Biomedical subjects
Publications and source records attributed to T F Havel.
We report the implementation of a three-spin quantum disentanglement eraser on a liquid-state NMR quantum information processor. A key feature of this experiment was its use of pulsed magnetic field gradients to mimic projective measurements. This ability is an important step towards the development of an experimentally controllable system which can simulate any quantum dynamics, both coherent and decoherent.
The implementation of small prototype quantum computers has been studied through ensemble quantum computing via NMR measurements. In such laboratory studies it is convenient to have access to a wide array of logic gates. Here a systematic approach to reduce the logic gate to an NMR pulse sequence is introduced. This approach views the truth table for a quantum logic operation as a permutation matrix that corresponds to a propagator for an NMR transition. This propagator is then used as the starting point for the derivation of a pulse sequence. Pulse sequences for all the permutations of a four level system are reported along with implementations of representative examples on a two spin-1/2 system, 13C-labeled chloroform.
A quantum computer (QC) can operate in parallel on all its possible inputs at once, but the amount of information that can be extracted from the result is limited by the phenomenon of wave function collapse. We present a new computational model, which differs from a QC only in that the result of a measurement is the expectation value of the observable, rather than a random eigenvalue thereof. Such an expectation value QC can solve nondeterministic polynomial-time complete problems in polynomial time. This observation is significant precisely because the computational model can be realized, to a certain extent, by NMR spectroscopy on macroscopic ensembles of quantum spins, namely molecules in a test tube. This is made possible by identifying a manifold of statistical spin states, called pseudo-pure states, the mathematical description of which is isomorphic to that of an isolated spin system. The result is a novel NMR computer that can be programmed much like a QC, but in other respects more closely resembles a DNA computer. Most notably, when applied to intractable combinatorial problems, an NMR computer can use an amount of sample, rather than time, which grows exponentially with the size of the problem. Although NMR computers will be limited by current technology to exhaustive searches over only 15 to 20 bits, searches over as much as 50 bits are in principle possible, and more advanced algorithms could greatly extend the range of applicability of such machines.
This paper introduces a novel computational method for estimating relaxation rates among pairs of spin orders. This method simultaneously estimates all the auto- and cross-relaxation rates from the same measurements, and avoids the ill-conditioning problems associated with multiexponential fits. The method models the relaxation dynamics by a system of linear differential equations, and assumes that measurements of the spin orders have been made at an equally spaced sequence of time points. It computes a nonlinear least-squares fit of the exponential of the rate matrix at the shortest time point to these measurements. Preliminary estimates of the exponential matrix and initial spin orders from which to start the computations are obtained by solving simpler linear-least-squares problems. The performance of the method on simulated 2 x 2 test problems indicates that when measurements at eight or more equally spaced times spanning the maximum and inflection points of the build-up curves are available, the relative errors in the rates are usually less than the relative errors in the measurements. The method is further demonstrated by applying it to the problem of determining the cross correlation-induced cross-relaxation rates between the in-phase and antiphase coherence of the amide groups in the 15N-labeled protein oxidized flavodoxin. Finally, the possibility of extending the method to other kinds of relaxation measurements and larger spin systems is discussed.
A few years ago, lattice model studies indicated that compactness could induce polymer chains to develop protein-like secondary structures. Subsequent off-lattice studies have found the amounts of induced structure to be relatively small. Here we use distance geometry to generate random conformations of compact poly-alanine chains of various chain lengths. The poly-alanine chains are subjected only to compactness and excluded volume constraints; no other energies or conformational propensities are included in the chain generation procedure. We find that compactness leads to considerable stabilization of secondary structure, but the absolute amount of secondary structure depends strongly on the criteria used to define helices and sheets. By loose criteria, much secondary structure arises from compactness, but by strict criteria, little does. The stabilization free energy of secondary structure provided by compactness, however, appears to be independent of criteria. Since real helices and sheets in proteins can be identified by strict criteria, we introduced small energy perturbations to compact poly-alanine chains using the AMBER force field. Small refinements produced good alpha-helices. For beta-sheets, however, larger refinements are necessary. Compactness appears to impart stability, but not much structural specificity, to secondary structures in proteins. Compactness acts more like diffusion as a force, a result of ensemble statistics, than like pair interactions such as hydrogen bonding.
Two-dimensional NMR spectra are rectangular arrays of real numbers, which are commonly regarded as digitized images to be analyzed visually. If one treats them instead as mathematical matrices, linear algebra techniques can also be used to extract valuable information from them. This matrix approach is greatly facilitated by means of a physically significant decomposition of these spectra into a product of matrices--namely, S = PAPT. Here, P denotes a matrix whose columns contain the digitized contours of each individual peak or multiple in the one-dimensional spectrum, PT is its transpose, and A is an interaction matrix specific to the experiment in question. The practical applications of this decomposition are considered in detail for two important types of two-dimensional NMR spectra, double quantum-filtered correlated spectroscopy and nuclear Overhauser effect spectroscopy, both in the weak-coupling approximation. The elements of A are the signed intensities of the cross-peaks in a double quantum-filtered correlated spectrum, or the integrated cross-peak intensities in the case of a nuclear Overhauser effect spectrum. This decomposition not only permits these spectra to be efficiently simulated but also permits the corresponding inverse problems to be given an elegant mathematical formulation to which standard numerical methods are applicable. Finally, the extension of this decomposition to the case of strong coupling is given.
A computational method is described that takes an initial estimate of the chemical shifts, line widths and scalar coupling constants for the protons in a molecule, and refines this estimate so as to improve the least-squares fit between an experimental COSY spectrum and the spectrum simulated from these parameters in the weak-coupling approximation. In order to evaluate the potential of such refinements for estimating these parameters from COSY experiments, the method has been applied to a large number of sample problems which were themselves simulated from standard conformations of the amino acids, along with 25 near-native conformations of the protein bovine pancreatic trypsin inhibitor. The results of this evaluation show that: (i) if the chemical shifts are known to within ca. 0.01 ppm and no noise or artifacts are present in the data, the method is capable of recovering the correct coupling constants, starting from essentially arbitrary values, to within 0.1 Hz in almost all cases. (ii) Although the precision of these estimates of the coupling constants is degraded by the limited resolution, noise and artifacts present in most experimental spectra, the large majority of coupling constants can still be recovered to within 1.0 Hz; the local minimum problem is not made significantly worse by such defects in the data. (iii) The method assigns an 'effective' line width to all the resonances, and in the process can resolve overlapping cross peaks. (iv) The method is not capable of determining the chemical shifts a priori, due to the presence of numerous local minima in the least-squares residual as a function of these parameters.
A new computational method for simultaneously estimating all the proton-proton coupling constants in a molecule from COSY spectra [Yang, J.-X. and Havel, T.F. (1994) J. Biomol. NMR, 4, 807-826] is applied to experimental data from two polypeptides. The first of these is a cyclic hexapeptide denoted as VDA (-D-Ala1-Phe2-Trp3-Lys(Z)4-Val5-Phe6-), in deuterated DMSO, while the second is a 39-residue protein, called decorsin, in aqueous solution. The effect of different data processing strategies and different initial parameter values on the accuracy of the coupling constants was explored. In the case of VDA, most of the coupling constants did not depend strongly on the initial values chosen for the optimization or on how the data were processed. This, together with our previous experience using simulated data, implies strongly that these values are accurate estimates of the coupling constants. They also differ by an average of only 0.36 Hz from the values of the 14 coupling constants that could be measured independently by established methods. In the case of decorsin, many of the coupling constants exhibited a moderate dependence on their initial values and a strong dependence on how the data were processed. With the most successful data processing strategy, the amide-alpha coupling constants differed by an average of 1.11 Hz from the 21 values that could be measured by established methods, while two thirds of the three-bond coupling constants fell within 1.0 Hz of the ranges obtained by applying the Karplus relation to an independently computed ensemble of distance geometry structures. The averages of the coupling constants over multiple optimizations using random initial values were computed in order to obtain the best possible estimates of the coupling constants. Most clearly incorrect averages can be identified by large standard deviations in the coupling constants or the associated line widths and chemical shifts, and can be explained by strong coupling and/or overlap with the water signal, the diagonal peaks or other cross peaks.
A method is proposed for defining a probability distribution on an ensemble of protein conformations from a 2D NOE spectrum, while at the same time back-calculating the experimental spectrum from the ensemble. This enables one to assess the relative quality and significance of the conformations, and to test the consistency of the ensemble as a whole with the experimental spectrum. The method eliminates the need to integrate the cross-peak intensities and is surprisingly insensitive to random noise in the spectrum. In this communication, these advantages are demonstrated by applying the method to simulated data, for which the correct result is already known.
A high-precision solution structure of the elastase inhibitor eglin c was determined by NMR and distance geometry calculations. A large set of 947 nuclear Overhauser (NOE) distance constraints was identified, 417 of which were quantified from two-dimensional NOE spectra at short mixing times. In addition, a large number of homonuclear 1H-1H and heteronuclear 1H-15N vicinal coupling constants were used, and constraints on 42 chi 1 and 38 phi angles were obtained. Structure calculations were carried out using the distance geometry program DG-II. These calculations had a high convergence rate, in that 66 out of 75 calculations converged with maximum residual NOE violations ranging from 0.17 A to 0.47 A. The spread of the structures was characterized with average root mean square deviations ( ) between the structures and a mean structure. To calculate the unbiased toward any single structure, a new procedure was used for structure alignment. A canonical structure was calculated from the mean distances, and all structures were aligned relative to that. Furthermore, an angular order parameter S was defined and used to characterize the spread of structures in torsion angle space. To obtain an accurate estimate of the precision of the structure, the number of calculations was increased until the and the angular order parameters stabilized. This was achieved after approximately 40 calculations. The structure consists of a well-defined core whose backbone deviates from the canonical structure ca. 0.4 A, a disordered N-terminal heptapeptide whose backbone deviates by 0.8-12 A, and a proteinase-binding loop whose backbone deviates up to 3.0 A. Analysis of the angular order parameters and inspection of the structures indicates that a hinge-bending motion of the binding loop may occur in solution. Secondary structures were analyzed by comparison of dihedral angle patterns. The high precision of the structure allows one to identify subtle differences with four crystal structures of eglin c determined in complexes with proteinases.
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ZFY, a sex-related Zn-finger protein encoded by the human Y chromosome, is distinguished from the general class of Zn-finger proteins by the presence of a two-finger repeat. Whereas odd-numbered domains and linkers fit a general consensus, even-numbered domains and linkers exhibit systematic differences. Because this alternation may have fundamental implications for the mechanism of protein-DNA recognition, we have undertaken biochemical and structural studies of fragments of ZFY. We describe here the solution structure of a representative nonconsensus (even-numbered) Zn finger based on 2D NMR studies of a 30-residue peptide. Structural modeling by distance geometry and simulated annealing (DG/SA) demonstrates that this peptide folds as a miniglobular domain containing a C-terminal beta--hairpin and N-terminal alpha-helix (beta beta alpha motif). These features are similar to (but not identical with) those previously described in consensus-type Zn fingers (derived from ADR1 and Xfin); the similarities suggest that even and odd ZFY domains bind DNA by a common mechanism. A model of the protein-DNA complex (designated the "jumping-linker" model) is presented and discussed in terms of the ZFY two-finger repeat. In this model every other linker is proposed to cross the minor groove by means of a putative finger/linker submotif HX4HX3-hydrophobic residue-X3. Analogous use of a hydrophobic residue in a linker that spans the minor groove has recently been described in crystallographic and 3D NMR studies of homeodomain-DNA complexes. The proposed model of ZFY is supported in part by the hydroxyl radical footprint of the TFIIIA-DNA complex [Churchill, M.E.A., Tullius, T.D., & Klug, A. (1990) Proc. Natl. Acad. Sci. U.S.A. 87, 5528-5532].
We describe a largely automatic procedure for building protein structures from sequence alignments with homologues of known structure. This procedure uses simple rules by which multiple sequence alignments can be translated into distance and chirality constraints, which are then used as input for distance geometry calculations. By this means one obtains an ensemble of conformations for the unknown structure that are compatible with the rules employed, and the differences among these conformations provide an indication of the reliability of the structure prediction. The overall approach is demonstrated here by applying it to several Kazal-type trypsin inhibitors, for which experimentally determined structures are available. On the basis of our experience with these test problems, we have further predicted the conformation of the human pancreatic secretory trypsin inhibitor, for which no experimentally determined structure is presently available.
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Given a sufficiently good empirical potential function for the internal energy of molecules, prediction of the preferred conformations is nearly impossible for large molecules because of the enormous number of local energy minima. Energy embedding has been a promising method for locating extremely good local minima, if not always the global minimum. The algorithm starts by locating a very good local minimum when the molecule is in a high-dimensional Euclidean space, and then it gradually projects down to three dimensions while allowing the molecule to relax its energy throughout the process. Now we present a variation on the method, called rotational energy embedding, where the descent into three dimensions is carried out by a sequence of internal rotations that are the multidimensional generalization of varying torsion angles in three dimensions. The new method avoids certain kinds of difficulties experienced by ordinary energy embedding and enables us to locate conformations very near the native for avian pancreatic polypeptide and apamin, given only their amino acid sequences and a suitable potential function.
An important component of computer programs for determining the solution conformation of proteins and other flexible molecules from nuclear magnetic resonance data are the so-called "bound smoothing algorithms", which compute lower and upper limits on the values of all the interatomic distances from the relatively sparse set which can usually be measured experimentally. To date, the only methods efficient enough for use in large problems take account of only the triangle inequality, but an appreciable improvement in the precision of the limits is possible if the algebraic relations between the distances among each quadruple of atoms are also considered. The goal of this paper is to use a recently improved algorithm for computing these "tetrangle inequality limits" to determine just how much improvement really is possible, given the types of experimental data that are usually available.
The solution conformation of plastocyanin from the green alga Scenedesmus obliquus has been determined from distance and dihedral angle constraints derived by nuclear magnetic resonance (NMR) spectroscopy. Structures were generated with distance geometry and restrained molecular dynamics calculations. A novel molecular replacement method was also used with the same NMR constraints to generate solution structures of S. obliquus plastocyanin from the x-ray structure of the homologous poplar protein. Scenedesmus obliquus plastocyanin in solution adopts a beta-barrel structure. The backbone conformation is well defined and is similar overall to that of poplar plastocyanin in the crystalline state. The distinctive acidic region of the higher plant plastocyanins, which functions as a binding site for electron transfer proteins and inorganic complexes, differs in both shape and charge in S. obliquus plastocyanin.
A set of conformational restraints derived from nuclear magnetic resonance (n.m.r.) measurements on solutions of the basic pancreatic trypsin inhibitor (BPTI) was used as input for distance geometry calculations with the programs DISGEO and DISMAN. Five structures obtained with each of these algorithms were systematically compared among themselves and with the crystal structure of BPTI. It is clear that the protein architecture observed in single crystals of BPTI is largely preserved in aqueous solution, with local structural differences mainly confined to the protein surface. The results confirm that protein conformations determined in solution by combined use of n.m.r. and distance geometry are a consequence of the experimental data and do not depend significantly on the algorithm used for the structure determination. The data obtained further provide an illustration that long intramolecular distances in proteins, which are comparable with the radius of gyration, are defined with high precision by relatively imprecise nuclear Overhauser enhancement measurements of a large number of much shorter distances.