Systematic derivation of partition functions for ligand binding to two-dimensional lattices

The Ising problem consists in finding the analytical solution of the partition function of a lattice once the interaction geometry among its elements is specified. No general analytical solution is available for this problem, except for the one-dimensional case. Using site-specific thermodynamics, it is shown that the partition function for ligand binding to a two-dimensional lattice can be obtained from those of one-dimensional lattices with known solution. The complexity of the lattice is reduced recursively by application of a contact transformation that involves a relatively small number of steps. The transformation implemented in a computer code solves the partition function of the lattice by operating on the connectivity matrix of the graph associated with it. This provides a powerful new approach to the Ising problem, and enables a systematic analysis of two-dimensional lattices that model many biologically relevant phenomena. Application of this approach to finite two-dimensional lattices with positive cooperativity indicates that the binding capacity per site diverges as Na (N = number of sites in the lattice) and experiences a phase-transition-like discontinuity in the thermodynamic limit N → ∞. The zeroes of the partition function tend to distribute on a slightly distorted unit circle in complex plane and approach the positive real axis already for a 5×5 square lattice. When the lattice has negative cooperativity, its properties mimic those of a system composed of two classes of independent sites with the apparent population of low-affinity binding sites increasing with the size of the lattice, thereby accounting for a phenomenon encountered in many ligand-receptor interactions.

The solution structure of the N-terminal domain of α2-macroglobulin receptor-associated protein

The three-dimensional structure of the N-terminal domain (residues 18–112) of α2-macroglobulin receptor-associated protein (RAP) has been determined by NMR spectroscopy. The structure consists of three helices composed of residues 23–34, 39–65, and 73–88. The three helices are arranged in an up-down-up antiparallel topology. The C-terminal 20 residues were shown not to be in a well defined conformation. A structural model for the binding of RAP to the family of low-density lipoprotein receptors is proposed. It defines a role in binding for both the unordered C terminus and the structural scaffold of the core structure. Pathogenic epitopes for the rat disease Heymann nephritis, an experimental model of human membranous glomerulonephritis, have been identified in RAP and in the large endocytic receptor gp330/megalin. Here we provide the three-dimensional structure of the pathogenic epitope in RAP. The amino acid residues known to form the epitope are in a helix–loop–helix conformation, and from the structure it is possible to rationalize the published results obtained from studies of fragments of the N-terminal domain.

Attenuated T2 relaxation by mutual cancellation of dipole–dipole coupling and chemical shift anisotropy indicates an avenue to NMR structures of very large biological macromolecules in solution

Fast transverse relaxation of 1H, 15N, and 13C by dipole-dipole coupling (DD) and chemical shift anisotropy (CSA) modulated by rotational molecular motions has a dominant impact on the size limit for biomacromolecular structures that can be studied by NMR spectroscopy in solution. Transverse relaxation-optimized spectroscopy (TROSY) is an approach for suppression of transverse relaxation in multidimensional NMR experiments, which is based on constructive use of interference between DD coupling and CSA. For example, a TROSY-type two-dimensional 1H,15N-correlation experiment with a uniformly 15N-labeled protein in a DNA complex of molecular mass 17 kDa at a 1H frequency of 750 MHz showed that 15N relaxation during 15N chemical shift evolution and 1HN relaxation during signal acquisition both are significantly reduced by mutual compensation of the DD and CSA interactions. The reduction of the linewidths when compared with a conventional two-dimensional 1H,15N-correlation experiment was 60% and 40%, respectively, and the residual linewidths were 5 Hz for 15N and 15 Hz for 1HN at 4°C. Because the ratio of the DD and CSA relaxation rates is nearly independent of the molecular size, a similar percentagewise reduction of the overall transverse relaxation rates is expected for larger proteins. For a 15N-labeled protein of 150 kDa at 750 MHz and 20°C one predicts residual linewidths of 10 Hz for 15N and 45 Hz for 1HN, and for the corresponding uniformly 15N,2H-labeled protein the residual linewidths are predicted to be smaller than 5 Hz and 15 Hz, respectively. The TROSY principle should benefit a variety of multidimensional solution NMR experiments, especially with future use of yet somewhat higher polarizing magnetic fields than are presently available, and thus largely eliminate one of the key factors that limit work with larger molecules.

Linking genome and proteome by mass spectrometry: Large-scale identification of yeast proteins from two dimensional gels

The function of many of the uncharacterized open reading frames discovered by genomic sequencing can be determined at the level of expressed gene products, the proteome. However, identifying the cognate gene from minute amounts of protein has been one of the major problems in molecular biology. Using yeast as an example, we demonstrate here that mass spectrometric protein identification is a general solution to this problem given a completely sequenced genome. As a first screen, our strategy uses automated laser desorption ionization mass spectrometry of the peptide mixtures produced by in-gel tryptic digestion of a protein. Up to 90% of proteins are identified by searching sequence data bases by lists of peptide masses obtained with high accuracy. The remaining proteins are identified by partially sequencing several peptides of the unseparated mixture by nanoelectrospray tandem mass spectrometry followed by data base searching with multiple peptide sequence tags. In blind trials, the method led to unambiguous identification in all cases. In the largest individual protein identification project to date, a total of 150 gel spots—many of them at subpicomole amounts—were successfully analyzed, greatly enlarging a yeast two-dimensional gel data base. More than 32 proteins were novel and matched to previously uncharacterized open reading frames in the yeast genome. This study establishes that mass spectrometry provides the required throughput, the certainty of identification, and the general applicability to serve as the method of choice to connect genome and proteome.

The two-dimensional IR nonlinear spectroscopy of a cyclic penta-peptide in relation to its three-dimensional structure

A form of two-dimensional (2D) vibrational spectroscopy, which uses two ultrafast IR laser pulses, is used to examine the structure of a cyclic penta-peptide in solution. Spectrally resolved cross peaks occur in the off-diagonal region of the 2D IR spectrum of the amide I region, analogous to those in 2D NMR spectroscopy. These cross peaks measure the coupling between the different amide groups in the structure. Their intensities and polarizations relate directly to the three-dimensional structure of the peptide. With the help of a model coupling Hamiltonian, supplemented by density functional calculations, the spectra of this penta-peptide can be regenerated from the known solution phase structure. This 2D-IR measurement, with an intrinsic time resolution of less than 1 ps, could be used in all time regimes of interest in biology.

Solution 19F nuclear Overhauser effects in structural studies of the cytoplasmic domain of mammalian rhodopsin

19F nuclear Overhauser effects (NOEs) between fluorine labels on the cytoplasmic domain of rhodopsin solubilized in detergent micelles are reported. Previously, high-resolution solution 19F NMR spectra of fluorine-labeled rhodopsin in detergent micelles were described, demonstrating the applicability of this technique to studies of tertiary structure in the cytoplasmic domain. To quantitate tertiary contacts we have applied a transient one-dimensional difference NOE solution 19F NMR experiment to this system, permitting assessment of proximities between fluorine labels specifically incorporated into different regions of the cytoplasmic face. Three dicysteine substitution mutants (Cys-140–Cys-316, Cys-65–Cys-316, and Cys-139–Cys-251) were labeled by attachment of the trifluoroethylthio group through a disulfide linkage. Each mutant rhodopsin was prepared (8–10 mg) in dodecylmaltoside and analyzed at 20°C by solution 19F NMR. Distinct chemical shifts were observed for all of the rhodopsin 19F labels in the dark. An up-field shift of the Cys-316 resonance in the Cys-65–Cys-316 mutant suggests a close proximity between the two residues. When analyzed for 19F-19F NOEs, a moderate negative enhancement was observed for the Cys-65–Cys-316 pair and a strong negative enhancement was observed for the Cys-139–Cys-251 pair, indicating proximity between these sites. No NOE enhancement was observed for the Cys-140–Cys-316 pair. These NOE effects demonstrate a solution 19F NMR method for analysis of tertiary contacts in high molecular weight proteins, including membrane proteins.

Determining RNA solution structure by segmental isotopic labeling and NMR: application to Caenorhabditis elegans spliced leader RNA 1.

Recent developments in multidimensional heteronuclear NMR spectroscopy and large-scale synthesis of uniformly 13C- and 15N-labeled oligonucleotides have greatly improved the prospects for determination of the solution structure of RNA. However, there are circumstances in which it may be advantageous to label only a segment of the entire RNA chain. For example, in a larger RNA molecule the structural question of interest may reside in a localized domain. Labeling only the corresponding nucleotides simplifies the spectrum and resonance assignments because one can filter proton spectra for coupling to 13C and 15N. Another example is in resolving alternative secondary structure models that are indistinguishable in imino proton connectivities. Here we report a general method for enzymatic synthesis of quantities of segmentally labeled RNA molecules required for NMR spectroscopy. We use the method to distinguish definitively two competing secondary structure models for the 5' half of Caenorhabditis elegans spliced leader RNA by comparison of the two-dimensional [15N] 1H heteronuclear multiple quantum correlation spectrum of the uniformly labeled sample with that of a segmentally labeled sample. The method requires relatively small samples; solutions in the 200-300 microM concentration range, with a total of 30 nmol or approximately 40 micrograms of RNA in approximately 150 microliters, give strong NMR signals in a short accumulation time. The method can be adapted to label an internal segment of a larger RNA chain for study of localized structural problems. This definitive approach provides an alternative to the more common enzymatic and chemical footprinting methods for determination of RNA secondary structure.

Definition of a metal-dependent/Li(+)-inhibited phosphomonoesterase protein family based upon a conserved three-dimensional core structure.

Inositol polyphosphate 1-phosphatase, inositol monophosphate phosphatase, and fructose 1,6-bisphosphatase share a sequence motif, Asp-Pro-(Ile or Leu)-Asp-(Gly or Ser)-(Thr or Ser), that has been shown by crystallographic and mutagenesis studies to bind metal ions and participate in catalysis. We compared the six alpha-carbon coordinates of this motif from the crystal structures of these three phosphatases and found that they are superimposable with rms deviations ranging from 0.27 to 0.60 A. Remarkably, when these proteins were aligned by this motif a common core structure emerged, defined by five alpha-helices and 11 beta-strands comprising 155 residues having rms deviations ranging from 1.48 to 2.66 A. We used the superimposed structures to align the sequences within the common core, and a distant relationship was observed suggesting a common ancestor. The common core was used to align the sequences of several other proteins that share significant similarity to inositol monophosphate phosphatase, including proteins encoded by fungal qa-X and qutG, bacterial suhB and cysQ (identical to amtA), and yeast met22 (identical to hal2). Evolutionary comparison of the core sequences indicate that five distinct branches exist within this family. These proteins share metal-dependent/Li(+)-sensitive phosphomonoesterase activity, and each predicted tree branch exhibits unique substrate specificity. Thus, these proteins define an ancient structurally conserved family involved in diverse metabolic pathways including inositol signaling, gluconeogenesis, sulfate assimilation, and possibly quinone metabolism. Furthermore, we suggest that this protein family identifies candidate enzymes to account for both the therapeutic and toxic actions of Li+ as it is used in patients treated for manic depressive disease.