Timothy F. Havel

Protein structures in solution by nuclear magnetic resonance and distance geometry. The polypeptide fold of the basic pancreatic trypsin inhibitor determined using two different algorithms, DISGEO and DISMAN

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.

Solution conformation of proteinase inhibitor IIA from bull seminal plasma by 1H nuclear magnetic resonance and distance geometry.

A determination of the solution conformation of the proteinase inhibitor IIA from bull seminal plasma (BUSI IIA) is described. Two-dimensional nuclear Overhauser enhancement spectroscopy (NOESY) was used to obtain a list of 202 distance constraints between individually assigned hydrogen atoms of the polypeptide chain, to identify the positions of the three disulfide bridges, and to locate the single cis peptide bond. Supplementary geometric constraints were derived from the vicinal spin-spin couplings and the locations of certain hydrogen bonds, as determined by nuclear magnetic resonance (n.m.r.). Using a new distance geometry program (DISGEO) which is capable of computing all-atom structures for proteins the size of BUSI IIA, five conformers were computed from the NOE distance constraints alone, and another five were computed with the supplementary constraints included. Comparison of the different structures computed from the n.m.r. data among themselves and with the crystal structures of two homologous proteins shows that the global features of the conformation of BUSI IIA (i.e. the overall dimensions of the molecule and the threading of the polypeptide chain) were well-defined by the available n.m.r. data. In the Appendix, we describe a preliminary energy refinement of the structure, which showed that the constraints derived from the n.m.r. data are compatible with a low energy spatial structure.

The theory and practice of distance geometry

The mathematics of distance geometry constitutes the basis of a group of algorithms for revealing the structural consequences of diverse forms of information about a macromolecules conformation. These algorithms are of proven utility in the analysis of experimental conformational data. This paper presents the basic theorems of distance geometry in Euclidean space and gives formal proofs of the correctness and, where possible, of the complexity of these algorithms. The implications of distance geometry for the energy minimization of macromolecules are also discussed.

An evaluation of the combined use of nuclear magnetic resonance and distance geometry for the determination of protein conformations in solution

An evaluation of the potential of nuclear magnetic resonance (n.m.r.) as a means of determining polypeptide conformation in solution is performed with the aid of a new distance geometry program which is capable of computing complete spatial structures for small proteins from n.m.r. data. Ten sets of geometric constraints which simulate the results available from n.m.r. experiments of varying precision and completeness were extracted from the crystal structure of the basic pancreatic trypsin inhibitor, and conformers consistent with these constraints were computed. Comparison of these computed structures with each other and with the original crystal structure shows that it is possible to determine the global conformation of a polypeptide chain from the distance constraints which are available from n.m.r. experiments. The results obtained with the different data sets also provide a standard by which the quality of protein structures computed from n.m.r. data can be evaluated when no crystal structure is available, and indicate directions in which n.m.r. experiments for protein structure determination could be further improved.

A distance geometry program for determining the structures of small proteins and other macromolecules from nuclear magnetic resonance measurements of intramolecular1H−1H proximities in solution

DISGEO is a new implementation of a distance geometry algorithm which has been specialized for the calculation of macromolecular conformation from distance measurements obtained by two-dimensional nuclear Overhauser enhancement spectroscopy. The improvements include (1) a decomposition of the complete embedding process into two successive, more tractable calculations by the use of “substructures”, (2) a compact data structure for storing incomplete distance information on a structure, (3) a more efficient shortest-path algorithm for computing the triangle inequality limits on all distances from this information, (4) a new algorithm for selecting random metric spaces from within these limits, (5) the use of chirality constraints to obtain good covalent geometry without the use ofad hoc weights or excessive optimization. The utility of the resultant program with nuclear magnetic resonance data is demonstrated by embedding complete spatial structures for the protein basic pancreatic trypsin inhibitor vs all 508 intramolecular, interresidue proton-proton contacts shorter than 4.0 A that were present in its crystal structure. The crystal structure could be reproduced from this data set to within 1.3 A minimum root mean square coordinate difference between the backbone atoms. We conclude that the information potentially available from nuclear magnetic resonance experiments in solution is sufficient to define the spatial structure of small proteins.

EXPERIMENTAL QUANTUM ERROR CORRECTION

Quantum error correction is required to compensate for the fragility of the state of a quantum computer. We report the first experimental implementations of quantum error correction and confirm the expected state stabilization. A precise analysis of the decay behavior is performed in alanine and a full implementation of the error correction procedure is realized in trichloroethylene. In NMR computing, however, a net improvement in the signal to noise would require very high polarization. The experiment implemented the three-bit code for phase errors using liquid state NMR.

Nuclear magnetic resonance spectroscopy: an experimentally accessible paradigm for quantum computing

Abstract We present experimental results which demonstrate that nuclear magnetic resonance spectroscopy is capable of emulating many of the capabilities of quantum computers, including unitary evolution and coherent superpositions, but without attendant wave-function collapse. This emulation is made possible by two facts. The first is that the spin active nuclei in each molecule of a liquid sample are largely isolated from the spins in all other molecules, so that each molecule is effectively an independent quantum computer. The second is the existence of a manifold of statistical spin states, called pseudo-pure states, whose transformation properties are identical to those of true pure states. These facts enable us to operate on coherent superpositions over the spins in each molecule using full quantum parallelism, and to combine the results into deterministic macroscopic observables via thermodynamic averaging. We call a device based on these principles an ensemble quantum computer . Our results show that it is indeed possible to prepare a pseudo-pure state in a macroscopic liquid sample under ambient conditions, to transform it into a coherent superposition, to apply elementary quantum logic gates to this superposition, and to convert it into the equivalent of an entangled state. Specifically, we have: • - implemented the quantum XOR gate in two different ways, one using Pound-Overhauser double resonance, and the other using a spin-coherence double resonance pulse sequence; • - demonstrated that the square root of the Pound-Overhauser XOR corresponds to a conditional rotation, thus confirming that NMR spectroscopy provides a universal set of gates; • - devised a spin-coherence implementation of the Toffoli gate, and confirmed that it transforms the equilibrium state of a four-spin system as expected; • - used standard gradient-pulse techniques in NMR to equalize all but one of the populations in a two-spin system, thus obtaining the basic pseudo-pure state that corresponds to |00〉; • - validated that one can identify which basic pseudo-pure state is present by transforming it into one-spin superpositions, whose associated spectra jointly characterize the state; • - applied the spin-coherence XOR gate to a one-spin superposition to create an entangled state, and confirmed its existence by detecting the associated double-quantum coherence via gradient-echo methods.

Stable calculation of coordinates from distance information

A new method is described for the calculation of Cartesian coordinates for n points given the n × n matrix of interpoint distances. The algorithm is faster than some earlier methods, and it is remarkably stable with respect to both numerical roundoff errors and errors in the given distance matrix. The resultant coordinates have their origin near the center of mass and axes approximately along the three principal rotational axes. The calculation is described of distances to the center of mass directly from the distance matrix. Results of computer trials of the algorithm are given.

NMR Based Quantum Information Processing: Achievements and Prospects

Nuclear magnetic resonance (NMR) provides an experimental setting to explore physical implementations of quantum information processing (QIP). Here we introduce the basic background for understanding applications of NMR to QIP and explain their current successes, limitations and potential. NMR spectroscopy is well known for its wealth of diverse coherent manipulations of spin dynamics. Ideas and instrumentation from liquid state NMR spectroscopy have been used to experiment with QIP. This approach has carried the field to a complexity of about 10 qubits, a small number for quantum computation but large enough for observing and better understanding the complexity of the quantum world. While liquid state NMR is the only present-day technology about to reach this number of qubits, further increases in complexity will require new methods. We sketch one direction leading towards a scalable quantum computer using spin 1/2 particles. The next step of which is a solid state NMR-based QIP capable of reaching 10-30 qubits.

A new method for building protein conformations from sequence alignments with homologues of known structure

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.