Orders-of-Magnitude Larger Force Demonstrated for Dielectrophoresis of Proteins Enabling High-Resolution Separations Based on New Mechanisms.

Proteins are perhaps the most important yet frustratingly complicated and difficult class of compounds to analyze, manipulate, and use. One very attractive option to characterize and differentially concentrate proteins is dielectrophoresis, but according to accepted theory, the force on smaller particles the size of proteins is too low to overcome diffusive action. Here, three model proteins, immunoglobulin G, α-chymotrypsinogen A, and lysozyme, are shown to generate forces much larger than predicted by established theory are more consistent with new theoretical constructs, which include the dipole moment and interfacial polarizability. The forces exerted on the proteins are quantitatively measured against well-established electrophoretic and diffusive processes and differ for each. These forces are orders of magnitude larger than previously predicted and enable the selective isolation and concentration of proteins consistent with an extremely high-resolution separation and concentration system based on the higher-order electric properties. The separations occur over a small footprint, happen quickly, and can be made in series or parallel (and in any order) on simple devices.

Online Hydrophobic Interaction Chromatography-Mass Spectrometry for Top-Down Proteomics.

Recent progress in top-down proteomics has led to a demand for mass spectrometry (MS)-compatible chromatography techniques to separate intact proteins using volatile mobile phases. Conventional hydrophobic interaction chromatography (HIC) provides high-resolution separation of proteins under nondenaturing conditions but requires high concentrations of nonvolatile salts. Herein, we introduce a series of more-hydrophobic HIC materials that can retain proteins using MS-compatible concentrations of ammonium acetate. The new HIC materials appear to function as a hybrid form of conventional HIC and reverse phase chromatography. The function of the salt seems to be preserving protein structure rather than promoting retention. Online HIC-MS is feasible for both qualitative and quantitative analysis. This is demonstrated with standard proteins and a complex cell lysate. The mass spectra of proteins from the online HIC-MS exhibit low charge-state distributions, consistent with those commonly observed in native MS. Furthermore, HIC-MS can chromatographically separate proteoforms differing by minor modifications. Hence, this new HIC-MS combination is promising for top-down proteomics.

Sensitive, high throughput detection of proteins in individual, surfactant-stabilized picoliter droplets using nanoelectrospray ionization mass spectrometry.

Droplet-based fluidics is emerging as a powerful platform for single cell analysis, directed evolution of enzymes, and high throughput screening studies. Due to the small amounts of compound compartmentalized in each droplet, detection has been primarily by fluorescence. To extend the range of experiments that can be carried out in droplets, we have developed the use of electrospray ionization mass spectrometry (ESI-MS) to measure femtomole quantities of proteins in individual pico- to nanoliter droplets. Surfactant-stabilized droplets containing analyte were produced in a flow-focusing droplet generation microfluidic device using fluorocarbon oil as the continuous phase. The droplets were collected off-chip for storage and reinjected into microfluidic devices prior to spraying the emulsion into an ESI mass spectrometer. Crucially, high quality mass spectra of individual droplets were obtained from emulsions containing a mixture of droplets at >150 per minute, opening up new routes to high throughput screening studies.

Rapid and highly sensitive protein extraction via cobalt oxide nanoparticle-based liquid-liquid microextraction coupled with MALDI mass spectrometry.

A new approach for rapid and highly sensitive protein extraction using cobalt oxide nanoparticles modified with cetyltrimethylammonium (Co(3)O(4)/CTA(+) NP) using nanoparticle-based liquid-liquid microextraction (NP-LLME) coupled with matrix-assisted laser desorption/ionization mass spectrometry (MALDI-MS) has been successfully demonstrated. For the first time, the metal oxide NPs (Co(3)O(4)/CTA(+) NP) prepared in the organic phase (toluene) have been successfully applied for the extraction and preconcentration of proteins from sample solutions and complex samples via electrostatic forces involved between the metal oxide NP and proteins. Lysozyme was used as the model protein to investigate the optimal extraction parameters of the current approach. The optimal conditions were obtained at pH > pI for 10 min of incubation time (extraction time) with 3% salt (NaCl) addition. The Co(3)O(4)/CTA(+) NP was successfully applied for the highly sensitive analysis of an array proteins such as insulin, chymotrypsinogen and lysozyme from aqueous solution, protein mixture and milk samples in nanoparticle-based liquid-phase microextraction coupled with MALDI-MS. The potentiality of the NP-LLME using Co(3)O(4)/CTA(+) NP for the extraction of proteins was also compared with other types of NP-liquid phase microextraction (LPME) methods. The current approach offers distinct advantages including rapidity, straightforwardness, high sensitivity for washing- and separation-free MALDI-MS analysis of proteins.

Delayed Desorption Improves Protein Analysis by Desorption Electrospray Ionization Mass Spectrometry.

Protein analysis by desorption electrospray ionization mass spectrometry (DESI-MS) is limited and often accompanied by a mass-dependent loss in sensitivity as protein molecular weight increases. Previously, incomplete dissolution was identified as a potential contributing factor to this limitation for larger proteins. Here, we developed a unique two-step configuration in which a prewetting solvent is applied to the sample surface proximal to DESI analysis by a wetting quill to increase dissolution time and the detection of larger proteins. After optimizing the system with a mixture of proteins containing cytochrome c, myoglobin, and chymotripsinogen, we demonstrate the ability of delayed desorption to improve the analysis of larger proteins such as bovine serum albumin. Albumin and other serum proteins, including even larger ones, were also detected directly from diluted goat serum. An additional feature of this technique is the ability to deliver multiple solvents with potential synergistic or cooperative effects. For example, when using acetonitrile solutions of formic acid and ammonium bicarbonate as the prewetting and DESI spray solvent, respectively, the intensity of chymotrypsinogen improved dramatically compared to controls but less so for smaller proteins such as myoglobin and cytochrome c. Adduct removal was also observed for all proteins. These early results demonstrate the ability of this two-step technique for the use of multiple additives and increased dissolution times compared to standard DESI-MS experiments.

Immunocytochemical localization of secretory proteins in bovine pancreatic exocrine cells.

The bovine exocrine pancreatic cell produces a variety of enzymes and proenzymes for export. Biochemical studies by Greene L.J., C.H. Hirs, and G.E. Palade (J. Biol. Chem. 1963. 238:2054) have shown that the mass proportions of several of these proteins in resting pancreatic juice and zymogen granule fractions are identical. In this study we have used immunocytochemical techniques at the electron microscope level to determine whether regional differences exist in the bovine gland with regard to production of individual secretory proteins and whether specialization of product handling occurs at the subcellular level. The technique used is a modification of one previously reported (McLean, J.D., and S.J. Singer. 1970. Proc. Natl. Acad. Sci U.S.A. 69:1771) in which immunocytochemical reagents are applied to thin sections of bovine serum albumin-imbedded tissue and zymogen granule fractions. A double antibody technique was used in which the first step consisted of rabbit F(ab')2 antibovine secretory protein and the detection step consisted of sheep (F(ab')2 antirabbit F(ab')2 conjugated to ferritin. The results showed that all exocrine cells in the gland, and all zymogen granules and Golgi cisternae in each cell, were qualitatively alike with regard to their content of secretory proteins examined (trypsinogen, chymotrypsinogen A, carboxypeptidase A, RNase, and DNase). The data suggest that these secretory proteins are transported through the cisternae of the Golgi complex where they are intermixed before copackaging in zymogen granules; passage through the Golgi complex is apparently obligatory for these (and likely all) secretory proteins, and is independent of extent of glycosylation, e.g., trypsinogen, a nonglycoprotein vs. DNase, a glycoprotein.

Calcium and pancreatic secretion. I. Subcellular distribution of calcium and magnesium in the exocrine pancreas of the guinea pig.

The distribution of calcium and magnesium has been studied in the acinar cells of the pancreas of the guinea pig. Most of the magnesium was found to be associated with the rough microsomes (probably bound to the ribosomes) and with the postmicrosomal supernate. In contrast, calcium was distributed among all the particulate fractions, primarily the mitochondria, microsomes (especially smooth surfaced), zymogen granules, and the plasmalemma, and was low in the postmicrosomal supernate. Most of the calcium recovered in the particulate fractions was found to be membrane bound. The highest concentrations were found in the membranes of the zymogen granules and in the plasmalemma. By means of control experiments using -45Ca as the tracer, it was established that a considerable redistribution of calcium occurs during homogenization and cell fractionation. At least some of the resulting artifacts were estimated quantitatively and the data were corrected accordingly. The biochemical results were confirmed with the cytochemical antimonate technique carried out on the tissue as well as on isolated fractions. The role of calcium associated with the zymogen granules and with their limiting membranes is discussed in relation to the architecture of the granule and to the functionality of the pancreatic juice.

Single cell analysis in full body quartz glass chips with native UV laser-induced fluorescence detection.

In order to investigate the individual and inhomogenous cellular response, e.g. to external stimuli, single cell analysis is mandatory and may provide new cognitions in proteomics as well as in other fields of systems biology in the future. Here, we report on novel chip architectures for single cell analysis based on full body quartz glass microfluidic chips (QG chips) that extend our previous studies in polydimethylsiloxane (PDMS) chips, and enhance the detection sensitivity of native UV laser-induced fluorescence (UV-LIF) detection. Detection of a 10nM tryptophan solution with an S/N ratio of 11.9, which gives a theoretical limit of detection of 2.5 nM (with S/N=3), was possible. With these optimizations the three proteins alpha-chymotrypsinogen A, ovalbumin and catalase each at a concentration of 100 microg/mL (equal to 4 microM, 0.4 microM and 2.2 microM) were injected electrokinetically and could be separated with nearly baseline resolution. Furthermore, fluorescence spectra (excitation wavelength, lambda(ex) = 266 nm) clearly demonstrate the favourable properties like the very high UV transparency and the nearly vanishing background fluorescence of the QG chips as compared to PDMS chips and to PDMS quartz window (PQW) chips. Finally we exploit the improved sensitivity for single cell electropherograms of Spodoptera frugiperda (Sf9) insect cells.

Glomerular charge barrier and development of proteinuria in passive Heymann nephritis.

BACKGROUND/AIM: Passive Heymann nephritis (PHN) in rats is a commonly used model of membranous glomerulonephritis in man where the cause of proteinuria is not fully resolved. This study was designed to investigate the role of the glomerular charge barrier in development of PHN proteinuria. METHODS: We studied female Sprague-Dawley rats (n = 33) at days 0, 2, 5 and 14 after induction of PHN by injection of antiserum against renal tubular epithelial antigens (anti-Fx1A). Measuring clearance of chymotrypsinogen A (Chym, MW 25,000, 21 A) and similar sized anionic chymotrypsinogen (aChym), together with (51)Cr-EDTA, we hypothesized an increased sieving coefficient (theta) of aChym in the early phase of PHN due to impairment of the glomerular charge barrier. RESULTS: No proteinuria was seen at day 2 (5.8 +/- 1.4 mg/ 24 h, p > 0.05), while protein excretion increased to 23.2 +/- 2.9 mg/24 h (p < 0.05) at day 5 (84 +/- 2% albumin) and further to 544.3 +/- 51.1 mg/24 h (p < 0.01) at day 14 (60 +/- 1% albumin; p < 0.01, day 5 vs. day 14). theta aChym was similar to control at day 2 (0.49 +/- 0.03, p > 0.05), increased at day 5 to 0.62 +/- 0.02 (p < 0.01) but decreased at day 14 to 0.39 +/- 0.02 (p < 0.01). The sieving coefficient of Chym (theta Chym) was decreased at day 14 (p < 0.05). The ratio of theta aChym to theta Chym was increased at day 5 (p < 0.01) but was elsewhere similar to control. CONCLUSION: The increased ratio of theta aChym to theta Chym and selective albuminuria at day 5 indicates an initial impairment of the glomerular charge barrier in PHN.

Sub-2 microm porous and nonporous particles for fast separation in reversed-phase high performance liquid chromatography.

One approach to achieve fast and efficient separations in packed column liquid chromatography (LC) is to reduce eddy diffusion and mass transfer resistance in the mobile phase using short columns packed with small particles. In this study, efficiencies of columns packed with 1.5 and 3.0 microm nonporous and porous particles were compared in reversed-phase LC using nitromethane and a protein as analytes. Nonporous particles provided overall higher efficiency at high linear velocities when nitromethane was used as solute; however, the efficiency difference diminished significantly when the particle size was reduced from 3 to 1.5 microm. Efficiencies for 1.5 microm nonporous particles were considerably higher than those for 1.5 microm porous particles at high linear velocities when a protein, alpha-chymotrypsinogen A (MW 25,000), was used as solute. In addition, the average retention factor for amylbenzene in a column packed with ACQUITY C(18) porous particles was approximately 16 fold higher than for Micra C(18) nonporous particles for aqueous mobile phase compositions containing from 40 to 75% acetonitrile. Pressure drop, sample loading capacity, and separation power were also evaluated and compared for porous and nonporous particles under practical conditions.

Evaluation and comparison of alternatives to Protein A chromatography Mimetic and hydrophobic charge induction chromatographic stationary phases.

In this paper Protein A mimetic and hydrophobic charge induction chromatographic (HCIC) stationary phases are characterized in terms of their protein adsorption characteristics and their selectivity is compared with Protein A chromatography using a set of Chinese hamster ovary-derived monoclonal antibodies and Fc-fusion proteins. Linear retention experiments were employed to compare the selectivities of these resins for both non-IgG model proteins as well as antibodies and the fusion proteins. While none of the non-IgG model proteins were observed to bind to the Protein A resin, most of them did in fact bind to the alternative resins. In addition, while the elution pH was similar for the model proteins and antibodies on the HCIC resin, the mimetic resins did exhibit higher binding for the antibodies under these linear pH gradient conditions. A mixed mode preparative isotherm model previously developed for HCIC was shown to accurately describe the adsorption behavior of the mimetic materials as well. Host cell protein clearance profiles were also investigated under preparative conditions using complex biological feeds and the results indicated that while some selectivity was observed for both the HCIC and the mimetic materials, the purification factors were in general significantly less than those obtained with Protein A. It is important to note, however, that the selectivity of the mimetic and HCIC materials was also observed to be antibody specific indicating that further optimization may well result in increased selectivities for these materials.

Novel adsorptive polyamine coating for enhanced capillary electrophoresis of basic proteins and peptides.

In capillary electrophoresis (CE), the anionic and hydrophobic nature of the fused-silica capillary surface has long been known to present a problem in protein and peptide analysis. The use of capillary surface coating is one of the approaches to avoid the analyte-wall interactions. In this study, a new polymer, poly-LA 313, has been synthesized, physico-chemical characterized, and applied as polyamine coating for CE separations. The coating process is highly reproducible and provides fast separations of peptides and proteins in a few minutes and with high efficiency. The physically adsorbed polymer gives rise to a durable coating in the range of pH 2-10, in the presence of organic modifiers (acetonitrile and methanol) and with complex biological samples. The efficiency of the new cationic polymer was also tested performing protein and peptide separations with capillary electrophoresis-electrospray ionization-mass spectrometry (CE-ESI-MS).

Human pancreatic chymotrypsinogen A: a non-competitive enzyme immunoassay, and molecular forms in serum and amniotic fluid.

A sandwich enzyme immunoassay has been developed for human pancreatic chymotrypsin(ogen) using polystyrene balls coated with specific IgG as the first antibody and peroxidase-labelled IgG as the second antibody. The detection limit was 0.5 microgram/l. A good parallelism was observed with the curves obtained from standard chymotrypsinogen A and chymotrypsin(ogen) present in pancreatic juice; however, a slight discrepancy in parallelism with chymotrypsin(ogen) present in serum and amniotic fluid was noticed. Chymotrypsinogen concentration in pancreatic juice was evaluated to represent 9% of total proteins. Mean values of chymotrypsin(ogen) in human sera were 24.6 +/- 8.3 micrograms/l in adults and 20.9 +/- 8.8 micrograms/l in newborns. In amniotic fluid at the 18th week of pregnancy the values were scattered (5-70 micrograms/l). The molecular forms of immunoreactive chymotrypsin(ogen) in normal serum and amniotic fluid have been investigated by gel filtration on Sephadex G-100. Two peaks of immunoreactive chymotrypsin(ogen) were observed in normal serum; the first peak elutes in a position consistent with a complex of chymotrypsin with serum inhibitor (Mr 76,000), and the second peak elutes with a molecular weight of approx. 25,000 corresponding to the elution position of free chymotrypsin(ogen). In normal amniotic fluid three peaks of immunoreactive material were present; the first and second peaks elute in the same position as in serum, and the third peak with a molecular weight of about 14,500 may represent a degraded form of chymotrypsin.

Isolation and partial characterization of a complex of several (Pro-) endopeptidases from whole porcine pancreatic extract and from purified zymogen granules.

Pancreatic zymogen granules contain exportable proteins at a very high concentration. The mechanism leading to this condensation is unknown. On the other hand, it is known that aqueous extract of pancreatic acetone powder precipitates at low ionic strength and acidic pH. The precipitable fraction is called 'euglobulin' in the literature. We thought that euglobulin could serve as a simplified model to study the condensation of some of the pancreatic exportable proteins. We have compared quantitatively and qualitatively the composition of euglobulins prepared from porcine pancreatic acetone powder and from lysates of purified pancreatic zymogen granules. They were found to be nearly identical, consisting of glycoprotein(s) and/or proteoglycan(s) associated to a proesterase activity, chymotrypsinogens C and D and proelastase. We conclude therefore, that the interactions between the constituents of euglobulin must be specific, since they can occur in the complex protein mixture of the whole organ to a similar extent as in the zymogen granules themselves. We have tried to identify the nature of these specific interactions. We were able to demonstrate that neither the granule membranes, nor the high-molecular-weight proteoglycan present in the granules (Reggio, H.A. and Palade, C.E. (1978) J. Cell. Biol. 77,288-314) were responsible for the observed aggregation. Electrostatic interactions between acidic and basic proteins (Thomson, A. and Denniss, I.S. (1976) Biochim. Biophys. Acta 429, 581-590) were demonstrated between proelastase and chymotrypsinogens C and D. However, the possible roles of the glycoprotein(s) and/or proteoglycan(s) in the condensation process remain unknown.

Stimulation of protein synthesis in isolated pancreatic acini from chronically ethanol-fed rats is due to alterations in post-transcriptional regulation.

In an earlier study, we reported that isolation of acini from the pancreas of rats fed ethanol chronically, led to a 2- to 3-fold increase in the rate of protein synthesis compared to acini from rats fed the control diet. In the present study, we wanted to investigate whether the enhanced rate of protein synthesis was due to an increased rate of degranulation, reflecting a stimulation of cellular signal transduction processes, and/or to changes at the level of transcription/translation. The rate of degranulation was monitored by initially prelabelling the secretory proteins in vivo with [3H]leucine followed by determination of their fate in the intact tissue as well as in the subsequently isolated acini. The recovery of the label in isolated acini as a fraction of that incorporated into the tissue was similar for control and ethanol-fed groups, suggesting that ethanol feeding had no effect on the rate of degranulation during the isolation of acini. The rate of incorporation of [3H]uridine into total RNA was about 70% higher in acini from the ethanol-fed group as compared to the control group, suggesting a higher rate of transcription. However, the steady-state level of mRNA for trypsinogen, a representative digestive enzyme mRNA, showed only a moderate increase of 20% in acini from the ethanol-fed group compared to those from the intact tissue. These results suggest that the increased rate of protein synthesis in isolated acini from ethanol-fed rat pancreas is primarily due to post-transcriptional modifications.

Displacement chromatography of proteins using a retained pH front in a hydrophobic charge induction chromatography column.

The chromatographic separation of two proteins into a displacement train of two adjoined rectangular bands was accomplished using a novel method for hydrophobic charge induction chromatography (HCIC) which employs a self-sharpening pH front as the displacer. This method exploits the fact that protein elution in HCIC is promoted by a pH change, but is relatively independent of salt effects, so that a retained pH front can be used in place of a traditional displacer in displacement chromatography. The retained pH front was produced using the two adsorbed buffering species tricine and acetic acid. The separation of lysozyme and α-chymotrypsinogen A into adjoined, rectangular bands was accomplished with overall recoveries based on the total mass injected greater than 90 and 70%, respectively. The addition of urea to the buffer system increased the sharpness of the pH front by 36% while the yields of lysozyme and α-chymotrypsinogen A based on the total mass eluted increased from 76% to 99% and from 37% to 85%, respectively, when the purities of both proteins in their product fractions were fixed at 85%. The results demonstrate that the method developed in this study is a useful variant of HCIC and is also a useful alternative to other displacement chromatography methods.

Direct measurement of protein osmotic second virial cross coefficients by cross-interaction chromatography.

The importance of weak protein interactions, such as protein self-association, is widely recognized in a variety of biological and technological processes. Although protein self-association has been studied extensively, much less attention has been devoted to weak protein cross-association, mainly due to the difficulties in measuring weak interactions between different proteins in solution. Here a framework is presented for quantifying the osmotic second virial cross coefficient directly using a modified form of self-interaction chromatography called cross-interaction chromatography. A theoretical relationship is developed between the virial cross coefficient and the chromatographic retention using statistical mechanics. Measurements of bovine serum albumin (BSA)/lysozyme cross-association using cross-interaction chromatography agree well with the few osmometry measurements available in the literature. Lysozyme/alpha-chymotrypsinogen interactions were also measured over a wide range of solution conditions, and some counterintuitive trends were observed that may provide new insight into the molecular origins of weak protein interactions. The virial cross coefficients presented in this work may also provide insight into separation processes that are influenced by protein cross-interactions, such as crystallization, precipitation, and ultrafiltration.

The bovine pro-carboxypeptidase A-S6 ternary complex: a rare case of a secreted protein complex.

Up to now, a non-covalent ternary complex in which the pro-carboxypeptidase A (subunit I) is associated to two functionally different proteins (subunits II and III) has only been found in the pancreas of ruminant species. In the other species studied so far, the pro-carboxypeptidase A is secreted either as a monomer or as a binary association with a functionally different protein. Subunit I is the immediate precursor of carboxypeptidase A. Subunit II is a chymotrypsinogen of the C-type, involved, like subunit I, in the degradation of proteins and peptides. Although closely related to the pancreatic serine endopeptidases, subunit III appears to be devoid of any specific enzymatic activity. Information about the spatial organization of the subunits in the ternary complex has been deduced from the sequential dissociation of the complex. In contrast to the mechanism of activation of subunits I and II, which is independent of their aggregation state, the catalytic properties of the resulting enzymes are sensitive to their aggregation state. Moreover, the structural basis of inactivity of subunit III as well as the physiological role of the ternary complex are also discussed in this review.

A quantitative immuno-electronmicroscopic study of amylase and chymotrypsinogen in peri- and tele-insular cells of the rat exocrine pancreas.

Malaisse-Lagae demonstrated in 1975 that peri-insular (PI) cells and tele-insular (TI) cells produce amylase (Am) and chymotrypsinogen (Ch) in a different ratio. These biochemical measurements are in contradiction with recent observations of Bendayan (1985), who found that the Am/Ch ratio measured with the protein A-gold technique applied to ultrathin Epon sections was the same in PI and TI cells. We have previously shown (Posthuma et al., 1984) that experimentally induced changes in Am and Ch content of rat pancreas are quantitatively reflected by immuno-gold labeling of zymogen granules in cryosections. Here we applied the same technique to compare the Am/Ch labeling density ratios in PI and TI pancreatic cells. To ascertain constancy of experimental conditions, we used ultrathin cryosections from tissue blocks consisting of TI and PI tissue elements. Consecutive sections of these blocks were alternatively immunolabeled for Am and Ch, using protein A-gold as marker. The density of gold particles over zymogen granules of both PI and TI cells was measured. It appeared that the Am/Ch labeling density ratio was significantly lower in PI than in TI cells. This difference resulted from a lower Am labeling as well as higher Ch labeling density over zymogen granules in PI cells.

Immunocytochemical assays of amylase and chymotrypsinogen in rat pancreas secretory granules. Efficacy of using immunogold-labeled ultrathin cryosections to estimate relative protein concentrations.

An exploration was conducted as to whether the relative concentration of two intracellular proteins could be evaluated quantitatively from their labeling densities in ultrathin cryosections labeled with the immunogold technique. As a model rat pancreatic cells were used in which the content of amylase (Am) and chymotrypsinogen (Ch) was experimentally altered. Rats were fed either normal laboratory chow or food containing soybean trypsin inhibitor (STI), which affects the Am/Ch ratio in the tissues. The changes in Am and Ch protein levels and enzyme activities were measured biochemically in cell suspension homogenates or in zymogen granule fractions. Within 5 days a maximal change in the Am/Ch was observed as a result of adaptation to the STI diet. The Am/Ch ratio determined biochemically was compared with that from counts of gold particles bound to the respective protein in immunogold-labeled cryosections. The two data sets matched fairly well, indicating that the intensity of the immunoreaction is a reliable reflection of antigen concentration in this system.