Nanodomain-induced chain folding in poly(gamma-benzyl-L-glutamate)-b-polyglycine diblock copolymers

We report on the self-assembly mechanism and dynamics in a series of poly(gamma-benzyl-l-glutamate)-b-poly(glycine) (PBLG-b-PGly) diblock copolymers within the composition range 0.67 < or = f(PBLG) < or = 0.97 and the temperature (T) range 303 < T < 433 K. Small- and wide-angle X-ray scattering, (13)C NMR, and differential scanning calorimetry are used for the structure investigation coupled with dielectric spectroscopy for both the peptide secondary structure and the associated dynamics. These techniques provide not only the nanophase morphology but also the type and persistence of peptide secondary structures. The thermodynamic confinement of the blocks within the nanodomains and the disparity in their packing efficiency results in multiple chain folding of the PGly secondary structure that effectively stabilize a lamellar morphology for high f(PBLG). Nanoscale confinement proves to be important in controlling the persistence length of secondary peptide motifs.     

Facile preparation of well-defined AB2 Y-shaped miktoarm star polypeptide copolymer via the combination of ring-opening polymerization and click chemistry

Well-defined AB2 Y-shaped miktoarm star polypeptide copolymer, PZLL-b-(PBLG)2, was synthesized via a combination of ring-opening polymerization (ROP) of alpha-amino acid N-carboxyanhydride (NCA) and click chemistry, where PZLL is poly(epsilon-benzyloxycarbonyl-L-lysine) and PBLG is poly(gamma-benzyl-L-glutamate). First, two types of primary-amine-containing initiators, N-aminoethyl 3,5-bis(propargyloxyl)-benzamide and 3-azidopropylamine, were synthesized and employed for the ROP of NCA, leading to the formation of dialkynyl-terminated PZLL and azide-terminated PBLG, dialkynyl-PZLL and PBLG-N3, respectively. The subsequent copper(I)-catalyzed cycloaddition reaction between dialkynyl-PZLL and slightly excess PBLG-N3 led to facile preparation of PZLL-b-(PBLG)2 Y-shaped miktoarm star polypeptide copolymer. The excess PBLG-N3 was scavenged off by reacting with alkynyl-functionalized Wang resin. The obtained Y-shaped miktoarm star polypeptide copolymer was characterized by gel permeation chromatograph (GPC), Fourier transform-infrared spectroscopy (FT-IR), and (1)H NMR. Moreover, after the hydrolysis of protecting benzyl and benzyloxycarbonyl groups of PZLL-b-(PBLG)2, water-soluble pH-responsive Y-shaped miktoarm star polypeptide copolymer, PLL-b-(PLGA)2, was obtained, where PLL is poly(L-lysine) and PLGA is poly(L-glutamic acid). It can self-assemble into PLGA-core micelles at acidic pH and PLL-core micelles at alkaline pH, accompanied with the coil-to-helix transition of PLGA and PLL sequences, respectively. The spontaneous pH-responsive supramolecular assembly of PLL-b-(PLGA)2 miktoarm star polypeptide copolymer has been investigated via a combination of (1)H NMR, laser light scattering (LLS), transmission electron microscopy (TEM), and circular dichroism (CD) spectroscopy.     

Stimuli-responsive zwitterionic block copolypeptides: poly(N-isopropylacrylamide)-block-poly(lysine-co-glutamic acid)

Synthesis of novel zwitterionic block copolypeptides, poly(N-isopropylacrylamide)-block-poly(L-glutamic acid-co-L-lysine) [PNiPAM(n)(PLG(x)-co-PLLys(y))m , where n is the number-average degree of polymerization (DP(n)) of PNiPAM block, x and y are the mole fraction of glutamic acid and lysine residues, respectively, and m is the total DP(n) of the peptide block], and their stimuli-responsiveness to temperature and pH variation in aqueous solutions are described. Initiated with the amino-terminated poly(N-isopropylacrylamide) (PNiPAM(n)-NH2), ring-opening polymerization (ROP) of a mixture of gamma-benzyl-L-glutamate N-carboxyanhydride (BLG-NCA), and Boc-L-lysine N-carboxyanhydride (BLLys-NCA) afforded the block copolypeptides PNiPAM(n)(PBLG(x)-co-PBLLys(y))m, with a poly(N-isopropylacrylamide) block together with a random copolypeptide block, which was then deprotected with HBr/trifluoroacetic acid into the double hydrophilic block copolypeptides, PNiPAM(n)(PLG(x)-co-PLLys(y))m. Their block ratios and lengths, as well as the amino acid residue ratios in the random copolypeptide block are varied (n = 360, x = 0.4-0.5, y = 0.4-0.6, and m = 220-252). The secondary structures of the copolypeptides in aqueous solution at different pH conditions were examined. Phase transitions in aqueous solutions induced by both pH and temperature variation were investigated by (1)H NMR spectroscopy. The transitions induced by temperature were also explored by turbidity measurements using UV/vis spectroscopy for their lower critical aggregation temperature (LCAT) determination. Furthermore, these aggregation processes were followed by dynamic light scattering measurements.     

Molecular blending by polymerization of intercalated solvent. Poly(gamma-benzyl-L-glutamate)/benzyl methacrylate as a model system

The aim of the present research is to obtain blending between a polymer and a (polymerized) solvent on the molecular level. Because of its rigid rod structure, poly(gamma-benzyl-L-glutamate) (PBLG) is chosen as the polymer. Benzyl methacrylate (BzMA) has been chosen as the solvent for two reasons. First, the structure of the solvent is very similar to the structure of the side chain of PBLG, favoring interactions between the two materials. Second, the solvent can be polymerized, because of the presence of a C=C bond. In cast films of PBLG and BzMA separate zones of the polymer and solvent are present. Wide-angle X-ray diffraction and Raman results show that upon heating the cast films homogenization occurs and solvent molecules intercalate between the helices of PBLG. At 150 degrees C a hexagonal packing is obtained. The dimensions of the obtained packing depend on the solvent concentration, which confirms that solvent molecules are indeed present within the crystalline lattice. DSC experiments imply that the observed changes upon heating correspond to thermodynamic processes. On cooling the homogeneous samples, disordering of the hexagonal packing occurs. Polymerization of the homogeneous samples results in a disordering of the hexagonal packing and in a contraction of the unit cell. The latter once more confirms that solvent molecules are indeed present within the crystalline lattice. The applied principle of polymerization of a solvent in a molecular homogeneous system can be favorable for many applications, for which morphology control at the molecular level is required.     

Hierarchical ionic self-assembly of rod-comb block copolypeptide-surfactant complexes

Novel hierarchical nanostructures based on ionically self-assembled complexes of diblock copolypeptides and surfactants are presented. Rod-coil diblock copolypeptide poly(gamma-benzyl-L-glutamate)-block-poly(L-lysine), PBLG-b-PLL (Mn = 25,000 and 8000 for PBLG and PLL, respectively, polydispersity index 1.08), was complexed with anionic surfactants dodecanesulfonic acid (DSA) or dodecyl benzenesulfonic acid (DBSA), denoted as PBLG-b-PLL(DSA)1.0 and PBLG-b-PLL(DBSA)1.0, respectively. The complexation leading to supramolecular rod-comb architectures was studied by transmission electron microscopy (TEM), small-angle X-ray scattering (SAXS), Fourier transform infrared spectroscopy (FTIR), and polarized optical microscopy (POM). PBLG-b-PLL, PBLG-b-PLL(DBSA)1.0, and PBLG-b-PLL(DSA)1.0 self-assemble with alternating PBLG lamellae and PLL-containing lamellae with a periodicity of 27-33 nm. Within the PBLG lamellae, the rod-like PBLG helices pack with a periodicity of ca. 1.3 nm. The internal structure of the PLL-containing lamellae depends on the complexation. For pure PBLG-b-PLL, the PLL chains adopt a random coil conformation and the PLL domains are disordered. For PBLG-b-PLL(DSA)1.0, lamellar self-assembly of periodicity of 3.7 nm within the PLL(DSA)1.0 domains is observed due to crystalline packing of the linear n-dodecyl tails. For PBLG-b-PLL(DBSA)1.0 with branched dodecyl tails, a distinct SAXS reflection is observed, suggesting self-assembly within the PLL(DBSA)1.0 domains with a periodicity of 2.9 nm. However, due to the absence of higher order reflections, the internal structure cannot be conclusively assigned. The efficient plasticization which leads to fluid-like liquid crystallinity in PBLG-b-PLL(DBSA)1.0 and an alpha-helical conformation according to FTIR allows us to suggest that the PLL(DBSA)1.0 domains have a hexagonal internal structure. The interplay of self-assembly at different length scales combined with rod-like liquid crystallinity can open new routes to design functional materials.     

Subcutaneous Construction of Engineered Adipose Tissue with Fat Lobule-Like Structure Using Injectable Poly-Benzyl-L-Glutamate Microspheres Loaded with Adipose-Derived Stem Cells

Porous microcarriers were fabricated from synthesized poly(γ-benzyl-L-glutamate) (PBLG) polymer to engineer adipose tissue with lobule-like structure via the injectable approach. The adipogenic differentiation of human adipose-derived stem cells (hASCs) seeded on porous PBLG microcarriers was determined by adipogenic gene expression and glycerol-3-phosphate dehydrogenase enzyme activity. In vitro adipogenic cultivation was performed for 7 days, and induced hASC/PBLG complex (Adi-ASC/PBLG group) was subcutaneously injected into nude mice. Injections of PBLG microcarriers alone (PBLG group) and non-induced hASC/PBLG complex (ASC/PBLG group) served as controls. Newly formed tissues were harvested after 4 and 8 weeks. Generation of subcutaneous adipose tissue with typical lobule-like structure separated by fibrous septa was observed upon injection of adipogenic-induced hASC/microsphere complex. Adipogenesis significantly increased in the Adi-ASC/PBLG group compared with the control groups. The angiogenesis in the engineered adipose tissue was comparable to that in normal tissue as determined by capillary density and luminal diameter. Cell tracking assay demonstrated that labeled hASCs remained detectable in the neo-generated tissues 8 weeks post-injection using green fluorescence protein-labeled hASCs. These results indicate that adipose tissue with typical lobule-like structure could be engineered using injectable porous PBLG microspheres loaded with adipogenic-induced hASCs.     

Conformational properties of a peptide model for unfolded alpha-helices

Models of protein folding often hypothesize that the first step is local secondary structure formation. The assumption is that unfolded polypeptide chains possess an intrinsic propensity to form these local secondary structures. On the basis of this idea, it is tempting to model the local conformational properties of unfolded proteins using well-established residue secondary structure propensities, in particular, alpha-helix forming propensities. We have used spectroscopic methods to investigate the conformational behavior of a host-guest series of peptides designed to model unfolded alpha-helices. A suitable peptide model for unfolded alpha-helices was determined from studies of the length dependence of the conformational properties of alanine-based peptides. The chosen host peptide possessed a small, detectable, alpha-helix content. Substituting various representative guest residues into the central position of the host peptide at times changed the conformational behavior dramatically, and often in ways that could not be predicted from known alpha-helix forming propensities. The data presented can be used to rationalize some of these propensities. However, it is clear that secondary structure propensities cannot be used to predict the local conformational properties of unfolded proteins.     

Conformational study on poly [gamma-(alpha-phenethyl)-L-glutamate] using vibrational circular dichroism spectroscopy

Vibrational circular dichroism (VCD) and IR absorption spectra are obtained in a chloroform solution for poly[gamma-((R)-alpha-phenethyl)-L-glutamate] (PRPLG) and poly[gamma-((S)-alpha-phenethyl)-L-glutamate] (PSPLG), whose only structural difference is an opposite chiral center in the side chain. Their characteristic amide A, I, and II bands show VCD patterns quite similar to those of poly[gamma-benzyl-L-glutamate] (PBLG), indicating that the secondary structure of these polypeptides is a right-handed alpha-helix. The VCD spectra in the CH stretching region exhibit different patterns for PRPLG and PSPLG, reflecting the chirality difference in the side chains. This difference is interpreted on the basis of the additivity of optical activity contributions from the main chain conformation and the chirality difference in the side chains. The results indicate that a VCD difference spectrum of the CH stretching region is a useful diagnostic tool for elucidating local chirality differences.     

A conserved alpha helical domain at the N-terminus of Pex14p is required for PTS1 and PTS2 protein import in Hansenula polymorpha

We have analyzed the highly conserved N-terminus of Hansenula polymorpha Pex14p for its function in peroxisomal matrix protein import. The region comprising aa 10-54 of HpPex14p is predicted to contain three alpha-helices. Its alpha-helical structure was confirmed by CD analysis of a synthetic peptide, corresponding to residues 8-58. Deletion of aa 1-21 of HpPex14p, but not of aa 1-9, completely abolished PTS1 and PTS2 matrix protein import. An extensive mutational analysis of the first alpha-helix (aa 10-21) demonstrated that its secondary structure, as well as residues Phe20 and Leu21, are essential for PTS1 and PTS2 matrix protein import.     

Secondary structure of peptides. 18. 15N-nmr and 13C-nmr CP/MAS investigation of the primary and secondary structure of (Ala/Val) copolypeptides

Various copolypeptides were prepared by benzylamine or tertiary amine-initiated copolymerizations of alanine–N-carboxyanhydride (Ala-NCA) and valine–N-carboxyanhydride (Val-NCA). The number-average molecular weights of these copolypeptides were detemined by ¹H-nmr spectroscopic end-group analyses and viscosity measurements. The sequences were characterized by ¹⁵N-nmr spectra in solution, and the average lengths of the homogeneous blocks were determined from the signal intensities. The 50.3-and 75.4-MHz ¹³C-nmr CP/MAS spectra of the solid copolypeptides are not sensitive to sequence effects, but allow qualitative and quantitative analyses of the secondary structures. In contrast to other methods, the ¹³C-nmr spectra allow determination of the extent to which individual amino acids are incorporated into β-sheet or α-helix phases. Depending on primary structure and molecular weight, the secondary structure of (Ala/Val) copolypeptides may vary significantly. Both monomer units may be predominantly helical or predominantly β-sheet structure, or the Val units may prefer the β-sheet structure with most Ala-units forming β-helices. However, these secondary structures are more or less thermodynamically unstable and revert to the stable conformations on reprecipitation from trifluoroacetic acid/water.     

The effect of peptide glycation on local secondary structure

Protein glycation is a non-enzymatic reaction between reducing sugars and amino groups that occurs in vivo and has been implicated in a number of disease states and pathologies including Alzheimer's and diabetes. Although glycation is thought to alter protein structure and function, there is currently little information on the structural consequences of this modification. We have used a model alpha-helix and a model beta-hairpin peptide, and NMR analysis, to investigate the effects of glycation upon secondary structure. Glycation of the dilysine motif within the alpha-helix peptide occurred preferentially at one lysine residue and resulted in severe disruption to the local secondary structure. The area immediately around the site of modification was extremely flexible and the peptide did not adopt a preferred conformation in this area of the helix in 30% TFE. Significant glycation of the beta-hairpin peptide was not detected and the structure was unchanged. These results show that glycation results in local secondary structure distortion of alpha-helices and that preferential glycation occurs in a sequence specific manner. The findings will allow us to interrogate the local environment in other peptides/proteins to predict the likelihood of glycation, and to model the potential effects such modification might have upon structure/function.     

Secondary and tertiary structure characteristics of Megasphaera elsdenii flavodoxin in the reduced state as determined by two-dimensional 1H NMR

The secondary structure of two-electron-reduced Megasphaera elsdenii flavodoxin has been determined by visual, qualitative inspection of the sequential connectivities involving C alpha H, C beta H and NH protons observed in NOESY (two-dimensional nuclear Overhauser enhancement spectroscopy) spectra. Results from an amide proton exchange experiment were used to confirm the secondary structure assignment and to demonstrate the compactness and stability of the protein. After the secondary structure elements were established, the global fold of the protein and the flavin binding site have been determined using nonsequential interresidual NOE connectivities as primary source of information. The secondary structure and the global fold of M. elsdenii and Clostridium MP flavodoxin appeared to be very similar, differences are observed however. M. elsdenii flavodoxin consists of a central parallel beta-sheet including five strands surrounded on both sides by a pair of alpha-helices.     

Structural roles of the active site iron(III) ions in catechol 1,2-dioxygenases and differential secondary structure changes in isoenzymes A and B from Acinetobacter radioresistens S13

The reversible active site metal ion removal process for two catechol 1,2-dioxygenase isoenzymes (IsoA and IsoB) isolated from Acinetobacter radioresistens S13 has been monitored using circular dichroism and fluorescence spectroscopic techniques. IsoA and IsoB are homodimers, containing one iron(III) ion per subunit. Their amino acid sequence identity is 48.4%. Previous experiments suggested that structural diversities could be responsible for the differential thermal and pH stabilities of the two isoenzymes and of their distinct demetallation kinetics. The far-UV CD spectra of IsoA and IsoB catechol 1,2-dioxygenases from A. radioresistens S13 provide information on their secondary structures. IsoB appears to have a content of alpha-helices higher than IsoA. Upon metal ion removal, both proteins reversibly lose part of their secondary structure following distinct pathways. CD spectra simulations allowed us to estimate the content of alpha-helices, beta-sheets, and turns for each isoenzyme and to monitor the secondary structure rearrangements. The metal ion withdrawal has large influence on the secondary structure: in particular a significant reduction of alpha-helices content is observed for both isoenzymes. Intrinsic fluorescence emission spectra clearly support such results, adding information on the local environment changes of the tryptophan residues. The positioning of Trp250 in IsoB has been shown to be of particular interest for monitoring the local structure changes occurring upon metal ion removal. For the first time these studies allow to underline the role of active site iron ions on dioxygenases folding and stability, further evidencing the differences in structural assembling between the two isoenzymes from A. radioresistens S13.     

Buoyant and potentiometric titrations of synthetic polpeptides. II. Five copolypeptides and two nonionizable homopolypeptides in CsCl solutions.

The buoyant density titrations of five ionizable copolypeptides in concentrated CsCl solutions have been determined. The results are used to formulate models for predicting the buoyant density titration behavior of copolypeptides and proteins using the previously reported homopolypeptide buoyant density titration curves. It was determined for these copolypeptides that the best predictive model must include not only the buoyant densities of the constituent amino acid residues and the relative composition, but also hydration and salt binding. Hydrations determined for the homopolypeptides are used in the copolypeptide predictive model. The hydrations of the neutral homopolypeptides were readily calculable since their buoyant densities are thermodynamically defined in terms of their partial specific volumes and hydrations. For the case of a charged macromolecule, an expression for the buoyant density as a function of the number and nature of the bound ions, its partial specific volume, and its relative hydration has also been available for some time. This heretofore intuitive relationship is now derived from thermodynamic principles and allows calculations of hydrations to charged macromolecules which bind either cations, anions, or both. The potentiometric titrations of three of the five copolypeptides in concentrated CsCl solutions were determined in order to study the effect of residue interaction and solvation effects on their ionization behavior. The potentiometric results are also combined directly with the buoyant density titration results to determine the correlation of the buoyant density with the degree of ionization. As in the cases of poly(Glu) and poly(His), the buoyant density of the copolypeptides changed linearily with the degree of ionization. The buoyant density titrations of two nonionizable homopolypeptides, poly(Gly) and poly(Ala), were determined in concentrated CsCl solutions. The buoyant density was found to increase with increasing pH, despite the fact that side chains do not contain ionizable groups. This is the first evidence from homopolypeptide or copolypeptide data that buoyant density changes can be observed from effects other than side-chain ionizations.     

Extracellular guanyl-specific ribonuclease Sa from the actinomycete Streptomyces aureofaciens. Primary structure and homology with ribonucleases from bacteria and fungi

The complete amino acid sequence of a guanyl-specific RNAse from Streptomyces aureofaciens has been established using a rapid method of primary structure analysis which eliminates the peptide fractionation. The automated Edman degradation of the carboxymethylated RNAse Sa and of non-fractionated peptide mixtures produced by tryptic and staphylococcal protease digests of the modified protein were used. The RNAse contains 96 amino acid residues, Mr 10,566. The secondary structures of RNAse Sa and microbial RNAses have been calculated using a modified Chou--Fasman procedure. A comparison of the primary and secondary structures of the RNAses revealed different degrees of sequence homology and a similar distribution of predicted structural regions (alpha-helices, beta-structure and beta-turn). The predicted secondary structure patterns are discussed in the light of the RNAse X-ray analysis date.     

Influence of pH on NMR structure and stability of the human prion protein globular domain

The NMR structure of the globular domain of the human prion protein (hPrP) with residues 121-230 at pH 7.0 shows the same global fold as the previously published structure determined at pH 4.5. It contains three alpha-helices, comprising residues 144-156, 174-194, and 200-228, and a short anti-parallel beta-sheet, comprising residues 128-131 and 161-164. There are slight, strictly localized, conformational changes at neutral pH when compared with acidic solution conditions: helix alpha1 is elongated at the C-terminal end with residues 153-156 forming a 310-helix, and the population of helical structure in the C-terminal two turns of helix alpha 2 is increased. The protonation of His155 and His187 presumably contributes to these structural changes. Thermal unfolding monitored by far UV CD indicates that hPrP-(121-230) is significantly more stable at neutral pH. Measurements of amide proton protection factors map local differences in protein stability within residues 154-157 at the C-terminal end of helix alpha 1 and residues 161-164 of beta-strand 2. These two segments appear to form a separate domain that at acidic pH has a larger tendency to unfold than the overall protein structure. This domain could provide a "starting point" for pH-induced unfolding and thus may be implicated in endosomic PrPC to PrPSc conformational transition resulting in transmissible spongiform encephalopathies.     

Secondary structure and structure-activity relationships of peptides corresponding to the subunit interface of herpes simplex virus DNA polymerase

The interaction of the catalytic subunit of herpes simplex virus DNA polymerase with the processivity subunit, UL42, is essential for viral replication and is thus a potential target for antiviral drug discovery. We have previously reported that a peptide analogous to the C-terminal 36 residues of the catalytic subunit, which are necessary and sufficient for its interaction with UL42, forms a monomeric structure with partial alpha-helical character. This peptide and one analogous to the C-terminal 18 residues specifically inhibit UL42-dependent long chain DNA synthesis. Using multidimensional (1)H nuclear magnetic resonance spectroscopy, we have found that the 36-residue peptide contains partially ordered N- and C-terminal alpha-helices separated by a less ordered region. A series of "alanine scan" peptides derived from the C-terminal 18 residues of the catalytic subunit were tested for their ability to inhibit long-chain DNA synthesis and by circular dichroism for secondary structure. The results identify structural aspects and specific side chains that appear to be crucial for interacting with UL42. These findings may aid in the rational design of new drugs for the treatment of herpesvirus infections.     

Limits on alpha-helix prediction with neural network models.

Using a backpropagation neural network model we have found a limit for secondary structure prediction from local sequence. By including only sequences from whole alpha-helix and non-alpha-helix structures in our training and test sets--sequences spanning boundaries between these two structures were excluded--it was possible to investigate directly the relationship between sequence and structure for alpha-helix. A group of non-alpha-helix sequences, that was disrupting overall prediction success, was indistinguishable to the network from alpha-helix sequences. These sequences were found to occur at regions adjacent to the termini of alpha-helices with statistical significance, suggesting that potentially longer alpha-helices are disrupted by global constraints. Some of these regions spanned more than 20 residues. On these whole structure sequences, 10 residues in length, a comparatively high prediction success of 78% with a correlation coefficient of 0.52 was achieved. In addition, the structure of the input space, the distribution of beta-sheet in this space, and the effect of segment length were also investigated.     

Toward intrinsically fluorescent proteomimetics: fluorescent probe response to alpha helix structure of poly-gamma-benzyl-L-glutamate

A fluorescent probe (1), developed for recognition of alpha helical secondary structure, shows a large fluorescence change upon titration with the synthetic protein PBLG. Compared to fluorophores of similar size and shape, 1 displayed the smallest dissociation constant (K(D)=80microM) when titrated with PBLG. These preliminary studies are directed toward developing small molecule proteomimetics that have intrinsic fluorescence and are specific for helical-protein binding-sites.     

Protein similarity from knot theory: geometric convolution and line weavings.

Shape similarity is one of the most elusive and intriguing questions of nature and mathematics. Proteins provide a rich domain in which to test theories of shape similarity. Proteins can match at different scales and in different arrangements. Sometimes the detection of common local structure is sufficient to infer global alignment of two proteins; at other times it provides false information. Proteins with very low sequence identity may share large substructures, or perhaps just a central core. There are even examples of proteins with nearly identical primary sequences in which alpha-helices have become beta-sheets. Shape similarity can be formulated (i) in terms of global metrics, such as RMSD or Hausdorff distance, (ii) in terms of subgraph isomorphisms, such as the detection of shared substructures with similar relative locations, or (iii) purely topologically, in terms of structure preserving transformations. Existing protein structure detection programs are built on the first two types of similarity. The third forms the foundations of knot theory. The thesis of this paper is this: Protein similarity detection leads naturally to algorithms operating at the metric, relational, and isotopic scales. The paper introduces a definition of similarity based on atomic motions that preserve local backbone topology without incurring significant distance errors. Such motions are motivated by the physical requirements for rearranging subsequences of a protein. Similarity detection then seeks rigid body motions able to overlay pairs of substructures, each related by a substructure-preserving motion, without necessarily requiring global structure preservation. This definition is general enough to span a wide range of questions: One can ask for full rearrangement of one protein into another while preserving global topology, as in drug design; or one can ask for rearrangements of sets of smaller substructures, preserving local but not global topology, as in protein evolution. In the appendix, we exhibit an algorithm for answering the general rearrangement question. That algorithm has the complexity of robot motion planning. In the text, we consider a more common case in which one seeks protein similarity by rearrangements of relatively short peptide segments. We exhibit two algorithms, one based on writhing numbers and one based on line weavings. The algorithms have time complexities O(n (4)) and O(s (11)), respectively, where n is the maximum number of residues in the proteins being compared and s is the number of secondary structure elements. In practice, the running times were nearly interactive. We report results obtained with a dozen pairs of proteins, exhibiting a range of typical features.