Integrating NOE and RDC using sum-of-squares relaxation for protein structure determination.

We revisit the problem of protein structure determination from geometrical restraints from NMR, using convex optimization. It is well-known that the NP-hard distance geometry problem of determining atomic positions from pairwise distance restraints can be relaxed into a convex semidefinite program (SDP). However, often the NOE distance restraints are too imprecise and sparse for accurate structure determination. Residual dipolar coupling (RDC) measurements provide additional geometric information on the angles between atom-pair directions and axes of the principal-axis-frame. The optimization problem involving RDC is highly non-convex and requires a good initialization even within the simulated annealing framework. In this paper, we model the protein backbone as an articulated structure composed of rigid units. Determining the rotation of each rigid unit gives the full protein structure. We propose solving the non-convex optimization problems using the sum-of-squares (SOS) hierarchy, a hierarchy of convex relaxations with increasing complexity and approximation power. Unlike classical global optimization approaches, SOS optimization returns a certificate of optimality if the global optimum is found. Based on the SOS method, we proposed two algorithms-RDC-SOS and RDC-NOE-SOS, that have polynomial time complexity in the number of amino-acid residues and run efficiently on a standard desktop. In many instances, the proposed methods exactly recover the solution to the original non-convex optimization problem. To the best of our knowledge this is the first time SOS relaxation is introduced to solve non-convex optimization problems in structural biology. We further introduce a statistical tool, the Cramér-Rao bound (CRB), to provide an information theoretic bound on the highest resolution one can hope to achieve when determining protein structure from noisy measurements using any unbiased estimator. Our simulation results show that when the RDC measurements are corrupted by Gaussian noise of realistic variance, both SOS based algorithms attain the CRB. We successfully apply our method in a divide-and-conquer fashion to determine the structure of ubiquitin from experimental NOE and RDC measurements obtained in two alignment media, achieving more accurate and faster reconstructions compared to the current state of the art.

A peptide mimic blocks the cross-reaction of anti-DNA antibodies with glomerular antigens.

Anti-DNA antibodies play a pivotal role in the pathogenesis of lupus nephritis by cross-reacting with renal antigens. Previously, we demonstrated that the binding affinity of anti-DNA antibodies to self-antigens is isotype-dependent. Furthermore, significant variability in renal pathogenicity was seen among a panel of anti-DNA isotypes [derived from a single murine immunoglobulin (Ig)G3 monoclonal antibody, PL9-11] that share identical variable regions. In this study, we sought to select peptide mimics that effectively inhibit the binding of all murine and human anti-DNA IgG isotypes to glomerular antigens. The PL9-11 panel of IgG anti-DNA antibodies (IgG1, IgG2a, IgG2b and IgG3) was used for screening a 12-mer phage display library. Binding affinity was determined by surface plasmon resonance. Enzyme-linked immunosorbent assay (ELISA), flow cytometry and glomerular binding assays were used for the assessment of peptide inhibition of antibody binding to nuclear and kidney antigens. We identified a 12 amino acid peptide (ALWPPNLHAWVP, or 'ALW') which binds to all PL9-11 IgG isotypes. Preincubation with the ALW peptide reduced the binding of the PL9-11 anti-DNA antibodies to DNA, laminin, mesangial cells and isolated glomeruli significantly. Furthermore, we confirmed the specificity of the amino acid sequence in the binding of ALW to anti-DNA antibodies by alanine scanning. Finally, ALW inhibited the binding of murine and human lupus sera to dsDNA and glomeruli significantly. In conclusion, by inhibiting the binding of polyclonal anti-DNA antibodies to autoantigens in vivo, the ALW peptide (or its derivatives) may potentially be a useful approach to block anti-DNA antibody binding to renal tissue.

Novel mechanism of regulation of the non-receptor protein tyrosine kinase Csk: insights from NMR mapping studies and site-directed mutagenesis.

Csk (C-terminal Src kinase), a protein tyrosine kinase, consisting of the Src homology 2 and 3 (SH2 and SH3) domains and a catalytic domain, phosphorylates the C-terminal tail of Src-family members, resulting in downregulation of the Src family kinase activity. The Src family kinases share 37 % homology with Csk but, unlike Src-family kinases, the catalytic domain of Csk alone is weakly active and can be stimulated in trans by interacting with the Csk-SH3 domain, suggesting a mode of intradomain regulation different from that of Src family kinases. The structural determinants of this intermolecular interaction were studied by nuclear magnetic resonance (NMR) and site-directed mutagenesis techniques. Chemical shift perturbation of backbone nuclei (H' and (15)N) has been used to map the Csk catalytic domain binding site on the Csk-SH3. The experimentally determined interaction surface includes three structural elements: the N-terminal tail, a small part of the RT-loop, and the C-terminal SH3-SH2 linker. Site-directed mutagenesis revealed that mutations in the SH3-SH2 linker of the wild-type Csk decrease Csk kinase activity up to fivefold, whereas mutations in the RT-loop left Csk kinase activity largely unaffected. We conclude that the SH3-SH2 linker plays a major role in the activation of the Csk catalytic domain.

A novel, specific interaction involving the Csk SH3 domain and its natural ligand.

C-terminal Src kinase (Csk) takes part in a highly specific, high affinity interaction via its Src homology 3 (SH3) domain with the proline-enriched tyrosine phosphatase PEP in hematopoietic cells. The solution structure of the Csk-SH3 domain in complex with a 25-residue peptide from the Pro/Glu/Ser/Thr-rich (PEST) domain of PEP reveals the basis for this specific peptide recognition motif involving an SH3 domain. Three residues, Ala 40, Thr 42 and Lys 43, in the SH3 domain of Csk specifically recognize two hydrophobic residues, Ile 625 and Val 626, in the proline-rich sequence of the PEST domain of PEP. These two residues are C-terminal to the conventional proline-rich SH3 domain recognition sequence of PEP. This interaction is required in addition to the classic polyproline helix (PPII) recognition by the Csk-SH3 domain for the association between Csk and PEP in vivo. NMR relaxation analysis suggests that Csk-SH3 has different dynamic properties in the various subsites important for peptide recognition.

Peptide chemical ligation inside living cells: in vivo generation of a circular protein domain.

Here we describe the first example of a peptide chemical ligation reaction performed inside a living cell. A cell-based native chemical ligation approach was developed and used to generate a circular version of the N-terminal Src homology 3 (SH3) domain from the murine c-Crk adapter protein inside Escherichia coli cells. The in vivo cyclization reaction was extremely efficient and the resulting circular protein domain was fully biologically active and able to adopt the native SH3 folded structure. This work represents an important step towards the in vivo generation of small backbone cyclic peptides for use in basic biological research.

Simulated and NMR-derived backbone dynamics of a protein with significant flexibility: a comparison of spectral densities for the betaARK1 PH domain.

A 7.6 ns molecular dynamics trajectory of the betaARK1 PH domain in explicit water with appropriate ions was calculated at 300 K. Spectral densities at omega = 0, omega(N), and 0.87omega(H) and the model-free parameters were evaluated from the experimental as well as the simulated data, taking the anisotropic overall motion of the protein into account. Experimental and simulated spectral densities are in reasonable general agreement for NH bond vectors, where the corresponding motions have converged within the simulation time. A sufficient sampling of the motions for NH bonds within flexible parts of the protein requires a longer simulation time. The simulated spectral densities J(0) and J(omega(N)) are, on average, 4.5% and 16% lower than the experimental data; the corresponding numbers for the core residues are about 6%; the high-frequency spectral densities J(0.87omega(H)) are lower by, on average, 16% (21% for the core). The simulated order parameters, S(2), are also lower, although the overall disagreement between the simulation and experiment is less pronounced: 1% for all residues and 6% for the core. The observed systematic decrease of simulated spectral density and the order parameters compared to the experimental data can be partially attributed to the ultrafast librational motion of the NH bonds with respect to their peptide plane, which was analyzed in detail. This systematic difference is most pronounced for J(0.87omega(H)), which appears to be most sensitive to the slow, subnanosecond time scale of internal motion, whereas J(0) and J(omega(N)) are dominated by the overall rotational tumbling of the protein. Similar discrepancies are observed between the experimentally measured (15)N relaxation parameters (R(1), R(2), NOE) and their values calculated from the simulated spectral densities. The analysis of spectral densities provides additional information regarding the comparison of the simulated and experimental data, not available from the model-free analysis.

Nuclear magnetic resonance relaxation in determination of residue-specific 15N chemical shift tensors in proteins in solution: protein dynamics, structure, and applications of transverse relaxation optimized spectroscopy.

We developed several approaches to direct determination of the 15N CSA from relaxation measurements in uniformly 15N-labeled proteins in solution. These methods are based on multiple-field measurements and could be extended to other nuclei in proteins and other molecules. Combined with the isotropic chemical shift measurements, this provides an experimental approach to full characterization of chemical shift tensors in proteins in their native milieu, which is likely to provide valuable information on the nature of chemical shifts and their relation to protein structure. Knowledge of 15N CSA is essential for an accurate characterization of protein dynamics from relaxation measurements.

Rescuing a destabilized protein fold through backbone cyclization.

We describe the physicochemical characterization of various circular and linear forms of the approximately 60 residue N-terminal Src homology 3 (SH3) domain from the murine c-Crk adapter protein. Structural, dynamic, thermodynamic, kinetic and biochemical studies reveal that backbone circularization does not prevent the adoption of the natural folded structure in any of the circular proteins. Both the folding and unfolding rate of the protein increased slightly upon circularization. Circularization did not lead to a significant thermodynamic stabilization of the full-length protein, suggesting that destabilizing enthalpic effects (e.g. strain) negate the expected favorable entropic contribution to overall stability. In contrast, we find circularization results in a dramatic stabilization of a truncated version of the SH3 domain lacking a key glutamate residue. The ability to rescue the destabilized mutant indicates that circularization may be a useful tool in protein engineering programs geared towards generating minimized proteins.

Determination of the rotational diffusion tensor of macromolecules in solution from nmr relaxation data with a combination of exact and approximate methods--application to the determination of interdomain orientation in multidomain proteins.

In this paper we present a method for determining the rotational diffusion tensor from NMR relaxation data using a combination of approximate and exact methods. The approximate method, which is computationally less intensive, computes values of the principal components of the diffusion tensor and estimates the Euler angles, which relate the principal axis frame of the diffusion tensor to the molecular frame. The approximate values of the principal components are then used as starting points for an exact calculation by a downhill simplex search for the principal components of the tensor over a grid of the space of Euler angles relating the diffusion tensor frame to the molecular frame. The search space of Euler angles is restricted using the tensor orientations calculated using the approximate method. The utility of this approach is demonstrated using both simulated and experimental relaxation data. A quality factor that determines the extent of the agreement between the measured and predicted relaxation data is provided. This approach is then used to estimate the relative orientation of SH3 and SH2 domains in the SH(32) dual-domain construct of Abelson kinase complexed with a consolidated ligand.

The structure of the IgE Cepsilon2 domain and its role in stabilizing the complex with its high-affinity receptor FcepsilonRIalpha.

The stability of the complex between IgE and its high-affinity receptor, FcepsilonRI, on mast cells is a critical factor in the allergic response. The long half-life of the complex of IgE bound to this receptor in situ ( approximately 2 weeks, compared with only hours for the comparable IgG complex) contributes to the permanent sensitization of these cells and, hence, to the immediate response to allergens. Here we show that the second constant domain of IgE, Cepsilon2, which takes the place of the flexible hinge in IgG, contributes to this long half-life. When the Cepsilon2 domain is deleted from the IgE Fc fragment, leaving only the Cepsilon3 and Cepsilon4 domains (Cepsilon3-4 fragment), the rate of dissociation from the receptor is increased by greater than 1 order of magnitude. We report the structure of the Cepsilon2 domain by heteronuclear NMR spectroscopy and show by chemical shift perturbation that it interacts with FcepsilonRIalpha. By sedimentation equilibrium we show that the Cepsilon2 domain binds to the Cepsilon3-4 fragment of IgE. These interactions of Cepsilon2 with both FcepsilonRIalpha and Cepsilon3-4 provide a structural explanation for the exceptionally slow dissociation of the IgE-FcepsilonRIalpha complex.

The virtual NMR spectrometer: a computer program for efficient simulation of NMR experiments involving pulsed field gradients.

This paper presents a software program, the Virtual NMR Spectrometer, for computer simulation of multichannel, multidimensional NMR experiments on user-defined spin systems. The program is capable of reproducing most features of the modern NMR experiment, including homo- and heteronuclear pulse sequences, phase cycling, pulsed field gradients, and shaped pulses. Two different approaches are implemented to simulate the effect of pulsed field gradients on coherence selection, an explicit calculation of all coherence transfer pathways, and an effective approximate method using integration over multiple positions in the sample. The applications of the Virtual NMR Spectrometer are illustrated using homonuclear COSY and DQF COSY experiments with gradient selection, heteronuclear HSQC, and TROSY. The program uses an intuitive graphical user interface, which resembles the appearance and operation of a real spectrometer. A translator is used to allow the user to design pulse sequences with the same programming language used in the actual experiment on a real spectrometer. The Virtual NMR Spectrometer is designed as a useful tool for developing new NMR experiments and for tuning and adjusting the experimental setup for existing ones prior to running costly NMR experiments, in order to reduce the setup time on a real spectrometer. It will also be a useful aid for learning the general principles of magnetic resonance and contemporary innovations in NMR pulse sequence design.

Direct determination of changes of interdomain orientation on ligation: use of the orientational dependence of 15N NMR relaxation in Abl SH(32).

The relative orientation and motions of domains within many proteins are key to the control of multivalent recognition, or the assembly of protein-based cellular machines. Current methods of structure determination have limited applicability to macromolecular assemblies, characterized by weak interactions between the constituents. Crystal structures of such complexes might be biased by packing forces comparable to the interdomain interactions, while the precision and accuracy of the conventional NMR structural approaches are necessarily limited by the restricted number of NOE contacts and by interdomain flexibility rendering the available NOE information uninterpretable. NMR relaxation studies are capable of providing "long-range" structural information on macromolecules in their native milieu. Here we determine directly the change in domain orientation between unligated and dual ligated subdomains of the SH(32) segment of Abelson kinase in solution, using the orientational dependence of nuclear spin relaxation. These results demonstrate that the change in domain orientation between unligated and ligated forms can be measured directly in solution.

Accurate quantitation of protein expression and site-specific phosphorylation.

A mass spectrometry-based method is described for simultaneous identification and quantitation of individual proteins and for determining changes in the levels of modifications at specific sites on individual proteins. Accurate quantitation is achieved through the use of whole-cell stable isotope labeling. This approach was applied to the detection of abundance differences of proteins present in wild-type versus mutant cell populations and to the identification of in vivo phosphorylation sites in the PAK-related yeast Ste20 protein kinase that depend specifically on the G1 cyclin Cln2. The present method is general and affords a quantitative description of cellular differences at the level of protein expression and modification, thus providing information that is critical to the understanding of complex biological phenomena.

Impact of Cl- and Na+ ions on simulated structure and dynamics of betaARK1 PH domain.

A nonzero net charge of proteins at pH 7 is usually compensated by the addition of charge-balancing counter ions during molecular dynamics simulation, which reduces electrostatic interactions. For highly charged proteins, like the betaARK1 PH domain used here, it seems reasonable to also add explicit salt ions. To assess the impact of explicit salt ions, two molecular dynamics simulations of solvated betaARK1 PH domain have been carried out with different numbers of Cl- and Na+ ions, based on the Cornell et al. force field and the Ewald summation, which was used in the treatment of long-range electrostatic interactions. Initial positions of ions were obtained from the AMBER CION program. Increasing the number of ions alters the average structure in loop regions, as well as the fluctuation amplitudes of dihedral angles. We found unnaturally strong interactions between side chains in the absence of salt ions. The presence of salt ions reduces these electrostatic interactions. The time needed for the equilibration of the ionic environment around the protein, after initial placement of ions close to oppositely charged side chains, is in the nanosecond time range, which can be shortened by using a higher ionic strength. Our results also suggest selecting those methods that do not place the ions initially close to the protein surface.

Flexibility of interdomain contacts revealed by topological isomers of bivalent consolidated ligands to the dual Src homology domain SH(32) of abelson.

Src homology (SH)2 and SH3 domains are found in a variety of proteins involved in the control of cellular signaling and architecture. The possible interrelationships between domains are not easily investigated, even though several cases of multiple domain-containing constructs have been studied structurally. As a complement to direct structural methods, we have developed consolidated ligands and tested their binding to the Abl SH(32) complex. Consolidated ligands combine in the same molecule peptide sequences recognized by SH2 and SH3 domains, i.e., Pro-Val-pTyr-Glu-Asn-Val and Pro-Pro-Ala-Tyr-Pro-Pro-Pro-Pro-Val-Pro, respectively; these are joined by oligoglycyl linkers. Four types of ligands were chemically synthesized, representing all the possible relative orientations of ligands. Their affinities were found to vary with binding portion topologies and linker lengths. Two of these types were shown to bind to both SH2 and SH3 dual domains with high affinities and specificities, showing increases of one order of magnitude, as compared to the most strongly bound monovalent equivalent. These results suggest that the relative orientation of SH2 and SH3 in Abl SH(32) is not fixed, and this synthetic approach may be generally useful for determining the structures of ligated complexes and for developing reagents with high affinities and specificities.

Solution structure of the proapoptotic molecule BID: a structural basis for apoptotic agonists and antagonists.

Members of the BCL2 family of proteins are key regulators of programmed cell death, acting either as apoptotic agonists or antagonists. Here we describe the solution structure of BID, presenting the structure of a proapoptotic BCL2 family member. An analysis of sequence/structure of BCL2 family members allows us to define a structural superfamily, which has implications for general mechanisms for regulating proapoptotic activity. It appears two criteria must be met for proapoptotic function within the BCL2 family: targeting of molecules to intracellular membranes, and exposure of the BH3 death domain. BID's activity is regulated by a Caspase 8-mediated cleavage event, exposing the BH3 domain and significantly changing the surface charge and hydrophobicity, resulting in a change of cellular localization.

The effect of noncollinearity of 15N-1H dipolar and 15N CSA tensors and rotational anisotropy on 15N relaxation, CSA/dipolar cross correlation, and TROSY.

Current approaches to 15N relaxation in proteins assume that the 15N-1H dipolar and 15N CSA tensors are collinear. We show theoretically that, when there is significant anisotropy of molecular rotation, different orientations of the two tensors, experimentally observed in proteins, nucleic acids, and small peptides, will result in differences in site-specific correlation functions and spectral densities. The standard treatments of the rates of longitudinal and transverse relaxation of amide 15N nuclei, of the 15N CSA/15N-1H dipolar cross correlation, and of the TROSY experiment are extended to account for the effect of noncollinearity of the 15N-1H dipolar and 15N CSA (chemical shift anisotropy) tensors. This effect, proportional to the degree of anisotropy of the overall motion, (D parallel/D perpendicular - 1), is sensitive to the relative orientation of the two tensors and to the orientation of the peptide plane with respect to the diffusion coordinate frame. The effect is negligible at small degrees of anisotropy, but is predicted to become significant for D parallel/D perpendicular > or = 1.5, and at high magnetic fields. The effect of noncollinearity of 15N CSA and 15N-1H dipolar interaction is sensitive to both gross (hydrodynamic) properties and atomic-level details of protein structure. Incorporation of this effect into relaxation data analysis is likely to improve both precision and accuracy of the derived characteristics of protein dynamics, especially at high magnetic fields and for molecules with a high degree of anisotropy of the overall motion. The effect will also make TROSY efficiency dependent on local orientation in moderately anisotropic systems.

Chemical ligation of folded recombinant proteins: segmental isotopic labeling of domains for NMR studies.

A convenient in vitro chemical ligation strategy has been developed that allows folded recombinant proteins to be joined together. This strategy permits segmental, selective isotopic labeling of the product. The src homology type 3 and 2 domains (SH3 and SH2) of Abelson protein tyrosine kinase, which constitute the regulatory apparatus of the protein, were individually prepared in reactive forms that can be ligated together under normal protein-folding conditions to form a normal peptide bond at the ligation junction. This strategy was used to prepare NMR sample quantities of the Abelson protein tyrosine kinase-SH(32) domain pair, in which only one of the domains was labeled with 15N. Mass spectrometry and NMR analyses were used to confirm the structure of the ligated protein, which was also shown to have appropriate ligand-binding properties. The ability to prepare recombinant proteins with selectively labeled segments having a single-site mutation, by using a combination of expression of fusion proteins and chemical ligation in vitro, will increase the size limits for protein structural determination in solution with NMR methods. In vitro chemical ligation of expressed protein domains will also provide a combinatorial approach to the synthesis of linked protein domains.