Slow internal dynamics in proteins: application of NMR relaxation dispersion spectroscopy to methyl groups in a cavity mutant of T4 lysozyme

Recently developed carbon transverse relaxation dispersion experiments (Skrynnikov, N. R.; et al. J. Am. Chem. Soc. 2001, 123, 4556-4566) were applied to the study of millisecond to microsecond time scale motions in a cavity mutant of T4 lysozyme (L99A) using methyl groups as probes of dynamics. Protein expressed in E. coli cells with (13)CH(3)-pyruvate as the sole carbon source contained high levels of (13)C enrichment at a total of 80 Val gamma, Leu delta, Ile gamma (2), Ala beta, and Met epsilon methyl positions with little extraneous incorporation. Data for 72 methyl groups were available for analysis. Dispersion profiles with large amplitudes were measured for many of these residues and were well fit to a two-state exchange model. The interconversion rates and populations of the states, obtained from fitting relaxation dispersion profiles of each individual probe, were remarkably homogeneous and data for nearly all methyl groups in the protein could be collectively fit to a single cooperative conformational transition. The present study demonstrates the general applicability of methyl relaxation dispersion measurements for the investigation of millisecond time scale protein motions at a large number of side-chain positions. Potential artifacts associated with the experiments are described and methods to minimize their effects presented. These experiments should be particularly well suited for probing dynamics in high molecular weight systems due to the favorable NMR spectroscopic properties of methyl groups.     

A “multigrid” extension of theFFT for the numerical inversion of Fourier and Laplace Transforms

An algorithm for accurate numerical inversion of slowly convergent Fourier and Laplace Transforms is studied. It makes use of several equidistant grids with the same number of points, covering different symmetric intervals of the time and frequency axes. Typically, the number of operations per computed function value is about twice as large as for an ordinary FFT. The distribution of points is, however, for many applications much more adequate because, globally, the union of the grids is an approximately equidistant point set on a logarithmic scale.Dedicated to Gene H. Golub on the occasion of his 60'th birthday     

On the design of nested iterations for elliptic difference equations

By Richardson extrapolation from 2h andh toh/2 the results of computations with coarse grids are used for the construction of an initial approximation on finer grid. After a rather small number of iterations high accuracy is obtained. Numerical results are given for the two-dimensional Laplace equation.     

A special stability problem for linear multistep methods

The trapezoidal formula has the smallest truncation error among all linear multistep methods with a certain stability property. For this method error bounds are derived which are valid under rather general conditions. In order to make sure that the error remains bounded ast , even though the product of the Lipschitz constant and the step-size is quite large, one needs not to assume much more than that the integral curve is uniformly asymptotically stable in the sense of Liapunov.The preparation of this paper was partly sponsored by the Office of Naval Research and the US Army Research Office (Durham). Reproduction in whole or in part is permitted for any purpose of the US Government.     

A randomly generated program for automatic identity checking

A method for making secret programs for automatic identity checking with very high demands for security, is described. The consistency of the sequence of digits, which identifies the person, is tested by a sequence of transformations, chosen by means of a stored secret random table. The method has been implemented for a system of unattended cash dispenser terminals, equipped with microprocessors.     

Probing slow time scale dynamics at methyl-containing side chains in proteins by relaxation dispersion NMR measurements: application to methionine residues in a cavity mutant of T4 lysozyme.

A relaxation dispersion-based NMR experiment is presented for the measurement and quantitation of micros-ms dynamic processes at methyl side-chain positions in proteins. The experiment measures the exchange contribution to the 13C line widths of methyl groups using a constant-time CPMG scheme. The effects of cross-correlated spin relaxation between dipole-dipole and dipole-CSA interactions as well as the effects of scalar coupling responsible for mixing of magnetization modes during the course of the experiment have been investigated in detail both theoretically and through simulations. It is shown that the complex relaxation properties of the methyl spin system do not complicate extraction of accurate exchange parameters as long as care is taken to ensure that appropriate magnetization modes are interchanged in the middle of the constant-time CPMG period. An application involving the measurement of relaxation dispersion profiles of methionine residues in a Leu99Ala substitution of T4 lysozyme is presented. All of the methionine residues are sensitive to an exchange event with a rate on the order of 1200 s(-1) at 20 degrees C that may be linked to a process in which hydrophobic ligands are able to rapidly bind to the cavity that is present in this mutant.     

Transient deflection response in microcantilever array integrated with polydimethylsiloxane (PDMS) microfluidics

We report the integration of a nanomechanical sensor consisting of 16 silicon microcantilevers with polydimethylsiloxane (PDMS) microfluidics. For microcantilevers positioned near the bottom of a microfluidic flow channel, a transient differential analyte concentration for the top versus bottom surface of each microcantilever is created when an analyte-bearing fluid is introduced into the flow channel (which is initially filled with a non-analyte containing solution). We use this effect to characterize a bare (nonfunctionalized) microcantilever array in which the microcantilevers are simultaneously read out with our recently developed high sensitivity in-plane photonic transduction method. We first examine the case of non-specific binding of bovine serum albumin (BSA) to silicon. The average maximum transient microcantilever deflection in the array is -1.6 nm, which corresponds to a differential surface stress of only -0.23 mN m(-1). This is in excellent agreement with the maximum differential surface stress calculated based on a modified rate equation in conjunction with finite element simulation. Following BSA adsorption, buffer solutions with different pH are introduced to further study microcantilever array transient response. Deflections of 20-100 nm are observed (2-14 mN m(-1) differential surface stress). At a flow rate of 5 μL min(-1), the average measured temporal width (FWHM) of the transient response is 5.3 s for BSA non-specific binding and 0.74 s for pH changes.