How the Sequence of a Gene Specifies Structural Symmetry in Proteins

Internal symmetry is commonly observed in the majority of fundamental protein folds. Meanwhile, sufficient evidence suggests that nascent polypeptide chains of proteins have the potential to start the co-translational folding process and this process allows mRNA to contain additional information on protein structure. In this paper, we study the relationship between gene sequences and protein structures from the viewpoint of symmetry to explore how gene sequences code for structural symmetry in proteins. We found that, for a set of two-fold symmetric proteins from left-handed beta-helix fold, intragenic symmetry always exists in their corresponding gene sequences. Meanwhile, codon usage bias and local mRNA structure might be involved in modulating translation speed for the formation of structural symmetry: a major decrease of local codon usage bias in the middle of the codon sequence can be identified as a common feature; and major or consecutive decreases in local mRNA folding energy near the boundaries of the symmetric substructures can also be observed. The results suggest that gene duplication and fusion may be an evolutionarily conserved process for this protein fold. In addition, the usage of rare codons and the formation of higher order of secondary structure near the boundaries of symmetric substructures might have coevolved as conserved mechanisms to slow down translation elongation and to facilitate effective folding of symmetric substructures. These findings provide valuable insights into our understanding of the mechanisms of translation and its evolution, as well as the design of proteins via symmetric modules.     

A calculation strategy for the structure determination of symmetric demers by 1H NMR

The structure determination of symmetric dimers by NMR is impeded by the ambiguity of inter- and intramonomer NOE crosspeaks. In this paper, a calculation strategy is presented that allows the calculation of dimer structures without resolving ther ambuguity by additional experiments (like asymmetric labeling). The strategy employs a molecular dynamic-based simulated annealing approach to minimize a traget function. The experimental part of the target function contains distance restraints that correctly describe the ambiguity of the NOE peaks, and a novel term that restrains the symmetry of the dimer without requiring the knowledge of the symmetry axis. The use of the method is illustrated by three examples, using experimentally obtained data and model data derived from a known structure. For the purpose of testing the method, it is assumed that every NOE crosspeak is ambiguous in all three cases. It is shown that the structure of a homologous protein is known and in ab intio structure determination. The method can be extended to higher order symmetric multimers. © 1993 Wiley-Liss, Inc.     

New Approach of Plasmonically Induced Reflectance in a Planar Metamaterial for Plasmonic Sensing Applications

We theoretically demonstrate and investigate plasmonically induced reflectance (PIR) in a new planar metamaterial with two completely different approaches. Here, we not only show that broken symmetry is a general strategy to create electromagnetically induced reflectance (EIR)-like effect but also demonstrate that the nanoplasmonic EIR can be realized even without broken symmetry via the excitation of the higher-order plasmonic modes in the same designed planar metamaterial. In nanophotonics, plasmonic structures enable large field strengths within small mode volumes. Therefore, combining EIR with nanoplasmonics would open up the way toward ultracompact sensors with extremely high sensitivity. In the second approach of creating the PIR of our proposed nanostructure, the restrictions on size are partially relaxed, making fabrication much easier. Their interactions and coupling between plasmonic modes are investigated in detail by analyzing field distributions and spectral responses. Also, we show that the PIR frequency position depended very sensitively on the dielectric surrounding. Furthermore, the narrow and fully modulated PIR features due to the extraordinary reduction of damping may serve for designing novel devices in the field of chemical and biomedical sensing.

     

Calculation of symmetric multimer structures from NMR data using a priori knowledge of the monomer structure, co-monomer restraints, and interface mapping: The case of leucine zippers

Summary NMR studies of symmetric multimers are problematic due to the difficulty in distinguishing between intra-, inter-, and co-monomer (mixed) NOE signals. Previously, one of us described a general calculation strategy called dynamic assignment by which this difficulty can be overcome [Nilges, M. (1993) Proteins, 17, 297–309]. Here we describe extensions to the method for handling many co-monomer NOEs and for taking advantege of prior knowledge of monomer structures. The new protocol was developed for the particularly difficult case of leucine zipper (LZ) homodimers, for which the previous protocol proved inefficient. In addition to the problem of dimer symmetry, LZs have a particularly high proportion of co-monomer NOE signals and a high degree of repetition in sequence and structure, leading to significant spectral overlap. Furthermore, the leucine zipper is a rather extended (as opposed to globular) protein domain; accurately determining such a structure based only on the very short distances obtainable by NMR is clearly a challenge to the NMR structure determination method. We have previously shown that, for LZ homodimers, many of the backbone-backbone NOESY cross peaks can be unambiguously assigned as intra-monomer, enabling approximate monomer structures to be calculated. Using model and experimental data sets, we verified that the new protocol converges to the correct dimer structure. The results show that short-range NMR distance data can be sufficient to define accurately the extended LZ. The protocol has been used to derive a novel solution structure of the c-Jun LZ domain. Based on these calculations, we propose the protocol as a prototype for the general case of symmetric multimers where the monomer structure is known.Abbreviations 3D three-dimensional - GCN4-c crystal structure of the GCN4 LZ homodimer - GCN4-s solution structures of GCN4 - GSYM global symmetry - Jun-m model structure of the Jun LZ homodimer - Jun-s solution structure of Jun - LZ leucine zipper - MFP mean force potential - MDSA molecular dynamical simulated annealing - NCS noncrystallographic symmetry - NOE nuclear Overhauser enhancement - rmsd root-mean-square deviation - vdW van der Waals     

The portal protein of bacteriophage SPP1: a DNA pump with 13-fold symmetry.

Electron microscopy in combination with image processing is a powerful method for obtaining structural information on non-crystallized biological macromolecules at the 10-50 A resolution level. The processing of noisy microscopical images requires advanced data processing methodologies in which one must carefully avoid the introduction of any form of bias into the data set. Using a novel multivariate statistical approach to the analysis of symmetry, we studied the structure of the bacteriophage SPP1 portal protein oligomer. This portal structure, ubiquitous in icosahedral bacteriophages which package dsDNA, is located at the site of symmetry mismatch between a 5-fold vertex of the icosahedral shell and the 6-fold symmetric (helical) tail. From previous studies such 'head-to-tail connector' structures were generally accepted to be homododecamers assembled in a 12-fold symmetric ring around a central channel. Using a new analysis methodology we have found that the phage SPP1 portal structure exhibits 13-fold cyclical symmetry: a new point group organization for oligomeric proteins. A model for the DNA packaging mechanism by 13-fold symmetric portal protein assemblies is presented which attributes a coherent functional meaning to their unusual symmetry.     

Structure determination of symmetric homo-oligomers by a complete search of symmetry configuration space, using NMR restraints and van der Waals packing

Structural studies of symmetric homo-oligomers provide mechanistic insights into their roles in essential biological processes, including cell signaling and cellular regulation. This paper presents a novel algorithm for homo-oligomeric structure determination, given the subunit structure, that is both complete, in that it evaluates all possible conformations, and data-driven, in that it evaluates conformations separately for consistency with experimental data and for quality of packing. Completeness ensures that the algorithm does not miss the native conformation, and being data-driven enables it to assess the structural precision possible from data alone. Our algorithm performs a branch-and-bound search in the symmetry configuration space, the space of symmetry axis parameters (positions and orientations) defining all possible C(n) homo-oligomeric complexes for a given subunit structure. It eliminates those symmetry axes inconsistent with intersubunit nuclear Overhauser effect (NOE) distance restraints and then identifies conformations representing any consistent, well-packed structure to within a user-defined similarity level. For the human phospholamban pentamer in dodecylphosphocholine micelles, using the structure of one subunit determined from a subset of the experimental NMR data, our algorithm identifies a diverse set of complex structures consistent with the nine intersubunit NOE restraints. The distribution of determined structures provides an objective characterization of structural uncertainty: backbone RMSD to the previously determined structure ranges from 1.07 to 8.85 A, and variance in backbone atomic coordinates is an average of 12.32 A(2). Incorporating vdW packing reduces structural diversity to a maximum backbone RMSD of 6.24 A and an average backbone variance of 6.80 A(2). By comparing data consistency and packing quality under different assumptions of oligomeric number, our algorithm identifies the pentamer as the most likely oligomeric state of phospholamban, demonstrating that it is possible to determine the oligomeric number directly from NMR data. Additional tests on a number of homo-oligomers, from dimer to heptamer, similarly demonstrate the power of our method to provide unbiased determination and evaluation of homo-oligomeric complex structures.     

Beyond bilateral symmetry: geometric morphometric methods for any type of symmetry

Background

Studies of symmetric structures have made important contributions to evolutionary biology, for example, by using fluctuating asymmetry as a measure of developmental instability or for investigating the mechanisms of morphological integration. Most analyses of symmetry and asymmetry have focused on organisms or parts with bilateral symmetry. This is not the only type of symmetry in biological shapes, however, because a multitude of other types of symmetry exists in plants and animals. For instance, some organisms have two axes of reflection symmetry (biradial symmetry; e.g. many algae, corals and flowers) or rotational symmetry (e.g. sea urchins and many flowers). So far, there is no general method for the shape analysis of these types of symmetry.

Results

We generalize the morphometric methods currently used for the shape analysis of bilaterally symmetric objects so that they can be used for analyzing any type of symmetry. Our framework uses a mathematical definition of symmetry based on the theory of symmetry groups. This approach can be used to divide shape variation into a component of symmetric variation among individuals and one or more components of asymmetry. We illustrate this approach with data from a colonial coral that has ambiguous symmetry and thus can be analyzed in multiple ways. Our results demonstrate that asymmetric variation predominates in this dataset and that its amount depends on the type of symmetry considered in the analysis.

Conclusions

The framework for analyzing symmetry and asymmetry is suitable for studying structures with any type of symmetry in two or three dimensions. Studies of complex symmetries are promising for many contexts in evolutionary biology, such as fluctuating asymmetry, because these structures can potentially provide more information than structures with bilateral symmetry.     

Common occurrence of internal repeat symmetry in membrane proteins

Symmetry plays significant roles in protein structure and function. Particularly, symmetric interfaces are known to act as switches for two-state conformational change. Membrane proteins often undergo two-state conformational change during the transport process of ion channels or the active/inactive transitions in receptors. Here, we provide the first comprehensive analyses of internal repeat symmetry in membrane proteins. We examined the known membrane protein structures and found that, remarkably, nearly half of them have internal repeat symmetry. Moreover, we found that the conserved cores of these internal repeats are positioned at the interface of symmetric units when they are mapped on structures. Because of the large sequence divergence that occurs between internal repeats, the inherent symmetry present in protein sequences often has only been detected after structure determination. We therefore developed a sensitive procedure to predict the internal repeat symmetry from sequence information and identified 4653 proteins that are likely to have internal repeat symmetry.     

Opening and closing of a toroidal group II chaperonin revealed by a symmetry constrained elastic network model

Recently, the atomic structures of both the closed and open forms of Group 2 chaperonin protein Mm‐cpn were revealed through crystallography and cryo‐electron microscopy. This toroidal‐like chaperonin is composed of two eightfold rings that face back‐to‐back. To gain a computational advantage, we used a symmetry constrained elastic network model (SCENM), which requires only a repeated subunit structure and its symmetric connectivity to neighboring subunits to simulate the entire system. In the case of chaperonin, only six subunits (i.e., three from each ring) were used out of the eight subunits comprising each ring. A smooth and symmetric pathway between the open and closed conformations was generated by elastic network interpolation (ENI). To support this result, we also performed a symmetry‐constrained normal mode analysis (NMA), which revealed the intrinsic vibration features of the given structures. The NMA and ENI results for the representative single subunit were duplicated according to the symmetry pattern to reconstruct the entire assembly. To test the feasibility of the symmetry model, its results were also compared with those obtained from the full model. This study allowed the folding mechanism of chaperonin Mm‐cpn to be elucidated by SCENM in a timely manner.     

Extent of structural asymmetry in homodimeric proteins: prevalence and relevance

Most homodimeric proteins have symmetric structure. Although symmetry is known to confer structural and functional advantage, asymmetric organization is also observed. Using a non-redundant dataset of 223 high-resolution crystal structures of biologically relevant homodimers, we address questions on the prevalence and significance of asymmetry. We used two measures to quantify global and interface asymmetry, and assess the correlation of several molecular and structural parameters with asymmetry. We have identified rare cases (11/223) of biologically relevant homodimers with pronounced global asymmetry. Asymmetry serves as a means to bring about 2:1 binding between the homodimer and another molecule; it also enables cellular signalling arising from asymmetric macromolecular ligands such as DNA. Analysis of these cases reveals two possible mechanisms by which possible infinite array formation is prevented. In case of homodimers associating via non-topologically equivalent surfaces in their tertiary structures, ligand-dependent mechanisms are used. For stable dimers binding via large surfaces, ligand-dependent structural change regulates polymerisation/depolymerisation; for unstable dimers binding via smaller surfaces that are not evolutionarily well conserved, dimerisation occurs only in the presence of the ligand. In case of homodimers associating via interaction surfaces with parts of the surfaces topologically equivalent in the tertiary structures, steric hindrance serves as the preventive mechanism of infinite array. We also find that homodimers exhibiting grossly symmetric organization rarely exhibit either perfect local symmetry or high local asymmetry. Binding of small ligands at the interface does not cause any significant variation in interface asymmetry. However, identification of biologically relevant interface asymmetry in grossly symmetric homodimers is confounded by the presence of similar small magnitude changes caused due to artefacts of crystallisation. Our study provides new insights regarding accommodation of asymmetry in homodimers.     

Probabilistic approach to the design of symmetric protein quaternary structures

Probabilistic methods have been developed that estimate the site-specific probabilities of the amino acids in sequences likely to fold to a particular target structure, and such information can be used to guide the de novo design of proteins and to probe sequence variability. An extension of these methods for the design of symmetric homo-oligomeric quaternary structures is presented. The theory is in excellent agreement with the results of studies on exactly solvable lattice models. Application to an atomically detailed representation of proteins verifies the utility of a symmetry assumption, which greatly simplifies and accelerates the calculations. The method may be applied to a wide variety of symmetric and periodic protein structures.     

A graphical method for analyzing distance restraints using residual dipolar couplings for structure determination of symmetric protein homo-oligomers

High-resolution structure determination of homo-oligomeric protein complexes remains a daunting task for NMR spectroscopists. Although isotope-filtered experiments allow separation of intermolecular NOEs from intramolecular NOEs and determination of the structure of each subunit within the oligomeric state, degenerate chemical shifts of equivalent nuclei from different subunits make it difficult to assign intermolecular NOEs to nuclei from specific pairs of subunits with certainty, hindering structural analysis of the oligomeric state. Here, we introduce a graphical method, DISCO, for the analysis of intermolecular distance restraints and structure determination of symmetric homo-oligomers using residual dipolar couplings. Based on knowledge that the symmetry axis of an oligomeric complex must be parallel to an eigenvector of the alignment tensor of residual dipolar couplings, we can represent distance restraints as annuli in a plane encoding the parameters of the symmetry axis. Oligomeric protein structures with the best restraint satisfaction correspond to regions of this plane with the greatest number of overlapping annuli. This graphical analysis yields a technique to characterize the complete set of oligomeric structures satisfying the distance restraints and to quantitatively evaluate the contribution of each distance restraint. We demonstrate our method for the trimeric E. coli diacylglycerol kinase, addressing the challenges in obtaining subunit assignments for distance restraints. We also demonstrate our method on a dimeric mutant of the immunoglobulin-binding domain B1 of streptococcal protein G to show the resilience of our method to ambiguous atom assignments. In both studies, DISCO computed oligomer structures with high accuracy despite using ambiguously assigned distance restraints.     

The PIR domain of Grb14 is an intrinsically unstructured protein: implication in insulin signaling

Grb14 belongs to the Grb7 family of adapter proteins and was identified as a negative regulator of insulin signal transduction. Its inhibitory effect on the insulin receptor kinase activity is controlled by a newly discovered domain called PIR. To investigate the biochemical and biophysical characteristics of this new domain, we cloned and purified recombinant PIR-SH2, PIR, and SH2 domains. The isolated PIR and PIR-SH2 domains were physiologically active and inhibited insulin-induced reinitiation of meiosis in the Xenopus oocytes system. However, NMR experiments on (15)N-labelled PIR revealed that it did not present secondary structure. These results suggest that the PIR domain belongs to the growing family of intrinsically unstructured proteins.     

Bundles of amphipathic transmembrane alpha-helices as a structural motif for ion-conducting channel proteins: studies on sodium channels and acetylcholine receptors

Channel proteins are transmembrane symmetric (or pseudosymmetric) oligomers organized around a central ionic pore. We present here a molecular model of the pore forming structures of two channel proteins with different primary structures and oligomeric size: the voltage-sensitive sodium channel and the nicotinic cholinergic receptor. We report low-energy arrangements of alpha-helical bundles calculated by semiempiricial potential energy functions and optimization routines and further refined using molecular dynamics. The ion-conducting pore is considered to be a symmetric or pseudosymmetric homooligomer of 3-5 amphipathic alpha-helices arranged such that the polar residues line a central hydrophilic pathway and the apolar residues face the hydrophobic bilayer interior. The channel lining exposes either charged (Asp, Glu, Arg, Lys) or polar-neutral (Ser, Thr) residues. A bundle of four parallel helices constrained to C4 symmetry, the helix axis aligned with the symmetry axis, and the helices constrained to idealized dihedral angles, produces a structure with a pore of the size inferred for the sodium channel protein (area approximately 16 A2). Similarly, a pentameric array optimized with constraints to maintain C5 symmetry and backbone torsions characteristic of alpha-helices adopts a structure that appears well suited to form the lining of the nicotinic cholinergic receptor (pore area approximately 46 A2). Thus, bundles of amphipathic alpha-helices satisfy the structural, energetic, and dynamic requirements to be the molecular structural motif underlying the function of ionic channels.     

A geometric arrangement algorithm for structure determination of symmetric protein homo-oligomers from NOEs and RDCs

Nuclear magnetic resonance (NMR) spectroscopy is a primary tool to perform structural studies of proteins in physiologically-relevant solution conditions. Restraints on distances between pairs of nuclei in the protein, derived from the nuclear Overhauser effect (NOE), provide information about the structure of the protein in its folded state. NMR studies of symmetric protein homo-oligomers present a unique challenge. Using X-filtered NOESY experiments, it is possible to determine whether an NOE restrains a pair of protons across different subunits or within a single subunit, but current experimental techniques are unable to determine in which subunits the restrained protons lie. Consequently, it is difficult to assign NOEs to particular pairs of subunits with certainty, thus hindering the structural analysis of the oligomeric state. Computational approaches are needed to address this subunit ambiguity, but traditional solutions often rely on stochastic search coupled with simulated annealing and simulations of simplified molecular dynamics, which have many tunable parameters that must be chosen carefully and can also fail to report structures consistent with the experimental restraints. In addition, these traditional approaches rarely provide guarantees on running time or solution quality. We reduce the structure determination of homo-oligomers with cyclic symmetry to computing geometric arrangements of unions of annuli in a plane. Our algorithm, disco, runs in expected O(n2) time, where n is the number of distance restraints, potentially assigned ambiguously. disco is guaranteed to report the exact set of oligomer structures consistent with the distance restraints and also with orientational restraints from residual dipolar couplings (RDCs). We demonstrate our method using two symmetric protein complexes: the trimeric E. coli diacylglycerol kinase (DAGK) and a dimeric mutant of the immunoglobulin-binding domain B1 of streptococcal protein G (GB1). In both cases, disco computes oligomer structures with high precision and also finds distance restraints that are either mutually inconsistent or inconsistent with the RDCs. The entire protocol DISCO has been completely automated in a software package that is freely available and open-source at www.cs.duke.edu/donaldlab/software.php.     

Structure and stability effects of mutations designed to increase the primary sequence symmetry within the core region of a β-trefoil

Human acidic fibroblast growth factor (FGF-1) is a member of the beta-trefoil hyperfamily and exhibits a characteristic threefold symmetry of the tertiary structure. However, evidence of this symmetry is not readily apparent at the level of the primary sequence. This suggests that while selective pressures may exist to retain (or converge upon) a symmetric tertiary structure, other selective pressures have resulted in divergence of the primary sequence during evolution. Using intra-chain and homologue sequence comparisons for 19 members of this family of proteins, we have designed mutants of FGF-1 that constrain a subset of core-packing residues to threefold symmetry at the level of the primary sequence. The consequences of these mutations regarding structure and stability were evaluated using a combination of X-ray crystallography and differential scanning calorimetry. The mutational effects on structure and stability can be rationalized through the characterization of "microcavities" within the core detected using a 1.0A probe radius. The results show that the symmetric constraint within the primary sequence is compatible with a well-packed core and near wild-type stability. However, despite the general maintenance of overall thermal stability, a noticeable increase in non-two-state denaturation follows the increase in primary sequence symmetry. Therefore, properties of folding, rather than stability, may contribute to the selective pressure for asymmetric primary core sequences within symmetric protein architectures.     

Production and characterization of two hemolysins of Bacillus cereus.

Bacillus cereus strain B-48 produced two hemolysins with molecular weights of 52,000 (H-I) and 31,000 (H-II). A mutant was isolated that produced only H-II but was identical with the wild type in all other respects. We exploited this mutant to produce H-II for study that was free of contamination by H-I. By manipulation of media composition, we produced H-I in the absence of H-II. The hemolysins were precipitated differently by ammonium sulfate, and both exhibited the Arrhenius effect when heated. Both hemolysins attached rapidly to erythrocytes; however, lysis by H-I was immediate, while lysis by H-II followed after a lag. Hemolysis by H-I and H-II increased in rate with increasing temperature and was absent at 0 degrees C. Only H-I was inhibited by cholesterol. The hemolysins of B. cereus appeared similar to the hemolysins of B. thuringiensis. H-I probably is identical with cereolysin.     

Symmetric primary and tertiary structure mutations within a symmetric superfold: a solution, not a constraint, to achieve a foldable polypeptide

In previous studies designed to increase the primary structure symmetry within the hydrophobic core of human acidic fibroblast growth factor (FGF-1) a combination of five mutations were accommodated, resulting in structure, stability and folding kinetic properties similar to wild-type (despite the symmetric constraint upon the set of core residues). A sixth mutation in the core, involving a highly conserved Met residue at position 67, appeared intolerant to substitution. Structural analysis suggested that the local packing environment of position 67 involved two regions of apparent insertions that distorted the tertiary structure symmetry inherent in the beta-trefoil architecture. It was postulated that a symmetric constraint upon the primary structure within the core could only be achieved after these insertions had been deleted (concomitantly increasing the tertiary structure symmetry). The deletion of these insertions is now shown to permit mutation of position 67, thereby increasing the primary structure symmetry relationship within the core. Furthermore, despite the imposed symmetric constraint upon both the primary and tertiary structure, the resulting mutant form of FGF-1 is substantially more stable. The apparent inserted regions are shown to be associated with heparin-binding functionality; however, despite a marked reduction in heparin-binding affinity the mutant form of FGF-1 is surprisingly approximately 70 times more potent in 3T3 fibroblast mitogenic assays. The results support the hypothesis that primary structure symmetry within a symmetric protein superfold represents a possible solution, rather than a constraint, to achieving a foldable polypeptide.