now been taken and preliminary data are presented. These include computer graphics to outline hydrophobic clusters in globular protein structures, high resolution 1H-NMR experiments at variable hydrostatic pressure and 13C-NMR relaxation measurements. At the present early stage of these new investigations it appears that the hydrophobic cluster model for globular proteins is compatible with the data obtained.     

Neural influence on the postnatal changes in acetylcholine receptor distribution at nerve-muscle junctions in the mouse

The effect of denervation at different stages of development on the pattern of junctional AChR molecules has been examined in hindlimb muscles of the mouse using fluorescent α-bungarotoxin. Denervation at birth leads in a few days to a marked dispersal of the junctional AChR cluster. The mechanism of dispersal is unknown but appears to be too slow to be explained by free diffusion of individual AChR molecules. Following birth, the morphological stability of the cluster increases so that denervation at 2 weeks of age, when the mature form of the cluster begins to develop, leads to little increase in cluster size. The changes in the pattern of receptors seen when the nerve is intact are arrested by denervation.     

2. A Theory for the Displacement of Proteins and Viruses with Polyethylene Glycol

ABSTRACT

The displacement action of polyethylene glycol of different molecular weights may be linked to the ability of the polymers to form coiled particles in solution. From conclusions drawn from their sedimentating properties in centrifugal fields the polyethylene glycols of low molecular weights, as expected, are less randomly coiled than those of higher molecular weight. It is suggested that protein molecules have the ability to diffuse into the coils of the polyethylene glycol from which they are excluded when the random coiling increases with increasing polymer concentration. From considerations based on the interaction of the polymer filament with the displaced particle the distribution of the substance between the coils and the intermolecular spaces may be predicted semi-quantitatively.     

Hydrophobic molecules in lecithin-water systems. I. Formation of reversed hexagonal phases at high and low water contents.

The system dioleoylphosphatidylcholine (DOPC)-n-dodecane-2H2O was investigated with different nuclear magnetic resonance (NMR) techniques: (a) a tentative phase diagram was determined by 2H- and 31P-NMR, (b) translational diffusion coefficients were determined for the three components with the pulsed magnetic field gradient NMR technique, and (c) order parameters for perdeuterated n-dodecane were obtained by 2H-NMR. n-Dodecane induces the formation of reversed hexagonal (HII) phases at low and high water concentrations, and cubic phases at low water contents. The translational diffusion coefficients of n-dodecane in a cubic phase with 6 mol water per mol DOPC, and in an HII phase with 48 mol water per mol DOPC, were just approximately 2.5 times lower than in pure dodecane. Perdeuterated dodecane gave large quadrupole splittings in a lamellar phase, much smaller in an HII phase at low water contents, and a narrow single peak in an HII phase at high water contents. This latter observation indicates that a large fraction of the dodecane molecules is located in separate regions between the water cylinders. Our results support the model given by Gruner concerning the aggregation of membrane lipids in the presence of hydrophobic molecules.     

Permanent dipole moment of tRNA''s and variation of their structure in solution.

The structure of six different tRNA molecules has been analyzed in solution by electrooptical measurements and by bead model simulations. The electric dichroism measured as a function of the field strength shows that tRNA's are associated with substantial permanent dipole moments, which are in the range of 1 x 10(-27) cm(identical to 300 D; before correction for the internal directing field). Rotational diffusion time constants of tRNA molecules in their native state at 2 degrees C show a considerable variation. A particularly large value found for tRNA(Tyr) (50 ns) can be explained by its nine additional nucleotide residues. However, remarkable variations remain for tRNA molecules with the standard number of 76 nucleotide residues (tRNA(Phe) [yeast] 41.6 ns, tRNA(Val) [Escherichia coli] 44.9 ns, tRNA(Glu) [E. coli] 46.8 ns; tRNA(Phe) [E. coli] 48.3 ns). These variations indicate modulations of the tertiary structure, which may be due to a change of the L-hinge angle. Bead models are used to simulate both electric and hydrodynamic parameters of tRNA molecules according to the crystal structure of tRNA(Phe) (yeast). The asymmetric distribution of phosphate charges with respect to the center of diffusion leads, under the assumption of a constant charge reduction to 15% by ion condensation, to a theoretical dipole moment of 7.2 x 10(-28) cm, which is in reasonable agreement with the measurements. The dichroism decay curve calculated for tRNA(Phe) (yeast) is also consistent with the measurements and thus the structure in solution and in the crystal must be very similar in this case. However, our measurements also indicate that the structure of some other tRNA's in solution is different, even in cases with the same number of nucleotide residues.     

Maximum-entropy determination of self-association distribution functions; daunorubicin and ATP.

In the present paper we show how one can use the perturbation of some molecular optical property (for example circular dichroism or chemical shift) as a function of concentration to construct cluster distribution functions describing the self-association of molecules in solution. The optical data are first converted into data giving the variation of the average extent of clustering as a function of the total concentration and then, using straightforward thermodynamics, a set of moments of the cluster distribution function can be obtained. Utilizing the maximum-entropy method, the moments are then used to calculate approximate distribution functions, where the more moments that are used the better the approximation obtained. Given the probability distribution for clusters of different sizes one can then calculate the equilibrium constant for each stage of association. Thus one converts average degree of association into equilibrium constants without having to use any specific model. By this method one can clearly tell whether the equilibrium constants remain constant, increase, or decrease with the number of molecules in a cluster. We apply the method to literature data for two systems, namely daunorubicin, which has a strong tendency to cluster in solution, and Mg(ATP)(2-) which forms weaker clusters. We find that the successive equilibrium constants for adding a monomer to a cluster are approximately constant for daunorubicin but clearly decrease as a function of increasing cluster size for Mg(ATP)(2-).     

Changing cellular location of CheZ predicted by molecular simulations

In the chemotaxis pathway of the bacterium Escherichia coli, signals are carried from a cluster of receptors to the flagellar motors by the diffusion of the protein CheY-phosphate (CheYp) through the cytoplasm. A second protein, CheZ, which promotes dephosphorylation of CheYp, partially colocalizes with receptors in the plasma membrane. CheZ is normally dimeric in solution but has been suggested to associate into highly active oligomers in the presence of CheYp. A model is presented here and supported by Brownian dynamics simulations, which accounts for these and other experimental data: A minority component of the receptor cluster (dimers of CheA_short) nucleates CheZ oligomerization and CheZ molecules move from the cytoplasm to a bound state at the receptor cluster depending on the current level of cellular stimulation. The corresponding simulations suggest that dynamic CheZ localization will sharpen cellular responses to chemoeffectors, increase the range of detectable ligand concentrations, and make adaptation more precise and robust. The localization and activation of CheZ constitute a negative feedback loop that provides a second tier of adaptation to the system. Subtle adjustments of this kind are likely to be found in many other signaling pathways.