Designing materials for plasmonic systems: the alkali-noble intermetallics.

We use electronic structure calculations based upon density functional theory to search for ideal plasmonic materials among the alkali-noble intermetallics. Importantly, we use density functional perturbation theory to calculate the electron-phonon interaction and from there use a first order solution to the Boltzmann equation to estimate the phenomenological damping frequency in the Drude dielectric function. We discuss the necessary electronic features of a plasmonic material and investigate the optical properties of the alkali-noble intermetallics in terms of some generic plasmonic system quality factors. We conclude that at low negative permittivities, KAu, with a damping frequency of 0.0224 eV and a high optical gap to bare plasma frequency ratio, outperforms gold and to some extent silver as a plasmonic material. Unfortunately, a low plasma frequency (1.54 eV) reduces its utility in modern plasmonics applications. We also discuss, briefly, the effect of local fields on the optical properties of these materials.

A review of the optical properties of alloys and intermetallics for plasmonics.

Alternative materials are required to enhance the efficacy of plasmonic devices. We discuss the optical properties of a number of alloys, doped metals, intermetallics, silicides, metallic glasses and high pressure materials. We conclude that due to the probability of low frequency interband transitions, materials with partially occupied d states perform poorly as plasmonic materials, ruling out many alloys, intermetallics and silicides as viable. The increased probability of electron-electron and electron-phonon scattering rules out many doped and glassy metals.

Optical properties of intermetallic compounds from first principles calculations: a search for the ideal plasmonic material.

First principles calculations have been used to predict the optical properties for a range of intermetallic compounds for which little or no experimental optical data are currently available. Density functional theory combined with the random phase approximation is used to calculate the dielectric functions for these compounds. The aim of this work is to investigate how the band edge and plasma frequency vary with composition in order to identify materials with promising plasmonic properties. Towards this end the intermetallic compounds chosen are composed of elements which on their own have reasonable optical properties for plasmonic applications. The position of the band edge relative to the plasma frequency is most favourable in the simple binary compounds formed from the alkali plus noble metals NaAu, KAu and KAg. In particular, for KAu the band edge and plasma frequency occur at almost the same frequency, and hence the imaginary part of the dielectric function is practically zero for frequencies below the plasma frequency. In addition, the plasma frequency in this compound is at relatively low frequency, promising a material with strong plasmon response in the infrared.

Dynamic role of kallikrein 6 in traumatic spinal cord injury.

Kallikrein 6 (K6) is a member of the kallikrein gene family that comprises 15 structurally and functionally related serine proteases. In prior studies we showed that, while this trypsin-like enzyme is preferentially expressed in neurons and oligodendroglia of the adult central nervous system (CNS), it is up-regulated at sites of injury due to expression by infiltrating immune and resident CNS cells. Given this background we hypothesized that K6 is a key contributor to the pathophysiology of traumatic spinal cord injury (SCI), influencing neural repair and regeneration. Examination of K6 expression following contusion injury to the adult rat cord, and in cases of human traumatic SCI, indicated significant elevations at acute and chronic time points, not only at the injury site but also in cord segments above and below. Elevations in K6 were particularly prominent in macrophages, microglia and reactive astrocytes. To determine potential effects of elevated K6 on the regeneration environment, the ability of neurons to adhere to and extend processes on substrata which had been exposed to recombinant K6 was examined. Limited (1 h) or excess (24 h) K6-mediated proteolytic digestion of a growth-facilitatory substrate, laminin, significantly decreased neurite outgrowth. By contrast, similar hydrolysis of a growth-inhibitory substrate, aggrecan, significantly increased neurite extension and cell adherence. These data support the hypothesis that K6 enzymatic cascades mediate events secondary to spinal cord trauma, including dynamic modification of the capacity for axon outgrowth.

Potential scope of action of tissue kallikreins in CNS immune-mediated disease.

The objective of this study was to define the potential scope of action of tissue kallikreins in T cell-mediated disease of the CNS. We demonstrate quantitatively the differential expression of all 15 human tissue kallikreins within brain, spinal cord and immune compartments. In human Jurkat T cells we demonstrate differential regulation of select kallikreins by CD3 receptor, Concanavilin A (Con A), interleukin 2 (IL2), and lipopolysaccharide (LPS)-mediated activation and by exposure to steroid hormones, dexamethasone, norgestrel, androstan and estradiol. The patterns of co-expression and co-regulation described point to novel effector roles for select tissue kallikreins in neurological disorders involving T cells, such as multiple sclerosis.

Structural and energetic consequences of mutations in a solvated hydrophobic cavity.

The structural and energetic consequences of modifications to the hydrophobic cavity of interleukin 1-beta (IL-1beta) are described. Previous reports demonstrated that the entirely hydrophobic cavity of IL-1beta contains positionally disordered water. To gain a better understanding of the nature of this cavity and the water therein, a number of mutant proteins were constructed by site-directed mutagenesis, designed to result in altered hydrophobicity of the cavity. These mutations involve the replacement of specific phenylalanine residues, which circumscribe the cavity, with tyrosine, tryptophan, leucine and isoleucine. Using differential scanning calorimetry to determine the relative stabilities of the wild-type and mutant proteins, we found all of the mutants to be destabilizing. X-ray crystallography was used to identify the structural consequences of the mutations. No clear correlation between the hydrophobicities of the specific side-chains introduced and the resulting stabilities was found.

Distinct promoters regulate tissue-specific and differential expression of kallikrein 6 in CNS demyelinating disease.

Kallikrein 6 is a serine protease expressed abundantly in normal adult human and rodent CNS, and therein is regulated by injury. In the case of CNS demyelinating disease, K6 expression in CNS occurs additionally in perivascular and parenchymal inflammatory cells suggesting a role in pathogenesis. Herein we describe two unique transcripts that occur within the human and mouse K6 genes that differ in their 5'-untranslated regions. These transcripts have identical translation initiation sites in exon 3, are expressed in a tissue-specific fashion and are differentially regulated in response to CNS injury. While the human and mouse 5'-transcripts differ in sequence they are identical in genomic organization and tissue-specific expression. The most 5'-transcript, designated transcript 1, includes exon 1-7, and was detectable in all CNS regions, but not in any non-CNS tissues examined (spleen, thymus, liver, kidney, pancreas, submandibular gland and peripheral nerve). In contrast, transcript 2 lacks exon 1, but contains a unique sequence at the 5'-end of exon 2, designated exon 2A. Transcript 2 was expressed both in CNS and in each peripheral tissue. In a murine model of human CNS demyelinating inflammatory disease induced by Theiler's picornovirus, mouse K6 transcript 1 was up-regulated in brain and spinal cord at acute and more chronic phases of CNS inflammation and demyelination, while overall transcript 2 expression was not significantly altered. However, in isolated splenocyte cultures, transcript 2 was up-regulated two-fold by cellular activation. Tissue-specific expression patterns and differential regulation in CNS disease indicates that each K6 5'-transcript is probably regulated by unique promoter elements and may serve as a molecular target to treat inflammatory demyelinating disease.

Activity of a newly identified serine protease in CNS demyelination.

We have identified a novel serine protease, myelencephalon-specific protease (MSP), which is preferentially expressed in the adult CNS, and therein, is abundant in both neurones and oligodendroglia. To determine the potential activity of MSP in CNS demyelination, we examined its expression in multiple sclerosis lesions and in two animal models of multiple sclerosis: Theiler's murine encephalomyelitis virus (TMEV) and myelin oligodendrocyte glycoprotein (MOG)-induced experimental allergic encephalomyelitis (EAE) in marmosets. High levels of MSP were present within infiltrating mononuclear cells, including macrophages and T cells, which characteristically fill sites of demyelination, both in multiple sclerosis lesions and in animal models of this disease. The functional consequence of excess MSP on oligodendroglia was determined in vitro by evaluating the effects of recombinant MSP (r-MSP) on oligodendrocyte survival and process number. Application of excess r-MSP resulted in a dramatic loss of processes from differentiated oligodendrocytes, and a parallel decrease in process outgrowth from immature cells. Transfection of oligodendrocyte progenitors with an MSP-green fluorescent protein construct produced similar changes in oligodendrocyte process number. Importantly, r-MSP did not affect oligodendrocyte survival or differentiation towards the sulphatide-positive lineage. We further demonstrate that myelin basic protein, and to a lesser extent myelin oligodendrocyte glycoprotein, can serve as MSP substrates. These studies support the hypothesis that excess MSP, as is present in inflammatory CNS lesions, promotes demyelination.

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

Structural assembly of the active site in an aldo-keto reductase by NADPH cofactor.

A 1.9 A resolution X-ray structure of the apo-form of Corynebacterium 2,5-diketo-d-gluconic acid reductase A (2,5-DKGR A), a member of the aldo-keto reductase superfamily, has been determined by molecular replacement using the NADPH-bound form of the same enzyme as the search model. 2,5-DKGR A catalyzes the NADPH-dependent stereo-specific reduction of 2,5-diketo-d-gluconate (2,5-DKG) to 2-keto-l-gulonate, a precursor in the industrial production of vitamin C. An atomic-resolution structure for the apo-form of the enzyme, in conjunction with our previously reported high-resolution X-ray structure for the holo-enzyme and holo/substrate model, allows a comparative analysis of structural changes that accompany cofactor binding. The results show that regions of the active site undergo coordinated conformational changes of up to 8 A. These conformational changes result in the organization and structural rearrangement of residues associated with substrate binding and catalysis. Thus, NADPH functions not only to provide a hydride ion for catalytic reduction, but is also a critical structural component for formation of a catalytically competent form of DKGR A.

Reduction of wobble-position GC bases in Corynebacteria genes and enhancement of PCR and heterologous expression.

Corynebacteria codon usage exhibits an overall GC content of 67%, and a wobble-position GC content of 88%. Escherichia coli, on the other hand has an overall GC content of 51%, and a wobble-position GC content of 55%. The high GC content of Corynebacteria genes results in an unfavorable codon preference for heterologous expression, and can present difficulties for polymerase-based manipulations due to secondary-structure effects. Since these characteristics are due primarily to base composition at the wobble-position, synthetic genes can, in principle, be designed to eliminate these problems and retain the wild-type amino acid sequence. Such genes would obviate the need for special additives or bases during in vitro polymerase-based manipulation and mutant host strains containing uncommon tRNA's for heterologous expression. We have evaluated synthetic genes with reduced wobble-position G/C content using two variants of the enzyme 2,5-diketo-D-gluconic acid reductase (2,5-DKGR A and B) from Corynebacterium. The wild-type genes are refractory to polymerase-based manipulations and exhibit poor heterologous expression in enteric bacteria. The results indicate that a subset of codons for five amino acids (alanine, arginine, glutamate, glycine and valine) contribute the greatest contribution to reduction in G/C content at the wobble-position. Furthermore, changes in codons for two amino acids (leucine and proline) enhance bias for expression in enteric bacteria without affecting the overall G/C content. The synthetic genes are readily amplified using polymerase-based methodologies, and exhibit high levels of heterologous expression in E. coli.

Thermodynamic characterization of mutants of human fibroblast growth factor 1 with an increased physiological half-life.

Human acidic fibroblast growth factor (FGF-1) is a potent mitogen and angiogenic factor, with reportedly poor thermal stability and a relatively short in vivo half-life. However, certain mutants of FGF-1 have been described that exhibit a significant increase in half-life in tissue culture-based assays. FGF-1 contains three cysteine residues, two of which are highly conserved and buried within the protein core. Mutant forms of FGF-1 that substitute a serine residue at these cysteine positions have been reported to increase the protein's half-life and specific activity as well as decrease the dependence upon heparin for full activity. However, the underlying physical basis for this increase in half-life has not been determined. Possible effects include stabilization of protein structure and elimination of sulfhydryl chemistry at these positions. Here we have used differential scanning calorimetry and isothermal equilibrium denaturation to characterize thermodynamic parameters of unfolding for individual, and combination, cysteine to serine mutations in human FGF-1. The results show that substitution by serine is destabilizing at each cysteine position in wild-type FGF-1. Thus, the increased half-life previously reported for these mutations does not correlate with thermal stability and is most likely due to elimination of sulfhydryl chemistry. The results also suggest a method by which protein half-life may be modulated by rational design.

Preferential expression of myelencephalon-specific protease by oligodendrocytes of the adult rat spinal cord white matter.

Myelencephalon-specific protease (MSP) is a novel serine protease that is expressed predominantly in the nervous system. In the adult rat spinal cord, MSP mRNA expression was dramatically upregulated, in both the white and gray matter, after systemic exposure to the glutamate receptor agonist, kainic acid (KA) (Scarisbrick et al. J Neurosci 17: 8156-8168, 1997b). To determine the cell-specific expression patterns of MSP, we generated MSP-specific monoclonal antibodies. These have been used in immunohistochemical and in situ hybridization colocalization studies, to demonstrate that MSP mRNA and protein are produced predominantly by CNP-immunoreactive oligodendroglia, but not by GFAP-immunoreactive astrocytes, in the white matter of the normal adult cord. In vitro, the soma of oligodendrocytes were also densely MSP immunoreactive, as were their growth tips, while astrocytes were associated with lower levels. These findings suggest that the enzymatic activity of MSP is likely to be important in the biology of oligodendrocytes and/or in the maintenance of the nerve fiber tracts of the adult spinal cord.

Molecular modeling of substrate binding in wild-type and mutant Corynebacteria 2,5-diketo-D-gluconate reductases.

2,5-diketo-D-gluconic acid reductase (2,5-DKGR; E.C. 1.1.1.-) catalyzes the Nicotinamide adenine dinucleotide phosphate (NADPH)-dependent stereo-specific reduction of 2, 5-diketo-D-gluconate (2,5-DKG) to 2-keto-L-gulonate (2-KLG), a precursor in the industrial production of vitamin C (L-ascorbate). Microorganisms that naturally ferment D-glucose to 2,5-DKG can be genetically modified to express the gene for 2,5-DKGR, and thus directly produce vitamin C from D-glucose. Two naturally occurring variants of DKGR (DKGR A and DKGR B) have been reported. DKGR B exhibits higher specific activity toward 2,5-DKG than DKGR A; however, DKGR A exhibits a greater selectivity for this substrate and significantly higher thermal stability. Thus, a modified form of DKGR, combining desirable properties from both enzymes, would be of substantial commercial interest. In the present study we use a molecular dynamics-based approach to understand the conformational changes in DKGR A as the active site is mutated to include two active site residue changes that occur in the B form. The results indicate that the enhanced kinetic properties of the B form are due, in part, to residue substitutions in the binding pocket. These substitutions augment interactions with the substrate or alter the alignment with respect to the putative proton donor group. Proteins 2000;39:68-75.

Reversible thermal denaturation of human FGF-1 induced by low concentrations of guanidine hydrochloride.

Human acidic fibroblast growth factor (FGF-1) is a powerful mitogen and angiogenic factor with an apparent melting temperature (Tm) in the physiological range. FGF-1 is an example of a protein that is regulated, in part, by stability-based mechanisms. For example, the low Tm of FGF-1 has been postulated to play an important role in the unusual endoplasmic reticulum-independent secretion of this growth factor. Despite the close relationship between function and stability, accurate thermodynamic parameters of unfolding for FGF-1 have been unavailable, presumably due to effects of irreversible thermal denaturation. Here we report the determination of thermodynamic parameters of unfolding (DeltaH, DeltaG, and DeltaCp) for FGF-1 using differential scanning calorimetry (DSC). The thermal denaturation is demonstrated to be two-state and reversible upon the addition of low concentrations of added guanidine hydrochloride (GuHCl). DeltaG values from the DSC studies are in excellent agreement with values from isothermal GuHCl denaturation monitored by fluorescence and circular dichroism (CD) spectroscopy. Furthermore, the results indicate that irreversible denaturation is closely associated with the formation of an unfolding intermediate. GuHCl appears to promote reversible two-state denaturation by initially preventing aggregation of this unfolding intermediate, and at subsequently higher concentrations, by preventing formation of the intermediate.

Disordered water within a hydrophobic protein cavity visualized by x-ray crystallography.

Water in the hydrophobic cavity of human interleukin 1beta, which was detected by NMR spectroscopy but was invisible by high resolution x-ray crystallography, has been mapped quantitatively by measurement and phasing of all of the low resolution x-ray diffraction data from a single crystal. Phases for the low resolution data were refined by iterative density modification of an initial flat solvent model outside the envelope of the atomic model. The refinement was restrained by the condition that the map of the difference between the electron density distribution in the full unit cell and that of the atomic model be flat within the envelope of the well ordered protein structure. Care was taken to avoid overfitting the diffraction data by maintaining phases for the high resolution data from the atomic model and by a resolution-dependent damping of the structure factor differences between data and model. The cavity region in the protein could accommodate up to four water molecules. The refined solvent difference map indicates that there are about two water molecules in the cavity region. This map is compatible with an atomic model of the water distribution refined by using XPLOR. About 70% of the time, there appears to be a water dimer in the central hydrophobic cavity, which is connected to the outside by two constricted channels occupied by single water molecules approximately 40% of the time on one side and approximately 10% on the other.

Crystal structure of 2,5-diketo-D-gluconic acid reductase A complexed with NADPH at 2.1-A resolution.

The three-dimensional structure of Corynebacterium 2, 5-diketo-D-gluconic acid reductase A (2,5-DKGR A; EC 1.1.1.-), in complex with cofactor NADPH, has been solved by using x-ray crystallographic data to 2.1-A resolution. This enzyme catalyzes stereospecific reduction of 2,5-diketo-D-gluconate (2,5-DKG) to 2-keto-L-gulonate. Thus the three-dimensional structure has now been solved for a prokaryotic example of the aldo-keto reductase superfamily. The details of the binding of the NADPH cofactor help to explain why 2,5-DKGR exhibits lower binding affinity for cofactor than the related human aldose reductase does. Furthermore, changes in the local loop structure near the cofactor suggest that 2,5-DKGR will not exhibit the biphasic cofactor binding characteristics observed in aldose reductase. Although the crystal structure does not include substrate, the two ordered water molecules present within the substrate-binding pocket are postulated to provide positional landmarks for the substrate 5-keto and 4-hydroxyl groups. The structural basis for several previously described active-site mutants of 2,5-DKGR A is also proposed. Recent research efforts have described a novel approach to the synthesis of L-ascorbate (vitamin C) by using a genetically engineered microorganism that is capable of synthesizing 2,5-DKG from glucose and subsequently is transformed with the gene for 2,5-DKGR. These modifications create a microorganism capable of direct production of 2-keto-L-gulonate from D-glucose, and the gulonate can subsequently be converted into vitamin C. In economic terms, vitamin C is the single most important specialty chemical manufactured in the world. Understanding the structural determinants of specificity, catalysis, and stability for 2,5-DKGR A is of substantial commercial interest.

X-ray crystal structure of human acidic fibroblast growth factor.

Fibroblast growth factors (FGFs) are mitogenic and chemotactic agents for a wide variety of cell types and play a primary role in the regulation of angiogenesis. Angiogenesis is involved in a variety of critical physiological events including organogenesis, wound healing, ischemic collateral circulation, and solid tumor growth. High-resolution structural information is key to understanding the mechanism of action of these growth factors. We report here the X-ray crystal structure of human acidic FGF (aFGF), with data extending to 2.0 angstroms resolution. The crystal contains four independent molecules in the asymmetric unit. Each molecule contains a single bound sulfate ion, in similar juxtapositions. The bound sulfate is stabilized through hydrogen-bond interactions with residues Asn 18, Lys 113, and Lys 118 and defines a potential heparin binding site. The hydrogen bond with the N delta 2 moiety of Asn 18 appears to be the most conserved interaction, being similar to those observed for sulfate ion bound to human basic FGF (bFGF) and similar but not identical to interactions observed for bovine aFGF with heparin analogs. Of the added solvent groups, five ordered water molecules are conserved in each of the four independent structures of human aFGF. These water molecules, located at buried positions, provide hydrogen bonding partnerships with several buried polar groups in the core of the protein. A central interior cavity exists in each of the four structures, with sizes ranging from approximately 20 to 50 angstroms3. The cavity sizes appear to be significantly smaller than that observed in the related protein interleukin-1 beta. The region comprising the high affinity FGF receptor binding site is structurally very similar to the corresponding region from human bFGF, whereas the low affinity site is structurally quite different. The results provide a structural basis for the role of the low affinity binding site in FGF receptor discrimination.

Alanine scanning mutagenesis of the alpha-helix 115-123 of phage T4 lysozyme: effects on structure, stability and the binding of solvent.

A series of individual alanine mutations has been constructed in the helical region 115 to 123 in phage T4 lysozyme in order to evaluate the contribution to protein stability of the different side-chains within this region. Pairwise alanine mutations and a combination mutant with seven alanine substitutions were constructed to evaluate the additive effects upon structure and stability. Only three residues within this region (Ser117, Leu118 and Leu121) have a substantial influence upon stability (change in free energy of unfolding greater than 1.0 kcal/mol). Replacement of Ser117 with alanine results in an increase in protein stability of 1.27 kcal/mol, apparently due to the release of strain present in the wild-type protein. Replacement of the buried residues Leu118 and Leu121 is destabilizing. Substitution of the remaining six residues with alanine has relatively little effect on stability. This is consistent with prior studies showing that only 20 to 30% of the residues in amphipathic helices in T4 lysozyme are critical for stability. For some of the pairwise alanine mutants the effects on stability are additive. For most of these mutants, however, there is a slight (approximately 0.15 to 0.25 kcal/mol) non-additivity such that the double mutant is more stable than the sum of the constituent single mutants. This effect is consistently observed for residues with positions i, i +4; i.e. adjacent, but in consecutive turns of the helix, suggesting a weak but significant interaction between these amino acid residues. A more pronounced non-additivity (approximately 0.5 kcal/mol) is seen in the seven-alanine combination mutant. This non-additivity is due to a modest "collapse" or "repacking" that occurs for the combination mutants (especially the multiple alanine mutant) but is not possible for the single replacements. The truncation of some side-chains permits an increase in solvent accessibility of main-chain amide and carbonyl groups. This effect is most pronounced for the seven-alanine combination mutant, where two solvent molecules, not present in wild-type, hydrogen bond to main-chain carbonyl groups in the middle region of the helix. It has been suggested that the binding of such water molecules might represent the first step in solvent-mediated unfolding of an alpha-helix. The appearance of ordered solvent, however, appears to have very little effect on stability (approximately less than 0.2 kcal/mol).

Accommodation of amino acid insertions in an alpha-helix of T4 lysozyme. Structural and thermodynamic analysis.

One to four alanines were inserted by site-directed mutagenesis at three different locations within the alpha-helix comprising residues 39 to 50 in bacteriophage T4 lysozyme. All insertion mutants were correctly folded and catalytically active although the insertions led to a thermal destabilization by 1.1 to 4.2 kcal/mol when compared to wild-type. Variants that restored part of the loss in stability associated with the initial alanine insertions could be found by randomizing the inserted amino acids. In selected cases, directed mutagenesis of adjacent residues was also used to regain stability. Structural information obtained from X-ray crystallography and/or 2D-NMR for 10 different variants showed two distinct ways in which the protein responded to the amino acid insertions: (1) The inserted amino acids were incorporated into the helix by replacing preceding wild-type amino acids and causing a shift in register towards the N terminus. As a consequence, wild-type amino acids were translocated from the helix into the preceding loop. (2) Insertions caused a "looping out" within the alpha-helix. In this case the perturbation was confined to a minimal region in the immediate vicinity of the insertion. No change in the length of the helix was detected in either case. The structural response appears to be determined by the maintenance of the hydrophobic interface between the helix and the rest of the protein. This interface remains essentially intact in all variant structures. The results exemplify the plasticity and the adaptability of the protein structure which allows the incorporation of additional amino acids into a secondary structure element without large structural perturbations, as long as vital internal interactions are preserved. They also suggest that loops in proteins related by evolution can vary in length not only because of insertions within the loops themselves but also as a consequence of insertions within neighboring secondary structure elements.