A Comparison of the Self-association Behavior of the Plant Cyclotides Kalata B1 and Kalata B2 via Analytical Ultracentrifugation*

The recently discovered cyclotides kalata B1 and kalata B2 are miniproteins containing a head-to-tail cyclized backbone and a cystine knot motif, in which disulfide bonds and the connecting backbone segments form a ring that is penetrated by the third disulfide bond. This arrangement renders the cyclotides extremely stable against thermal and enzymatic decay, making them a possible template onto which functionalities can be grafted. We have compared the hydrodynamic properties of two prototypic cyclotides, kalata B1 and kalata B2, using analytical ultracentrifugation techniques. Direct evidence for oligomerization of kalata B2 was shown by sedimentation velocity experiments in which a method for determining size distribution of polydisperse molecules in solution was employed. The shape of the oligomers appears to be spherical. Both sedimentation velocity and equilibrium experiments indicate that in phosphate buffer kalata B1 exists mainly as a monomer, even at millimolar concentrations. In contrast, at 1.6 mm, kalata B2 exists as an equilibrium mixture of monomer (30%), tetramer (42%), octamer (25%), and possibly a small proportion of higher oligomers. The results from the sedimentation equilibrium experiments show that this self-association is concentration dependent and reversible. We link our findings to the three-dimensional structures of both cyclotides, and propose two putative interaction interfaces on opposite sides of the kalata B2 molecule, one involving a hydrophobic interaction with the Phe6, and the second involving a charge-charge interaction with the Asp25 residue. An understanding of the factors affecting solution aggregation is of vital importance for future pharmaceutical application of these molecules.

The recently discovered cyclotides kalata B1 and kalata B2 are miniproteins containing a head-to-tail cyclized backbone and a cystine knot motif, in which disulfide bonds and the connecting backbone segments form a ring that is penetrated by the third disulfide bond. This arrangement renders the cyclotides extremely stable against thermal and enzymatic decay, making them a possible template onto which functionalities can be grafted. We have compared the hydrodynamic properties of two prototypic cyclotides, kalata B1 and kalata B2, using analytical ultracentrifugation techniques. Direct evidence for oligomerization of kalata B2 was shown by sedimentation velocity experiments in which a method for determining size distribution of polydisperse molecules in solution was employed. The shape of the oligomers appears to be spherical. Both sedimentation velocity and equilibrium experiments indicate that in phosphate buffer kalata B1 exists mainly as a monomer, even at millimolar concentrations. In contrast, at 1.6 mM, kalata B2 exists as an equilibrium mixture of monomer (30%), tetramer (42%), octamer (25%), and possibly a small proportion of higher oligomers. The results from the sedimentation equilibrium experiments show that this self-association is concentration dependent and reversible. We link our findings to the three-dimensional structures of both cyclotides, and propose two putative interaction interfaces on opposite sides of the kalata B2 molecule, one involving a hydrophobic interaction with the Phe 6 , and the second involving a charge-charge interaction with the Asp 25 residue. An understanding of the factors affecting solution aggregation is of vital importance for future pharmaceutical application of these molecules.
The cyclotides (1) are a recently discovered family of circular proteins that have been isolated from various Rubiaceae and Violaceae plants. They are one of several groups of naturally occurring circular proteins discovered in a wide range of microand higher organisms over recent years (2,3). To date, around 50 different cyclotides are known, ranging in size from 28 to 37 amino acids. In addition to their head-to-tail cyclized peptide backbones, they all share a high sequence similarity as well as the striking feature of a cystine knot: two disulfide bonds and their connecting backbone segments form a ring that is penetrated by the third disulfide bond. This cyclic cystine knot (CCK) 1 motif (4), i.e. the combination of circular peptide backbone and knotted disulfide arrangement, renders the cyclotides extremely stable, both against thermal degradation and enzymatic digest. Anecdotal evidence from the 1970s, for example, indicates that African tribeswomen prepared a birth-facilitating tea by boiling the leaves of a local plant, Oldenlandia affinis. On investigation of this uterotonic agent it was shown that its main components were macrocyclic peptides, predominantly kalata B1 and kalata B2 (5). In addition to this uterotonic effect, cyclotides show a broad range of other biological activities, including antimicrobial (6), cytotoxic (7), and anti-HIV activity (8,9) as well as neurotensin antagonism (10). Their natural function in plants appears to be as defense molecules (11).
Synthetic cyclization is widely used in the pharmaceutical industry to enhance the stability and biological lifetime of small peptides. It is proposed that because of their exceptional stability the cyclotides may serve as useful protein templates for biopharmaceutical applications (12). The aim is to graft pharmacologically relevant peptide epitopes onto the stable CCK framework. Since knowledge of protein oligomerization and self-association behavior under various solution conditions will be vital in the evaluation of its suitability as a biopharmaceutical, we studied the sedimentation properties of two prototypic cyclotides, kalata B1 and kalata B2, with the purpose of shedding light on their properties in solution. These molecules were the first cyclotides to be discovered, are the most abundant peptides in the native plant O. affinis, and have dissimilar solution behaviors.
In this study we employed analytical ultracentrifugation techniques, where absorbance (for low concentrations) and interference optics (for high concentrations) were used to access a broad range of protein concentrations for the characterization of these cyclotides and their oligomers. Analytical ultracentrifugation provides important information about the solution behavior of biomolecules, including the overall size and shape of the molecules and their propensity to self-associate. We utilized sedimentation velocity experiments to resolve the nature of the aggregation behavior employing a newly applied method for determining the continuous size distribution of polydisperse macromolecules in solution (13,14). We also characterized the hydrodynamic properties of these cyclotides, including the sedimentation coefficient (s), the translational diffusion coefficient (D), as well as molecular mass and shape in solution. Sedimentation equilibrium experiments were performed to confirm the identities of the oligomeric species that were detected from the sedimentation velocity experiments, as well as to ascertain the reversibility and determine association constants of the selfassociation reactions.
Based on the NMR structure coordinates of kalata B1 and kalata B2, a comparison of the protein surface residues was made. Special attention was given to residues that affect the properties of those protein surfaces that may play a role in oligomerization (15). Analysis of the structures led us to propose locations of putative self-interaction sites that would explain the solution behavior of these fascinating circular proteins.

EXPERIMENTAL PROCEDURES
Sample Preparation-The limiting solubility of a freshly prepared solution of kalata B2 in buffer is ϳ6.5 mg/ml. This solution was stable over a 2-week period during which the analytical ultracentrifugation experiments were carried out at 20°C. However, on storage at low temperature over time the solution becomes colloidal, with some precipitation occurring. By contrast, kalata B1 solutions appear to be less susceptible to precipitation. All sedimentation experiments were done with freshly prepared solutions.
Analytical Ultracentrifugation-Sedimentation equilibrium and velocity experiments were carried out using an Optima XL-A/XL-I analytical ultracentrifuge (Beckman Coulter, Fullerton, CA), equipped with both absorbance and interference optical detection systems, using a Beckman An-60 Ti rotor with cells containing sapphire windows, and titanium double-sector centerpieces (pathlength 1.2 cm) (Nanolytics GmbH, Dallgow, Germany). The value of the radial distance of the bottom of the cell is between 7.13 and 7.15 cm (not stretched). Kalata B1 and kalata B2 were isolated from the aerial parts of O. affinis as described previously (1) and purified by repeated reverse phase HPLC. Prior to centrifugation, the peptides were either dissolved in or dialyzed into 100 mM sodium phosphate buffer, pH 7.4. The molar extinction coefficient at 280 nm (5875 M Ϫ1 cm Ϫ1 ), partial specific volumes (0.702 liters/g), and molecular masses for both kalata B1 and B2 (2,892 and 2,955 Da, respectively) were calculated based on its amino acid composition using the program Sednterp (16). In experiments using interference optics, 3.33 fringes were taken as equal to 1 mg/ml protein.
Sedimentation Velocity-For sedimentation velocity experiments, samples (340 l, concentrations between 0.5 and 6.5 mg/ml) and reference solutions (350 l) were loaded into cells. The rotor temperature was equilibrated at 20°C in the vacuum chamber for 1-2 h prior to the start of the run. Experiments were conducted at 20°C and rotor speeds of 60,000 rpm. Interference scans were collected at time intervals of 1 min. Data were analyzed with the software Sedfit Version 8.52, and errors reported are from replicate experiments.
Continuous Size Distribution Analysis-The continuous size distribution analysis of the sedimentation velocity data of the kalata proteins was performed with Sedfit (Version 8.52). In this analysis a differential sedimentation coefficient distribution c(s) that deconvolutes diffusion effects, based on the direct boundary modeling with distributions of Lamm equation solutions (13) is determined. A sedimentation coefficient distribution c(s) can be defined as in Equation 1, a͑r,t) ϭ ͵ c(s)(s,D(s),r,t)ds ϩ (Eq. 1) with the measured absorbance or interference profiles a(r,t) denoting the observed sedimentation data, c(s) the concentration of species with sedimentation coefficients between s and s ϩ ds, (s,D,r,t) the solution of the Lamm equation described above (17) and ⑀ the noise components. The Lamm equation was solved by finite element methods on a static or moving frame of reference (18,19). For each species, the diffusion coefficient D(s) was estimated as a function of the sedimentation s based on the known partial specific volume of the protein, and on an estimated anhydrous frictional ratio (f/f o ) (14). The c(s) distribution was converted into a molar mass distribution c(M) (13,14).
All size distributions were solved on a radial grid of 1000 radius values between the meniscus and bottom, a confidence level of p ϭ 0.68, and a resolution N of 300 sedimentation coefficients between 0.1 and 10 s (or molar masses between 500 and 100,000 Da).
Rapid Monomer-Tetramer-Octamer Self-association Model-The sedimentation velocity analysis was performed with Sedfit (Version 8.52) using a model for rapid reversible monomer-tetramer-octamer self-association by calculating finite element solutions of the Lamm equation according to methods described by Claverie (18), combined with local weight-average sedimentation coefficients and gradient average diffusion coefficients (20) and a two-step propagation scheme as described by Schuck (19). In modeling the experimental data the association constants and species sedimentation coefficients were treated as floating parameters.
Sedimentation Equilibrium-For the sedimentation equilibrium experiments the cells were filled with 130 -150 l of sample at loading concentrations between 1.0 -6.5 mg/ml and reference (140 -160 l) solutions. Sedimentation equilibrium was attained at 24 h at a rotor temperature of 20°C, and at rotor speeds of 40,000, 45,000, 50,000, and 60,000 rpm respectively. Interferometric patterns were recorded with only water in the cell at appropriate speeds and used for correcting for radial-dependent fluctuation in Rayleigh response across the cell (21). Data analysis was performed by global analysis of 9 datasets obtained at different loading concentrations and rotor speeds using XL-A/XL-I Data Analysis Software Version 4.0 (Beckman Instruments, Inc. Beckman Coulter, Fullerton, CA) for fitting the self-association models. Estimates of the weight-average molar masses (M r ) were obtained from the least-squares fits that were based on the Boltzmann distributions of ideal species in the centrifugal field as shown in Equation 2, where S(r) is the experimentally observed concentration signal in absorbance or fringes at radius r, S(r 0 ) the concentration signal at the reference radius r 0, ϭ M r (1 Ϫ )( 2 /2RT) (where M r is the weightaverage molar mass of the monomer, the partial specific volume of the solute, the solvent density, the rotor angular velocity, R the gas constant, and T the temperature in Kelvin) and E the baseline offset, and models found in the data analysis software involving multiple species (22)(23)(24).

RESULTS
In previous NMR spectroscopic studies we had noted that a well determined NMR structure of kalata B1 could be obtained in aqueous solution at millimolar concentrations, while kalata B2 required 20 -30% of an organic co-solvent to achieve a similar quality structure. One possible explanation would be an increased propensity of kalata B2 to aggregate, but it was not possible to determine this from the NMR data. Analytical ultracentrifugation techniques were therefore employed to compare the hydrodynamic properties and resolve the oligomeric structures of kalata B1 and kalata B2. This was achieved by fitting the sedimentation velocity data to a continuous size distribution (sedimentation coefficient and molar mass), noninteracting discrete species and rapid monomer-tetramer-octamer self-association models. In addition, sedimentation equilibrium data over a wide range of solution conditions were fitted to non-interacting discrete species model, as well as a number of self-association models.
Sedimentation Velocity-The sedimentation velocity experiments for kalata B1 and kalata B2 were conducted at a concentration of 5.0 mg/ml. The data, obtained at time intervals of 1 min (Fig. 1), show an excellent fit to a continuous size distribution model (Equation 1). The best-fit sedimentation profiles shown in panel A are of very high quality (r.m.s.d. ϭ 0.018, which represents a fit with a relative error of approx. 0.1%), as reflected in the small, randomly distributed residuals and virtually no systematic deviation visible in the residuals bitmap ( Fig. 1, B   a Best-fit weight-average anhydrous frictional ratio (f/f 0 ). b Sedimentation coefficient taken from the ordinate maximum of each peak in the best-fit c(s) distribution (Fig. 3). c Molar mass values taken from the ordinate maximum of each peak in the best-fit c(M) distribution (13,14). d Diffusion coefficient calculated using the best-fit values for sedimentation coefficient, frictional ratio and molar mass.  Table I. The presence of up to 90% monomer was evident, even at millimolar concentrations. The molar mass determined by this analysis is close to the known molecular mass of kalata B1 (2892 Da), based on its amino acid composition, and verified by mass spectrometry.
For comparison, the sedimentation profiles of kalata B2 at concentrations of 0.5, 2.0, 5.0, and 6.5 mg/ml were fitted to a continuous size distribution model. A single best-fit weightaverage frictional ratio for all species at different concentrations was extracted from the data by virtue of the criterion of the quality of the fit. The results of the analysis are also summarized in Table I. At a loading protein concentration of 5 mg/ml, Fig. 2 reveals the presence of three major species, with sedimentation coefficients of ϳ0.70 (30% of the total), 1.91 (42%), and 2.60 S (25%). These s 20 values correspond to molar masses of 3,054, 13,810, and 22,108 Da. It thus appears that the solution is a mixture of monomers, with tetramers and octomers. The oligomers appear to be very stable, as confirmed by similar size distribution measurements made 2 weeks apart. The mass of the 13,810 Da species (4.67 times the monomer molar mass) could be attributed to either a tetramer or a pentamer. Additional analysis of the sedimentation velocity and equilibrium data suggests that this species is most likely a tetramer and that the 22,108 Da species is an octamer (see below). Fig. 3 shows a comparison of the continuous size distribution profiles, c(s) in panels A-C of kalata B2 at initial protein concentrations of 0.5, 2.0, and 6.5 mg/ml. At low concentration kalata B2 (0.5 mg/ml, panel A) is present mainly as a single monomeric species in solution with an s 20 of 0.70 S, a diffusion coefficient (D 20 ) of 2.0 ϫ 10 Ϫ6 cm 2 /s, and an apparent molar mass of 2,895 Da. The apparent molar mass value is consistent with that deduced from its amino acid composition (2,955 Da), and experimentally verified by mass spectrometry. When the concentration is increased to 2 mg/ml (panel B), a species of a molecular mass that corresponds to a tetramer (12,269 Da), corresponding to ϳ24% of the total, also appears in solution. At 6.5 mg/ml (Fig. 3, panel C) a third aggregate, in addition to the monomer (ϳ19%) and the putative tetramer (ϳ47%), corresponding to an approximate molar mass of an octamer of 23,891 Da (27%) becomes apparent.
To determine whether a rapid reversible equilibrium exists between the kalata B2 species, the sedimentation velocity data at an initial protein concentration of 5.0 mg/ml were fitted to a monomer-tetramer-octamer rapid self-association model (Sedfit Version 8.5) as shown in Fig. 4. For this fit, the respective values obtained for s 20 from fits to the continuous size distri-bution model (Table I), and association constants from fits of the sedimentation equilibrium data to a monomer-tetrameroctamer model (see below), were used as starting values. For the monomer, tetramer, and octamer, respectively, the calculated best-fit sedimentation profiles converge to s 20 values of 0.7, 1.6 and 2.6 S, with association constant values of K 1,4 ϭ 8 ϫ 10 7 M Ϫ3 (0.006 in fringe units) and K 1,8 ϭ 4 ϫ 10 15 M Ϫ7 (1 ϫ 10 Ϫ6 in fringe units). The fit is good (r.m.s.d. of 0.04, which represents a fit with a relative error of 0.23%) with randomly distributed residuals, and only minor systematic deviation visible in the residuals of the bitmap (Fig. 4, B and C).
The oligomeric states of kalata B2, the Stokes radius and dimensions of equivalent hydrodynamic ellipsoids (oblate and prolate) of each oligomer were estimated from the experimental sedimentation coefficients, and are shown in Table II. In terms of gross hydrodynamic shape, with an estimated hydration ratio of 0.3 g/g, calculated from the amino acid composition (16,25), these values correspond to either an equivalent oblate ellipsoid with major and minor axes of 2.40 ϫ 1.70 nm (monomer), 4.55 ϫ 1.81 nm (tetramer) and 5.82 ϫ 2.21 nm (octamer) or to an equivalent prolate ellipsoid with dimensions of 2.63 ϫ 1.89 nm (monomer), 6.06 ϫ 2.49 nm (tetramer), and 7.88 ϫ 3.08 nm (octamer).
Sedimentation Equilibrium -Figs. 5, A and B show the sedimentation equilibrium data for kalata B1 fitted to a single a Calculated from the theoretical molar mass and sedimentation coefficient. b Axial ratios for oblate or prolate ellipsoid calculated by the v method (16) using the program SEDNTERP and employing theoretical molar masses with their respective sedimentation coefficients (Table I) and a theoretical estimate for hydration of 0.30 g/g as predicted from the amino acid composition (16,25). c Overall dimensions, calculated with the assumption of a hydration of 0.3 g/g.
FIG. 4. Sedimentation velocity data of kalata B2 compared with sedimentation profiles of a rapid monomer-tetramer-octamer self-association model. Panel A, sedimentation of kalata B2 as shown in Fig. 2 (open circles), and calculated best-fit sedimentation profiles of the rapid monomer-tetramer-octamer self-association model (solid lines), which converged to s 20 values of 0.70, 1.6, and 2.6 S for the monomer, tetramer, and octamer, respectively. The association constants were determined as K 1,4 ϭ 1.4 ϫ 10 9 M Ϫ3 (0.006 fringe units) and monomeric species, acquired at a loading concentrations of 1.25, 2.5, and 5.0 mg/ml and rotorspeeds of 40,000, 50,000, and 60,000 rpm. The data fit well to a single monomeric species (Equation 2), with molar masses of 2,952, 3,008, and 2,841 Da respectively, close to its calculated molar mass of 2,892 Da. The fits improved slightly when the data were modeled to a monomer-tetramer self-association model (K 1,4 ϭ 8 ϫ 10 6 M Ϫ3 (3.5 ϫ 10 Ϫ5 in fringe units) with a r.m.s.d. of 0.029. This represents no more than 10% of a tetrameric species at very high concentration protein (5.0 mg/ml). Thus the equilibrium results support the results of the analysis obtained from sedimentation velocity experiments.
Sedimentation equilibrium experiments were performed on kalata B2 to confirm the identities of the oligomeric species detected in sedimentation velocity experiments, as well as to ascertain the reversibility and association constants of the self-association reaction that the analysis of the velocity data seems to indicate. To distinguish between self-association and polydispersity, sedimentation equilibrium experiments for kalata B2 were performed at a rotor speed of 40,000, 45,000, and 50,000 rpm using loading concentrations between 1.0 and 6.5 mg/ml. The plots of apparent molecular weight versus con-centration coincide, which is diagnostic for a self-associating system. Thus, a reversible equilibrium on the time scale of the experiment is suggested for the self-interaction of kalata B2. Fig. 5C shows the global fit of the sedimentation equilibrium data at three rotor speeds (40,000, 45,000, and 50,000 rpm) and three loading concentrations (1.0, 3.0, and 6.5 mg/ml) to a monomer-tetramer-octamer equilibrium. The residuals for the global fit of all the data are plotted in Fig. 5D. The association constants for the monomer-tetramer-octamer self-association model was determined as K 1,4 ϭ 4 ϫ 10 9 M Ϫ3 (0.017 fringe units) and Surface-exposed Residues-In order to explain the difference in the solution behavior of kalata B1 and kalata B2, their three-dimensional structures, obtained from solution NMR experiments, were compared. The amino acid sequences of kalata B1 (26) and kalata B2 (1) differ in only five residues, so particular attention was given to the properties and the extent of surface exposure of those residues. The locations of the five amino acid "substitutions" (V6F, T16S, S18T, V21I, and N25D) FIG. 5. Sedimentation equilibrium of kalata B1 and kalata B2. Panel A, fringe displacements at equilibrium are plotted versus the distance from the axis of rotation for kalata B1. Samples at initial concentrations of 1.25 (circle), 2.5 (square), and 5 mg/ml (triangle) in 100 mM sodium phosphate, pH 7.4, were centrifuged at 20°C for least 24 h at 40,000, 50,000, and 60,000 rpm, respectively. For clarity only data at rotor speeds of 40,000 (all offset by 2 fringes and Ϫ0.1 cm) and 60,000 rpm are shown. The solid line represents the global nonlinear least squares best-fit to the data to mainly a single monomeric species (Equation 1) with an r.m.s.d. of 0.029. Panel B, residuals for the nonlinear least squares best-fits at all concentrations and all rotor speeds are plotted versus the distance from the axis of rotation. Panel C, fringe displacement at equilibrium is plotted versus the distance from the axis of rotation for kalata B2. Samples at initial concentrations of 1.0 (circle), 3.0 (square), and 6.5 mg/ml (triangle) in 100 mM sodium phosphate, pH 7.4, were centrifuged at 20°C for at least 24 h at 40,000, 45,000, and 60,000 rpm, respectively. For clarity only data at a rotor speed of 40,000 (all offset by 2 fringes and Ϫ0.1 cm) and 50,000 rpm are shown. The solid lines represent the global nonlinear least squares best-fits to the data at all concentrations and all rotor speeds according to a monomer-tetrameroctamer model. Panel D, residuals for the nonlinear least squares best-fits at all concentrations and all rotor speeds are plotted versus the distance from the axis of rotation. The r.m.s.d. was 0.033. of kalata B2 compared with kalata B1, along with the overall amino acid sequence, are displayed in Fig. 6. The overall threedimensional structures of the two peptides are almost identical, as might be expected, because both contain a cystine knot motif (27) that strongly influences the core structure. We therefore turned to an analysis of the surface properties of the molecules. Fig. 7A shows the surfaces of kalata B1 and B2 with residues color-coded into categories of positive, negative, polar or hydrophobic. The cysteine residues are colored separately from the other polar residues for convenience. This makes it clear that most of the cystine residues are buried in the core of the molecule, with only Cys 10 and Cys 17 surface-exposed. This exposure occurs only on one face of the molecule and forms part of a polar or hydrophilic region. Surface-exposed hydrophobic residues dominate the opposite face of the molecule, presumably forced to the surface because there is no room for them in the protein core because of the cystine knot. Differences in the extent of this hydrophobic patch between the two molecules are only revealed by a comparison of the average solvent accessible surface areas of kalata B1 and kalata B2. This comparison, given in Å 2 and a percentage of the total surface area, and sorted by amino acid properties is summarized in Table III. There is an almost 115 Å 2 increase in the hydrophobic solvent accessible surface area of kalata B2 compared with kalata B1, which accounts for most of the increase in the overall solvent exposed area of 125 Å 2 , the other being an increase of 10 Å 2 in the hydrophilic area. The increase in hydrophobic area is largely due to the substitution of V 6 in kalata B1 for a Phe in kalata B2, which leads to an increase in the solvent exposed area by an average 62 Å 2 . This is one of two hydrophobichydrophobic substitutions, the other being the Val 21 for Ile on the same face of the protein. Phe 6 and Ile 21 form part of an extended hydrophobic patch, which also includes Gly 7 , Gly 8 , Trp 19 , and Pro 20 , covering 28% of the overall surface of kalata B2.
The other noticeable difference between the surfaces of the two peptides is in the charge distribution, as illustrated in Fig.  7B, which shows that the oppositely charged residues Arg 24 and Asp 25 are in close proximity in kalata B2, creating an exposed bipolar patch on one end of the molecule that does not exist in kalata B1. This bipolar region is also almost completely solvent-exposed. We therefore suggest that this solvent-exposed bipolar patch, involving Asp 25 , in combination with the hydrophobic patch, involving Phe 6 , might be involved in the oligomerization of kalata B2 in solution.
Molecular modeling studies were carried out to assist in predicting the way in which the bipolar region and hydrophobic patch might be involved in self-association. Fig. 8 illustrates the potential self-interaction interfaces that might lead to tetramer formation. Fig. 8A focuses on the potential chargecharge interactions between the bipolar patches of different monomers. Fig. 8B shows a possible relative orientation of the two putative self-interaction surfaces of each monomer in the tetramer. The key interacting regions that distinguish kalata FIG. 6. Ribbon representation of the overall fold of kalata B1 and B2. The C␣ atoms of amino acids common to both peptides are shown as balls labeled with one-letter code (residues other than cysteine) or numbered according to their position in the peptide sequence (cysteine residues) and colored according to the properties of the amino acids (hydrophobic, gray; hydrophilic, light green; acidic, red; basic, light blue; cysteine, yellow). For residues that differ in kalata B1 and kalata B2, the amino acid side chains are shown as ball and stick (in blue for kalata B1, in green for kalata B2) and labeled with their one-letter codes and residue numbers in the corresponding color.  B2 from kalata B1 are the bipolar-bipolar interface involving the Arg 24 and Asp 25 residues, and the hydrophobic-hydrophobic interface, involving the Phe 6 -Phe 6 interaction. Stacking of two such tetramer units would produce an octamer with a geometry consistent with the analyzed ultracentrifugation data.

DISCUSSION
In the current study we have shown that the two prototypical plant cyclotides kalata B1 and kalata B2 display marked differences in their degree of self-association in aqueous solution. Kalata B1 exists in a monomeric state under a wide range of solution conditions, while kalata B2 self-associates mainly into tetramers and octamers besides monomers. From an examination of the structural basis for this difference in solution behavior, we hypothesize that the two residues Phe 6 and Asp 25 , situated on opposite sides of the kalata B2 molecule, are involved in this self-interaction.
We resolved the oligomeric forms of these cyclotides in aqueous buffer by the application of sedimentation equilibrium and sedimentation velocity experiments, employing a new method for determining the continuous size distribution of polydisperse macromolecules (14); that has been shown to be the best means to detect and quantitatively characterize self-association of macromolecules in solution (14,28). A detailed comparison of the hydrodynamic properties and solution behavior of cyclo-tides has not previously been undertaken. Since these proteins possess a CCK scaffold that has been proposed as a potential template onto which desirable properties can be grafted, our results show that in the design of such modified templates, changes in aggregation behavior should also be taken into account. Furthermore, aggregation in vivo is likely to be enhanced, since these peptides are intended to perform their function in biological environments that are generally characterized by high total concentrations of macromolecules, referred to as "crowded" (29,30).
We found that the self-assembly of kalata B2 into multimers takes place in a reversible concentration-dependent manner, i.e. at very low concentrations only the monomeric species is present, at intermediate concentrations most likely tetramers appear, and at high concentrations octamers and possibly higher order oligomers emerge. The analysis consistently reveals the presence of three major species at high concentration with sedimentation coefficients of ϳ0.7, 1.91, and 2.6 S (Table  I). Furthermore, the peak of the monomer does not shift significantly (Fig. 3), which shows that there is no significant concentration dependence of the sedimentation coefficient, an indication of ideal sedimentation.
Although the number and relative concentration of individual kalata B2 oligomers can be ascertained by using the continuous size distribution method, it was difficult to be certain about the oligomeric identity of the 1.91 S peak, i.e. either a tetramer or a pentamer. Possible errors can be introduced when transforming the c(s) distribution into molar mass distribution c(M) (14). In addition, the minor systematic error in the fit indicates that either the oligomers are in reversible equilibrium with each other, possibly on the time scale of the sedimentation process, or that the oligomers differ slightly in their shape, in which case the c(s) assumption of a single weight-average frictional ratio is not strictly fulfilled. There is some indication that this 1.91 S peak represents a tetramer if the analysis of additional sedimentation velocity and equilibrium data is taken into account. For instance the velocity data fits well to a rapid monomer-tetramer-octamer model of selfassociation (Fig. 4). This model of self-association is also supported by the analysis of equilibrium data (Fig. 5, B and C) that fit well to a monomer in equilibrium with tetramer and octamer, but not with a pentamer. This strongly suggests that a monomer-tetramer-octamer self-association pattern is mainly the manner in which kalata B2 self-associates.
The sedimentation data enabled an estimation of the shape and asymmetry of each oligomer. The overall dimensions of the monomer were calculated as 2.40 ϫ 1.70 nm (equivalent an oblate ellipsoid) or 2.63 ϫ 1.89 nm (equivalent to a prolate ellipsoid), with both corresponding very well to the dimensions measured from its NMR structure (2.5 ϫ 1.9 ϫ 1.5 nm). The Stokes radius of 1.06 nm, with the axial ratio values of the monomer being Ͻ2, suggests that kalata B2 is spatially compact and has a roughly spherical shape. Thus, the structural information on kalata B2 supports our hydrodynamic findings. The finding that an increase in oligomeric size causes only a slight increase in the axial ratios (Table II), would suggest that the monomers are arranged mainly in a symmetrical fashion that is compatible with a spherical kalata B2 oligomer. The data rule out a linear oligomerization pattern that would result in asymmetric multimeric structures in solution.
To try to explain the difference in solution behavior, the properties of the surface exposed residues of the two cyclotides were examined, with particular attention given to differences in the amino acid sequence. There are two surface areas on these proteins with distinguishing properties and features that might explain the difference in their solution behavior. One is FIG. 8. Hypothetical oligomer formation of kalata B2. A, details of hypothetical oligomer formation that illustrate the charge-charge interactions involving the Arg 24 and Asp 25 residues of kalata B2, with the peptide backbone in green and disulfide bonds in yellow. The amino acid side chains of the charged residues creating the bipolar patch (Arg 24 and Asp 25 ) are given as ball and stick, with the nitrogen atoms of Arg 24 colored in blue and the oxygen atoms of Asp 25 in red. B, potential tetramer of kalata B2 showing a possible relative orientation of the two putative interaction surfaces, involving Phe 6 -Phe 6 and Arg 24 -Asp 25 . The amino acids are colored according to their properties (see Fig. 7), charged residues and residues of the hydrophobic interaction area are labeled with the one-letter code and residue number. the bipolar area that includes the N25D substitution, and the other, on the opposite side of the molecule, is the hydrophobic surface patch that includes the V6F substitution (Fig. 7). The bipolar patch created by the N25D substitution, Arg 24 -Asp 25 , might theoretically facilitate intermolecular ionic self-interaction of kalata B2 (as depicted in Fig. 8A) but not kalata B1, since the latter lacks this second negatively charged amino acid. To support the notion of a charge-charge interaction between different kalata B2 molecules, there are many examples where salt bridges exist between two associating molecules in buffer solution. One such instance is the affinity of an antibody for lyzozyme via a Glu-Arg salt bridge, confirmed in analytical ultracentrifugation studies (31).
With respect to the V6F substitution, a recent analysis has shown that Phe has a high probability of being found in many types of protein-protein interfaces, while Val does not (15). It is thus possible to hypothesize that the V6F substitution in kalata B2 facilitates self-association. The two surface regions discussed are substantially solvent-exposed, which makes them good candidates for interaction areas. Moreover, a model of the tetramer (Fig. 8B), showing a possible relative orientation of the two putative self-interaction surfaces, illustrates that the Phe 6 -Phe 6 interaction in the hydrophobic patch interface is possible while maintaining the bipolar patch interactions. It is noted that in this model the other hydrophobic substitution, V21I, is also present in this hydrophobic patch interface and that the Ile lines up favorably for an Ile 21 -Ile 21 interaction. Furthermore, Ile is preferred (only slightly), as is Phe (highly), over Val in self-interaction complexes (15). It is thus possible that, in addition to Phe 6 , Ile 21 may also contribute to the self-aggregation of kalata B2. As illustrated in Fig.  8B, several other hydrophobic residues that are conserved in both kalata B1 and B2 line the putative interaction surface.
We therefore propose a hypothetical model of self-association that involves a Phe 6 -Phe 6 , and possibly an Ile 21 -Ile 21 , as well as an Arg 24 -Asp 25 interaction between different kalata B2 molecules to form a tetramer, as depicted in Fig. 8B. The dimensions of this theoretical model (5 ϫ 4 ϫ 1.5 nm) are in good accordance with the data derived from ultracentrifugation experiments, if an oblate ellipsoid is assumed. As indicated in the model, the protein-protein interface is highly populated with hydrophobic residues, providing ample opportunity for hydrophobic interactions. On the other hand, the surface that our model of a hypothetical tetramer presents to the aqueous environment shows large hydrophilic areas. Moreover, our suggestion that Phe 6 -Phe 6 and Arg 24 -Asp 25 interactions are involved in tetramer formation is supported by studies on residues that are generally preferred in the most common types of protein-protein interfaces. Specifically, both these residueresidue interactions are among the most favored in many protein-protein interfaces (15).
Two tetrameric units stacked on top of each other may then form a globular octamer. Again, the overall dimensions of this theoretical model are in good accordance with experimental data. The proposed model is also consistent with the fact that no dimers are observed, as each of the proposed interactions is in itself rather weak and their synergistic effects only become apparent in the tetramer.
In conclusion, we have shown that kalata B2 assembles into a monomer-tetramer-octamer self-association pattern, while kalata B1 exists as a monomer in solution, even at relatively high concentration. Furthermore, we have determined that the kalata B2 oligomers are most likely globular rather then elongated. Based on the properties of the surface exposed residues, and residues highly likely to be found in self-interaction interfaces (15), we have proposed two putative self-association surface areas on opposite sides of the circular protein kalata B2. These two substantially solvent exposed areas, where the V6F and the N25D changes are found, represent the most distinguishing features of kalata B2 relative to kalata B1. Being on opposites sides of the protein, Phe 6 -Phe 6 and Arg 24 -Asp 25 interactions between different kalata B2 molecules to form a globular tetramer are sterically feasible.