Accumulation of embedded solitons in systems with quadratic nonlinearity.

Previous numerical studies have revealed the existence of embedded solitons (ESs) in a class of multiwave systems with quadratic nonlinearity, families of which seem to emerge from a critical point in the parameter space, where the zero solution has a fourfold zero eigenvalue. In this paper, the existence of such solutions is studied in a three-wave model. An appropriate rescaling casts the system in a normal form, which is universal for models supporting ESs through quadratic nonlinearities. The normal-form system contains a single irreducible parameter epsilon, and is tantamount to the basic model of type-I second-harmonic generation. An analytical approximation of Wentzel-Kramers-Brillouin type yields an asymptotic formula for the distribution of discrete values of epsilon at which the ESs exist. Comparison with numerical results shows that the asymptotic formula yields an exact value of the scaling index, -65, and a fairly good approximation for the numerical factor in front of the scaling term.

Fast 3D motif search of EM density maps using a locally normalized cross-correlation function.

Three-dimensional motif search is becoming increasingly important both in the search for molecular signatures within a tomographic reconstruction, at low resolution, and in the search for atomic structures within high-resolution cryo-EM maps of macromolecular complexes. The present work describes the implementation of a fast local correlation algorithm suitable for template matching in the SPIDER environment. Two examples are given, one in each of the areas of application: (i). within a 7.8A single-particle reconstruction of the Escherichia coli ribosome, four proteins and one RNA structure were located with high accuracy; (ii). within a cryo-tomogram of sarcoplasmic reticulum vesicles, ryanodine receptors were located in positions that agreed with expert knowledge.

Electron tomography of frozen-hydrated isolated triad junctions.

Cryoelectron microscopy and tomography have been applied for the first time to isolated, frozen-hydrated skeletal muscle triad junctions (triads) and terminal cisternae (TC) vesicles derived from sarcoplasmic reticulum. Isolated triads were selected on the basis of their appearance as two spherical TC vesicles attached to opposite sides of a flattened vesicle derived from a transverse tubule (TT). Foot structures (ryanodine receptors) were resolved within the gap between the TC vesicles and TT vesicles, and some residual ordering of the receptors into arrays was apparent. Organized dense layers, apparently containing the calcium-binding protein calsequestrin, were found in the lumen of TC vesicles underlying the foot structures. The lamellar regions did not directly contact the sarcoplasmic reticulum membrane, thereby creating an approximately 5-nm-thick zone that potentially constitutes a subcompartment for achieving locally elevated [Ca(2+) ] in the immediate vicinity of the Ca(2+)-conducting ryanodine receptors. The lumen of the TT vesicles contained globular mass densities of unknown origin, some of which form cross-bridges that may be responsible for the flattened appearance of the transverse tubules when viewed in cross-section. The spatial relationships among the TT membrane, ryanodine receptors, and calsequestrin-containing assemblage are revealed under conditions that do not use dehydration, heavy-metal staining, or chemical fixation, thus exemplifying the potential of cryoelectron microscopy and tomography to reveal structural detail of complex subcellular structures.

Three-dimensional reconstruction of the recombinant type 3 ryanodine receptor and localization of its amino terminus.

Recombinant type 3 ryanodine receptor (RyR3) has been purified in quantities sufficient for structural characterization by cryoelectron microscopy and three-dimensional (3D) reconstruction. Two cDNAs were prepared and expressed in HEK293 cells, one encoding the wild-type RyR3 and the other encoding RyR3 containing glutathione S-transferase (GST) fused to its amino terminus (GST-RyR3). RyR3 was purified from detergent-solubilized transfected cells by affinity chromatography using 12.6-kDa FK506-binding protein in the form of a GST fusion as the affinity ligand. Purification of GST-RyR3 was achieved by affinity chromatography by using glutathione-Sepharose. Purified recombinant RyR3 and GST-RyR3 proteins exhibited high-affinity [(3)H]ryanodine binding that was sensitive to activation by Ca(2+) and caffeine and to inhibition by Mg(2+). 3D reconstructions of both recombinant RyR3 and GST-RyR3 appeared very similar to that of the native RyR3 purified from bovine diaphragm. Comparison of the 3D reconstructions of RyR3 and GST-RyR3 revealed that the GST domains and, hence, the amino termini of the RyR3 subunits are located in the "clamp" structures that form the corners of the square-shaped cytoplasmic region of homotetrameric RyR3. This study describes the 3D reconstruction of a recombinant ryanodine receptor and it demonstrates the potential of this technology for characterizing functional and structural perturbations introduced by site-directed mutagenesis.

Calcium transport across the sarcoplasmic reticulum: structure and function of Ca2+-ATPase and the ryanodine receptor.

Contraction of striated muscle results from a rise in cytoplasmic calcium concentration in a process termed excitation/contraction coupling. Most of this calcium moves back and forth across the sarcoplasmic-reticulum membrane in cycles of contraction and relaxation. The channel responsible for release from the sarcoplasmic reticulum is the ryanodine receptor, whereas Ca2+-ATPase effects reuptake in an ATP-dependent manner. The structures of these two molecules have been studied by cryoelectron microscopy, with helical crystals in the case of Ca2+-ATPase and as isolated tetramers in the case of ryanodine receptor. Structures of Ca2+-ATPase at 8-A resolution reveal the packing of transmembrane helices and have allowed fitting of a putative ATP-binding domain among the cytoplasmic densities. Comparison of ATPases in different conformations gives hints about the conformational changes that accompany the reaction cycle. Structures of ryanodine receptor at 30-A resolution reveal a multitude of isolated domains in the cytoplasmic portion, as well as a distinct transmembrane assembly. Binding sites for various protein ligands have been determined and conformational changes induced by ATP, calcium and ryanodine have been characterized. Both molecules appear to use large conformational changes to couple interactions in their cytoplasmic domains with calcium transport through their membrane domains, and future studies at higher resolution will focus on the mechanisms for this coupling.

Three-dimensional structure of ryanodine receptor isoform three in two conformational states as visualized by cryo-electron microscopy.

Using cryo-electron microscopy and single particle image processing techniques, we present the first three-dimensional reconstructions of isoform 3 of the ryanodine receptor/calcium release channel (RyR3). Reconstructions were carried out on images obtained from a purified, detergent-solubilized receptor for two different buffer conditions, which were expected to favor open and closed functional states of the channel. As for the heart (RyR2) and skeletal muscle (RyR1) receptor isoforms, RyR3 is a homotetrameric complex comprising two main components, a multidomain cytoplasmic assembly and a smaller ( approximately 20% of the total mass) transmembrane region. Although the isoforms show structural similarities, consistent with the approximately 70% overall sequence identity of the isoforms, detailed comparisons of RyR3 with RyR1 showed one region of highly significant difference between them. This difference indicated additional mass present in RyR1, and it likely corresponds to a region of the RyR1 sequence (residues 1303-1406, known as diversity region 2) that is absent from RyR3. The reconstructions of RyR3 determined under "open" and "closed" conditions were similar to each other in overall architecture. A difference map computed between the two reconstructions reveals subtle changes in conformation at several widely dispersed locations in the receptor, the most prominent of which is a approximately 4 degrees rotation of the transmembrane region with respect to the cytoplasmic assembly.

Amino acid residues 4425-4621 localized on the three-dimensional structure of the skeletal muscle ryanodine receptor.

We have localized a region contained within the sequence of amino acid residues 4425-4621 on the three-dimensional structure of the skeletal muscle ryanodine receptor (RyR). Mouse monoclonal antibodies raised against a peptide comprising these residues have been complexed with ryanodine receptors and imaged in the frozen-hydrated state by cryoelectron microscopy. These images, along with images of antibody-free ryanodine receptor, were used to compute two-dimensional averaged images and three-dimensional reconstructions. Two-dimensional averages of immunocomplexes in which the ryanodine receptor was in the fourfold symmetrical orientation disclosed four symmetrical regions of density located on the edges of the receptor's cytoplasmic assembly that were absent from control averages of receptor without added antibody. Three-dimensional reconstructions revealed the antibody-binding sites to be on the so-called handle domains of the ryanodine receptor's cytoplasmic assembly, near their junction with the transmembrane assembly. This study is the first to demonstrate epitope mapping on the three-dimensional structure of the ryanodine receptor.

Three-dimensional location of the imperatoxin A binding site on the ryanodine receptor.

Cryo-electron microscopy and three-dimensional, single-particle image analysis have been used to reveal the specific binding site of imperatoxin A (IpTx(a)) on the architecture of the calcium release channel/ryanodine receptor from skeletal muscle (RyR1). IpTx(a) is a peptide toxin that binds with high affinity to RyR1 and affects its functioning. The toxin was derivatized with biotin to enhance its detection with streptavidin. IpTx(a) binds to the cytoplasmic moiety of RyR1 between the clamp and handle domains, 11 nm away from the transmembrane pore. The proposed mimicry by IpTx(a) of the dihydropyridine receptor (DHPR) II-III loop, thought to be a main physiological excitation-contraction trigger, suggests that the IpTx(a) binding location is a potential excitation-contraction signal transduction site.

Cryoelectron microscopy and image analysis of the cardiac ryanodine receptor.

The three-dimensional structure of the cardiac muscle ryanodine receptor (RyR2) is described and compared with its skeletal muscle isoform (RyR1). Previously, structural studies of RyR2 have not been as informative as those for RyR1 because optimal conditions for electron microscopy, which require low levels of phospholipid, are destabilizing for RyR2. A simple procedure was devised for diluting RyR2 (in phospholipid-containing buffer) into a lipid-free buffer directly on the electron microscope grid, followed by freezing within a few seconds. Cryoelectron microscopy of RyR2 so prepared yielded images of sufficient quality for analysis by single particle image processing. Averaged projection images for RyR2, as well as for RyR1, prepared under the same conditions, were found to be nearly identical in overall dimensions and appearance at the resolution attained, approximately 30 A. An initial three-dimensional reconstruction of RyR2 was determined (resolution approximately 41 A) and compared with previously reported reconstructions of RyR1. Although they looked similar, which is consistent with the similarity found for the projection images, and with expectations based on the 66% amino acid sequence identity of the two isoforms, structural differences near the corners of the cytoplasmic assembly were observed in both two- and three-dimensional studies.

Purification and characterization of ryanodine receptor 3 from mammalian tissue.

The ryanodine receptors are intracellular Ca2+ release channels that play a key role in cell signaling via Ca2+. There are three isoforms. Isoform 1 from skeletal muscle and isoform 2 from heart have been characterized. Isoform 3 is widely distributed in many mammalian tissues although in minuscule amounts. Its low abundance has hampered its study. We now describe methodology to isolate mammalian isoform 3 in amounts sufficient for biochemical and biophysical characterization. Bovine diaphragm sarcoplasmic reticulum fractions enriched in terminal cisternae containing both isoforms 1 (>95%) and 3 (<5% of the ryanodine binding) served as starting source. Isoform 3 was selectively immunoprecipitated from the 3-[(3-cholamidopropyl)-dimethylammonio]-1-propanesulfonic acid (CHAPS)-solubilized fraction and eluted with peptide epitope. Isoform 3 thus prepared is highly purified as characterized by SDS-polyacryamide gel electrophoresis, Coomassie Blue staining, and by high affinity ryanodine binding. The purified isoform 3 was incorporated into planar lipid bilayers, and its channel properties were studied. Channel characteristics in common with the other two isoforms are slope conductance, higher selectivity to Ca2+ versus K+ (PCa/K approximately 6), and response to drugs and ligands. In its response to Ca2+ and ATP, it more closely resembles isoform 2. The first two-dimensional structure of isoform 3 was obtained by cryoelectron microscopy and image enhancement techniques.

Contributions of electron microscopy and single-particle techniques to the determination of the ryanodine receptor three-dimensional structure.

The ryanodine receptor is the main intracellular calcium release channel from the sarcoplasmic reticulum in striated muscle. It is the largest ion channel known, composed of four identical major subunits of 565 kDa and four smaller 12-kDa subunits, identified as FK-506 binding protein. The successful isolation of the ryanodine receptor together with the development of cryoelectron microscopy and single-particle image processing techniques have enabled major progress to be made in the determination of the receptor's structure over the past decade. Three-dimensional reconstruction shows the receptor to be composed of two main parts, a large square shaped cytoplasmic assembly and a smaller transmembrane assembly. The cytoplasmic assembly has an unusual architecture in which about 10 domain-like structures are interconnected in a loosely packed manner. Subsequent studies have started to reveal conformational changes associated with channel gating and the localization of binding sites for some proteins with which the receptor interacts (calmodulin, and FK-506 binding protein). It is becoming clear that long-range induced conformational changes must be involved in the mechanisms of modulation of the receptor's gating properties.

Ryanodine receptors: structure and macromolecular interactions.

Ryanodine receptors (RyRs), a class of intracellular calcium release channels, are the largest ion channels known. Recently, cryoelectron microscopy and image reconstructions of isolated receptors have shown that most of the protein mass forms a porous, multidomain cytoplasmic assembly. Evidence is mounting that suggests that the cytoplasmic assembly communicates with the transmembrane regions over distances of 100 or greater. RyRs are centrally important in excitation-contraction coupling, which occurs at specialized regions where the sarcoplasmic reticulum, containing the RyRs, and the plasma membrane/transverse-tubule system form junctions. Numerous proteins are present at these junctions, some of which interact directly with the RyR.

Assembly and full functionality of recombinantly expressed dihydrolipoyl acetyltransferase component of the human pyruvate dehydrogenase complex.

The dihydrolipoyl acetyltransferase (E2) component of mammalian pyruvate dehydrogenase complex (PDC) consists of 60 COOH-terminal domains as an inner assemblage and sequentially via linker regions an exterior pyruvate dehydrogenase (E1) binding domain and two lipoyl domains. Mature human E2, expressed in a protease-deficient Escherichia coli strain at 27 degrees , was prepared in a highly purified form. Purified E2 had a high acetyltransferase activity, was well lipoylated based on its acetylation, and bound a large complement of bovine E1. Electron micrographs demonstrated that the inner core was assembled in the expected pentagonal dodecahedron shape with E1 binding around the inner core periphery. With saturating E1 and excess dihydrolipoyl dehydrogenase (E3) but no E3-binding protein (E3BP), the recombinant E2 supported the overall PDC reaction at 4% of the rate of bovine E2.E3BP subcomplex. The lipoates of assembled human E2 or its free bilipoyl domain region were reduced by E3 at rates proportional to the lipoyl domain concentration, but those of the E2.E3BP were rapidly used in a concentration-independent manner consistent with bound E3 rapidly using a set of lipoyl domains localized nearby. Given this restriction and the need for E3BP for high PDC activity, directed channeling of reducing equivalents to bound E3 must be very efficient in the complex. The recombinant E2 oligomer increased E1 kinase activity by up to 4-fold and, in a Ca2+-dependent process, increased phospho-E1 phosphatase activity more than 15-fold. Thus the E2 assemblage fully provides the molecular intervention whereby a single E2-bound kinase or phosphatase molecule rapidly phosphorylate or dephosphorylate, respectively, many E2-bound E1. Thus, we prepared properly assembled, fully functional human E2 that mediated enhanced regulatory enzyme activities but, lacking E3BP, supported low PDC activity.

Locations of calmodulin and FK506-binding protein on the three-dimensional architecture of the skeletal muscle ryanodine receptor.

Isolated skeletal muscle ryanodine receptors (RyRs) complexed with the modulatory ligands, calmodulin (CaM) or 12-kDa FK506-binding protein (FKBP12), have been characterized by electron cryomicroscopy and three-dimensional reconstruction. RyRs are composed of 4 large subunits (molecular mass 565 kDa) that assemble to form a 4-fold symmetric complex that, architecturally, comprises two major substructures, a large ( approximately 80% of the total mass) cytoplasmic assembly and a smaller transmembrane assembly. Both CaM and FKBP12 bind to the cytoplasmic assembly at sites that are 10 and 12 nm, respectively, from the putative entrance to the transmembrane ion channel. FKBP12 binds along the edge of the square-shaped cytoplasmic assembly near the face that interacts in vivo with the sarcolemma/transverse tubule membrane system, whereas CaM binds within a cleft that faces the junctional face of the sarcoplasmic reticulum membrane at the triad junction. Both ligands interact with a domain that connects directly to a cytoplasmic extension of the transmembrane assembly of the receptor, and thus might cause structural changes in the domain which in turn modulate channel gating.

Cryoelectron microscopy resolves FK506-binding protein sites on the skeletal muscle ryanodine receptor.

A 12-kDa immunophilin (FKBP12) is an integral component of the skeletal muscle ryanodine receptor (RyR). The RyR is a hetero-oligomeric complex with structural formula (FKBP)4(Ryr1)4, where Ryr1 is the 565-kDa product of the Ryr1 gene. To aid in the detection of the immunophilin's location in the receptor, we exchanged the FKBP12 present in RyR-enriched vesicles derived from sarcoplasmic reticulum with an engineered construct of FKBP12 fused to glutathione S-transferase and then isolated the complexes. Cryoelectron microscopy and image averaging of the complexes (in an orientation displaying the RyR's fourfold symmetry) revealed four symmetrically distributed, diffuse density regions that were located just outside the boundary defining the cytoplasmic assembly of the RyR. These regions are attributed to the glutathione transferase portion of the fusion protein because they are absent from receptors lacking the fusion protein. To more precisely define the location of FKBP12, we similarly analyzed complexes of RyR containing FKBP12 itself. Apparently some FKBP is lost during the purification or storage of the RyR because, to detect the receptor-bound immunophilin, it was necessary to add FKBP12 to the purified receptor before electron microscopy. Averaged images of these complexes showed a region of density that had not been observed previously in images of isolated receptors, and its position, along the edges of the transmembrane assembly, agreed with the position of the FKBP12 deduced from the experiments with the fusion protein. The proposed locations for FKBP12 are about 10 nm from the transmembrane baseplate assembly that contains the ion channel of the RyR.

Three-dimensional architecture of the skeletal muscle ryanodine receptor.

Recent advances in determining the three-dimensional architecture of the skeletal muscle ryanodine receptor/calcium release channel (RyR) by cryo-electron microscopy and three-dimensional reconstruction are discussed. The tetrameric receptor is characterized by a large 4-fold symmetric cytoplasmic assembly that consists of many domains separated by solvent-containing crevices and holes. Experimental evidence suggests that at least one regulatory ligand, calmodulin, binds to sites on the cytoplasmic assembly that are at least 10 nanometers from the transmembrane channel.

Localization of calmodulin binding sites on the ryanodine receptor from skeletal muscle by electron microscopy.

Calmodulin (CaM) is a regulator of the calcium release channel (ryanodine receptor) of the sarcoplasmic reticulum of skeletal and cardiac muscle. The locations where CaM binds on the surface of the skeletal muscle ryanodine receptor were determined by electron microscopy. Wheat germ CaM was labeled specifically at Cys-27 with a maleimide derivative of a 1.4-nm-diameter gold cluster, and the gold-cluster-labeled CaM was bound to the purified ryanodine receptor. The complexes were imaged in the frozen-hydrated state by cryoelectron microscopy with no stains or fixatives present. In the micrographs, gold clusters were frequently observed near the corners of the square-shaped images of the ryanodine receptors. In some images, all four corners of the receptor were occupied by gold clusters. Image averaging allowed the site of CaM binding to be determined in two dimensions with an estimated precision of 4 nm. No changes were apparent in the quaternary structure of the ryanodine receptor upon binding CaM to the resolution attained, about 3 nm. Side views of the ryanodine receptor, in which the receptor is oriented approximately perpendicular to the much more frequent fourfold symmetric views, were occasionally observed, and showed that the CaM binding site is most likely on the surface of the receptor that faces the cytoplasm. We conclude that the CaM binding site is at least 10 nm from the transmembrane channel of the receptor and, consequently, that long-range conformational changes are involved in the modulation of the calcium channel activity of the receptor by CaM.

Cryo-electron microscopy and three-dimensional reconstruction of the calcium release channel/ryanodine receptor from skeletal muscle.

The calcium release channel (CRC) from skeletal muscle is an unusually large tetrameric ion channel of the sarcoplasmic reticulum, and it is a major component of the triad junction, the site of excitation contraction coupling. The three-dimensional architecture of the CRC was determined from a random conical tilt series of images extracted from electron micrographs of isolated detergent-solubilized channels prepared in a frozen-hydrated state. Three major classes of fourfold symmetric images were identified, and three-dimensional reconstructions were determined for two of these. The two independent reconstructions were almost identical, being related to each other by a 180 degrees rotation about an axis in the plane of the specimen grid. The CRC consists of a large cytoplasmic assembly (29 x 29 x 12 nm) and a smaller transmembrane assembly that protrudes 7 nm from one of its faces. A cylindrical low-density region, 2-3 nm in apparent diameter, extends down the center of the transmembrane assembly, and possibly corresponds to the transmembrane Ca(2+)-conducting pathway. At its cytoplasmic end this channel-like feature appears to be plugged by a globular mass of density. The cytoplasmic assembly is apparently constructed from 10 or more domains that are loosely packed together such that greater than 50% of the volume enveloped by the assembly is occupied by solvent. The cytoplasmic assembly is suggestive of a scaffolding and seems well adapted to maintain the structural integrity of the triad junction while allowing ions to freely diffuse to and away from the transmembrane assembly.

Three-dimensional structures of the human alpha 2-macroglobulin-methylamine and chymotrypsin complexes.

The three-dimensional structures of chymotrypsin- and methylamine-treated negatively stained human alpha 2-macroglobulin have been determined by weighted back projection from electron microscope data. Projections of the reconstructions show good concordance with two-dimensional averages of both stained and frozen-hydrated molecules. The reconstructions reveal that the H-shaped front projection of the molecule is related to the smaller ellipsoidal end view by a rotation of 90 degrees about the crossbar (minor axis) of the H. This finding is in agreement with tilt studies. The reconstruction of the alpha 2-macroglobulin-methylamine reveals an hour-glass shaped void which is filled by the two proteinase molecules in the reconstruction of alpha 2-macroglobulin-chymotrypsin. Protein plugs which appear to block the exterior entrances to the cavity may function to prevent access of proteins to the encapsulated proteinase and serve to block its escape. Extensive thresholding of each reconstruction leaves a "backbone" consisting of two side-by-side rod-like structures, suggesting that this is the arrangement of the two protomeric units which form the molecule. Both structures show some departure from the expected symmetry. The asymmetries are robust features of the reconstructions and may reflect structurally asymmetric features of the transformation from the native to the chymotrypsin-treated form of the molecule.

Configuration of interdomain linkers in pyruvate dehydrogenase complex of Escherichia coli as determined by cryoelectron microscopy.

The dihydrolipoyl transacetylase (E2p) component of the pyruvate dehydrogenase complex (PDC) of Escherichia coli is a multidomain polypeptide comprising a catalytic domain, a domain that binds dihydrolipoyl dehydrogenase (E3-binding domain), and three domains containing lipoic acid (lipoyl domains). In PDC 24 subunits of E2p associate by means of interactions involving the catalytic domains to form the structural core of PDC. From cryoelectron microscopy and computer image analysis of frozen-hydrated isolated E2p cores it appears that the lipoyl domains are located peripherally about the core complex and do not assume fixed positions. To further test this interpretation the visibility of the lipoyl domains in electron micrographs was enhanced by specifically biotinylating the lipoic acids and labeling them with streptavidin. In agreement with the studies of native, unlabeled E2p cores, cryoelectron microscopy of the streptavidin-labeled E2p cores showed that the lipoic acid moieties are capable of extending approximately 13 nm from the surface of the core. Localization of the E3-binding domains was accomplished by cryoelectron microscopy of E2p-E3 subcomplexes prepared by reconstitution in vitro. Frequently an apparent gap of several nanometers separated the bound E3 from the surface of the core. The third component of PDC, pyruvate dehydrogenase (E1p), appeared to bind to the E2p core in a manner similar to that observed for E3. These results support a structural model of the E2p core in which the catalytic, E3-binding, and three lipoyl domains are interconnected by linker sequences that assume extended and flexible conformations.