Brownian Tumbling Research Articles

Path to Collagenolysis: COLLAGEN V TRIPLE-HELIX MODEL BOUND PRODUCTIVELY AND IN ENCOUNTERS BY MATRIX METALLOPROTEINASE-12

Collagenolysis is essential in extracellular matrix homeostasis, but its structural basis has long been shrouded in mystery. We have developed a novel docking strategy guided by paramagnetic NMR that positions a triple-helical collagen V mimic (synthesized with nitroxide spin labels) in the active site of the catalytic domain of matrix metalloproteinase-12 (MMP-12 or macrophage metalloelastase) primed for catalysis. The collagenolytically productive complex forms by utilizing seven distinct subsites that traverse the entire length of the active site. These subsites bury ∼1,080 Å(2)of surface area, over half of which is contributed by the trailing strand of the synthetic collagen V mimic, which also appears to ligate the catalytic zinc through the glycine carbonyl oxygen of its scissile G∼VV triplet. Notably, the middle strand also occupies the full length of the active site where it contributes extensive interfacial contacts with five subsites. This work identifies, for the first time, the productive and specific interactions of a collagen triple helix with an MMP catalytic site. The results uniquely demonstrate that the active site of the MMPs is wide enough to accommodate two strands from collagen triple helices. Paramagnetic relaxation enhancements also reveal an extensive array of encounter complexes that form over a large part of the catalytic domain. These transient complexes could possibly facilitate the formation of collagenolytically active complexes via directional Brownian tumbling.

The "long tail" of the protein tumbling correlation function: observation by (1)H NMR relaxometry in a wide frequency and concentration range.

Inter-protein interactions in solution affect the auto-correlation function of Brownian tumbling not only in terms of a simple increase of the correlation time, they also lead to the appearance of a weak slow component (“long tail”) of the correlation function due to a slowly changing local anisotropy of the microenvironment. The conventional protocol of correlation time estimation from the relaxation rate ratio R1/R2 assumes a single-component tumbling correlation function, and thus can provide incorrect results as soon as the “long tail” is of relevance. This effect, however, has been underestimated in many instances. In this work we present a detailed systematic study of the tumbling correlation function of two proteins, lysozyme and bovine serum albumin, at different concentrations and temperatures using proton field-cycling relaxometry combined with R1ρ and R2 measurements. Unlike high-field NMR relaxation methods, these techniques enable a detailed study of dynamics on a time scale longer than the normal protein tumbling correlation time and, thus, a reliable estimate of the parameters of the “long tail”. In this work we analyze the concentration dependence of the intensity and correlation time of the slow component and perform simulations of high-field 15N NMR relaxation data demonstrating the importance of taking the “long tail” in the analysis into account.Electronic supplementary materialThe online version of this article (doi:10.1007/s10858-015-0001-1) contains supplementary material, which is available to authorized users.

Solid-State NMR Approaches to Internal Dynamics of Proteins: From Picoseconds to Microseconds and Seconds

Solid-state nuclear magnetic resonance (NMR) spectroscopy has matured to the point that it is possible to determine the structure of proteins in immobilized states, such as within microcrystals or embedded in membranes. Currently, researchers continue to develop and apply NMR techniques that can deliver site-resolved dynamic information toward the goal of understanding protein function at the atomic scale. As a widely-used, natural approach, researchers have mostly measured longitudinal (T1) relaxation times, which, like in solution-state NMR, are sensitive to picosecond and nanosecond motions, and motionally averaged dipolar couplings, which provide an integral amplitude of all motions with a correlation time of up to a few microseconds. While overall Brownian tumbling in solution mostly precludes access to slower internal dynamics, dedicated solid-state NMR approaches are now emerging as powerful new options. In this Account, we give an overview of the classes of solid-state NMR experiments that have expanded the accessible range correlation times from microseconds to many milliseconds. The measurement of relaxation times in the rotating frame, T1ρ, now allows researchers to access the microsecond range. Using our recent theoretical work, researchers can now quantitatively analyze this data to distinguish relaxation due to chemical-shift anisotropy (CSA) from that due to dipole-dipole couplings. Off-resonance irradiation allows researchers to extend the frequency range of such experiments. We have built multidimensional analogues of T2-type or line shape experiments using variants of the dipolar-chemical shift correlation (DIPSHIFT) experiment that are particularly suited to extract intermediate time scale motions in the millisecond range. In addition, we have continuously improved variants of exchange experiments, mostly relying on the recoupling of anisotropic interactions to address ultraslow motions in the ms to s ranges. The NH dipolar coupling offers a useful probe of local dynamics, especially with proton-depleted samples that suppress the adverse effect of strong proton dipolar couplings. We demonstrate how these techniques have provided a concise picture of the internal dynamics in a popular model system, the SH3 domain of α-spectrin. T1-based methods have shown that large-amplitude bond orientation fluctuations in the picosecond range and slower 10 ns low-amplitude motions coexist in these structures. When we include T1ρ data, we observe that many residues undergo low amplitude motions slower than 100 ns. On the millisecond to second scale, mostly localized but potentially cooperative motions occur. Comparing different exchange experiments, we found that terminal NH2 groups in side chains can even undergo a combination of ultraslow large-angle two-site jumps accompanied by small-angle fluctuations that occur 10 times more quickly.

Induction of Highly Curved Structures in Relation to Membrane Permeabilization and Budding by the Triterpenoid Saponins, α- and δ-Hederin

The interactions of triterpenoid monodesmosidic saponins, α-hederin and δ-hederin, with lipid membranes are involved in their permeabilizing effect. Unfortunately, the interactions of these saponins with lipid membranes are largely unknown, as are the roles of cholesterol or the branched sugar moieties (two for α-hederin and one for δ-hederin) on the aglycone backbone, hederagenin. The differences in sugar moieties are responsible for differences in the molecular shape of the saponins and the effects on membrane curvature that should be the most positive for α-hederin in a transbilayer direction. In large unilamellar vesicles and monocyte cells, we showed that membrane permeabilization was dependent on the presence of membrane cholesterol and saponin sugar chains, being largest for α-hederin and smallest for hederagenin. In the presence of cholesterol, α-hederin induced the formation of nonbilayer phases with a higher rate of Brownian tumbling or lateral diffusion. A reduction of Laurdan's generalized polarization in relation to change in order of the polar heads of phospholipids was observed. Using giant unilamellar vesicles, we visualized the formation of wrinkled borders, the decrease in liposome size, budding, and the formation of macroscopic pores. All these processes are highly dependent on the sugars linked to the aglycone, with α-hederin showing a greater ability to induce pore formation and δ-hederin being more efficient in inducing budding. Hederagenin induced intravesicular budding but no pore formation. Based on these results, a curvature-driven permeabilization mechanism dependent on the interaction between saponin and sterols and on the molecular shape of the saponin and its ability to induce local spontaneous curvature is proposed.

The nuclear magnetic resonance relaxation data analysis in solids: General R1/R1ρ equations and the model-free approach

The advantage of the solid state NMR for studying molecular dynamics is the capability to study slow motions without limitations: in the liquid state, if orienting media are not used, all anisotropic magnetic interactions are averaged out by fast overall Brownian tumbling of a molecule and thus investigation of slow internal conformational motions (e.g., of proteins) in solution can be conducted using only isotropic interactions. One of the main tools for obtaining amplitudes and correlation times of molecular motions in the μs time scale is measuring relaxation rate R(1)(ρ). Yet, there have been a couple of unresolved problems in the quantitative analysis of the relaxation rates. First, when the resonance offset of the spin-lock pulse is used, the spin-lock field can be oriented under an arbitrary angle in respect to B(0). Second, the spin-lock frequency can be comparable or even less than the magic angle spinning rate. Up to now, there have been no equations for R(1)(ρ) that would be applicable for any values of the spin-lock frequency, magic angle spinning rate and resonance offset of the spin-lock pulse. In this work such equations were derived for two most important relaxation mechanisms: heteronuclear dipolar coupling and chemical shift anisotropy. The validity of the equations was checked by numerical simulation of the R(1)(ρ) experiment using SPINEVOLUTION program. In addition to that, the applicability of the well-known model-free approach to the solid state NMR relaxation data analysis was considered. For the wobbling in a cone at 30° and 90° cone angles and two-site jump models, it has been demonstrated that the auto-correlation functions G(0)(t), G(1)(t), G(2)(t), corresponding to different spherical harmonics, for isotropic samples (powders, polycrystals, etc.) are practically the same regardless of the correlation time of motion. This means that the model-free approach which is widely used in liquids can be equally applied, at least assuming these two motional models, to the analysis of the solid state NMR relaxation data.

Two-particle random walk simulation of outer-sphere nuclear relaxation

We present a two-particle Monte Carlo method for computing the outer-sphere (OS) dipolar time correlation function (DTCF) of the relative position of a nuclear spin I on a diamagnetic molecule M(I) with respect to a nuclear or electronic spin S on a molecule M(S) when both molecules are anisotropic and undergo translational and rotational diffusion. As a first application, we question the validity of the appealing interspin procedure [L. P. Hwang, Mol. Phys. 51, 1235 (1984); A. Borel et al., Chem. Eur. J. 7, 600 (2001)] based on the solutions of a Smoluchowski diffusion equation, which conserve the interspin radial distribution function in the course of time. We show that the true random spatial motion of the interspin vector obtained by simulation can be very different from that given by the Smoluchowski solutions and lead to notable retardation of the time decay of the OS-DTCF. Then, we explore the influence of the solvation properties of M(S) on the decay rate of the DTCF. When M(S) is significantly larger than M(I), its rotation accelerates the decay only weakly, even if M(I) follows M(S) in its Brownian tumbling. By contrast, viscous solvation layers in OS pockets of M(S) can yield an important local slowdown of the relative translational diffusion of M(I), leading to a decay retardation of the DTCF, which adds to that due to the shape anisotropy of M(S). When M(S) is a Gd(3+)-based contrast agent, this retardation leads to a notable increase of the OS contribution to relaxivity even at rather high imaging field.

Intermolecular electrostatic interactions and Brownian tumbling in protein solutions

It is often implicitly assumed that the long-range intermolecular electrostatic interactions in homogeneous protein solutions either are negligible for affecting protein Brownian tumbling or cause its deceleration without changing the shape of rotational auto-correlation function. This review presents a wide set of experimental data (NMR relaxation, dielectric spectroscopy and Brownian dynamics simulations) demonstrating that the interprotein electrostatic steering leads to a complication of the rotational correlation function. The key point of this effect is the rotational anisotropy caused by the interaction of the electric dipole moment of a protein with the external electric field produced by charges of neighboring proteins. Taking this effect into account in some cases might be of critical importance for the correct interpretation of various experimental data.

Magnetic Resonance Imaging Guidance of Ablative Thermal Therapies

tive imaging technique because both the local chemical environment and relaxation properties of the nuclear spin system are intimately tied to Brownian motion and molecular tumbling, both directly affected by temperature. Several MRI parameters have been found useful for monitoring temperature changes. The 3 most studied parameters are the spin-lattice relaxation time, the apparent diffusion constant of water, and water’s proton resonance frequency (PRF). The temperature sensitivities asso

On the growth and shape of sodium taurodeoxycholate micellar aggregates: a spin-label and quasielastic light scattering investigation.

Electron spin resonance (ESR) and quasielastic laser scattering (QELS) measurements have been carried out on sodium taurodeoxycholate (NaTDC) micellar aqueous solutions. Computer simulation of the ESR line shape has been used to quantitatively analyze the rotational dynamics of the cholestan-spin label (CSL) dissolved by the NaTDC micellar aggregates as a function of temperature and NaCl concentration. The local reorientation of CSL has been accounted for motionally-averaged g- and A-tensors assuming fast oscillation around the spin-probe long molecular axis. The overall Brownian tumbling of CSL-micelle complexes has been modeled by an axially symmetric rotational tensor. Good agreement with experimental spectra is obtained. Best-fit rotational parameters and QELS data suggest that, in the circumstance of large aggregation, NaTDC micelles have cylindrical shape and micellar growth occurs along the cylinder axis.

Phase Separation in Poly(N,N-diethylacrylamide)/D2O Solutions and Physical Gels as Studied by1H NMR Spectroscopy

The structural-dynamic changes during temperature-induced phase separation in poly(N,N-diethylacrylamide) (PDEAAm)/D 2 O solutions and physical gels in a broad range of concentrations (c = 0.5-50 wt.-%) were studied by conventional high-resolution and MAS 1 H NMR spectra. In the whole concentration range, irrespective of whether the studied system is a solution (c 5 wt.-%), the phase transition is manifested by line brondening (linewidth 3.6 kHz) of a major part of PDEAAm anits, evidently due to the formation of compact globular-like structures. 1 H. MAS NMR spectra have shown that this broadening is not due to near-static dipolar interactions. The respective motion is effectively isotropic with correlation time 1 μs, probably corresponding to Brownian tumbling of the whole globular particles. The thermotropic phase transition, as revealed by NMR, is not discontinuous, but 6 K broad (302-308 K). Above the LCST transition, the fraction p * of PDEAAm segments in globular-like structures is between 0.94-1.0, independent of the polymer concentration. At temperatures below the LCST a certain preaggregation of PDEAAm is indicated by smaller line broadening (linewidths 100 Hz) in the 1 H NMR spectra.

Study of the Dynamic Structure of Native and Hydrophobized Glucose Oxidase by Time-Domain Dielectric Spectroscopy

The dynamic structures of native and hydrophobized (by covalent attachment of palmitoyl chains) glucose oxidase were studied by time-domain dielectric spectroscopy (TDDS). Analysis of the dipole correlation function for both types of the enzyme showed that the decay of the correlation function of the macromolecule motion can be presented as a sum of components corresponding to different kinds of protein motion: isotropic rotation of the protein molecule as a whole, anisotropic Brownian tumbling of subunits, and anisotropic intramolecular motion of polar groups and substructures. The slowest relaxation time was found to be longer for the modified enzyme than for the native enzyme. The dielectric strengths for all relaxation processes, as well as the dipole moment and the molecular volume, were also larger for the modified glucose oxidase. The observed differences between various types of the dipole motion for the native and modified glucose oxidase are discussed.

Dielectric Relaxation, Molecular Motion and Interprotein Interactions in Myoglobin Solution

The results of the investigation of protein molecule dynamic in solution by Time Domain Dielectric Spectroscopy are presented. The horse myoglobin solutions in wide range of concentration from 0.6% to 54% at 20°C have been investigated. The result of analysis produced in the term of dipole correlation function has shown that the obtained correlation function of macromolecule motion may be presented as sum of three components corresponding to three kinds of protein motions: anisotropic intramolecular motion, anisotropic Brownian tumbling and isotropic slow motion. We suppose that the cause of protein tumbling anisotropy and the possibility to keep slow motion is the interprotein electrostatic interactions. The characteristic time of slow motion depends on the concentration of protein and perhaps is controlled by translational diffusion. The dipole moment of myoglobin calculated by the Onsager-Oncley equation is 200D for solutions less than 10% protein concentration. It is in a good agreement with the theoretical value.

Overall and internal protein dynamics in solution studied by the nonselective proton relaxation.

A new algorithm for the analysis of nonselective proton relaxation data in protein solution is presented. T1 and T2 of protein protons in lysozyme and RNase solutions were measured at three resonance frequencies--11, 27 and 90 MHz. In addition we measured water T1 dispersions in lysozyme solutions over the frequency range of 10 kHz--10 MHz on a field-cycling installation. It was found that the correlation function of protein Brownian tumbling as a whole is nonexponential: in addition to a component with the usual correlation time tau t it contained also a component with a correlation time exceeding tau t by approximately an order of magnitude and with a small relative amplitude. The experiment shows that the parameters of the slow component of the tumbling correlation function depend both on the concentration and on the pH of the protein solution. To explain the results obtained one must take into account the interprotein electrostatic interactions in solution. All protein molecules in solution experience electrostatic torques from their neighbors and this gives rise to an anisotropy in the protein Brownian tumbling. The lifetime of this anisotropy is controlled by the translational diffusion of proteins.

Effects of chemical exchange and dipole-dipole interactions on the proton relaxation rates of surface histidyl residues in human hemoglobins

Proton spin-spin and spin-lattice relaxation rates of several C2 protons of the histidyl residues located on the surfaces of human normal adult and sickle cell hemoglobins have been measured as a function of the hemoglobin concentration (10 to 16% (wt/ vol)), temperature ( 17 to 37°C), pH (5.7 to 9.0), and resonance frequency (300 to 600 MHz). The relaxation rates are compared to those calculated from the crystal coordinates of the hemoglobin molecule, assuming dipole-dipole interactions modulated by Brownian tumbling. We have found that the initial recoveries of the longitudinal magnetization of several of the C2 proton resonances of the surface histidyl residues investigated are in good agreement with the spin-lattice relaxation rates predicted by this model. On the other hand, the spin-spin relaxation rates are found to increase with the square of the resonance frequency and appear to be affected by the chemical exchange process between the ionized and unionized forms of the imidazole ring of the histidyl residue. From the experimental results, the lifetime of the exchange process is estimated to be 8 ± 3 μs for all the resonance lines studied in 10% deoxyhemoglobin at pH 7.0 and at 25°C.

A theory of measurement error and its implications for spatial and temporal gradient sensing during chemotaxis. II. The effects of non-equilibrated ligand binding.

Cells generally chemotax along a direction in which their receptor occupancy gradient--whether spatial or temporal--is maximum. Occupancy differentials are, however, often so small as to be masked by thermal noise; i.e., by fluctuations inherent in the stochastic nature of ligand binding. Such fluctuations therefore impose a fundamental limit on the sensitivity of a cell's ability to detect a chemoattractant gradient. In order to pursue the implications of this limit, fluctuation theories have been developed. The theories assume that the signal is some function of the receptor occupancy gradient, allow an estimate of the standard deviation about the mean signal, and permit an evaluation of, among other things, the extent to which a receptor defect can impair an effective response. Previous theories have assumed an equilibrated ligand-receptor interaction. In this paper we introduce a generalized definition of a signal caused by a receptor occupancy gradient that allows us to develop a non-equilibrium theory of thermal noise. We show that previous formulations are a special case of the current development. More specifically, we find the following. Swimming cells subject to Brownian tumbling must generally average their signals over a very long time period to achieve a signal-to-noise ratio less than or equal to 1. Spatial gradient detection is possible with ligand-receptor equilibrium constants less than 10(3)M-1, but since such ligands are rare, theory predicts that tumbling cells will generally not detect gradients by measuring spatial occupancy differentials. These conclusions hold irrespective of whether chemical equilibrium is achieved. For crawling cells not subject to Brownian tumbling, a range of affinities exists in which spatial or temporal gradient detection is possible. In general a spatial mechanism is more efficient for low affinity ligands (dissociation times less than 0.3 s), whereas a temporal mechanism is more efficient for higher K. In this case the detection of gradients in slowly dissociating ligand will be facilitated if signal processing begins prior to chemical equilibration. An important new parameter is indicated by the theory. The definitions of a temporal gradient signal is based on estimating and comparing average occupancy over two time intervals displaced by a time t1. The theory predicts an optimal t1, of order milliseconds, that leads to the shortest minimum averaging time. For t1 values at and longer than the optimum, and for all averaging times exceeding some minimum, the cell will detect a temporal signal.(ABSTRACT TRUNCATED AT 400 WORDS)

Effect of viscosity on the width of the methylene proton magnetic resonance line in sonicated phospholipid bilayer vesicles

Several experimenters [ l-41 have reported that the methylene proton magnetic resonance (PMR) linewidth in small single bilayer vesicles is constant for a wide range of viscosities. They have consequentially inferred that the only molecular motions responsible for narrowing of the methylene line in vesicles are rapid conformational isomerizations and other motions of the hydrocarbon chains rather than the diffusion of phospholipid molecules around the vesicles or vesicular Brownian tumbling, which should be a function of the viscosity of the suspending medium. Because the methylene PMR line is two orders of magnitude broader in large multilamellar phospholipid dispersions than in small vesicles, it was deduced that the degree of disorder resulting from acyl chain isomerizations is substantially greater in vesicles than in multilamellar dispersions. However, in a recent phosphorus magnetic resonance investigation [5], the phosphorus line from the headgroups of dipalmitoyl lecithin and egg yolk lecithin (EYL) in small vesicles was shown to exhibit a dependence on the medium viscosity which was entirely consistent with the phosphorus line being narrowed by vesicular Brownian tumbling and by phospholipid diffusion. Furthermore, values of the diffusion constant D for the phospholipid molecules calculated from the data were in good agreement with independent measurements of the diffusion constant in sonicated and unsonicated phospholipid dispersions by other methods [4,6&9]. In contradiction to published results we present in this communication clear experimental evidence that the PMR methylene linewidth in small vesicles is dependent on the viscosity of the suspending medium and we extract a diffusion constant for egg yolk lecithin molecules in bilayers in agreement with that obtained by other techniques. We shall conclude that the difference in widths between the methylene line in vesicles and in multilamellar dispersions is determined by Brownian tumbling and lateral diffusion and that there is no need to invoke large additional narrowing mechanisms.

Calculation of molecular motional correlation times from linewidths in nuclear magnetic resonance spectra of aggregated systems. Effect of particle size on spectra of phospholipid dispersions

Equations are developed which relate NMR linewidths for aggregates of macromolecules to the molecular motional parameters τ c (correlation time) and A (“anisotropy factor”). The effects of molecular motion can be isolated from those of Brownian tumbling of the aggregates by measuring linewidths at two solution viscosities or aggregate sizes. Where molecular motion is anisotropic ( A > 0), e.g., in membranes, aggregated proteins, and lipid dispersions, NMR linewidths are not simply related to τ c Systems with the same τ c but different values of A may exhibit different linewidths, as for the lecithin 31P resonance above and below the chain melting transition. The reduced linewidths observed from sonicated, compared with unsonicated, lecithin dispersions can be explained solely by the increased particle tumbling rates. Any differences in molecular motion within the bilayers are only minor. All the linewidth behavior reported for lecithin dispersions, including variations with vesicle radius and the only slight dependence on solution viscosity, are predicted by the theory developed here. It is shown that changes in A are greater than changes in τ c both along lecithin chains, and for lecithin phosphate groups at the chain melting transition.

Solvent proton magnetic relaxation dispersion in solutions of concanavalin A.

Concanavalin A, a protein isolated from jack beans, exhibits several important biological properties, all of which are related to its ability to bind and precipitate specific polysaccharides. Concanavalin A is a dimer at pH 5.6, and has one transition-metal and one calcium-ion binding site per monomer unit of molecular weight 27,000. Both metal-ion sites must be occupied for the protein to be active. It is of interest to determine the role of the transition metal ion in Concanavalin A and its relationship to the sugar binding activity of the protein. We report the magnetic field and temperature dependences of the spin-lattice magnetic relaxation rates of solvent protons in aqueous solutions of zinc and manganese derivatives of Concanavalin A, and the influence of monosaccharide binding on these rates. The results of a leastsquares fit of the data to the theory, with five adjustable parameters, indicate that there is one rapidly exchanging water molecule ligand on the Mn(2+) ion, with a residence lifetime of 2.5 musec at 25 degrees , and with its protons 0.27 nm (2.7 A) from the Mn(2+) ion. We find that at low magnetic fields (proton Larmor frequencies below about 10 MHz), the correlation time for the dipolar interaction between the Mn(2+) electronic spin moment and the protons on the water ligand is the spin-lattice relaxation time tau(S) of the Mn(2+) moment, but that at higher magnetic fields the correlation time for the dipolar interaction is determined by the Brownian rotational tumbling of the protein, because of the substantial variation of tau(S) with magnetic field. Monosaccharide binding to manganese Concanavalin A has little effect on the relaxation rates of solvent protons, a result that indicates that the sugars do not bind directly to the transition metal in the protein.

Effect of Anisotropic Hyperfine Interactions on Paramagnetic Relaxation in Liquids

A simple ``microcrystalline model'' is developed to discuss the effect of molecular motion in the liquid state on the paramagnetic relaxation of ions or molecules with spin S = ½. This theory relates the paramagnetic relaxation times T1 and T2′ to the anisotropy in g, Δg = gII — g⊥, to the anisotropy in the nuclear hyperfine interaction, A–B, and to the correlation time τc which describes the Brownian tumbling motion of the microcrystal in the liquid state. The contribution of the anisotropic hyperfine interaction to the paramagnetic relaxation turns out to depend on the nuclear spin quantum number Iz, so that different hyperfine multiplets in a paramagnetic resonance spectrum can show different line widths.