Aspects of the bond topology and chemical composition of a mineral may be incorporated into a general formula by writing the local topological details of each cation and anion, along with their chemical identity, as a general expression called a structure-generating function. Here, this procedure is described for polysomatic T–O–T and H–O–H structures. We may write tetrahedrally coordinated cations and their associated anions as {T2nΘm}. For {T2nΘm} to be a chain or ribbon, 5n < m ≤ 6n, and we may write m as 5n + N, where N is an integer. Within the {T2nΘ(5n+N)} unit, we may recognize three types of anion vertices: (1) bridging anions, Θbr, that are bonded to two T cations; (2) apical anions, Θap, that are involved in linkage to other cations out of the plane of the bridging anions; and (3) linking anions, Θl, that link to non-T cations in the plane of the bridging anions. We may incorporate the connectivity of the cations in our algebraic representation of the chain as follows: {T2nΘbraΘapbΘlc} where a + b + c = 5n + N. The apical anions of the T- or H-sheets provide some anions of the layer of octahedra. We may use the handshaking di-lemma of graph theory to examine the interaction between the two types of layers, and write a Structure-Generating Function, S(N;n), that gives both the stoichiometry and aspects of the bond topology of the structures.

Where N = 1, the T-sheet consists of ribbons of the form {T2nΘ(5n+1)} = {T2nΘbr(3n–1)Θap2nΘl2}. Each T–Θbr–T linkage spans an octahedron, and hence there are (3n – 1) octahedrally coordinated cations between opposing {T2nΘbr(3n–1)Θap2nΘl2} ribbons. There are an additional (n–1) vertices, Ψ, required to complete the coordination of the M cations on one side of the O-sheet, and we may write the structure-generating function for biopyriboles as follows: S(1;n) = Xi[M(3n–1)Ψ2(n–1){T2nΘbr(3n–1)Θap2nΘl2}2] = [M(3n–1)Ψ2(n–1){T2nΘ(5n+1)}2]. Where N = 2, the general form of the T-ribbon is {T2nΘ(5n+2)}, a component of the H-sheet in the polysomatic H–O–H minerals in which the T-ribbons are linked laterally by [5]- or [6]-coordinated high-valence cations, D, which have the coordination (Dφ41φapφt), where ft may or may not be present depending on the coordination number, [6] or [5], of the D cation. The general formula for an H-sheet is [Dφap{T2nΘbr(3n–2)Θap2nΘl4}φt0–1], where φt (written after the T-sheet) occurs on the outside of the H-sheet and may be involved in linkage between adjacent H–O–H blocks. The H-sheet links via its apical anions to the O-sheet, giving the general formula of an H–O–H block as [M(3n+1)(DφapΨn{T2nΘ(5n+2)}φt0–1)2]. These H–O–H blocks may link directly or indirectly through the φt anions of the (DΘl4φapφt) octahedra, giving S(2;n) = Xi[M(3n+1)Ψ2n(D2φap2{T2nΘbr(3n–2)Θap2nΘl4}2)φt0–2]. Combining the expressions for the structure-generating functions gives a single function for T–O–T and H–O–H structures:

S(N;n) = Xi[M(3n+2N–3)?2(n+N–2)(D2(N–1)f2ap(N–1){T2nT(3n–N)brT2napT2N1}2)f0–2(N–1)t]

This expression also generates mixed-ribbon polysomatic structures. Thus S(1;2+3) gives the chemical composition and structure of the mixed-chain pyribole chesterite, and S(2;1+4) gives the chemical composition and structure of the mixed-chain H–O–H mineral, veblenite.

Two-dimensional nets may be used to generate the stoichiometry and structure of single-layer and double-layer sheet-silicate minerals. Many sheet-silicate minerals are based on the 3-connected plane nets 63, 4.82, (4.6.8)2(6.82)1and (52.8)1(5.82)1, and some more complicated nets, e.g. (5.6.7)4(5.72)1(62.7)1, (4.122)2(42.12)1, (52.8)1(5.62)1(5.6.8)2(62.8)1,have one or two representative structures. Many complicated sheet-silicate minerals are based on sheets of 2-, 3- and 4-connected tetrahedra that may be developed from 3- and 4-connected plane nets by a series of oikodoméic operations on 3- or 4-connected nets that change the topologyof the parent net. There are three classes of oikodoméic operations: (1) insertion of 2- and 3-connected vertices into 3- and 4-connected plane nets; (2,3) replication of single-layer sheets by topological mirror or two-fold-rotation operators, and condensation of the resulting twosingle-layer sheets to form double-layer sheets. The topological aspects of these sheet structures may be described by functions that express stoichiometry in terms of tetrahedron connectivities (formula-generating functions) and functions that associate these formula-generating functionswith specific two-dimensional nets. Using these functions, we may generate formulae and structural arrangements of single-layer and double-layer silicate structures with specific local and long-range topological features.

Biotin and lipoic acid moieties are the covalently attached coenzyme cofactors of several multicomponent enzyme complexes that catalyze key metabolic reactions. Attachment of these moieties to the biotinyl- and lipoyl-dependent enzymes is post-translationally catalyzed by specific biotinylating and lipoylating protein enzymes. In Escherichia coli, two different enzymes, LplA and LipB, catalyze independent pathways for the lipoylation of the relevant enzymes, whereas only one enzyme, the BirA protein, is responsible for all the biotinylation. Counterparts of the E. coli BirA, LplA, and LipB enzymes have been previously identified in many organisms, but homology among the three families has never been reported. Computational analysis based on PSI-BLAST profiles and secondary structure predictions indicates, however, that lipoylating and biotinylating enzymes are evolutionarily related protein families containing a homologous catalytic module. Sequence conservation among the three families is very poor, but a single lysine residue is strictly conserved in all of them, which, according to the available X-ray crystal structure of the E. coli BirA protein, is expected to contribute to the binding of lipoic acid in the LplA and LipB enzymes.

A challenge in computational protein folding is to assemble secondary structure elements—helices and strands—into well-packed tertiary structures. Particularly difficult is the formation of β-sheets from strands, because they involve large conformational searches at the same time as precise packing and hydrogen bonding. Here we describe a method, called Geocore-2, that (1) grows chains one monomer or secondary structure at a time, then (2) disconnects the loops and performs a fast rigid-body docking step to achieve canonical packings, then (3) in the case of intrasheet strand packing, adjusts the side-chain rotamers; and finally (4) reattaches loops. Computational efficiency is enhanced by using a branch-and-bound search in which pruning rules aim to achieve a hydrophobic core and satisfactory hydrogen bonding patterns. We show that the pruning rules reduce computational time by 103- to 105-fold, and that this strategy is computationally practical at least for molecules up to about 100 amino acids long.

Escherichia coli NikR, a repressor with homologs in other bacteria and archaea, was identified as a potential new member of the ribbon-helix-helix (β-α-α) family of transcription factors in profile based sequence searches and in structure prediction experiments. Biophysical and biochemical characterization of the N-terminal domain of NikR show that it has many features expected of a β-α-α protein including α-helical content, dimeric solution form, concentration dependent thermal stability, and ability to bind DNA in sequence-specific manner. Mutation of a residue predicted to be important for DNA-binding reduces operator affinity but does not affect the secondary structure or stability of the protein.

The sequences of several members of the myosin family of molecular motors are evaluated using ASP (Ambivalent Structure Predictor), a new computational method. ASP predicts structurally ambivalent sequence elements by analyzing the output from a secondary structure prediction algorithm. These ambivalent sequence elements form secondary structures that are hypothesized to function as switches by undergoing conformational rearrangement. For chicken skeletal muscle myosin, 13 discrete structurally ambivalent sequence elements are identified. All 13 are located in the heavy chain motor domain. When these sequence elements are mapped into the myosin tertiary structure, they form two compact regions that connect the actin binding site to the adenosine 5′-triphosphate (ATP) site, and the ATP site to the fulcrum site for the force-producing bending of the motor domain. These regions, predicted by the new algorithm to undergo conformational rearrangements, include the published known and putative switches of the myosin motor domain, and they form plausible allosteric connections between the three main functional sites of myosin. The sequences of several other members of the myosin I and II families are also analyzed.

Methods for protein structure (3D)–sequence (1D) compatibility evaluation (threading) have been developed during the past decade. The protocol in which a sequence can recognize its compatible structure in the structural library (i.e., the fold recognition or the forward-folding search) is available for the structure prediction of new proteins. However, the reverse protocol, in which a structure recognizes its homologous sequences among a sequence database, named the inverse-folding search, is a more difficult application. In this study, we have investigated the feasibility of the latter approach. A structural library, composed of about 400 well-resolved structures with mutually dissimilar sequences, was prepared, and 163 of them had remote homologs in the library. We examined whether they could correctly seek their homologs by both forward- and inverse-folding searches. The results showed that the inverse-folding protocol is more effective than the forward-folding protocol, once the reference states of the compatibility functions are appropriately adjusted. This adjustment only slightly affects the ability of the forward-folding search. We noticed that the scoring, in which a given sequence is re-mounted onto a structure according to the 3D–1D alignment determined by the dynamic programming method, is only effective in the forward-folding protocol and not in the inverse-folding protocol. Namely, the inverse-folding search works significantly better with the score given by the 3D–1D alignment per se, rather than that obtained by the re-mounting. The implications of these results are discussed.

We describe an extensive test of Geocore, an ab initio peptide folding algorithm. We studied 18 short molecules for which there are structures in the Protein Data Bank; chains are up to 31 monomers long. Except for the very shortest peptides, an extremely simple energy function is sufficient to discriminate the true native state from more than 108 lowest energy conformations that are searched explicitly for each peptide. A high incidence of native-like structures is found within the best few hundred conformations generated by Geocore for each amino acid sequence. Predictions improve when the number of discrete φ/ψ choices is increased.