Identification of prekallikrein and high-molecular-weight kininogen as a complex in human plasma.

Prekallikrein and high-molecular-weight kininogen were found associated in normal human plasma at a molecular weight of 285,000 as assessed by gel filtration on Sephadex G-200. The molecular weight of prekallikrein in plasma that is deficient in high-molecular-weight kininogen was 115,000. This prekallikrein could be isolated at a molecular weight of 285,000 after plasma deficient in high-molecular-weight kininogen was combined with plasma that is congenitally deficient in prekallikrein. Addition of purified 125I-labeled prekallikrein and high-molecular-weight kininogen to the respective deficient plasma yielded a shift in the molecular weight of prekallikrein, and complex formation could be demonstrated by incubating prekallikrein with high-molecular weight kininogen. This study demonstrates that prekallikrein and high-molecular-weight kininogen are physically associated in plasma as a noncovalently linked complex and may therefore be adsorbed together during surface activation of Hageman factor. The complex is disrupted when these proteins are isolated by ion exchange chromatography.     

Role of surface in surface-dependent activation of Hageman factor (blood coagulation Factor XII)

The mechanism by which negatively charged substances such as celite, kaolin, or ellagic acid contribute to the surface-dependent activation of Hageman factor (Factor XII) was studied. Kinetic studies of the proteolytic activation of (125)I-labeled human Hageman factor by human plasma kallikrein, plasma, activated Factor XI, and trypsin were performed in the presence and absence of high molecular weight kininogen and surface materials such as celite, kaolin, or ellagic acid. The results showed that surface-bound Hageman factor was 500 times more susceptible than soluble Hageman factor to proteolytic activation by kallikrein in the presence of high molecular weight kininogen. Surface binding of Hageman factor enhanced its cleavage by plasmin, activated Factor XI, and trypsin by 100-fold, 30-fold, and 5-fold, respectively. On a molar basis, trypsin was twice as potent as kallikrein in the cleavage of the surface-bound Hageman factor, while plasmin and activated Factor XI were an order of magnitude less potent than kallikrein. Kallikrein even at concentrations as low as 0.5 nM (i.e., 1/1000th of the concentration of prekallikrein in plasma) was very potent in the limited proteolysis of the surface-bound Hageman factor. These results suggest that substances classically known as "activating surfaces" promote the activation of Hageman factor indirectly by altering its structure such that it is much more susceptible to proteolytic activation by other plasma or cellular proteases.     

Molecular assembly in the contact phase of the Hageman factor system.

Data obtained in the past few years have defined the molecular mechanisms of contact activation of the Hageman factor pathways of plasma, i.e., the kinin-forming, intrinsic clotting and fibrinolytic systems. Involved are four molecules: Hageman factor, high molecular weight (MW) kininogen, prekallikrein and factor XI. High MW kininogen serves as a surface cofactor to assemble prekallikrein or factor XI in proximity to surface-bound Hageman factor. Reciprocal proteolytic activation of Hageman factor and prekallikrein represents an essential step in the rapid activation of the contact phase. Although Hageman factor does undergo cleavage and activation in the absence of prekallikrein or high MW kininogen, the rate is approximately 50 and 100 times slower than when these molecules are present. Once Hageman factor is activated on the surface, it cleaves and activates clotting factor XI. Activated Hageman factor (HFa) exhibits two molecular forms. One of these, alpha HFa, activates prekallikrein and factor XI, and the intrinsic clotting system on the surface. alpha HFa and clotting factor XI remain surface bound. The other form of activated Hageman factor, beta HFa, leaves the surface, going into solution where it readily activates additional prekallikrein but not factor XI. Of perhaps even greater importance, kallikrein rapidly dissociates from the surface. Thus the formation of bradykinin and fibrinolysis is disseminated whereas clotting via the intrinsic system remains localized. Reviewed here is the molecular mechanism of contact activation of the Hageman factor pathways and discussed in the interaction of Hageman factor with the negatively charged surface, prekallikrein, factor XI and high MW kininogen. The multiple forms of activated Hageman factor and their potential biologic significance are also discussed.     

Mechanisms for the involvement of high molecular weight kininogen in surface-dependent reactions of Hageman factor.

The mechanisms by which human high molecular weight kininogen (HMKrK) contributes to the surface-dependent activation of the Hageman factor systems have been studied. The ability of various mixtures of purified human Hageman factor (coagulation factor XII), HMrK, prekallikrein, and kaolin to activate coagulation factor XI was determined with factor XIa (activated factor XI) clotting assays. Hageman factor, HMrK and prekallikrein were required for maximal rates of activation of factor XI. A certain optimal mixture of purified Hageman factor, HMrK, prekallikrein, and kaolin gave the same rapid initial rate of activation of purified factor XI as an equivalent aliquot of factor XI-deficient plasma. This suggests that potent, surface-mediated activation of factor XI in plasma is explicable in terms of Hageman factor, HMrK, and prekallikrein. By studying separately some of the surface-dependent reactions involving Hageman factor, it was found that HMrK accelerated by at least an order of magnitude the following reactions: (i) the activation of factor XI by activated Hageman factor; (ii) the activation of prekallikrein by activated Hageman factor; and (iii) the activation of Hageman factor by kallikrein. Stoichiometric rather than catalytic amounts of HMrK gave optimal activation of factor XI. These results are consistent with the hypothesis that HMrK and Hageman factor form a complex on kaolin which renders Hageman factor more susceptible to proteolytic activation by kallikrein and which facilitates the action of activated Hageman factor on its substrate proteins, factor XI and prekallikrein.     

The contact activation mechanism in human plasma: activation induced by dextran sulfate

Incubation of normal human plasma with dextran sulfate for 7 min at 4 degrees C generates kallikrein amidolytic activity. No kallikrein activity is generated in factor XII or prekallikrein-deficient plasma and only small amounts (8%) in high molecular weight (HMW) kininogen- deficient plasma. Addition of specific antisera directed against prekallikrein or HMW kininogen to normal plasma blocked the generation of kallikrein activity by dextran sulfate. Thus, factor XII, prekallikrein, and HMW kininogen are essential components for optimal activation of prekallikrein. The role of limited proteolysis in the activation of prekallikrein induced by dextran sulfate was studied by adding 125I-prekallikrein to plasma. The generation of kallikrein activity paralleled the proteolytic cleavage of prekallikrein as judged on SDS gels in the presence of reducing agents. The same cleavage fragments were observed as obtained by activation of purified prekallikrein by beta-factor-XIIa. Addition of 131I-HMW kininogen and 125I-factor XII or 131I-HMW kininogen and 125I-prekallikrein to normal plasma followed by activation with dextran sulfate and analysis on SDS gels indicated that the observed cleavage of prekallikrein and HMW kininogen is fast compared to the observed cleavage of factor XII, which is much slower and less extensive. During the first minutes of incubation of normal plasma with dextran sulfate, mainly alpha-factor- XIIa is formed. During prolonged incubation, beta-factor-XIIa is also formed.     

A different cleavage site for high molecular weight kininogen in vivo following intravenous injection of dextran sulfate in the rabbit

Purified radiolabeled rabbit Hageman factor, prekallikrein, and high molecular weight kininogen were used to examine Hageman factor system molecular dynamics after the intravenous injection of heparin-like dextran sulfate polymer in the rabbit. Hageman factor system proteins rapidly disappeared from the circulation following dextran sulfate injection, as measured by radial immunodiffusion, by kaolin-releasable kinin formation, and by measuring circulating levels of radiolabeled Hageman factor, prekallikrein, and high molecular weight kininogen. 125I-Hageman factor was distributed mainly to lung, liver, and spleen following dextran sulfate injection. Proteolysis of circulating 125I-Hageman factor occurred at a site within a disulfide loop into fragments of 50,000 and 30,000 molecular weight. Proteolysis of 125I-prekallikrein also occurred with visualization of a 50,000 molecular weight fragment. Although extensive proteolysis of 131I-high molecular weight kininogen was observed, the cleavage fragments were not the same as those generated during contact activation in vitro. The major fragment of high molecular weight kininogen observed in vivo was at 80,000 molecular weight, in contrast to the 65,000 molecular weight fragment generated by kallikrein in vitro. These results indicate that high molecular weight kininogen can undergo proteolysis in vivo into fragments not known to be associated with kinin release.     

In vitro activation of the contact (Hageman factor) system of plasma by heparin and chondroitin sulfate E

A large number of negatively charged macromolecules, including DNA, glycosaminoglycans, and proteoglycans, were tested as possible activators of the contact (Hageman factor) system in vitro. Activation was assessed by conversion of prekallikrein to kallikrein, as determined by amidolytic assay and by cleavage of 125I-Hageman factor into 52,000- and 28,000-dalton fragments. Of particular interest to these studies, heparin proteoglycan and glycosaminoglycan from rat peritoneal mast cells, and squid chondroitin sulfate E, which is representative of the glycosaminoglycan from cultured mouse bone marrow derived mast cells, induced the reciprocal activation between Hageman factor and prekallikrein. In addition, naturally occurring heparin glycosaminoglycans from pig mucosa, bovine lung, and rat mast cells also induced activation. In contrast, native connective tissue matrix glycosaminoglycans and proteoglycans from several sources were inactive, although when one such chondroitin sulfate was further sulfated in vitro, it gained activity. When the negative charge of the activating agents was blocked by the addition of hexadimethrine bromide, the cleavage of 125I-Hageman factor in the presence of prekallikrein was prevented. The active negatively charged macromolecules induced cleavage of 125I-high molecular weight kininogen in normal plasma but not in Hageman factor-deficient or prekallikrein- deficient plasmas. Reconstitution of prekallikrein-deficient plasma with purified prekallikrein restored the kininogen cleavage upon addition of the active proteoglycans. These results suggest that both heparin from connective tissue mast cells and highly sulfated chondroitin sulfate E from cultured mouse bone marrow derived mast cells (which are considered synonomous with mucosal mast cells) could activate the contact system of plasma subsequent to an activation secretion response.     

Endothelial cells produce a substance that inhibits contact activation of coagulation by blocking the activation of Hageman factor.

Human umbilical vein endothelial cells (HUVECs) produce a property that impairs the generation of coagulant and amidolytic activity initiated when normal human plasma is exposed to glass. This inhibitory property blocks the adsorption of Hageman factor (factor XII) to glass, thereby preventing the activation of Hageman factor, but does not impair the coagulant or amidolytic activity of already activated Hageman factor (factor XIIa). This property in HUVEC lysates could be neutralized by a purified preparation of Hageman factor but not by purified prekallikrein or high molecular mass kininogen. A partially purified inhibitory fraction from cell lysates exhibited a single homogeneous band in SDS/PAGE of approximately 22.5 kDa. Inhibitory activity was also found in concentrates of conditioned media from HUVECs, which also impaired the binding of Hageman factor to a surface; it may not be identical with that found in cell lysates.     

Plasma thromboplastin antecedent (PTA, factor XI): a specific and sensitive radioimmunoassay

A specific, sensitive, and reproducible radioimmunoassay for human plasma thromboplastin antecedent (PTA, factor XI) has been developed with purified PTA and monospecific rabbit antiserum. Precise measurements of PTA antigen were possible for concentrations as low as 0.3% of that in normal pooled plasma. Normal plasma contained approximately 6 microgram PTA/ml. A good correlation (correlation coefficient 0.68) existed between the PTA procoagulant assays and radioimmunoassays among 50 normal adults (25 males and 25 females). PTA antigen was markedly reduced in plasma of 13 patients with congenital homozygous PTA deficiency (range less than 0.003-0.128 U/ml) and 9 patients with hepatic cirrhosis (0.35+/-0.17 U/ml), but was normal in those of 9 patients under treatment with warfarin, 8 patients with disseminated intravascular coagulation and 16 patients with other congenital clotting factor abnormalities, including prekallikrein deficiency (Fletcher trait) and high molecular weight kininogen deficiency (Fitzgerald trait).     

Role of high-molecular-weight kininogen in surface-binding and activation of coagulation Factor XI and prekallikrein.

In the contact phase of activation of the kinin-forming, intrinsic clotting, and fibrinolytic systems, high-molecular-weight kininogen acts as a cofactor for the activation of Factor XI, prekallikrein, and Hageman factor. One mechanism by which high-molecular-weight kininogen acts as a cofactor has been studied by using 125I-labeled Factor XI and prekallikrein in kaolin-activated normal human plasma and plasmas deficient in high-molecular-weight kininogen and Hageman factor. High-molecular-weight kininogen was found to be essential for normal binding and cleavage of both Factor XI and prekallikrein on the kaolin surface. Hageman factor was essential for cleavage but not for binding of Factor XI and prekallikrein to kaolin. In normal plasma 80% of the activated Factor XI remained surface-bound, whereas 80% of the kallikrein was not surface-bound. These findings are consistent with the hypothesis that, in the initial phase of contact activation, high-molecular-weight kininogen links both Factor XI and prekallikrein to the exposed surface where they are activated by surface-bound activated Hageman factor. Once activated, the Factor XI molecules remain localized at the site of activation, in contrast to the kallikrein molecules which are found largely in the surrounding plasma.     

A unique precipitating autoantibody against plasma thromboplastin antecedent associated with multiple apparent plasma clotting factor deficiencies in a patient with systemic lupus erythematosus

A 42-yr-old woman with systemic lupus erythematosus without bleeding diathesis developed a prolonged activated partial thromboplastin time that was not corrected by normal plasma. An inhibitor that acted rapidly and inactivated 0.5 U/ml plasma thromboplastin antecedent (PTA, factor XI) at a 1:200 plasma dilution was demonstrated. In addition to a low titer of PTA (less than 0.01 U/ml), plasma assayed at 20-fold dilution also showed low titers of Hageman (factor XII, 0.02 U/ml), Fletcher (plasma prekallikrein, 0.02 U/ml), and Fitzgerald (high molecular weight kininogen, less than 0.01 U/ml) factors. The titer of these factors, except PTA, returned to normal upon further plasma dilution or upon removal of the inhibitor by protein A adsorption. Thus, the inhibitor appeared to interfere with these clotting factor assays, possibly by inactivating PTA in the substrate plasmas in the test system. Its specificity was further confirmed. The inhibitor did not interfere with surface-induced proteolytic cleavage of Hageman factor. Surface-induced generation of plasma kallikrein activity (amidolysis of H-D-pro-phe-arg-pNa and cold-promoted factor VII activity enhancement) requires only Hageman, Fletcher, and Fitzgerald factors and was normal. Reactions requiring all 4 contact phase factors, including PTA, such as surface-induced generation of plasmin activity (amidolysis of H-D-val-leu-lys-pNa) and activated Christmas factor (factor IXa) activity, were defective. Furthermore, the inhibitor bound to agarose-protein A inactivated and removed PTA selectively from normal plasma. The inhibitor was an IgG-lambda autoantibody that precipitated PTA. The inactivated activated PTA (factor XIa) without the requirement for an additional cofactor. Furthermore, it inhibited surface-induced activation of PTA by interfering with its proteolytic cleavage upon glass surface exposure and with its binding onto the reactive surfaces.     

Changes in plasma levels of prekallikrein, kallikrein, high molecular weight kininogen and kallikrein inhibitors during lethal endotoxin shock in dogs

Plasma levels of prekallikrein, kallikrein, high molecular weight kininogen and kallikrein inhibitors were measured in samples from dogs infused with E. coli endotoxin. Markedly reduced levels of prekallikrein and high molecular weight kininogen were seen at circulatory collapse and free kallikrein was detected. Both 'fast-reacting' and 'time-dependent' inhibitors of plasma kallikrein were significantly reduced. Fractionation of pre-infusion and collapse samples by gel filtration together with immunological procedures indicated that both alpha2-macroglobin and alpha1-antitrypsin were the major kallikrein inhibitors in dog plasma, and that they were significantly reduced in the collapse samples.     

Coagulation and fibrinolysis associated with contact phase in plasma with high molecular weight kininogen deficiency

Congenital deficiency of high molecular weight kininogen (HMWK), first reported by Saito et al. in 1975, is a rare disorder with homozygous defect of HMWK and only 14 cases have been reported so far. Prolonged partial thromboplastin time and depressed intrinsic fibrinolytic activity in plasma interacted with negatively charged surface were characterized in these patients without any bleeding problem. On the other hand, patients associated with hemorrhagic disorder, such as haemophiliacs, showed a markedly prolonged partial thromboplastin time but normal intrinsic fibrinolytic activity. These results give us a important suggestion on our understanding of why haemophiliacs bleed and why HMWK deficient patients do not. In immunological studies with specific antisera directed against human plasma HMWK and prekallikrein, HMWK in present in normal plasma in free form and a complexed form with prekallikrein, and whole prekallikrein in present in a complexed form with HMWK. This result is associated with diminished level of prekallikrein in plasma of patients with congenital HMWK deficiency. According to above-mentioned our experimental results and some reports, it is speculated that the deficiency of HMWK with normal level of prekallikrein is acquired.     

Amidolytic properties of single-chain activated Hageman factor.

Activation of Hageman factor (Factor XII) upon exposure to negatively charged agents has been attributed to proteolytic cleavage of this molecule. To examine this question, purified Hageman factor was exposed to Sephadex gels to which ellagic acid had been adsorbed. Such Hageman factor, separated from the gels and studied in the fluid phase, was amidolytic. Nonetheless, no cleavage of Hageman factor treated in this way could be demonstrated by sodium dodecyl sulfate/polyacrylamide gel electrophoresis. Thus, activation of Hageman factor by negatively charged agents was not necessarily accompanied by molecular scission.     

Severe fletcher factor (plasma prekallikrein) deficiency with partial deficiency of hageman factor (factor xii): Report of a case with observation on in vivo and in vitro leukocyte chemotaxis

A case of cross-reacting material-negative Fletcher trait with additional partial deficiency of Hageman factor (HF, Factor XII) is described. Although the patient presented with a recent history of frequent epistaxis, he had no other personal or family history of a tendency toward bleeding or infection. Similar to other cases of Fletcher trait, his plasma showed a markedly prolonged partial thromboplastin time which could be corrected by prolonged incubation with the surface-activator kaolin. Surface-induced fibrinolysis, amidolysis of α-N-benzoyl-proline-L -phenylalanine-L -arginine-p-nitro- anilide, and cold-promoted enhancement of factor VII activity, reactions requiring the presence in the plasma of Fletcher factor (pre-kallikrein), in addition to Hageman factor and Fitzgerald factor (high-molecular weight kininogen), were also defective. In vivo chemotaxis of polymorphonuclear leukocytes and monocytes (Rebuck's skin window technique) in response to skin abrasions was defective, but was normal when diphtheria-tetanus toxoid was also applied. In vitro leukocyte chemotaxis (Boyden chamber technique) in response to normal or patient's own serum activated with zymosan was normal. Together with previous observations that kallikrein generated chemotactic activity, possibly via activation of C5, the present observations suggest that prekallikrein activation may be important for in vivo leukocyte chemotactic response to skin abrasion. The inheritance of Fletcher trait in this patient is unclear. Although the father was an apparent heterozygote, the mother was completely normal for Fletcher factor procoagulant activity and antigen. The mild Hageman factor deficiency in the patient did not contribute significantly to the plasma defects described and was likely inherited from the father who had a low HF procoagulant activity.     

Plasma kallikrein/kinin system: a revised hypothesis for its activation and its physiologic contributions

Recent studies indicate that assembly of high molecular weight kininogen on its multiprotein receptor allows for prekallikrein activation. On endothelial cells, factor XII activation is secondary to prekallikrein activation and amplifies it. The immediate consequence of plasma prekallikrein activation is the cleavage of high molecular weight kininogen (HK) with liberation of bradykinin. Cleaved high molecular weight kininogen is antiangiogenic. Bradykinin stimulates tPA liberation and nitric oxide formation. In addition, formed plasma kallikrein promotes single-chain urokinase activation and subsequent plasminogen activation. Kininogens and their breakdown products also are antithrombins. The angiotensin converting enzyme breakdown product of bradykinin prevents canine coronary thrombosis. The author presents a new hypothesis for physiologic assembly and activation of the plasma kallikrein/kinin system and discusses its influence on vascular biology.     

Initiation of plasma prorenin activation by Hageman factor-dependent conversion of plasma prekallikrein to kallikrein.

Plasma prorenin is an inactive form of renin (EC 3.4.99.19) that can be converted to active renin in acid-treated plasma by an endogenous serine protease that is active at alkaline pH (alkaline phase activation). To identify this enzyme we first tested the ability of Hageman factor fragments, plasma kallikrein (EC 3.4.21.8), and plasmin (EC 3.4.21.7) to activate prorenin in acid-treated plasma. All three enzymes initiated prorenin activation; 50% activation was achieved with Hageman factor fragments at 1 microgram/ml, plasma kallikrein at 2-4 microgram/ml, or plasmin at 5-10 microgram/ml. We then showed that the alkaline phase of acid activation occurred normally in plasminogen-free plasma but was almost completely absent in plasmas deficient in either Hageman factor or prekallikrein; alkaline phase activation was restored to these latter plasmas when equal parts were mixed together. Therefore, both Hageman factor and prekallikrein were required for alkaline phase activation to occur. We then found that, although plasma kallikrein could activate prorenin in plasma deficient in either Hageman factor or prekallikrein, Hageman factor fragments were unable to activate prorenin in prekallikrein-deficient plasma. These studies demonstrate that alkaline phase prorenin activation is initiated by Hageman factor-dependent conversion of prekallikrein to kallikrein which, in turn, leads to activation of prorenin. In this fashion, we have revealed a possible link between the coagulation-kinin pathway and the renin-angiotensin system.     

Circulating inhibitors of blood coagulation associated with procainamide-induced lupus erythematosus

We studied a patient being treated with procainamide in whom we observed a high antinuclear antibody titer and prolonged activated partial thromboplastin (PTT), prothrombin (PT), and Stypven times (ST). Serum antibody concentrations against single-stranded DNA were elevated while those against native DNA were not elevated, suggesting the procainamide-induced lupus syndrome. Dilution of the patient's plasma with normal plasma failed to correct the PTT and PT, indicating the presence of an inhibitor(s) to blood coagulation. The anticoagulant activity was associated with the IgG fraction of the patient's serum. Addition of purified or partially purified human factors IX, X, VIII, VII, XIa, prekallikrein, high molecular weight kininogen, or phospholipids to the patient's plasma failed to correct the PTT, PT, or ST; however, purified human factor XII and prothrombin corrected the PTT and ST, respectively. These results indicate that production of antibodies directed against antigenic determinants on coagulation proteins can be a manifestation of procainamide-induced lupus erythematosus.     

Demonstration of kallikrein-like protease activity in nonactivated plasma of patients with Cooley''s anemia

Routine evaluation of 12 children with Cooley's anemia revealed that each one had a prolonged partial thromboplastin time. However, prothrombin time and thrombin time were within the normal range. Specific assays demonstrated low levels of the four contact factors: factors XI, XII, prekallikrein, and high molecular weight kininogen. Further investigation revealed activity against para-nitroanilide peptide substrates in unactivated plasma from all 12 patients. Following gel filtration on Sephadex G200, the activity emerged in one peak in the void volume, indicating a molecular weight of greater the 500,000. Activity was greatest against H-D-Pro-Phe-Arg-pNA, the substrate for plasma kallikrein, and was inhibited by diisopropyl fluorophosphate and trasolyl. It was unaffected by hirudin, soy bean trypsin inhibitor, and lima bean trypsin inhibitor. It was destroyed by heating at 56 degrees C. Specific antisera against human prekallikrein and human alpha-macroglobulin did not reduce the activity. It is concluded that a high molecular weight kallikrein-like protease, is present in the plasma of these patients. It is postulated that it is released into the circulation from tissue as a result of damage due to iron overload. It is further postulated that this protease brings about in vivo activation of the contrast factors, resulting in a fall in their circulating levels.     

Activation of factor XII by dextran sulfate: the basis for an assay of factor XII

A system was developed for studying the activation of factor XII (Hageman factor) in the presence of dextran sulfate (DS). Salient features of the system included low ionic strength (0.08), low concentration of factor XII (approximately 1/10,000 that in normal plasma), and an excess of exogenous prekallikrein (PK). In this system, factor XII was rapidly converted to the 80,000 molecular weight (mol wt) form of factor XIIa (alpha-factor-XIIa). Once formed, the factor XIIa converted PK to kallikrein at a rate that was proportional to the amount of factor XII originally present in the incubation mixture. This system was used to construct a simple sensitive assay for factor XII in plasma and other biologic samples. The kallikrein produced was measured spectrophotometrically with the chromogenic substrate (H-D-Pro-Phe-Arg- p-nitroanilide (S-2302). This assay was shown to be independent of the high molecular weight kininogen and the PK content of the sample being analyzed. The measurements obtained were consistent with fundamental enzymologic principles and, if desired, could be processed with a simple calculator program to achieve linear standard curves. When applied to the quantitation of factor XII in plasma, the assay yielded values in close agreement with those determined by coagulant assay or by radial immunodiffusion.