Lower Inhibitor Development in Hemophilia A Mice following Administration of Recombinant Factor VIII-O-Phospho-L-serine Complex

Abstract

Factor VIII is a multidomain protein composed of A1, A2, B, A3, C1, and C2 domains. Deficiency or dysfunction of factor VIII causes hemophilia A, a bleeding disorder. Administration of exogenous recombinant factor VIII as a replacement leads to development of inhibitory antibodies against factor VIII in 15–30% of hemophilia A patients. Hence, less immunogenic preparations of factor VIII are highly desirable. Inhibitory antibodies against factor VIII are mainly directed against immunodominant epitopes in C2, A3, and A2 domains. Further, several universal epitopes for CD4+ T-cells have been identified within the C2 domain. The C2 domain is also known to interact specifically with phosphatidylserine-rich lipid vesicles. Here, we have investigated the hypothesis that complexation of O-phospho-l-serine, the head group of phosphatidylserine, with the C2 domain can reduce the overall immunogenicity of factor VIII. The biophysical (circular dichroism and fluorescence) and biochemical studies (ELISA and size exclusion chromatography) showed that O-phospho-l-serine binds to the phospholipid-binding region in the C2 domain, and this interaction causes subtle changes in the tertiary structure of the protein. O-Phospho-l-serine also prevented aggregation of the protein under thermal stress. The immunogenicity of the factor VIII-O-phospho-l-serine complex was evaluated in hemophilia A mice. The total and inhibitory antibody titers were lower for factor VIII-O-phospho-l-serine complex compared with factor VIII alone. Moreover, factor VIII administered as a complex with O-phospho-l-serine retained in vivo activity in hemophilia A mice. Our results suggest that factor VIII-O-phospho-l-serine complex may be beneficial to increase the physical stability and reduce immunogenicity of recombinant factor VIII preparations. Factor VIII is a multidomain protein composed of A1, A2, B, A3, C1, and C2 domains. Deficiency or dysfunction of factor VIII causes hemophilia A, a bleeding disorder. Administration of exogenous recombinant factor VIII as a replacement leads to development of inhibitory antibodies against factor VIII in 15–30% of hemophilia A patients. Hence, less immunogenic preparations of factor VIII are highly desirable. Inhibitory antibodies against factor VIII are mainly directed against immunodominant epitopes in C2, A3, and A2 domains. Further, several universal epitopes for CD4+ T-cells have been identified within the C2 domain. The C2 domain is also known to interact specifically with phosphatidylserine-rich lipid vesicles. Here, we have investigated the hypothesis that complexation of O-phospho-l-serine, the head group of phosphatidylserine, with the C2 domain can reduce the overall immunogenicity of factor VIII. The biophysical (circular dichroism and fluorescence) and biochemical studies (ELISA and size exclusion chromatography) showed that O-phospho-l-serine binds to the phospholipid-binding region in the C2 domain, and this interaction causes subtle changes in the tertiary structure of the protein. O-Phospho-l-serine also prevented aggregation of the protein under thermal stress. The immunogenicity of the factor VIII-O-phospho-l-serine complex was evaluated in hemophilia A mice. The total and inhibitory antibody titers were lower for factor VIII-O-phospho-l-serine complex compared with factor VIII alone. Moreover, factor VIII administered as a complex with O-phospho-l-serine retained in vivo activity in hemophilia A mice. Our results suggest that factor VIII-O-phospho-l-serine complex may be beneficial to increase the physical stability and reduce immunogenicity of recombinant factor VIII preparations. Factor VIII (FVIII) is a multidomain protein that functions as a cofactor in the coagulation cascade. FVIII is composed of six domains, NH2-A1-A2-B-A3-C1-C2-COOH. It is synthesized as a 2351-residue single chain precursor protein, which is subsequently cleaved at residue 1680 to form the heavy chain (A1-A2-B) and the light chain (A3-C1-C2) (1Toole J.J. Knopf J.L. Wozney J.M. Sultzman L.A. Buecker J.L. Pittman D.D. Kaufman R.J. Brown E. Shoemaker C. Orr E.C. Amphlett G.W. Foster B.W. Coe M.L. Knutson G.J. Fass D.N. Hewick R.N. Nature. 1984; 312: 342-347Crossref PubMed Scopus (660) Google Scholar, 2Kaufman R.J. Wasley L.C. Dorner A.J. J. Biol. Chem. 1988; 263: 6352-6362Abstract Full Text PDF PubMed Google Scholar, 3Vehar G.A. Keyt B. Eaton D. Rodriguez H. O'Brien D.P. Rotblat F. Oppermann H. Keck R. Wood W.I. Harkins R.N. Tuddenham E.G.D. Lawn R.D. Capon D.J. Nature. 1984; 312: 337-342Crossref PubMed Scopus (658) Google Scholar). The light chain has a molecular mass of 80 kDa. The heavy chain undergoes further processing and is cleaved at several sites between the A2 and B domains, generating polypeptides with molecular masses ranging from 90 to 180 kDa (2Kaufman R.J. Wasley L.C. Dorner A.J. J. Biol. Chem. 1988; 263: 6352-6362Abstract Full Text PDF PubMed Google Scholar). The heavy chain and the light chain are held together by a divalent metal ion such as calcium (4Fay P.J. Arch. Biochem. Biophys. 1988; 262: 525-531Crossref PubMed Scopus (61) Google Scholar). The deficiency or dysfunction of FVIII activity causes hemophilia A, a life-threatening bleeding disorder. Replacement therapy with preparations of recombinant FVIII (rFVIII) 1The abbreviations used are: rFVIII, recombinant human factor VIII; ELISA, enzyme-linked immunosorbent assay; FVIII, factor VIII; OPLS, O-phospho-l-serine; PA, phosphatidic acid; PBT, phosphate buffer containing Tween; PC, phosphocholine; PHR, peak height ratio; PSP, plate-specific parameter; SEC, size exclusion chromatography; ITT, immune tolerance therapy. 1The abbreviations used are: rFVIII, recombinant human factor VIII; ELISA, enzyme-linked immunosorbent assay; FVIII, factor VIII; OPLS, O-phospho-l-serine; PA, phosphatidic acid; PBT, phosphate buffer containing Tween; PC, phosphocholine; PHR, peak height ratio; PSP, plate-specific parameter; SEC, size exclusion chromatography; ITT, immune tolerance therapy. is the treatment of choice (5VanAken W.G. Transfus. Med. Rev. 1997; 11: 6-14Crossref PubMed Scopus (10) Google Scholar). The administration of exogenous FVIII, however, leads to the development of inhibitory antibodies in 15–30% of hemophilia A patients, complicating the replacement therapy (6Jacquemin M.G. Saint-Remy J.M. Haemophilia. 1998; 4: 552-557Crossref PubMed Scopus (53) Google Scholar, 7Lollar P. Healey J.F. Barrow R.T. Parker E.T. Adv. Exp. Med. Biol. 2001; 489: 65-73Crossref PubMed Scopus (28) Google Scholar). Numerous treatment strategies, such as factor VIIa (a bypass agent), porcine FVIII (8Ingerslev J. Haematologica. 2000; 85: 15-20PubMed Google Scholar), immune tolerance therapy (ITT) with high doses of rFVIII (9Ho A.Y. Height S.E. Smith M.P. Drugs. 2000; 60: 547-554Crossref PubMed Scopus (43) Google Scholar), etc., are currently employed clinically to manage patients with inhibitors. However, rFVIII preparations that prevent the formation of inhibitors present alternate clinical approaches. The epitope regions and the mechanisms by which FVIII antibodies inhibit clotting activity are well understood. Most immunodominant epitopes of rFVIII are located in the C2, A3, and A2 domains of FVIII (7Lollar P. Healey J.F. Barrow R.T. Parker E.T. Adv. Exp. Med. Biol. 2001; 489: 65-73Crossref PubMed Scopus (28) Google Scholar, 10Gensana M. Altisent C. Aznar J.A. Casana P. Hernandez F. Jorquera J.I. Magallon M. Massot M. Puig L. Haemophilia. 2001; 7: 369-374Crossref PubMed Scopus (63) Google Scholar, 11Ananyeva N.M. Lacroix-Desmazes S. Hauser C.A. Shima M. Ovanesov M.V. Khrenov A.V. Saenko E.L. Blood Coagul. Fibrinolysis. 2004; 15: 109-124Crossref PubMed Scopus (72) Google Scholar). The immunoprecipitation and inhibitor neutralization assays of the inhibitor plasma from hemophilia A patients clearly indicated that the anti-light chain antibody titer was the highest (12Scandella D.H. Nakai H. Felch M. Mondorf W. Scharrer I. Hoyer L.W. Saenko E.L. Thromb. Res. 2001; 101: 377-385Abstract Full Text Full Text PDF PubMed Scopus (37) Google Scholar). More recently, Reding et al. (13Reding M.T. Okita D.K. Diethelm-Okita B.M. Anderson T.A. Conti-Fine B.M. J. Thromb. Haemost. 2003; 1: 1777-1784Crossref PubMed Scopus (86) Google Scholar) and Pratt et al. (14Pratt K.P. Qian J. Ellaban E. Okita D.K. Diethelm-Okita B.M. Conti-Fine B. Scott D.W. Thromb. Haemost. 2004; 92: 522-528Crossref PubMed Scopus (48) Google Scholar) have identified several universal epitopes for CD4+ T-cells in the 2291–2330 region of the C2 domain using proliferation assays with CD4+ cells from normal humans, hemophilia A patients (13Reding M.T. Okita D.K. Diethelm-Okita B.M. Anderson T.A. Conti-Fine B.M. J. Thromb. Haemost. 2003; 1: 1777-1784Crossref PubMed Scopus (86) Google Scholar), and mice (14Pratt K.P. Qian J. Ellaban E. Okita D.K. Diethelm-Okita B.M. Conti-Fine B. Scott D.W. Thromb. Haemost. 2004; 92: 522-528Crossref PubMed Scopus (48) Google Scholar). Three-dimensional models proposed based on crystallographic studies and mutational analysis show that the C2 domain also contains 2–4 hydrophobic loops and other charged residues that promote lipid binding (Fig. 1) (15Pratt K.P. Shen B.W. Takeshima K. Davie E.W. Fujikawa K. Stoddard B.L. Nature. 1999; 402: 439-442Crossref PubMed Scopus (285) Google Scholar, 16Gilbert G.E. Kaufman R.J. Arena A.A. Miao H. Pipe S.W. J. Biol. Chem. 2002; 277: 6374-6381Abstract Full Text Full Text PDF PubMed Scopus (100) Google Scholar, 17Stoilova-McPhie S. Villoutreix B.O. Mertens K. Kemball-Cook G. Holzenburg A. Blood. 2002; 99: 1215-1223Crossref PubMed Scopus (130) Google Scholar). Further, the C2 domain has structural features characteristic of universal immunodominant CD4+ epitopes (shown as sticks in Fig. 1) (18Raju R. Navaneetham D. Okita D. Diethelm-Okita B. McCormick D. Conti-Fine B.M. Eur. J. Immunol. 1995; 25: 3207-3214Crossref PubMed Scopus (39) Google Scholar). In the blood coagulation cascade, FVIII binds to the membrane surface of activated platelets via specific interaction between phosphatidylserine and the C2 domain (19Kemball-Cook G. Barrowcliffe T.W. Thromb. Res. 1992; 67: 57-71Abstract Full Text PDF PubMed Scopus (14) Google Scholar, 20Gilbert G.E. Furie B.C. Furie B. J. Biol. Chem. 1990; 265: 815-822Abstract Full Text PDF PubMed Google Scholar). The specificity of the interaction is mediated by O-phospho-l-serine (OPLS) the head group of phosphatidylserine (21Gilbert G.E. Drinkwater D. Biochemistry. 1993; 32: 9577-9585Crossref PubMed Scopus (88) Google Scholar). Since OPLS is known to interact with C2 domain that contains immunodominant epitopes, it would be of significance to know the effect of OPLS on the immunogenicity of rFVIII. Here we have investigated the effects of OPLS on the conformation, folding, and stability of rFVIII using physical and biochemical methods. We have also evaluated the impact of OPLS on the activity and immunogenicity of rFVIII in vivo in FVIII knock-out (hemophilia A) mice. The results suggest that binding of OPLS to immunodominant epitopes of rFVIII results in improved stability and reduction in immunogenicity of rFVIII in hemophilia A mice. We used recombinant human factor VIII (Baxter, Glendale, CA) for in vivo experiments. Monoclonal antibodies and were from coagulation plasma and FVIII plasma for the activity assays were from used in activated and assays was The activated and assays were using a coagulation OPLS, calcium and were from phosphate was from buffer were from and used further The of (OPLS) was for this form has been to interact with rFVIII to a the (21Gilbert G.E. Drinkwater D. Biochemistry. 1993; 32: 9577-9585Crossref PubMed Scopus (88) Google Scholar). The complex was by rFVIII in buffer composed of or OPLS, and The was at for rFVIII with or were as for complex by with buffer containing or immunogenicity were using and were to of rFVIII with OPLS can also be of rFVIII. rFVIII was by cells with the containing the of human The cells were in The was to a ion C. Parker E.T. Healey J.F. Barrow R.T. P. Thromb. Haemost. 2002; PubMed Scopus Google Scholar). The factor was on a and using a from in buffer containing containing rFVIII were on a and with a to in the The of the protein was by and size exclusion using a CA) to be It was also that of OPLS in the buffer the of rFVIII. rFVIII was used at a of in buffer and calcium OPLS was in and was to of OPLS at was in buffer containing rFVIII. by the of the were with a of rFVIII in buffer to of the was to for the was in tertiary structure of the protein in the of of OPLS were using a was at and was at K. Biophys. 2003; PubMed Scopus Google Scholar). was used to effect of Google Scholar). The at in the of a of OPLS was to the of rFVIII to the The is to rFVIII and lipid by the of 1) protein, is OPLS, is is OPLS is total protein is and is in The were as OPLS and using CA) with the from the to for The a of and a single binding of OPLS to the phospholipid-binding region of rFVIII was by the of OPLS to with antibody against the phospholipid-binding region of the C2 domain E.L. D. J. Biol. Chem. 1997; Full Text Full Text PDF PubMed Scopus Google Scholar) in a were with antibody by of the antibody at a of in buffer at The was with phosphate buffer containing of and The protein binding sites on the surface were by of buffer of in phosphate buffer of and for at The were with PBT, and of rFVIII in the or of OPLS in buffer was and at for The were with and with of at a and of a of in buffer at for The were with and of phosphate in buffer of and The were at for and the was by of at was using a was used to the of rFVIII thermal stress. were on a with was in the and in the of OPLS at a of from to 80 used were in was at and the was from to in a The was used to the of OPLS on rFVIII the of rFVIII was by the of OPLS of OPLS were investigated as it to the buffer It is to that thermal studies were in buffer of metal ion binding M. A. J. 2004; Full Text Full Text PDF PubMed Scopus Google Scholar). However, buffer has a high which causes changes at the changes at be to of and in the of rFVIII thermal in the and in the of OPLS were by a with a and The of the protein used was and a was used to the The was at and was to at was at a of were the of with a of were at and the was at and were at was using the of Google Scholar), with the to the is with the to the and is were as in as a of The in was as in the of the protein at and is the at a was to the of aggregation in the experiments. was using a CA) with exclusion of The was using a protein of known molecular from The of a with a a and buffer was used as the and was at of and of were of rFVIII in the and in the of OPLS at of thermal were by the protein at of were at and and at to the A of hemophilia A mice with a in of the FVIII was with from the L. S.E. 1995; PubMed Scopus Google Scholar). of and were used for the The of the has impact on the immune J. M. L. Hoyer L.W. Thromb. Haemost. 1999; PubMed Scopus Google Scholar). The in vivo activity of complex was by the in the hemophilia A mice R. W. J. Thromb. Haemost. 2003; 1: PubMed Scopus Google Scholar). of were administered with buffer or with rFVIII or complex The of rFVIII used was of protein The of the of was with a The were for the and the was at the of the and of hemophilia A mice of that were or of rFVIII or complex in of The of administration was investigated mainly to the immune Further, et al. B.M. Thromb. Haemost. 2000; PubMed Scopus Google Scholar) have that the were and administration in hemophilia A of immune for and Blood were in buffer at to by of rFVIII with or was also evaluated studies were in with the of the and at the at of and Inhibitory titers were by antibody in Scholar). were at with of rFVIII and subsequently with of of the and of antibody in buffer were at for The were and with of at a in buffer at for was for with of phosphate in buffer of and was by the of of at was using a The plate-specific was used to the to The for was as A of known antibody was for and used to the and of the between the and was as the A of the of of to of was used to the that to the The was the antibody titer for the Inhibitory antibody titers were using the of the as B. I. H. J. M. E. Thromb. Haemost. 1995; PubMed Scopus Google Scholar). of of plasma in human plasma were with of normal human plasma and at for activity at the of the was using activated A of the of activity of to of was to the with reduction in activity and was in analysis was using of OPLS and on the of to the effect of OPLS on the tertiary structure of the protein, the of the protein was in the of of A in of rFVIII at was in the of OPLS (Fig. in changes have been as for factor interaction with chain A. D. Biochemistry. 2002; PubMed Scopus Google Scholar). The were using under to the binding A high that OPLS interaction with rFVIII is with a hydrophobic chain such as phosphatidylserine showed a lower and the is to hydrophobic and It is to that the is a and may the binding of OPLS to rFVIII. of OPLS with studies were to OPLS binds to the region of the C2 domain. The that binds to the region was used as a that a region in the C2 domain was used as OPLS binds to the region of the protein, it would with to a reduction in rFVIII binding to (Fig. can be from the the binding of rFVIII to antibody with of OPLS, that the binding of OPLS and In to the from OPLS (a charged on the of on the a was OPLS was with to the of rFVIII. can be from the of Fig. the were and are of the of The that the reduction of rFVIII binding to with OPLS is mainly to between and OPLS for binding to rFVIII. of OPLS on of has been used to the and stability of several D. D. J. J. Biol. 1998; PubMed Scopus Google Scholar, W. Biophys. J. 2000; Full Text Full Text PDF PubMed Scopus Google Scholar). It has also been used to development 2000; Scholar) and to for protein J.M. B. M. Res. 1993; PubMed Scopus Google Scholar). The of the protein to is of the and immunogenicity of a protein rFVIII has been to be to aggregation subtle changes L. Biochemistry. 2001; PubMed Scopus Google Scholar), which may at the C2 domain the K. R. 2003; Scholar). In to the binding of OPLS to this region with aggregation of rFVIII, thermal studies of in the and in the of OPLS were of the rFVIII at in the of OPLS, showed a at that the protein is composed of L. Biochemistry. 2001; PubMed Scopus Google Scholar). The at a of at a of were used to the (Fig. in the was between and that the protein undergoes in the the with the increase in thermal exclusion studies at the thermal the of the and of the protein the A at is in Fig. the a and the in and was with the formation of L. Biochemistry. 2001; PubMed Scopus Google Scholar, J.L. T.W. J.F. J. 1998; Full Text PDF PubMed Scopus Google Scholar). in in at and the a as in Fig. thermal was in the of OPLS, the of was The analysis of rFVIII in the of OPLS and at showed that the characteristic features of were (Fig. that the of OPLS the and aggregation of rFVIII was further investigated by The of protein would be that of the protein to increase in the molecular of Google Scholar). In to OPLS with the formation of the of rFVIII in the and in the of OPLS were in the of rFVIII the in the of a further increase in in increase in the by studies (Fig. Since the of several and and of rFVIII, increase in indicated that the of size with In the of OPLS, the of changes is that OPLS the size of effect of OPLS on aggregation of rFVIII was further by rFVIII as a single peak at The the thermal were to to the with the of rFVIII show the of formation of was as a peak at which with (Fig. The peak height of the to protein the of the a of protein was rFVIII was to thermal In the of OPLS, the height of the protein peak is the peak that OPLS the formation of of rFVIII is a for the rFVIII W. D.N. Res. 2003; PubMed Scopus Google Scholar). rFVIII is to aggregation that may be by subtle changes in the tertiary structure L. Biochemistry. 2001; PubMed Scopus Google Scholar) in the C2 domain K. R. 2003; Scholar). on structure and mutational it has been proposed that the C2 domain contains 2–4 hydrophobic loops that are to (15Pratt K.P. Shen B.W. Takeshima K. Davie E.W. Fujikawa K. Stoddard B.L. Nature. 1999; 402: 439-442Crossref PubMed Scopus (285) Google Scholar, 16Gilbert G.E. Kaufman R.J. Arena A.A. Miao H. Pipe S.W. J. Biol. Chem. 2002; 277: 6374-6381Abstract Full Text Full Text PDF PubMed Scopus (100) Google Scholar, 17Stoilova-McPhie S. Villoutreix B.O. Mertens K. Kemball-Cook G. Holzenburg A. Blood. 2002; 99: 1215-1223Crossref PubMed Scopus (130) Google Scholar). Further, the C2 domain also several high (Fig. 1) (13Reding M.T. Okita D.K. Diethelm-Okita B.M. Anderson T.A. Conti-Fine B.M. J. Thromb. Haemost. 2003; 1: 1777-1784Crossref PubMed Scopus (86) Google Scholar). OPLS binding may this prevent and with the aggregation of rFVIII. We that effects may be beneficial and administration of rFVIII may reduce aggregation and surface to and of in to the activity and effect of rFVIII and complex studies were in hemophilia A mice. mice Hence, bleeding by the would in the of the in as for buffer alone. rFVIII and the complex and rFVIII were in coagulation of the of the rFVIII or to within of the that complexation of rFVIII with OPLS in of rFVIII, and protein the via to a to the of the in vivo activity a be A and analysis at the and activity of rFVIII in and is in of immunogenicity of complex and rFVIII was evaluated in the hemophilia A mice. A mice have been employed for the immunogenicity of FVIII immune is to that in J. M. L. Hoyer L.W. Thromb. Haemost. 1999; PubMed Scopus Google Scholar, M. J. Saint-Remy J.M. R. M. Thromb. Haemost. 2002; PubMed Scopus Google Scholar). Further, models are to immunogenicity of protein preparations A. L. J. Res. 1997; PubMed Scopus Google Scholar, A.J. M.L. 2004; PubMed Scopus Google Scholar). The total antibody titers and inhibitory titers in mice were by antibody and the of the (Fig. in hemophilia A mice administration in total antibody titer of for rFVIII and for at Further, of the six administered with antibody However, to the lower of immune administration A. L. J. Res. 1997; PubMed Scopus Google Scholar) and high a analysis be In administered antibodies were as as with rFVIII and the were at for preparations to the (Fig. analysis to in immune between and in the and was the of group was the of for mice with rFVIII, the total antibody titer was and the inhibitory antibody titer was The high inhibitory antibody titers may be to the administration of human protein in a mice The administration of the complex in a lower immune at the of compared with rFVIII. The total antibody titer and the inhibitory antibody titer for mice with the complex was and The of OPLS in the rFVIII inhibitory antibody formation by compared with rFVIII (Fig. Further, the immunogenicity of rFVIII administered with or as was also investigated to the specificity of OPLS The total antibody titers and inhibitory titers (Fig. and in the of or are with rFVIII and are that for the to have lower immunogenicity compared with rFVIII in hemophilia A mice to the specific interaction of OPLS with rFVIII. The for the lower immune with complex compared with rFVIII is However, we that the reduction in immunogenicity be to processing of the complex by the immune on structural the C2 domain region has several immunodominant epitopes for processing by cells (13Reding M.T. Okita D.K. Diethelm-Okita B.M. Anderson T.A. Conti-Fine B.M. J. Thromb. Haemost. 2003; 1: 1777-1784Crossref PubMed Scopus (86) Google Scholar). The binding of OPLS to this immunodominant epitope may subtle changes that may in processing of by the immune compared with rFVIII alone. complexation between rFVIII and OPLS is it is to that rFVIII would as a complex with Further, OPLS and factor to epitopes in the C2 domain E.L. Shima M. D. J. Biol. Chem. Full Text PDF PubMed Google Scholar, E.L. D. J. Biol. Chem. 1995; Full Text Full Text PDF PubMed Scopus Google Scholar). OPLS would be by factor in OPLS may to rFVIII a of administration with of may be rFVIII may be to processing by in may to changes in the of cells and H. Reding M. Qian J. Okita D.K. Parker E. P. Hoyer L.W. Conti-Fine B.M. Thromb. Haemost. 2001; 85: PubMed Scopus Google for antibody subtle changes in protein have been to the lower immunogenicity of the form of the antibody J. Biol. 2001; PubMed Scopus Google Scholar). the suggest that OPLS may be a beneficial for the development of less immunogenic rFVIII preparations. that OPLS is used as a in to with OPLS as is M. R. L. G. J. Res. 1993; Google Scholar). The present clearly a in the overall of the immune between rFVIII and We that this may to development of immunogenic rFVIII preparations. We the at for the of the dichroism and We and for We P. for of the and the of the for antibody titer using