Modeling the electrophoretic mobility and diffusion of weakly charged peptides

A bead model to determine the electrophoretic mobilities and translational diffusion constants of weakly charged peptides is developed that is based on a approximate structural model of peptides and is also grounded in electrohydrodynamic theory. A peptide made up of X amino acids is modeled as N=2X beads with 2 beads representing each amino acid in the chain. For the two beads representing a particular amino acid in a peptide, the radius of one bead is set to one-half the nearest neighbor Calpha-Calpha distance, and the radius of the other bead is chosen on the basis of the diffusion constant of the free amino acid. Peptide conformations, which are defined by a set of psi-phi dihedral angles, are randomly generated by using the transformation matrix approach of Flory (Flory, P. Statistical Mechanics of Chain Molecules; John Wiley: New York, 1969) and rejecting conformations which result in bead overlap. The mobility and diffusion constants are computed for each conformation and at least 100 independent conformations are examined for each peptide. In general, the mobility is found to depend only weakly on peptide conformation. Model and experimental mobilities are compared by examining the data of Janini and co-workers (Janini, G.; et al. J. Chromatogr. 1999, 848, 417-433). A total of 58 peptides consisting of from 2 to 39 amino acids are considered. The average relative error between experimental and model mobilities is found to be 1.0% and the rms relative error 7.7%. In specific cases, the discrepancy can be substantial and possible reasons for this are discussed. It should be emphasized that the input parameters of the peptide model are totally independent of experimental mobilities. It is hoped that the peptide model developed here will be useful in the prediction of peptide mobility as well as in using peptide mobilities to extract information about peptide structure, conformation, and charge. Finally, we show how simultaneous measurements of translational diffusion and mobility can be used to estimate peptide charge.     

Ion-interaction CZE: the presence of high concentrations of ion-pairing reagents demonstrates the complex mechanisms involved in peptide separations

We have furthered our understanding of the separative mechanism of a novel CE approach, termed ion-interaction CZE (II-CZE), developed in our laboratory for the resolution of mixtures of cationic peptides. Thus, II-CZE and RP-HPLC were applied to the separation of peptides differing by a single amino acid substitution in 10- and 12-residue synthetic model peptide sequences. Substitutions differed by a wide range of properties or side-chain type (e.g., alkyl side-chains, polar side-chains, etc.) at the substitution site. When carried out in high concentrations (400 mM) of pentafluoropropionic acid (PFPA), II-CZE separated peptides in order of increasing hydrophobicity when the substituted side-chains were of a similar type; when II-CZE was applied to the mixtures of peptides with substitutions of side-chains that differed in the type of functional group, there was no longer a correlation of electrophoretic mobility in II-CZE with relative peptide hydrophobicity, suggesting that a third factor is involved in the separative mechanism beyond charge and hydrophobicity. Interestingly, the hydrophobic PFPA- anion is best for separating peptides that differ in hydrophobicity with hydrophobic side-chains but high concentrations of the hydrophilic H2PO4- anion are best when separating peptides that differ in polar side-chains relative to hydrophobic side-chains. We speculate that differential hydration/dehydration properties of various side-chains in the peptide and the hydration/dehydration properties of the hydrophilic/hydrophobic anions as well as the electrostatic attractions between the peptide and the anions in solution all play a critical role in these solution-based effects.     

Peptide mapping by capillary zone electrophoresis: how close is theoretical simulation to experimental determination

A multi-variable computer model is presented for the prediction of the electrophoretic mobilities of peptides at pH 2.5 from known physico-chemical constants of their amino acid residues. The model is empirical and does not claim any theoretical dependencies; however, the results suggest that, at least at this pH, peptides may be theoretically represented as classical polymers of freely joined amino acid residues of unequal sizes. The model assumes that the electrophoretic mobility can be represented by a product of three functions that return the contributions of peptide charge, length and width, respectively to the mobility. The model relies on accurate experimental determination of the electrophoretic mobilities of a diverse set of peptides, by capillary zone electrophoresis (CZE), at 22 degrees C, with a 50 mM phosphate buffer, at pH 2.5. The electrophoretic mobilities of a basis set of 102 peptides that varied in charge from 0.65 to 16 and in size from two to 42 amino acid residues were accurately measured at these fixed experimental conditions using a stable 10% linear polyacrylamide-coated column. Data from this basis set was used to derive the peptide charge, length, and width functions respectively. The main purpose of this endeavor is to use the model for the prediction of peptide mobilities at pH 2.5, and for simulation of CZE peptide maps of protein digests. Excellent agreement was obtained between predicted and experimental electrophoretic mobilities for all categories of peptides, including the highly charged and the hydrophobic. To illustrate the utility of this model in protein studies it was used to simulate theoretical peptide maps of the digests of glucagon and horse cytochrome c. The resulting maps were compared and contrasted with their experimental counterparts. The potential of this approach and its limitations are discussed.     

The role of amino acid composition in the charge inversion of deprotonated peptides via gas-phase ion/ion reactions

Ion/ion charge inversion via multiple proton transfer reactions occurs via a long-lived intermediate. The intermediate can be observed if its lifetime is long relative to mechanisms for removal of excess energy (i.e., emission and collisional stabilization). The likelihood for formation of a stabilized intermediate is a function of characteristics of the reagent and analyte ions. This work is focused on the role acidic and basic sites of a deprotonated peptide play in the formation of a stabilized intermediate upon charge inversion with multiply protonated polypropyleniminediaminobutane dendrimers. A group of model peptides based on leucine enkephalin was used, which included YGGFL, YGGFLF, YGGFLK, YGGFLR and YGGFLH as well as methyl esterified and acetylated versions. Results showed that peptides containing basic amino acid residues charge inverted primarily by proton transfer from the DAB dendrimer to the peptide, whereas peptides without basic amino acids charge inverted primarily by complex formation with the DAB dendrimer. The modified versions of the peptides highlighted the importance of the presence of the C-terminus as well as the basicity of the peptide in the observation of a stabilized intermediate. These results provide new insights into the nature of the interactions that occur in the charge inversion of polypeptide anions via ion/ion reactions.     

Fluoroolefins as peptide mimetics: a computational study of structure, charge distribution, hydration, and hydrogen bonding

The design of peptide mimetic compounds is greatly facilitated by the identification of functionalities that can act as peptide replacements. The fluoroalkene moiety has recently been employed for that purpose. The purpose of this work is to characterize prototypical fluoroalkenes (fluoroethylene and 2-fluoro-2-butene) with respect to key properties of peptides (amides) including structure, charge distribution, hydration, and hydrogen bonding. The results are compared to those obtained for model peptides (formamide, N-methylacetamide). Calculations have been carried out at the MP2 and B3LYP levels of theory with the 6-311++G(2d,p) and 6-311++G(2d,2p) basis sets. The results suggest that the fluoroalkene is similar in steric requirements to a peptide bond but that there is less charge separation. Calculations of the hydration free energies with the PCM bulk continuum solvent model indicate that the fluoroalkene has much smaller hydration free energies than an amide but that the difference in solvation free energy for cis and trans isomers is comparable. In studies of complexes with water molecules, the fluoroalkene is found to engage in interactions that are analogous to backbone hydrogen-bonding interactions that govern many properties of natural peptides and proteins but with smaller interaction energies. In addition, key structural differences are noted when the fluoroalkene is playing the role of hydrogen-bond acceptor which may have implications in binding, aggregation, and conformational preferences in fluoroalkene peptidomimetics. The issue of cooperativity in hydrogen-bonding interactions in complexes with multiple waters has also been investigated. The fluoroalkene is found to exhibit cooperative effects that mirror those of the peptide but are smaller in magnitude. Thus, pairwise addivitity of interactions appears to more adequately describe the fluoroalkenes than the peptides they are intended to mimic.     

A computer program (COMPOST) for predicting mass spectrometric information from known amino acid sequences

A computer program (COMPOST) is described that carries out predictive computations on known amino acid sequences. The program is designed to be of use to mass spectrometrists with an interest in protein and peptide sequencing. Mass values (monoisotopic and average) for protonated peptide and protein molecules and elemental compositions are calculated. COMPOST also calculates mass to charge ratio values for protonated peptides expected from specified digests, locates specified amino acid subsequences or peptides of a specifIed molecular weight within a longer sequence, and predicts mass to charge ratio values for fragment ions from high-energy collision-induced dissociation of protonated peptides.     

Water hydrogen bond analysis on hydrophilic and hydrophobic biomolecule sites

Elastic and quasielastic neutron scattering experiments have been used to investigate the hydrogen bonding network dynamics of hydration water on hydrophilic and hydrophobic sites. To this end the evolution of hydration water dynamics of a prototypical hydrophobic amino acid with polar backbone, N-acetyl-leucine-methylamide (NALMA), and hydrophilic amino acid, N-acetyl-glycine-methylamide (NAGMA), has been investigated as a function of the molecular ratio water : peptide. The results suggest that the dynamical contribution of the intrinsic and low hydration molecules of water is characteristic of pure librational/rotational movement. The water molecule remains attached to the hydrophilic site with only the possibility of hindered rotations that eventually break the bond with the peptide and reform it immediately after. A gradual evolution from librational motions to hindered rotations is observed as a function of temperature. When the hydration increases, we observe (together with the hindered rotations of hydrogen bonds) a slow diffusion of water molecules on the surface of the peptides.     

Exploring the evaluation of net charge, hydrodynamic size and shape of peptides through experimental electrophoretic mobilities obtained from CZE

This work explores the validity of simple CZE models to analyze the electrophoretic mobilities of 102 peptides reported in literature. These models are based mainly on fundamental physicochemical theories providing analytical expressions amenable to relatively simple numerical analysis. Thus, the Linderstr?m-Lang capillary electrophoresis model (LLCEM) and its perturbed version (PLLCEM), proposed and applied previously to the CZE of globular proteins, are adapted and used here for peptides. Also the effects of pK-shifts on net charge, hydration and hydrodynamic size and shape of peptides are analyzed and discussed. Emphasis is placed on the fact that these parameters are physically coupled, and thus a variation in the net charge may produce an appreciable change in the hydrodynamic size of peptides. Within the framework of CZE, peptides may be assumed as having a hydrodynamic volume associated with either spherical or spheroidal particles. The effects on peptide net charge and hydrodynamic size, of electrostatic interaction between a pair of charged groups in the chain and electrical permitivitty around the peptide domain are studied. The predictions of the PLLCEM and LLCEM are in good agreement with results reported previously in the literature. Several limitations concerning these models and some needs for further research are also described.     

Sequence requirements and an optimization strategy for short antimicrobial peptides

Short antimicrobial host-defense peptides represent a possible alternative as lead structures to fight antibiotic resistant bacterial infections. Bac2A is a 12-mer linear variant of the naturally occurring bovine host defense peptide, bactenecin, and demonstrates moderate, broad-spectrum antimicrobial activity against Gram-positive and Gram-negative bacteria as well as against the yeast Candida albicans. With the assistance of a method involving peptide synthesis on a cellulose support, the primary sequence requirements for antimicrobial activity against the human pathogen Pseudomonas aeruginosa of 277 Bac2A variants were investigated by using a luciferase-based assay. Sequence scrambling of Bac2A led to activities ranging from superior or equivalent to Bac2A to inactive, indicating that good activity was not solely dependent on the composition of amino acids or the overall charge or hydrophobicity, but rather required particular linear sequence patterns. A QSAR computational analysis was applied to analyze the data resulting in a model that supported this sequence pattern hypothesis. The activity of selected peptides was confirmed by conventional minimal inhibitory concentration (MIC) analyses with a panel of human pathogen bacteria and fungi. Circular-dichroism (CD) spectroscopy with selected peptides in liposomes and membrane depolarization assays were consistent with a relationship between structure and activity. An additional optimization process was performed involving systematic amino acid substitutions of one of the optimal scrambled peptide variants, resulting in superior active peptide variants. This process provides a cost and time effective enrichment of new candidates for drug development, increasing the chances of finding pharmacologically relevant peptides.     

Charge location directs electron capture dissociation of peptide dications

The effect of peptide dication charge location on electron capture dissociation (ECD) fragmentation pattern is investigated. ECD fragmentation patterns are compared for peptides with amide and free acid C-terminal groups. ECD of free acid compared with C-terminally amidated peptides with basic residues near the N-terminus demonstrates increased formation of a-type ions. Similarly, ECD of free acid compared with C-terminally amidated peptides with basic residues near the C-terminus exhibits increased formation of y-type ions. Alteration of the peptide sequence to inhibit the formation of charged side chains (i.e., amino acid substitution and acetylation) provides further evidence for charge location effect on ECD. We propose that formation of zwitterionic peptide structures increases the likelihood of amide nitrogen protonation (versus basic side chains), which is responsible for the increase in a- and y-type ion formation.     

Sequential hydration of small protonated peptides

The sequential addition of water molecules to a series of small protonated peptides was studied by equilibrium experiments using electrospray ionization combined with drift cell techniques. The experimental data were compared to theoretical structures of selected hydrated species obtained by molecular mechanics simulations. The sequential water binding energies were measured to be of the order of 7-15 kcal/mol, with the largest values for the first water molecule adding to either a small nonarginine containing peptide (e.g., protonated dialanine) or to a larger peptide in a high charge state (e.g., triply protonated neurotensin). General trends are (a) that the first water molecules are more strongly bound than the following water molecules, (b) that very small peptides (2-3 residues) bind the first few water molecules more strongly than larger peptides, (c) that the first few water molecules bind more strongly to higher charge states than to lower charge states, and (d) that water binds less strongly to a protonated guanidino group (arginine containing peptides) than to a protonated amino group. Experimental differential entropies of hydration were found to be of the order of -20 cal/mol/K although values vary from system to system. At constant experimental conditions the number of water molecules adding to any peptide ion is strongly dependent on the peptide charge state (with higher charge states adding proportionally more water molecules) and only weakly dependent on the choice of peptide. For small peptides molecular mechanics calculations indicate that the first few water molecules add preferentially to the site of protonation until a complete solvation shell is formed around the charge. Subsequent water molecules add either to water molecules of the first solvation shell or add to charge remote functional groups of the peptide. In larger peptides, charge remote sites generally compete more effectively with charge proximate sites even for the first few water molecules.     

Hydration of small peptides

The results for the sequential hydration of small peptides (<15 residues) obtained in our group are reviewed and put in perspective with other work published in the literature where appropriate. Our findings are based on hydration equilibrium measurements in a high-pressure drift cell inserted into an electrospray mass spectrometer and on calculations employing molecular mechanics and density functional theory methods. It is found that the ionic functional groups typically present in peptides, the ammonium, guanidinium, and carboxylate groups, are the primary target of water molecules binding to peptides. Whereas the water–guanidinium binding energy is fairly constant at 9 ± 1 kcal/mol, the water binding energy of an ammonium group ranges from 7 to 15 kcal/mol depending on how exposed the ammonium group is. A five-residue peptide containing an ammonium group is in favorable cases large enough to fully self-solvate the charge, but a pentapeptide containing a guanidinium group is too small to efficiently shield the charge of this much larger ionic group. The water–carboxylate interaction amounts to 13 kcal/mol with smaller values for a shielded carboxylate group. Both water bound to water in a second solvation shell and charge remote water molecules on the surface of the peptide are bound by 7–8 kcal/mol. The presence of several ionic groups in multiply charged peptides increases the number of favorable hydration sites, but does not enhance the water–peptide binding energy significantly. Water binding energies measured for the first four water molecules bound to protonated bradykinin do not show the declining trend typically observed for other peptides but are constant at 10 kcal/mol, a result consistent with a molecule containing a salt bridge with several good hydration sites. Questions regarding peptide structural changes as a function of number of solvating water molecules are discussed. Not much is known at present about the effect of individual water molecules on the conformation of peptides and on the stability of peptide zwitterions.     

Aqueous Capillary Electrophoresis of Peptides Part 1: Conformational States, Volumes and Estimates of the Extent of Hydration

Summary A series of eighteen peptides have been modelled. Of the 380 low-energy viable conformers generated, 64 were selected, with 2–5 per peptide representing the range of structures and size. Using the results of previous investigations of this peptide group, it was possible to place an upper limit to the extent of hydration for each peptide. The modelled peptides were then hydrated in stepwise fashion. From the volumetric and dimensional data derived, in conjunction with published mobilities, the relationship between electrophoretic mobility ( _ep ) and the hydrodynamic radius (r) was used to objectively test the fit between the experimental ( _ep ) data and and the modelled size parameters over the range of hydration. Where the fit was tightest it was presumed that the fraction of the maximum reasonable hydration best represented the average degree of hydration of the set. Using ellipsoidal volumes, Connolly surfaces and excluded volumes the average degree of hydration was found to be in the mid range considered and corresponded to the mean of the bimodal distribution of hydration for the individual peptides according to charge-based calculations. For a peptide with two positive charges and a partial negative charge on the carboxy residue (pH=2.5), about 15 waters of hydration are indicated. With 3, 5 and 6 positive charges, the estimated waters are 28, 48 and 85, respectively. Van der Waals volumes were not helpful as the precise summation of the volumes associated with each bonded atom is a poor reflection of the effective volume of the migrating peptide. Conformational changes are examined as a function of the progressive hydration, and, as might be expected, the greatest changes occur in the early stages of hydration.     

Applicability of the critical chromatography concept to proteomics problems: Dependence of retention time on the sequence of amino acids

A peptide separation model based on the technique of liquid chromatography of macromolecules at the critical condition was proposed. In terms of this model, the array of experimental data on the separation of peptides is considered. The main phenomenological parameters of the model—effective adsorption energies of amino acid residues—were determined, thus allowing the influence of character of their alternation in the chain on retention times to be predicted. The model is applicable to investigation into the feasibility of separation in different chromatographic modes of not only peptides with the same amino acid composition and different sequences of units in the chain but also peptides containing amino acid isomers and mirror sequences with different terminal groups.     

Sequence modulation of tunneling barrier and charge transport across histidine doped oligo-alanine molecular junctions

Series tunneling across peptides composed of various amino acids is one of the main charge transport mechanisms for realizing the function of protein. Histidine, more frequently found in redox active proteins, has been proved to be efficient tunneling mediator. While how it exactly modulates charge transport in a long peptide sequence remains poorly explored. In this work, we studied charge transport of a model peptide junction, where oligo-alanine peptide was doped by histidine at different position, and the series of peptides were self-assembled into a monolayer on gold electrode with soft EGaIn as top electrode to form molecular junction. It was found that histidine increased the overall conductance of the peptide, meanwhile, its position modulated the conductance as well. Quantitative analysis by transport model and ultraviolet photoelectron spectroscopy (UPS) indicated a sequence dependent energy landscape of the tunneling barrier of the junction. Density-functional theory (DFT) calculation on the electronic structure of histidine doped oligo-alanine peptides revealed localized highest occupied molecular orbital (HOMO) on imidazole group of the histidine, which decreased charge transport barrier.     

Aqueous Capillary Electrophoresis of Peptides Part 2: An Investigation of Quantitative Determinants of Hydration and Solvation Relationships

Summary From the published electrophoretic data for a set of 58 peptides at pH 2.5 we have determined the excess hydration required to correct the deviations of the 31 higher-charged peptides from the Offord plot for the 27 singly-charged peptides. These values of the excess hydration were then used to test physical models by regression analysis. The dominant variable is the total excess positive charge, but the number of excess single positive charges and the number of pairs of positive charges – both at the end and internally – were significant determinants. The effect of acidic side chains was ambiguous throughout the analyses and this was presumed to arise from the ability of carboxy groups to be the sites of additional hydration or to diminish hydration via internal bonding with amino groups. A hydrophobicity index was included in he analysis, but surprisingly this too had little effect. In the last stage of the regressions, we also included coding for secondary structure within the peptides. This increased R² for the plots of the excess hydration versus values calculated from the regression constants (Y) from 0.95 to 0.97. Some solvation relationships were particularly good at modelling the hydration of the smaller, lesser-charged peptides, whilst others excelled in the opposite direction. The final model appeared to deal equally well with both extremes, but is not sufficiently sensitive to allow for all of the variations between peptides. As a result, the excess hydration was modelled very well for many of the peptides (±1–2 waters over the range of excess hydration form 5–276), but poorly for a few (± 100–200%). It was not possible to find another set of peptides that could be independently analysed in a similar fashion and compared. However, the regression constants were applied to an alternative set. Although appearing to fall in a generally reasonable range, various tests of the resultant calculated values indicated that this application was not valid. The second set of peptides were much more hydrophilic and the number of amino acid residues with an extended secondary structure appeared to be a contributing factor.     

Isotachophoretic analysis of peptides. Selection of electrolyte systems and determination of purity

Capillary isotachophoresis (ITP) was applied to the qualitative and quantitative analysis of both natural and synthetic oligo- and polypeptides. Based on the mathematical model of acid-base equilibria for a general ampholyte, a procedure and a computer program for the calculation of the pH dependence of the effective and specific charge and effective mobility of peptides with known amino acid sequence were developed which allow the selection of electrolyte systems for peptide isotachophoretic analysis to be rationalized. Basic peptides (bovine pancreatic trypsin inhibitor, bull seminal isoinhibitors of trypsin, arginine vasopressin and adamantylamide-alanylisoglutamine) were analysed with a cationic ITP system at acidic pH. Neutral and acidic peptides (insulin, proinsulin, bull seminal isoinhibitors of trypsin, cow colostrum isoinhibitors of trypsin) were analysed with an anionic ITP system, mostly at alkaline pH. Peptide purity (electrophoretic homogeneity) was determined from the ITP degree of purity defined by a peptide itself and the zone length ratio of its admixtures. Enrichment of peptide in the sample during the purification procedure was measured by its zone length relative to unit mass of the amount of sample analysed.     

Global conformations of proteins as predicted from the modeling of their CZE mobility data

Estimations of protein global conformations in well-specified physicochemical microenvironments are obtained through global structural parameters defined from polypeptide-scale analyses. For this purpose protein electrophoretic mobility data must be interpreted through a physicochemical CZE model to obtain estimates of protein equivalent hydrodynamic radius, effective and total charge numbers, hydration, actual ionizing pK and pH-near molecule. The electrical permittivity of protein domain is also required. In this framework, the solvent drag on proteins is obtained via the characteristic friction power coefficient associated with the number of amino acid residues defining the global chain conformation in solution. Also, the packing dimension related to the spatial distribution of amino acid residues within the protein domain is evaluated and discussed. These scaling coefficients together with the effective and total charge number fractions of proteins provide relevant interpretations of protein global conformations mainly from collapsed globule to hybrid chain regimes. Also, protein transport properties may be estimated within this framework. In this regard, the central role played by the friction power coefficient in the evaluation of these properties is highlighted.     

Biomolecular engineering by combinatorial design and high-throughput screening: small, soluble peptides that permeabilize membranes

Rational design and engineering of membrane-active peptides remains a largely unsatisfied goal. We have hypothesized that this is due, in part, to the fact that some membrane activities, such as permeabilization, are not dependent on specific amino acid sequences or specific three-dimensional peptide structures. Instead they depend on interfacial activity: the ability of a molecule to partition into the membrane-water interface and to alter the packing and organization of lipids. Here we test that idea by taking a nonclassical approach to biomolecular engineering and design of membrane-active peptides. A 16,384-member rational combinatorial peptide library, containing peptides of 9-15 amino acids in length, was screened for soluble members that permeabilize phospholipid membranes. A stringent, two-phase, high-throughput screen was used to identify 10 unique peptides that had potent membrane-permeabilizing activity but were also water soluble. These rare and uniquely active peptides do not share any particular sequence motif, peptide length, or net charge, but instead they share common compositional features, secondary structure, and core hydrophobicity. We show that they function by a common mechanism that depends mostly on interfacial activity and leads to transient pore formation. We demonstrate here that composition-space peptide libraries coupled with function-based high-throughput screens can lead to the discovery of diverse, soluble, and highly potent membrane-permeabilizing peptides.     

Role of the site of protonation in the low-energy decompositions of gas-phase peptide ions

The dissociation of singly or multiply protonated peptide ions by using low-energy collisional activation (CA) is highly dependent on the sites of protonation. The presence of strongly basic amino acid residues in the peptide primary structure dictates the sites of protonation, which generates a precursor ion population that is largely homogeneous with respect to charge sites. Attempts to dissociate this type of precursor ion population by low-energy CA result in poor fragmentation via few pathways. The work described here represents a systematic investigation of the effects of charge heterogeneity in the precursor ion population of a series of model peptides in low-energy CA experiments. Incorporation of acidic residues in the peptide RLC*IFSC*FR (where C* indicates a cysteic acid residue), for example, balances the charge on the basic arginine residues, which enables the ionizing protons to reside on a number of less basic sites along the peptide backbone. This results in a precursor ion population that is heterogeneous with respect to charge site. Low-energy CA of these ions results in diverse and efficient fragmentation. Molecular modeling has been utilized to demonstrate that energetically preferred conformations incorporate an intraionic interaction between arginine and cysteic acid residues.