On the specificity of interaction between the Saccharomyces cerevisiae clamp loader replication factor C and primed DNA templates during DNA replication

Replication factor C (RFC) catalyzes assembly of circular proliferating cell nuclear antigen clamps around primed DNA, enabling processive synthesis by DNA polymerase during DNA replication and repair. In order to perform this function efficiently, RFC must rapidly recognize primed DNA as the substrate for clamp assembly, particularly during lagging strand synthesis. Earlier reports as well as quantitative DNA binding experiments from this study indicate, however, that RFC interacts with primer-template as well as single- and double-stranded DNA (ssDNA and dsDNA, respectively) with similar high affinity (apparent K(d) approximately 10 nm). How then can RFC distinguish primed DNA sites from excess ssDNA and dsDNA at the replication fork? Further analysis reveals that despite its high affinity for various DNA structures, RFC selects primer-template DNA even in the presence of a 50-fold excess of ssDNA and dsDNA. The interaction between ssDNA or dsDNA and RFC is far less stable than between primed DNA and RFC (k(off) > 0.2 s(-1) versus 0.025 s(-1), respectively). We propose that the ability to rapidly bind and release single- and double-stranded DNA coupled with selective, stable binding to primer-template DNA allows RFC to scan DNA efficiently for primed sites where it can pause to initiate clamp assembly.     

Interaction of dimeric intercalating dyes with single-stranded DNA.

The unsymmetrical cyanine dye thiazole orange homodimer (TOTO) binds to single-stranded DNA (ssDNA, M13mp18 ssDNA) to form a fluorescent complex that is stable under the standard conditions of electrophoresis. The stability of this complex is indistinguishable from that of the corresponding complex of TOTO with double-stranded DNA (dsDNA). To examine if TOTO exhibits any binding preference for dsDNA or ssDNA, transfer of TOTO from pre-labeled complexes to excess unlabeled DNA was assayed by gel electrophoresis. Transfer of TOTO from M13 ssDNA to unlabeled dsDNA proceeds to the same extent as that from M13 dsDNA to unlabeled dsDNA. A substantial amount of the dye is retained by both the M13 ssDNA and M13 dsDNA even when the competing dsDNA is present at a 600-fold weight excess; for both dsDNA and ssDNA, the pre-labeled complex retains approximately one TOTO per 30 bp (dsDNA) or bases (ssDNA). Rapid transfer of dye from both dsDNA and ssDNA complexes is seen at Na+ concentrations > 50 mM. Interestingly, at higher Na+ or Mg2+ concentrations, the M13 ssDNA-TOTO complex appears to be more stable to intrinsic dissociation (dissociation in the absence of competing DNA) than the complex between TOTO and M13 dsDNA. Similar results were obtained with the structurally unrelated dye ethidium homodimer. The dsDNA- and ssDNA-TOTO complexes were further examined by absorption, fluorescence and circular dichroism spectroscopy. The surprising conclusion is that polycationic dyes, such as TOTO and EthD, capable of bis-intercalation, interact with dsDNA and ssDNA with very similar high affinity.     

The DNA binding preference of RAD52 and RAD59 proteins: implications for RAD52 and RAD59 protein function in homologous recombination

We examined the double-stranded DNA (dsDNA) binding preference of the Saccharomyces cerevisiae Rad52 protein and its homologue, the Rad59 protein. In nuclease protection assays both proteins protected an internal sequence and the dsDNA ends equally well. Similarly, using electrophoretic mobility shift assays, we found the affinity of both Rad52 and Rad59 proteins for DNA ends to be comparable with their affinity for internal sequences. The protein-DNA complexes were also directly visualized using atomic force microscopy. Both proteins formed discrete complexes, which were primarily found (90-94%) at internal dsDNA sites. We also measured the DNA end binding behavior of human Rad52 protein and found a slight preference for dsDNA ends. Thus, these proteins have no strong preference for dsDNA ends over internal sites, which is inconsistent with their function at a step of dsDNA break repair that precedes DNA processing. Therefore, we conclude that S. cerevisiae Rad52 and Rad59 proteins and their eukaryotic counterparts function by binding to single-stranded DNA formed as intermediates of recombination rather than by binding to the unprocessed DNA double-strand break.     

Quantitative analysis of monovalent counterion binding to random-sequence, double-stranded DNA using the replacement ion method

A variation of affinity capillary electrophoresis, called the replacement ion (RI) method, has been developed to measure the binding of monovalent cations to random sequence, double-stranded (ds) DNA. In this method, the ionic strength is kept constant by gradually replacing a non-binding ion in the solution with a binding ion and measuring the mobility of binding and non-binding analytes as a function of binding ion concentration. The method was validated by measuring the binding of Li+ ions to adenosine nucleotides; the apparent dissociation constants obtained by the RI method are comparable to literature values obtained by other methods. The binding of Tris+, NH4+, Li+, Na+, and K+ to dsDNA was then investigated. The apparent dissociation constants observed for counterion binding to a random-sequence 26-base pair (bp) oligomer ranged from 71 mM for Tris+ to 173 mM for Na+ and K+. Hence, positively charged Tris buffer ions will compete with other monovalent cations in Tris-buffered solutions. The bound cations identified in this study may correspond to the strongly correlated, tightly bound ions recently postulated to exist as a class of ions near the surface of dsDNA (Tan, Z.-J., and Chen, S.-J. (2006) Biophys. J. 91, 518-536). Monovalent cation binding to random-sequence dsDNA would be expected to occur in addition to any site-specific binding of cations to A-tracts or other DNA sequence motifs. Single-stranded DNA oligomers do not bind the five tested cations under the conditions investigated here.     

On-line post-capillary affinity detection of immunoglobulin G for capillary zone electrophoresis

To address the quality issues of antibody manufacturing, post-capillary affinity detection of immunoglobulin G (IgG) is developed for capillary zone electrophoresis. In analogy to a two-dimensional separation system, capillary zone electrophoresis (CZE), as the first dimension, resolves IgG variants based on their differences in molecular structure. IgG variants separated by CZE are discriminated against other serum and cellular proteins by affinity complex formation with protein A binding fragment in a post-capillary reactor. The analytical power of post-capillary affinity detection is demonstrated for rapid and selective heterogeneity analysis of human IgG subclasses and monoclonal antibodies in complex sample matrices. By comparing with pre-capillary formation of affinity complexes between IgG and protein A, post-capillary affinity detection clearly exhibit greater resolving power for examining IgG microheterogeneity. Affinity complex formation prior to CZE analysis, however, has the advantage of lower detection limits. Detection limits suffer with post-capillary affinity detection because of the high fluorescence background contributed by the fluorescently labeled protein A in the post-capillary reactor, and the need to determine a small change in the background level upon complex formation.     

Specificity and kinetics defining the interaction between a murine monoclonal autoantibody and DNA

Interactions between a murine monoclonal anti-DNA autoantibody (BV17-45) and DNA were examined by direct binding and competitive radioimmunoassays. Binding isotherms constructed by titration of purified BV17-45 with a series of distinct 32P-labeled double-stranded DNA ([32P]dsDNA) fragments were super-impossible, suggesting: 1) BV17-45/[32P]dsDNA binding is independent of dsDNA size using fragments greater than or equal to 192 base pairs in length, and 2) BV17-45 does not exhibit stringent sequence specificity. Single-stranded DNA-specific monoclonal antibody BV04-01 did not react with [32P]dsDNA, confirming its duplex character. In competition experiments, BV17-45 cross-reacted with phage (phi X174, M13) RF AND VIRION DNAS AT PICOMOLAR concentrations. Selectivity for B-form DNA was suggested by the ability of poly(dA) . poly(dT), but not other helical duplex forms, to block BV17-45/[32P] dsDNA binding. Among the four deoxyribohomopolymers, only deoxyadenylic acid polymers completely inhibited BV17-45/[32P]dsDNA complex formation. [32P]dsDNA binding was relatively insensitive to ionic strength, suggesting minimal contribution of electrostatic forces to the binding free energy. Measured BV17-45/[32P]dsDNA association and dissociation rate constants (4 degrees C) were 7.4 X 10(6) M-1 s-1 and 9.2 X 10(-5) s-1, respectively, yielding a functional affinity of 8 X 10(10) M-1. Results are discussed in terms of the relative contribution of B-DNA structural and substructural determinants to the mechanism of BV17-45 recognition.     

Replication protein A interactions with DNA. 2. Characterization of double-stranded DNA-binding/helix-destabilization activities and the role of the zinc-finger domain in DNA interactions

Human replication protein A (RPA) is a heterotrimeric single-stranded DNA-binding protein that is composed of subunits of 70, 32, and 14 kDa. RPA is required for multiple processes in cellular DNA metabolism. RPA has been reported to (1) bind with high affinity to single-stranded DNA (ssDNA), (2) bind specifically to certain double-stranded DNA (dsDNA) sequences, and (3) have DNA helix-destabilizing ("unwinding") activity. We have characterized both dsDNA binding and helix destabilization. The affinity of RPA for dsDNA was lower than that of ssDNA and precisely correlated with the melting temperature of the DNA fragment. The rates of helix destabilization and dsDNA binding were similar, and both were slow relative to the rate of binding ssDNA. We have previously mapped the regions required for ssDNA binding [Walther et al. (1999) Biochemistry 38, 3963-3973]. Here, we show that both helix-destabilization and dsDNA-binding activities map to the central DNA-binding domain of the 70-kDa subunit and that other domains of RPA are needed for optimal activity. We conclude that all types of RPA binding are manifestations of RPA ssDNA-binding activity and that dsDNA binding occurs when RPA destabilizes a region of dsDNA and binds to the resulting ssDNA. The 70-kDa subunit of all RPA homologues contains a highly conserved putative (C-X2-C-X13-C-X2-C) zinc finger. This motif directly interacts with DNA and contributes to dsDNA-binding/unwinding activity. Evidence is presented that a metal ion is required for the function of the zinc-finger motif.     

Recognition of template-primer and gapped DNA substrates by the human DNA polymerase beta

Interactions between human DNA polymerase beta and the template-primer, as well as gapped DNA substrates, have been studied using quantitative fluorescence titration and analytical ultracentrifugation techniques. In solution, human pol beta binds template-primer DNA substrates with a stoichiometry much higher than predicted on the basis of the crystallographic structure of the polymerase-DNA complex. The obtained stoichiometries can be understood in the context of the polymerase affinity for the dsDNA and the two ssDNA binding modes, the (pol beta)(16) and (pol beta)(5) binding modes, which differ by the number of nucleotide residues occluded by the protein in the complex. The analysis of polymerase binding to different template-primer substrates has been performed using the statistical thermodynamic model which accounts for the existence of different ssDNA binding modes and has allowed us to extract intrinsic spectroscopic and binding parameters. The data reveal that the small 8 kDa domain of the enzyme can engage the dsDNA in interactions, downstream from the primer, in both (pol beta)(16) and (pol beta)(5) binding modes. The affinity, as well as the stoichiometry of human pol beta binding to the gapped DNAs is not affected by the decreasing size of the ssDNA gap, indicating that the enzyme recognizes the ssDNA gaps of different sizes with very similar efficiency. On the basis of the obtained results we propose a plausible model for the gapped DNA recognition by human pol beta. The enzyme binds the ss/dsDNA junction of the gap, using its 31 kDa domain, with slight preference over the dsDNA. Binding only to the junction, but not to the dsDNA, induces an allosteric conformational transition of the enzyme and the entire enzyme-DNA complex which results in binding of the 8 kDa domain with the dsDNA. This, in turn, leads to the significant amplification of the enzyme affinity for the gap over the surrounding dsDNA, independent of the gap size. The presence of the 5'-terminal phosphate, downstream from the primer, has little effect on the affinity, but profoundly affects the ssDNA conformation in the complex. The significance of these results for the mechanistic model of the functioning of human pol beta is discussed.     

RPA phosphorylation in mitosis alters DNA binding and protein-protein interactions

The heterotrimeric DNA-binding protein, replication protein A (RPA), consists of 70-, 34-, and 14-kDa subunits and is involved in maintaining genomic stability by playing key roles in DNA replication, repair, and recombination. RPA participates in these processes through its interaction with other proteins and its strong affinity for single-stranded DNA (ssDNA). RPA-p34 is phosphorylated in a cell-cycle-dependent fashion primarily at Ser-29 and Ser-23, which are consensus sites for Cdc2 cyclin-dependent kinase. By systematically examining RPA-p34 phosphorylation throughout the cell cycle, we have found there are distinct phosphorylated forms of RPA-p34 in different cell-cycle stages. We have isolated and purified a unique phosphorylated form of RPA that is specifically associated with the mitotic phase of the cell cycle. The mitotic form of RPA (m-hRPA) shows no difference in ssDNA binding activity as compared with recombinant RPA (r-hRPA), yet binds less efficiently to double-stranded DNA (dsDNA). These data suggest that mitotic phosphorylation of RPA-p34 inhibits the destabilization of dsDNA by RPA complex, thereby decreasing the binding affinity for dsDNA. The m-hRPA also exhibits altered interactions with certain DNA replication and repair proteins. Using highly purified proteins, m-hRPA exhibited decreased binding to ATM, DNA pol alpha, and DNA-PK as compared to unphosphorylated recombinant RPA (r-hRPA). Dephosphorylation of m-hRPA was able to restore the interaction with each of these proteins. Interestingly, the interaction of RPA with XPA was not altered by RPA phosphorylation. These data suggest that phosphorylation of RPA-p34 plays an important role in regulating RPA functions in DNA metabolism by altering specific protein-protein interactions.     

Nonspecific electrostatic binding characteristics of the heparin-antithrombin interaction

We evaluated the role of nonspecific electrostatic binding in the interaction of antithrombin (AT) with heparin (Hp), a paradigmatic protein-glycosaminoglycan (GAG) system. To do so, we obtained the ionic-strength dependence of the binding constant, since a common feature in protein-polyelectrolyte systems is a maximum in affinity in the ionic strength range 10 mM 相似文献   

Effects of extracellular DNA on plasminogen activation and fibrinolysis

The increased levels of extracellular DNA found in a number of disorders involving dysregulation of the fibrinolytic system may affect interactions between fibrinolytic enzymes and inhibitors. Double-stranded (ds) DNA and oligonucleotides bind tissue-(tPA) and urokinase (uPA)-type plasminogen activators, plasmin, and plasminogen with submicromolar affinity. The binding of enzymes to DNA was detected by EMSA, steady-state, and stopped-flow fluorimetry. The interaction of dsDNA/oligonucleotides with tPA and uPA includes a fast bimolecular step, followed by two monomolecular steps, likely indicating slow conformational changes in the enzyme. DNA (0.1-5.0 μg/ml), but not RNA, potentiates the activation of Glu- and Lys-plasminogen by tPA and uPA by 480- and 70-fold and 10.7- and 17-fold, respectively, via a template mechanism similar to that known for fibrin. However, unlike fibrin, dsDNA/oligonucleotides moderately affect the reaction between plasmin and α(2)-antiplasmin and accelerate the inactivation of tPA and two chain uPA by plasminogen activator inhibitor-1 (PAI-1), which is potentiated by vitronectin. dsDNA (0.1-1.0 μg/ml) does not affect the rate of fibrinolysis by plasmin but increases by 4-5-fold the rate of fibrinolysis by Glu-plasminogen/plasminogen activator. The presence of α(2)-antiplasmin abolishes the potentiation of fibrinolysis by dsDNA. At higher concentrations (1.0-20 μg/ml), dsDNA competes for plasmin with fibrin and decreases the rate of fibrinolysis. dsDNA/oligonucleotides incorporated into a fibrin film also inhibit fibrinolysis. Thus, extracellular DNA at physiological concentrations may potentiate fibrinolysis by stimulating fibrin-independent plasminogen activation. Conversely, DNA could inhibit fibrinolysis by increasing the susceptibility of fibrinolytic enzymes to serpins.     

Enhanced DNA binding of 9-ω-amino alkyl ether analogs from the plant alkaloid berberine

To understand the structure-activity relationship of isoquinoline alkaloids, absorption, fluorescence, circular dichroism, and thermodynamics were employed to study the interaction of five C-9-ω-amino alkyl ether analogs from the plant alkaloid berberine with double-stranded calf thymus DNA. The C-9 derivatization resulted in dramatic enhancements in the fluorescence emission of these compounds. The most remarkable changes in the spectral and binding properties were in the BC4 and BC5 derivatives. Interactions of these analogs, which have an additional recognition motif with DNA, were evaluated through different spectroscopic and calorimetric titration experiments. The analogs remarkably enhanced the DNA binding affinity and the same was directly dependent on the alkyl chain length. The analog with six alkyl chains enhanced the DNA binding affinity by about 33 times compared with berberine. The binding became more entropically driven with increasing chain length. These results may be of potential use in the design of berberine derivatives and understanding of the structure-activity relationship for improved therapeutic applications.     

Fanconi anemia complementation group A (FANCA) protein has intrinsic affinity for nucleic acids with preference for single-stranded forms

The Fanconi anemia complementation group A (FANCA) gene is one of 15 disease-causing genes and has been found to be mutated in ～60% of Fanconi anemia patients. Using purified protein, we report that human FANCA has intrinsic affinity for nucleic acids. FANCA binds to both single-stranded (ssDNA) and double-stranded (dsDNA) DNAs; however, its affinity for ssDNA is significantly higher than for dsDNA in an electrophoretic mobility shift assay. FANCA also binds to RNA with an intriguingly higher affinity than its DNA counterpart. FANCA requires a certain length of nucleic acids for optimal binding. Using DNA and RNA ladders, we determined that the minimum number of nucleotides required for FANCA recognition is ～30 for both DNA and RNA. By testing the affinity between FANCA and a variety of DNA structures, we found that a 5'-flap or 5'-tail on DNA facilitates its interaction with FANCA. A patient-derived FANCA truncation mutant (Q772X) has diminished affinity for both DNA and RNA. In contrast, the complementing C-terminal fragment of Q772X, C772-1455, retains the differentiated nucleic acid-binding activity (RNA > ssDNA > dsDNA), indicating that the nucleic acid-binding domain of FANCA is located primarily at its C terminus, where most disease-causing mutations are found.     

Tau protein binds single-stranded DNA sequence specifically--the proof obtained in vitro with non-equilibrium capillary electrophoresis of equilibrium mixtures

Tau is a microtubule-associated protein, which plays an important role in physiology and pathology of neurons. Tau has been recently reported to bind double-stranded DNA (dsDNA) but not to bind single-stranded DNA (ssDNA) [Cell. Mol. Life Sci. 2003, 60, 413-421]. Here, we prove that tau binds not only dsDNA but also ssDNA. This finding was facilitated by using two kinetic capillary electrophoresis methods: (i) non-equilibrium capillary electrophoresis of equilibrium mixtures (NECEEM); (ii) affinity-mediated NECEEM. Using the new approach, we observed, for the first time, that tau could induce dissociation of strands in dsDNA by binding one of them in a sequence-specific fashion. Moreover, we determined the equilibrium dissociation constants for all tau-DNA complexes studied.     

Caffeine and other xanthines as cytochemical blockers and removers of heterocyclic DNA intercalators from chromatin

Caffeine (CAF) and other xanthines non-covalently bind with the cationic fluorescent dye acridine orange (AO) and with other heterocyclic mutagens and carcinogens that are known to intercalate into double-stranded DNA (dsDNA). Fluorescence microscopy and spectrofluorometry studies were employed to test the ability of caffeine and certain other methyl substituted xanthines, with different binding affinities for AO, to inhibit and to reverse the intercalation of AO and other heterocyclic agents from intercalation with the DNA of nuclear chromatin of air-dried cells. Results indicated that xanthines with binding affinity for AO greater than 150 m(-1) block the AO molecule in a concentration dependent manner and comply with mass action kinetics. Thus CAF and other xanthines can be used to either inhibit intercalation of AO into nuclear DNA or to remove AO once intercalated into nuclear DNA. The interactions between other planar heterocyclics, xanthines, and nuclear chromatin dsDNA were also found to be non-covalent. Studies are needed to determine the ability of CAF and other xanthines to block and/or remove polyaromatic hydrocarbon (PAH) intercalators from the DNA of living cells.     

Tyrosine phosphorylation enhances RAD52-mediated annealing by modulating its DNA binding

RAD52 protein has an important role in homology-directed DNA repair by mediating RAD51 nucleoprotein filament formation on single-stranded DNA (ssDNA) protected by replication protein-A (RPA) and annealing of RPA-coated ssDNA. In human, cellular response to DNA damage includes phosphorylation of RAD52 by c-ABL kinase at tyrosine 104. To address how this phosphorylation modulates RAD52 function, we used an amber suppressor technology to substitute tyrosine 104 with chemically stable phosphotyrosine analogue (p-Carboxymethyl-L-phenylalanine, pCMF). The RAD52(Y104pCMF) retained ssDNA-binding activity characteristic of unmodified RAD52 but showed lower affinity for double-stranded DNA (dsDNA) binding. Single-molecule analyses revealed that RAD52(Y104pCMF) specifically targets and wraps ssDNA. While RAD52(Y104pCMF) is confined to ssDNA region, unmodified RAD52 readily diffuses into dsDNA region. The Y104pCMF substitution also increased the ssDNA annealing rate and allowed overcoming the inhibitory effect of dsDNA. We propose that phosphorylation at Y104 enhances ssDNA annealing activity of RAD52 by attenuating dsDNA binding. Implications of phosphorylation-mediated activation of RAD52 annealing activity are discussed.     

Replication protein A interactions with DNA. III. Molecular basis of recognition of damaged DNA

Human replication protein A (RPA) is a heterotrimeric single-stranded DNA-binding protein (subunits of 70, 32, and 14 kDa) that is required for cellular DNA metabolism. RPA has been reported to interact specifically with damaged double-stranded DNA and to participate in multiple steps of nucleotide excision repair (NER) including the damage recognition step. We have examined the mechanism of RPA binding to both single-stranded and double-stranded DNA (ssDNA and dsDNA, respectively) containing damage. We show that the affinity of RPA for damaged dsDNA correlated with disruption of the double helix by the damaged bases and required RPAs ssDNA-binding activity. We conclude that RPA is recognizing single-stranded character caused by the damaged nucleotides. We also show that RPA binds specifically to damaged ssDNA. The specificity of binding varies with the type of damage with RPA having up to a 60-fold preference for a pyrimidine(6-4)pyrimidone photoproduct. We show that this specific binding was absolutely dependent on the zinc-finger domain in the C-terminus of the 70-kDa subunit. The affinity of RPA for damaged ssDNA was 5 orders of magnitude higher than that of the damage recognition protein XPA (xeroderma pigmentosum group A protein). These findings suggest that RPA probably binds to both damaged and undamaged strands in the NER excision complex. RPA binding may be important for efficient excision of damaged DNA in NER.     

DNA detection system using molecularly imprinted polymer as the gel matrix in electrophoresis

To develop a simple and inexpensive method for DNA detection, we prepared a molecularly imprinted polymer (MIP) for recognizing a specific double-stranded DNA (dsDNA) sequence and used it in an electrophoretic gel matrix. The MIP gel has many binding sites that are complementary in size, shape, and arrangement of functional groups of the target dsDNA sequence. During MIP gel electrophoresis (MIPGE), migration of the target dsDNA should be hindered by the capture effect of the binding sites in the MIP gel. This was confirmed by observation of deviations from the linear relationship between the migration distances of the DNA standard size markers in the polyacrylamide gel and those in the MIP gel. The migration distances of nontarget dsDNA maintained a linear relationship, however. In addition, the sequence selectivity of dsDNA in this method was investigated by using the Ha-ras gene and its point mutants. Except for A.T to T.A base pair substitution, mutant dsDNA (for example, substitution from A.T to C.G and from G.C to T.A) could be distinguished from the target (wild-type) dsDNA. Although some improvement in A.T (T.A) base pair distinction is still needed, this study is the first to demonstrate detection of a specific dsDNA sequence with MIPs and, as such, opens up a new realm for practical applications of MIPs.     

Small molecular ion adsorption on proteins and DNAs revealed by separation techniques

Ion binding is a term that assumes that the ion is included in the solvation sphere characterising the biomolecule. The binding forces are not clearly stated except for electrostatic attraction; weak forces (hydrogen bonds and Van der Waals forces) are likely involved. Many publications have dealt with ion binding to proteins and the consequences over the past 10 years, but only a few studies were performed using high-performance liquid chromatography (HPLC: ion exchange, reversed phase without the well-identified immobilised metal affinity chromatography) and capillary zone electrophoresis (CZE). This review focuses on the binding of proteins and DNAs mainly to the oxyanions (phosphate, borate, citrate) and amines used as buffers for both the HPLC eluent and the background electrolyte of CZE. Such specific ion adsorption on biomolecules is evidenced by physico-chemical characteristics such as the mobility or retention volume, closely associated with the net charge, which differ from the expected or experimental data obtained under the conditions of an indifferent electrolyte. It is shown that ion binding to proteins is a key parameter in the electrostatic repulsion between the free protein and a fouled membrane in the ultrafiltration separation of a protein mixture.