Structure and evolutionary origin of Ca(2+)-dependent herring type II antifreeze protein

In order to survive under extremely cold environments, many organisms produce antifreeze proteins (AFPs). AFPs inhibit the growth of ice crystals and protect organisms from freezing damage. Fish AFPs can be classified into five distinct types based on their structures. Here we report the structure of herring AFP (hAFP), a Ca(2+)-dependent fish type II AFP. It exhibits a fold similar to the C-type (Ca(2+)-dependent) lectins with unique ice-binding features. The 1.7 A crystal structure of hAFP with bound Ca(2+) and site-directed mutagenesis reveal an ice-binding site consisting of Thr96, Thr98 and Ca(2+)-coordinating residues Asp94 and Glu99, which initiate hAFP adsorption onto the [10-10] prism plane of the ice lattice. The hAFP-ice interaction is further strengthened by the bound Ca(2+) through the coordination with a water molecule of the ice lattice. This Ca(2+)-coordinated ice-binding mechanism is distinct from previously proposed mechanisms for other AFPs. However, phylogenetic analysis suggests that all type II AFPs evolved from the common ancestor and developed different ice-binding modes. We clarify the evolutionary relationship of type II AFPs to sugar-binding lectins.     

Low-temperature increases the yield of biologically active herring antifreeze protein in Pichia pastoris

Antifreeze proteins and antifreeze glycoproteins are structurally diverse molecules that share a common property in binding to ice crystals and inhibiting ice crystal growth. Type II fish antifreeze protein of Atlantic herring (Clupea harengus harengus) is unique in its requirement of Ca(2+) for antifreeze activity. In this study, we utilized the secretion vector pGAPZalpha A to express recombinant herring antifreeze protein (WT) and a fusion protein with a C-terminal six-histidine tag (WT-6H) in yeast Pichia pastoris wild-type strain X-33 or protease-deficient strain SMD1168H. Both recombinant proteins were secreted into the culture medium and properly folded and functioned as the native herring antifreeze protein. Furthermore, our studies demonstrated that expression at a lower temperature increased the yield of the recombinant protein dramatically, which might be due to the enhanced protein folding pathway, as well as increased cell viability at lower temperature. These data suggested that P. pastoris is a useful system for the production of soluble and biologically active herring antifreeze protein required for structural and functional studies.     

Structural basis for antifreeze activity of ice-binding protein from arctic yeast

Arctic yeast Leucosporidium sp. produces a glycosylated ice-binding protein (LeIBP) with a molecular mass of ～25 kDa, which can lower the freezing point below the melting point once it binds to ice. LeIBP is a member of a large class of ice-binding proteins, the structures of which are unknown. Here, we report the crystal structures of non-glycosylated LeIBP and glycosylated LeIBP at 1.57- and 2.43-? resolution, respectively. Structural analysis of the LeIBPs revealed a dimeric right-handed β-helix fold, which is composed of three parts: a large coiled structural domain, a long helix region (residues 96-115 form a long α-helix that packs along one face of the β-helix), and a C-terminal hydrophobic loop region ((243)PFVPAPEVV(251)). Unexpectedly, the C-terminal hydrophobic loop region has an extended conformation pointing away from the body of the coiled structural domain and forms intertwined dimer interactions. In addition, structural analysis of glycosylated LeIBP with sugar moieties attached to Asn(185) provides a basis for interpreting previous biochemical analyses as well as the increased stability and secretion of glycosylated LeIBP. We also determined that the aligned Thr/Ser/Ala residues are critical for ice binding within the B face of LeIBP using site-directed mutagenesis. Although LeIBP has a common β-helical fold similar to that of canonical hyperactive antifreeze proteins, the ice-binding site is more complex and does not have a simple ice-binding motif. In conclusion, we could identify the ice-binding site of LeIBP and discuss differences in the ice-binding modes compared with other known antifreeze proteins and ice-binding proteins.     

Calcium interacts with antifreeze proteins and chitinase from cold-acclimated winter rye

During cold acclimation, winter rye (Secale cereale) plants accumulate pathogenesis-related proteins that are also antifreeze proteins (AFPs) because they adsorb onto ice and inhibit its growth. Although they promote winter survival in planta, these dual-function AFPs proteins lose activity when stored at subzero temperatures in vitro, so we examined their stability in solutions containing CaCl2, MgCl2, or NaCl. Antifreeze activity was unaffected by salts before freezing, but decreased after freezing and thawing in CaCl2 and was recovered by adding a chelator. Ca2+ enhanced chitinase activity 3- to 5-fold in unfrozen samples, although hydrolytic activity also decreased after freezing and thawing in CaCl2. Native PAGE, circular dichroism, and Trp fluorescence experiments showed that the AFPs partially unfold after freezing and thawing, but they fold more compactly or aggregate in CaCl2. Ruthenium red, which binds to Ca(2+)-binding sites, readily stained AFPs in the absence of Ca2+, but less stain was visible after freezing and thawing AFPs in CaCl2. We conclude that the structure of AFPs changes during freezing and thawing, creating new Ca(2+)-binding sites. Once Ca2+ binds to those sites, antifreeze activity, chitinase activity and ruthenium red binding are all inhibited. Because free Ca2+ concentrations are typically low in the apoplast, antifreeze activity is probably stable to freezing and thawing in planta. Ca2+ may regulate chitinase activity if concentrations are increased locally by release from pectin or interaction with Ca(2+)-binding proteins. Furthermore, antifreeze activity can be easily maintained in vitro by including a chelator during frozen storage.     

Contribution of hydrophobic residues to ice binding by fish type III antifreeze protein

Type III antifreeze protein (AFP) is a 7-kDa globular protein with a flat ice-binding face centered on Ala 16. Neighboring hydrophilic residues Gln 9, Asn 14, Thr 15, Thr 18 and Gln 44 have been implicated by site-directed mutagenesis in binding to ice. These residues have the potential to form hydrogen bonds with ice, but the tight packing of side chains on the ice-binding face limits the number and strength of possible hydrogen bond interactions. Recent work with alpha-helical AFPs has emphasized the hydrophobicity of their ice-binding sites and suggests that hydrophobic interactions are important for antifreeze activity. To investigate the contribution of hydrophobic interactions between type III AFP and ice, Leu, Ile and Val residues on the rim of the ice-binding face were changed to alanine. Mutant AFPs with single alanine substitutions, L19A, V20A, and V41A, showed a 20% loss in activity. Doubly substituted mutants, L19A/V41A and L10A/I13A, had less than 50% of the activity of the wild type. Thus, side chain substitutions that leave a cavity or undercut the contact surface are almost as deleterious to antifreeze activity as those that lengthen the side chain. These mutations emphasize the importance of maintaining a specific surface contour on the ice-binding face for docking to ice.     

Enhancing the activity of a beta-helical antifreeze protein by the engineered addition of coils

The effectiveness of natural antifreeze proteins in inhibiting the growth of a seed ice crystal seems to vary with protein size. Here we have made use of the extreme regularity of the beta-helical antifreeze protein from the beetle Tenebrio molitor to explore systematically the relationship between antifreeze activity and the area of the ice-binding site. Each of the 12-amino acid, disulfide-bonded central coils of the beta-helix contains a Thr-Xaa-Thr ice-binding motif. By adding coils to, and deleting coils from, the seven-coil parent antifreeze protein, we have made a series of constructs with 6-11 coils. Misfolded forms of these antifreezes were removed by ice affinity purification to accurately compare the specific activity of each construct. There was a 10-100-fold gain in activity upon going from six to nine coils, depending on the concentration that was compared. Activity was maximal for the nine-coil construct, which gave a freezing point depression of 6.5 C degrees at 0.7 mg/mL, but actually decreased for the 10- and 11-coil constructs. This small loss in activity might result from the accumulation of a slight mismatch between the spacing of the ice-binding threonine residues and the O atoms of the ice lattice.     

Artificial antifreeze polypeptides: alpha-helical peptides with KAAK motifs have antifreeze and ice crystal morphology modifying properties.

Antifreeze polypeptides from fish are generally thought to inhibit ice crystal growth by specific adsorption onto ice surfaces and preventing addition of water molecules to the ice lattice. Recent studies have suggested that this adsorption results from hydrogen bonding through the side chains of polar amino acids as well as hydrophobic interactions between the non-polar domains on the ice-binding side of antifreeze polypeptides and the clathrate-like surfaces of ice. In order to better understand the activity of one of the antifreeze polypeptide families, namely the alpha-helical type I antifreeze polypeptides, four alpha-helical peptides having sequences not directly analogous to those of known antifreeze polypeptides and containing only positively charged and non-polar side chains were synthesized. Two peptides with regularly spaced lysine residues, GAAKAAKAAAAAAAKAAKAAAAAAAKAAKAAGGY-NH2 and GAALKAAKAAAAAALKAAKAAAAAALKAAKAAGGY-NH2, showed antifreeze activity, albeit weaker than seen in natural antifreeze polypeptides, by the criteria of freezing point depression (thermal hysteresis) and ice crystal modification to a hexagonal trapezohedron. Peptides with irregular spacing of Lys residues were completely inactive. Up to now, lysine residues have not been generally associated with antifreeze activity, though they have been implicated in some antifreeze polypeptides. This work also shows that lysine residues in themselves, when properly positioned on an alpha-helical polyalanine scaffold, have all the requisite properties needed for such an activity.     

Alternative roles for putative ice-binding residues in type I antifreeze protein

Two sets of variants of type I antifreeze protein have been synthesized to investigate the role of Leu and Asn in the activity of this 37-residue alpha-helix. Leu and Asn flank the central two of four regularly spaced ice-binding Thr in the i-1 and i + 3 positions, respectively. All three residues project from the same side of the helix to form the protein's putative ice-adsorption site and are considered in some models to act together as an "ice-binding motif". Replacement of Asn by residues with shorter side chains resulted in either a small loss (Ala) or gain (Thr) of antifreeze activity. However, substitution of Asn by its slightly larger homologue (Gln) abolished thermal hysteresis activity. The Gln-containing peptide was very soluble, largely monomeric, and fully helical. Of the three variants in which Leu was replaced by Ala, two of the three were more active than their Leu-containing counterparts, but all three variants began to precipitate as the peptide concentration increased. None of the seven variants tested showed dramatic differences in ice crystal morphology from that established by the wild type. These results are consistent with a primary role for Leu in preventing peptide aggregation at the antifreeze protein concentrations (10 mg/mL) normally present in fish serum. Similarly the role for Asn may have more to do with enhancing the solubility of these rather hydrophobic peptides than of making a stereospecific hydrogen-bonding match to the ice lattice as traditionally thought. Nevertheless, the dramatic loss of activity in the Asn-to-Gln replacement demonstrates the steric restriction on residues in or near the ice-binding site of the peptide.     

Effect of type III antifreeze protein dilution and mutation on the growth inhibition of ice.

Mutation of residues at the ice-binding site of type III antifreeze protein (AFP) not only reduced antifreeze activity as indicated by the failure to halt ice crystal growth, but also altered ice crystal morphology to produce elongated hexagonal bipyramids. In general, the c axis to a axis ratio of the ice crystal increased from approximately 2 to over 10 with the severity of the mutation. It also increased during ice crystal growth upon serial dilution of the wild-type AFP. This is in marked contrast to the behavior of the alpha-helical type I AFPs, where neither dilution nor mutation of ice-binding residues increases the c:a axial ratio of the ice crystal above the standard 3.3. We suggest that the ice crystal morphology produced by type III AFP and its mutants can be accounted for by the protein binding to the prism faces of ice and operating by step growth inhibition. In this model a decrease in the affinity of the AFP for ice leads to filling in of individual steps at the prism surfaces, causing the ice crystals to grow with a longer c:a axial ratio.     

A Ca2+-dependent bacterial antifreeze protein domain has a novel beta-helical ice-binding fold

AFPs (antifreeze proteins) are produced by many organisms that inhabit ice-laden environments. They facilitate survival at sub-zero temperatures by binding to, and inhibiting, the growth of ice crystals in solution. The Antarctic bacterium Marinomonas primoryensis produces an exceptionally large(>1 MDa) hyperactive Ca2+-dependent AFP. We have cloned,expressed and characterized a 322-amino-acid region of the protein where the antifreeze activity is localized that shows similarity to the RTX (repeats-in-toxin) family of proteins. The recombinant protein requires Ca2+ for structure and activity, and it is capable of depressing the freezing point of a solution in excess of 2 degrees C at a concentration of 0.5 mg/ml, therefore classifying it as a hyperactive AFP. We have developed a homology-guided model of the antifreeze region based partly on the Ca2+-bound beta-roll from alkaline protease. The model has identified both a novel beta-helical fold and an ice-binding site. The interior of the beta-helix contains a single row of bound Ca2+ ions down one side of the structure and a hydrophobic core down the opposite side. The ice binding surface consists of parallel repetitive arrays of threonine and aspartic acid/asparagine residues located down the Ca2+-bound side of the structure. The model was tested and validated by site-directed mutagenesis. It explains the Ca2+-dependency of the region, as well its hyperactive antifreeze activity. This is the first bacterial AFP to be structurally characterized and is one of only five hyperactive AFPs identified to date.AFPS     

Rational design of alpha-helical antifreeze peptides.

The alanine-rich alpha-helical antifreeze protein from the winter flounder Pseudopleuronectes americanus adsorbs to specific planes of ice guided by an ice lattice match to threonine residues regularly spaced 16.6 A apart. We report here that by redesigning the winter flounder antifreeze peptide to incorporate a 27.1-A spacing between putative 'ice-binding' threonines, the deduced binding alignment of the helical molecule on the ice lattice is changed from the Miller indices directional vector [1102 ] to [2203 ]. Subsequent ice-binding characteristics are altered, including changes in adsorption specificity, decreases in thermal hysteresis activity and the formation of rotated hexagonal bipyramid ice crystal morphology.     

Ice-binding surface of fish type III antifreeze.

We employed computational techniques, including molecular docking, energy minimization, and molecular dynamics simulation, to investigate the ice-binding surface of fish type III antifreeze protein (AFP). The putative ice-binding site was previously identified by mutagenesis, structural analysis, and flatness evaluation. Using a high-resolution x-ray structure of fish type III AFP as a model, we calculated the ice-binding interaction energy of 11 surface patches chosen to cover the entire surface of the protein. These various surface patches exhibit small but significantly different ice-binding interaction energies. For both the prism ice plane and an "ice" plane in which water O atoms are randomly positioned, our calculations show that a surface patch containing 14 residues (L19, V20, T18, S42, V41, Q9, P12, A16, M21, T15, Q44, I13, N14, K61) has the most favorable interaction energy and corresponds to the previously identified ice-binding site of type III AFP. Although in general agreement with the earlier studies, our results also suggest that the ice-binding site may be larger than the previously identified "core" cluster that includes mostly hydrophilic residues. The enlargement mainly results from the inclusion of peripheral hydrophobic residues and K61.     

Quantitative and qualitative analysis of type III antifreeze protein structure and function

Some cold water marine fishes avoid cellular damage because of freezing by expressing antifreeze proteins (AFPs) that bind to ice and inhibit its growth; one such protein is the globular type III AFP from eel pout. Despite several studies, the mechanism of ice binding remains unclear because of the difficulty in modeling the AFP-ice interaction. To further explore the mechanism, we have determined the x-ray crystallographic structure of 10 type III AFP mutants and combined that information with 7 previously determined structures to mainly analyze specific AFP-ice interactions such as hydrogen bonds. Quantitative assessment of binding was performed using a neural network with properties of the structure as input and predicted antifreeze activity as output. Using the cross-validation method, a correlation coefficient of 0.60 was obtained between measured and predicted activity, indicating successful learning and good predictive power. A large loss in the predictive power of the neural network occurred after properties related to the hydrophobic surface were left out, suggesting that van der Waal's interactions make a significant contribution to ice binding. By combining the analysis of the neural network with antifreeze activity and x-ray crystallographic structures of the mutants, we extend the existing ice-binding model to a two-step process: 1) probing of the surface for the correct ice-binding plane by hydrogen-bonding side chains and 2) attractive van der Waal's interactions between the other residues of the ice-binding surface and the ice, which increases the strength of the protein-ice interaction.     

Ice-binding mechanism of winter flounder antifreeze proteins

We have studied the winter flounder antifreeze protein (AFP) and two of its mutants using molecular dynamics simulation techniques. The simulations were performed under four conditions: in the gas phase, solvated by water, adsorbed on the ice (2021) crystal plane in the gas phase and in aqueous solution. This study provided details of the ice-binding pattern of the winter flounder AFP. Simulation results indicated that the Asp, Asn, and Thr residues in the AFP are important in ice binding and that Asn and Thr as a group bind cooperatively to the ice surface. These ice-binding residues can be collected into four distinct ice-binding regions: Asp-1/Thr-2/Asp-5, Thr-13/Asn-16, Thr-24/Asn-27, and Thr-35/Arg-37. These four regions are 11 residues apart and the repeat distance between them matches the ice lattice constant along the (1102) direction. This match is crucial to ensure that all four groups can interact with the ice surface simultaneously, thereby, enhancing ice binding. These Asx (x = p or n)/Thr regions each form 5-6 hydrogen bonds with the ice surface: Asn forms about three hydrogen bonds with ice molecules located in the step region while Thr forms one to two hydrogen bonds with the ice molecules in the ridge of the (2021) crystal plane. Both the distance between Thr and Asn and the ordering of the two residues are crucial for effective ice binding. The proper sequence is necessary to generate a binding surface that is compatible with the ice surface topology, thus providing a perfect "host/guest" interaction that simultaneously satisfies both hydrogen bonding and van der Waals interactions. The results also show the relation among binding energy, the number of hydrogen bonds, and the activity. The activity is correlated to the binding energy, and in the case of the mutants we have studied the number of hydrogen bonds. The greater the number of the hydrogen bonds the greater the antifreeze activity. The roles van der Waals interactions and the hydrophobic effect play in ice binding are also highlighted. For the latter it is demonstrated that the surface of ice has a clathratelike structure which favors the partitioning of hydrophobic groups to the surface of ice. It is suggested that mutations that involve the deletion of hydrophobic residues (e.g., the Leu residues) will provide insight into the role the hydrophobic effect plays in partitioning these peptides to the surface of ice.     

Secretory expression and site-directed mutagenesis studies of the winter flounder skin-type antifreeze polypeptides.

Winter flounder contains both liver-type, extracellular antifreeze polypeptides (wflAFPs) and less active skin-type, intracellular antifreeze polypeptides (wfsAFPs). The lower activity of wfsAFPs might be due to their lack of complete ice-binding motifs '-K-DT-'. In order to test the functional role of this putative ice-binding motif, mutations were introduced into the N-terminal or C-terminal regions of wfsAFP-2, which lack any presumptive ice-binding motifs. The wild-type and mutant wfsAFP-2 were secreted in Escherichia coli culture media as mature antifreeze proteins and purified to homogeneity. Surprisingly, the antifreeze activity decreased with the introduction of ice-binding motifs. However, there was a corresponding decrease in alpha-helical content as well as thermal stability and this would suggest a compromise in retaining helical structure with the presence of ice-binding motifs. These studies have brought new definitions of the roles of ice-binding motif residues in type I antifreeze proteins.     

Analysis of ice-binding sites in fish type II antifreeze protein by quantum mechanics

Many organisms living in cold environments can survive subzero temperatures by producing antifreeze proteins (AFPs) or antifreeze glycoproteins. In this paper we investigate the ice-binding surface of type II AFP by quantum mechanical methods, which, to the best of our knowledge, represents the first time that molecular orbital computational approaches have been applied to AFPs. Molecular mechanical approaches, including molecular docking, energy minimization, and molecular dynamics simulation, were used to obtain optimal systems for subsequent quantum mechanical analysis. We selected 17 surface patches covering the entire surface of the type II AFP and evaluated the interaction energy between each of these patches and two different ice planes using semi-empirical quantum mechanical methods. We have demonstrated the weak orbital overlay phenomenon and the change of bond orders in ice. These results consistently indicate that a surface patch containing 19 residues (K37, L38, Y20, E22, Y21, I19, L57, T56, F53, M127, T128, F129, R17, C7, N6, P5, G10, Q1, and W11) is the most favorable ice-binding site for both a regular ice plane and an ice plane where water O atoms are randomly positioned. Furthermore, for the first time the computation results provide new insights into the weakening of the ice lattice upon AFP binding, which may well be a primary factor leading to AFP-induced ice growth inhibition.     

Identification of the ice-binding face of antifreeze protein from Tenebrio molitor

The beetle Tenebrio molitor produces several isoforms of a highly disulfide-bonded beta-helical antifreeze protein with one surface comprised of an array of Thr residues that putatively interacts with ice. In order to use mutagenesis to identify the ice-binding face, we have selected an isoform that folds well and is tolerant of amino acid substitution, and have developed a heating test to monitor refolding. Three different types of steric mutations made to the putative ice-binding face reduced thermal hysteresis activity substantially while a steric mutation on an orthogonal surface had little effect. NMR spectra indicated that all mutations affected protein folding to a similar degree and demonstrated that most of the protein folded well. The large reductions in activity associated with steric mutations in the Thr array strongly suggest that this face of the protein is responsible for ice binding.     

Structure and function of antifreeze proteins

High-resolution three-dimensional structures are now available for four of seven non-homologous fish and insect antifreeze proteins (AFPs). For each of these structures, the ice-binding site of the AFP has been defined by site-directed mutagenesis, and ice etching has indicated that the ice surface is bound by the AFP. A comparison of these extremely diverse ice-binding proteins shows that they have the following attributes in common. The binding sites are relatively flat and engage a substantial proportion of the protein's surface area in ice binding. They are also somewhat hydrophobic -- more so than that portion of the protein exposed to the solvent. Surface-surface complementarity appears to be the key to tight binding in which the contribution of hydrogen bonding seems to be secondary to van der Waals contacts.     

Mechanism of the Ca2+-induced enhancement of the intrinsic factor VIIa activity

The intrinsic activity of coagulation factor VIIa (FVIIa) is dependent on Ca(2+) binding to a loop (residues 210-220) in the protease domain. Structural analysis revealed that Ca(2+) may enhance the activity by attenuating electrostatic repulsion of Glu(296) and/or by facilitating interactions between the loop and Lys(161) in the N-terminal tail. In support of the first mechanism, the mutations E296V and D212N resulted in similar, about 2-fold, enhancements of the amidolytic activity. Moreover, mutation of the Lys(161)-interactive residue Asp(217) or Asp(219) to Ala reduced the amidolytic activity by 40-50%, whereas the K161A mutation resulted in 80% reduction. Hence one of these Asp residues in the Ca(2+)-binding loop appears to suffice for some residual interaction with Lys(161), whereas the more severe effect upon replacement of Lys(161) is due to abrogation of the interaction with the N-terminal tail. However, Ca(2+) attenuation of the repulsion between Asp(212) and Glu(296) keeps the activity above that of apoFVIIa. Altogether, our data suggest that repulsion involving Asp(212) in the Ca(2+)-binding loop suppresses FVIIa activity and that optimal activity requires a favorable interaction between the Ca(2+)-binding loop and the N-terminal tail. Crystal structures of tissue factor-bound FVIIa(D212N) and FVIIa(V158D/E296V/M298Q) revealed altered hydrogen bond networks, resembling those in factor Xa and thrombin, after introduction of the D212N and E296V mutations plausibly responsible for tethering the N-terminal tail to the activation domain. The charge repulsion between the Ca(2+)-binding loop and the activation domain appeared to be either relieved by charge removal and new hydrogen bonds (D212N) or abolished (E296V). We propose that Ca(2+) stimulates the intrinsic FVIIa activity by a combination of charge neutralization and loop stabilization.     

Structural variations in the alanine-rich antifreeze proteins of the pleuronectinae

The sequence and activity of antifreeze proteins from two right eye flounder species were compared to assess the influence of structural variations on antifreeze capacity. The cDNA encoding the major serum antifreeze protein in the yellowtail flounder (Limanda ferruginea) was cloned from liver tissue. Its DNA sequence shows that the precursor to the antifreeze is a 97-residue preproportion. Edman degradation identified the N-terminus of the 48-amino-acid mature serum antifreeze protein and confirmed the sequence of the first 36 residues. A comparison with the previously determined winter flounder antifreeze protein and mRNA sequences shows strong homology through the 5' and 3' untranslated regions and in the peptide region. The mature protein section has the greatest sequence variation. Specifically, the yellowtail antifreeze protein, in contrast to that of the winter flounder, contains a fourth 11-amino-acid repeat and lacks several of the hydrophilic residues that have been postulated to aid in the binding of the protein to ice crystals. Intramolecular salt bridges are present in the antifreeze proteins from both species but in different registries with respect to the 11-amino-acid repeats. On a mass basis the yellowtail flounder antifreeze, though longer than that of the winter flounder, is only 80% as effective at depressing the freezing temperature of aqueous solutions. This lower activity might be due to the reduced number of hydrophilic ice-binding residues per molecule.