Peptides related to the antigenic determinant block T cell recognition of the native protein as processed by antigen-presenting cells

Discrepancy in CD3-Transmembrane Peptide Activity between In Vitro and In Vivo T-Cell Inhibition

Electrostatic amino acid interactions between receptor subunits within the T-cell antigen receptor (TCR) transmembrane domain are critical for the formation of the TCR-CD3 complex. Core peptide, a short peptide corresponding to the TCR-alpha transmembrane region, containing two positively charged amino acids, is known to inhibit T-cell function in vitro and in vivo. The aim of this study was to examine peptides corresponding to the syntactic transmembrane CD3 region binding to TCR-alpha for their ability to inhibit T-cell activation in vitro and in vivo. Three peptides matching the transmembrane sequence of CD3-delta, -epsilon and -gamma were synthesized and tested in different biological in vitro and in vivo systems for their effect on T-cell activity. The CD3-peptides had no impact on T-cell function in vitro, but surprisingly, decreased signs of inflammation in the adjuvant arthritis rat model in vivo. Preliminary evidence suggests that peptides with CD3 transmembrane-derived sequences can inhibit an immune response as assessed by adjuvant-induced arthritis. The lack of in vitro activity may lead to a wasteful disregard of active compounds in the process of drug discovery and development.

Potential biologic agents for treating rheumatoid arthritis

The encouraging clinical results observed in trials using anti-TNF therapy clearly warrant further studies to determine whether TNF inhibitors are capable of modifying the destructive component of this disease in long-term follow-up studies as well as to assess the safety of long-term use (see the article by Keystone in this issue). It is also reasonable to propose that interfering with the cytokine cascade earlier in the course of disease may be of even greater therapeutic benefit. As the pathogenetic mechanisms in RA are more clearly defined, especially in early disease and in those individuals destined to develop severe disease, the potential of other biologic agents to specifically inhibit these critical pathways may provide better treatments for our patients. Many potential targets in the immune-mediated process of RA are currently being rigorously evaluated in clinical trials. Use of combinations of biologic therapies, perhaps in human patients with RA, should be of considerable interest in future trials.

Signaling through the B cell antigen receptor regulates discrete steps in the antigen processing pathway

Antigen processing in B cells is initiated by antigen binding to the surface B cell antigen receptor (BCR). The BCR is a signaling receptor which also functions to endocytose bound antigen for subsequent intracellular processing and presentation with class II molecules. Previously, using subcellular fractionation, we showed that although the surface BCR constitutively traffics from the cell surface to the class II peptide-loading compartment (IIPLC), cross-linking the BCR regulates trafficking, resulting in a more rapid movement of the BCR to the IIPLC (Song et al., 1995, J. Immunol. 155, 4255). The rate of degradation of both the BCR and the bound antigen was also accelerated following BCR cross-linking. Here we provide evidence that the effect of cross-linking the BCR on antigen processing is in part dependent on signal cascades initiated by the BCR. We show that the protein kinase inhibitors Genistein and Chelerythrine, which block BCR signaling, reduce BCR-enhanced antigen processing in a dose-dependent manner. The kinase inhibitors have a small effect on the rate of internalization of the BCR and antigen following BCR cross-linking and significantly decrease the accelerated trafficking to the IIPLC. The increased rate of degradation of the BCR and antigen induced by BCR cross-linking is also decreased by the kinase inhibitors. BCR signaling does not appear to have a global effect on intracellular membrane trafficking as cross-linking the BCR did not alter the rate of trafficking of newly synthesized class II molecules to the IIPLC. Thus, the signaling function of the BCR appears to play a significant role in regulating discrete steps in the intracellular antigen processing pathway.

Differential sensitivity to antigenic competition in antigen-specific and -nonspecific antigen presentation by B cells

We have previously shown that a specific Ag presentation by B cells is different from a nonspecific one in the sensitivity to protein synthesis inhibition. In the present study we have compared the sensitivity of these Ag presentations to antigenic competition. A20-HL cells expressing TNP-specific IgM were pulsed with anti-mouse IgM goat IgG (aMGG) or trinitrophenylated goat IgG (TNP-NGG) as an Ag internalized through Ag receptor or NGG as an Ag internalized by fluid-phase pinocytosis. The pulsed cells induced IL-2 production by NGG-specific cloned T cells. The presence of dog IgG during pulsing A20-HL cells severely inhibited the presentation of NGG but not of aMGG or TNP-NGG. The presence did not decrease the internalization of 125I-NGG into A20-HL cells, suggesting that the inhibition was localized into the complex formation of antigenic peptides with MHC class II molecules. Thus, a specific Ag presentation by A20-HL cells is different from a nonspecific one in its sensitivity to antigenic competition.

Invariant chain peptides enhancing or inhibiting the presentation of antigenic peptides by major histocompatibility complex class II molecules

Two soluble invariant chain (Ii) peptides with overlapping sequences had contrasting effects on the presentation of antigenic peptides by murine Ad, Ak, Ed, and Ek major histocompatibility complex (MHC) class II molecules. Naturally produced class II-associated invariant chain peptides human (h)Ii81-104/murine (m)Ii80-103 inhibited antigen presentation on these MHC class II alleles in a manner consistent with competitive inhibition. The Ii-4 peptides hIi77-92/mIi76-91 enhanced presentation of antigenic peptides on I-E class II alleles by promoting the exchange of peptides at the cell surface. Treatment of antigen-presenting cells (APC) with Ii-4 before the addition of antigenic peptide greatly enhanced subsequent T cell responses, while treatment of APC with Ii-4 after antigenic peptide binding decreased subsequent T cell responses. The hIi81-104 and mIi80-103 peptides inhibited T cell responses in both types of assays. The binding of biotinylated antigenic peptide to MHC class II-transfected L cells, as measured by flow cytometry, was inhibited by mIi80-103 and enhanced by mIi-4. Segments of Ii fragments remaining associated with MHC class II, or released Ii peptides, appear to regulate the formation of stable antigenic peptide/MHC class II complexes either positively or negatively through interactions at or near the antigenic peptide binding site. These findings open a pathway for the design of novel therapeutics based on the structure and function of natural and rationally designed fragments of Ii.

MHC-binding peptides for immunotherapy of experimental autoimmune disease

It is now well accepted that T helper cells play a central role in the induction and maintenance of autoimmune disease. Many experimental models have emphasized this fact and have illustrated the efficacy of therapeutic strategies aimed at disrupting T cell recognition of autoantigens. Antibodies directed at either class II proteins of the major histocompatibility complex (MHC) or CD4 accessory molecules have been universally successful. However, the potential use of antibodies for therapy in humans is complicated by host anti-globulin and anti-idiotype responses. An alternative approach to anti-MHC blockade with antibodies is peptide blockade of MHC molecules. In addition, peptides may be used as agonists of autoantigens in order to modulate the autoimmune response. The use of synthetic peptides for therapy is an innovative yet relatively unexplored approach and will be the subject for discussion in this article.

Allo-cross-reactivity of a human neuraminidase-specific T cell clone dependent on presentation of an endogenous B cell-specific antigen

T cells specific for foreign antigen recognize a complex of peptides and self-major histocompatibility complex (MHC) molecules and can also cross-react with allo-MHC molecules. It remains controversial, however, what alloreactive T cells exactly recognize. It has been proposed that alloreactive T cells recognize endogenous peptides presented by allo-MHC molecules. To test this hypothesis, we examined an influenza virus-specific T cell clone (6H5), specific for neuraminidase N2 and restricted by HLA-DR1. In the absence of influenza virus, this clone cross-reacted with HLA-DR1Dw1+ but not with HLA-DR1Dw20+ Epstein-Barr virus-transformed lymphoblastoid cells (B-LCL). Cold target inhibition experiments and the rearrangement pattern of the T cell receptor beta chain indicated that 6H5 was a monoclonal T cell population most likely using the same T cell receptor for both responses. To determine whether determinants other than HLA-DR1Dw1+ B-LCL or activated B cells, but, surprisingly, not to other cell types expressed HLA-DR1Dw1, including monocytes and transfected L cells. These experiments further support the concept that recognition of allogeneic MHC (in this case HLA-DR1Dw1) may result from a cross-reactivity of T cells specific for a complex of foreign antigen and self-MHC (neuraminidase N2 and HLA-DR1Dw20). Furthermore, allorecognition of T cell clone 6H5 appears to depend upon the recognition of a complex of allogeneic MHC and a cell-type specific endogenous peptide presented by activated B cells.

Autoantibody production in hepatitis B e antigen transgenic mice elicited with a self T-cell peptide and inhibited with nonself peptides

Studies in hepatitis B e antigen (HBeAg)-expressing transgenic mice indicate that self tolerance to two T-cell determinants on the same transgenic self molecule can differ markedly. The dominant T-cell site on HBeAg is tolerogenic, whereas a proportion of T cells recognizing a second T-cell site evade tolerance induction, persist in the periphery, and can be activated in vivo by a single injection of a 12-residue T-cell self peptide. The self-reactive T cells mediate in vivo autoantibody production sufficient to neutralize detection of the autoantigen in serum. Furthermore, autoantibody production can be inhibited by nonself peptides that compete with the self peptide for binding to major histocompatibility complex molecules. This model illustrates that T cells specific for an immunogenic T-cell site on a nonsequestered autoantigen can escape tolerance induction and, more importantly, can mediate autoreactivity in vivo. Furthermore, these results suggest that synthetic T-cell sites may be useful as immunotherapeutic agents for the purpose of circumventing nonresponse to HBeAg during persistent hepatitis B virus infection.

Antigen presentation and self-nonself discrimination

Self-nonself discrimination is primarily carried out by T cells. Since the ligand recognized by T cells is a complex formed by antigenic peptides bound to MHC molecules, positive and negative selection of T lymphocytes must be based on the recognition of complexes formed by self-peptides bound to MHC molecules. This requires that self-antigens are continuously processed, bound by MHC molecules, and presented to T cells under conditions inducing both positive selection of T cells potentially able to recognize foreign antigens and negative selection, either by physical deletion or functional inactivation, of potentially autoreactive T cells. Self-nonself discrimination is not confined to intrathymic development of T lymphocytes, but it is a continuing process among peripheral T cells. Accordingly, autoimmunity is induced when self-antigens, or foreign antigens cross-reactive with self antigens, bound to MHC molecules, are presented under conditions able to activate self-reactive T cells. Based on these premises, a way of interfering with the induction of autoimmune diseases could rely on blocking the MHC binding site presenting the autoantigen.

Characteristics of peptides which compete for presented antigen-binding sites on antigen-presenting cells

The T cell recognition of globular protein antigens requires the cell surface presentation of the protein by Ia-expressing antigen-presenting cells (APC). The mechanisms by which APC function remain to be elucidated. To gain a better understanding of association of antigen with APC surfaces, a large panel of peptides of diverse physicochemical properties was assayed for the ability to compete with presented antigen for binding sites on the APC surface. Competition was measured by the ability of a peptide to block the I-Ek-restricted T cell response to pigeon cytochrome c (Pc) as presented by APC. The panel assayed included overlapping peptides representing the entire length of sperm whale myoglobin and the alpha and beta chains of human adult hemoglobin as well as synthetic conformational peptides of lactate dehydrogenase C4 exhibiting stable secondary, alpha-helical structures. The results presented here show that several peptides of this group compete with the presented form of Pc for binding sites on the APC. However, there is no single biochemical property or amino acid sequence algorithm which predicts the blocking ability. The peptides which compete with presented Pc are not predicted to assume the amphipathic alpha-helical conformation hypothesized by De Lisi and Berzofsky (Proc. Natl. Acad. Sci. USA 1986. 82: 7048) for T cell antigenic peptides. However, peptides designed and synthesized to adopt a stable alpha-helical secondary structure show more potent blocking activity than the corresponding linear peptides, suggesting that the secondary structure may indeed be a contributing factor in the ability of presented antigenic peptides to be bound by the APC. The results with the myoglobin and hemoglobin peptides show no connection between any particular secondary structure of the peptide in the native proteins and the ability of the peptides to block presentation. Further, there is no correlation between the major histocompatibility complex restriction of the competing peptides and their ability to block the I-Ek-restricted Pc-specific T cell response. This suggests that antigen presented by the APC may be bound to APC structures other than Ia prior to association with Ia. Such additional binding sites for presented antigen may be necessary to facilitate association with Ia.

Inhibition of antigen presentation in vitro and in vivo by MHC antagonist peptides

A series of analogue peptides have been generated, using as a template the core region of the OVA 323-339 peptide identified as critical in determining binding to I-Ad. Several of these "core extended" peptides had increased affinities for the I-Ad molecule compared to the native sequence, and were able to inhibit activation of an I-Ad-restricted T cell hybridoma in vitro. The induction of a T cell proliferative response to a peptide antigen could be inhibited by co-administration of core-extended peptide with antigen in the same adjuvant emulsion. Furthermore, inhibition also occurred when the inhibitor molecule was delivered separately one day before immunization. Finally, the induction of the autoimmune disease, experimental allergic encephalomyelitis (EAE), in susceptible mice could be reduced by the administration of a core-extended peptide with high affinity for the appropriate class II molecule. These findings have implications for the use of MHC antagonists in the control and treatment of MHC-associated autoimmune conditions in humans.

The presentation of L-tyrosine-azobenzenearsonate by different mouse Ia molecules uses a common agretope

The T cell response to L-tyrosine-azobenzenearsonate (ABA-tyr) has been studied using T cell lines and clones derived from three different mouse strains, B10.BR, B10.A (5R) and C57B1/6. In all cases, the arsonate group in conjunction with the amino group of tyrosine formed the functional T cell epitope. Molecules without any one or both of these groups are non-stimulatory. The hydrophobic moiety consisting of the azo-linked benzene rings forms the agretope of the molecule, as is evident from competitive inhibition of T cell stimulation by non-stimulatory analogues lacking the epitope. Substitutions on the benzene ring at ortho or meta positions resulted in decreases in ability to compete, indicating the likelihood of steric inhibition of binding of the agretope with the Ia molecule. This pattern was observed for clones and lines restricted by IAk, IAb and IEb/k MHC class II molecules. Peptides from lambda repressor protein, P84-98 and P73-88, showed haplotype specificity in their ability to inhibit ABA-tyr-induced proliferation of T cell clones, BRTC-4 and B6TC, respectively. The binding constants of ABA-tyr analogues were considered to be comparable to those of lambda repressor peptides because equimolar concentrations resulted in similar levels of competition. A cluster of aromatic amino acids on the floor of most MHC class II molecule binding sites might provide strong hydrophobic interaction with azo-linked benzene rings of ABA-tyr, thus accounting for its immunogenicity in all strains of mice studied.

A peptide binding protein having a role in antigen presentation is a member of the HSP70 heat shock family

The T cell recognition of globular protein antigens requires the processing and presentation of the antigen by Ia-expressing APCs. Processing is believed to involve the uptake of antigen into an acidic compartment where proteolysis occurs. The resulting peptides containing the T cell antigenic determinant are associated with Ia and presented at the cell surface to the specific T cells. The mechanisms by which antigenic peptides become associated with Ia is not known. We previously described a peptide binding protein of 72/74 x 10(3) Mr (PBP72/74) that plays a role in antigen presentation as shown by the ability of an antiserum raised in rabbits to affinity-purified PBP72/74 to block presentation of cytochrome c to a cytochrome c-specific T cell hybrid. Here we show that PBP72/74 is recognized by mAbs specific for members of the HSP70 family of proteins. In Western blots PBP72/74 is bound by mAb 7.10, specific for an evolutionarily conserved epitope of HSP proteins and by mAb N27, specific for both the constitutively expressed and inducible 72/73 x 10(3) Mr HSP70 proteins. In addition, PBP72/74 shares a second common feature of the HSP proteins, that of binding to ATP. Indeed, ATP causes the release of PBP72/74 from binding to a peptide fragment of cytochrome c (Pc 81-104) and PBP72/74 can be eluted from ATP columns by Pc 81-104. Finally, a portion of PBP72/74 is shown to be present on B cell surfaces by immunofluorescence staining. Thus, it appears that characteristics of the heat shock proteins are shared by a protein playing a role in antigen presentation, suggesting some commonality in function.

Antigen-presenting function of B lymphocytes

Here we review our current results studying B cells as APC and the mechanisms by which processed antigen is transported to and held on the cell surface for recognition by the specific T cell along with the MHC class II molecules. These studies were carried out using the globular protein cytochrome c as antigen for which the T-cell antigenic determinant was localized to a C-terminal 10-amino acid peptide fragment. For certain analyses, native cytochrome c or antigenic peptide fragments were covalently coupled to antibodies directed toward B-cell surface structures, allowing the targeting of antigen to the APC surface. Our findings indicate that all B cells function as APC and that the APC function is not differentially regulated in defined B-cell subpopulations. Using cytochrome c-antibody conjugates, it was shown that the surface Ig plays two significant roles in augmenting the B-cell APC function following antigen binding: signalling for enhanced APC function and concentrating antigen for subsequent internalization and processing. Both IgM and IgD appear to function identically in facilitating antigen processing in both immune and nonimmune B-cell populations. Furthermore, the surface Ig does not appear to be specially differentiated to function in concentrating antigen, as antigen artificially bound to other B-cell surface structures including MHC class I and class II molecules is also effectively presented. Lastly, evidence is presented that a previously described B-cell activating factor activity is strongly associated with the membranes of activated but not unactivated helper T cells, providing a mechanism by which the T-cell helper function can be focused on the specific antigen-presenting B cell. Concerning the mechanism by which processed antigen is presented at the B-cell surface, evidence is presented suggesting a role of peptide-binding chaperone proteins which may function to transport peptide to the APC surface and facilitate its association with the appropriate Ia. One candidate protein, PBP72/74, is described which binds peptides but not native antigens, is a member of the hsp70 family and appears to play a role in antigen presentation by the ability of antisera raised against it to block APC functions. Peptide-antibody conjugates were used to explore the spacial restrictions on MHC-restricted peptide presentation and it was shown that peptides covalently coupled to antibodies specific for Ig, class I or class II molecules are effective antigens in vitro even in the absence of processing.(ABSTRACT TRUNCATED AT 400 WORDS)

Direct evidence for functional self-protein/Ia-molecule complexes in vivo

Through the development of a panel of murine hybridomas reactive to murine hemoglobin, we have been able to study the processing and presentation of self antigens by antigen-presenting cells. Our results demonstrate that peritoneal macrophages in vivo can process and potentially present the self-antigen hemoglobin. We have extended this finding to show that, directly after removal from the mouse, antigen-presenting cells from a variety of tissues stimulate our hemoglobin-specific hybridomas without any manipulation or addition of exogenous antigen. This constitutes direct functional proof that in a nondisease state self proteins are processed constitutively and can be presented in a fashion similar to that in which foreign antigens are presented. Our demonstration that antigen-presenting cells can process and potentially present self as well as foreign molecules implies that self-tolerance occurs at the level of the T cell. This constitutive processing and presentation of self antigens has potentially far-reaching implications in self-tolerance, autoimmunity, and alloreactivity.

T cell activation by processed antigen is equally blocked by I-E and I-A-restricted immunodominant peptides

The T cell response to a soluble protein requires the processing of the native antigen by an antigen-presenting cell (APC) to a peptide containing an antigenic determinant, which is transported to and bound on the antigen-presenting cell surface, where it is subsequently recognized by the specific T cell in the context of the appropriate Ia molecule. Investigating the response of a pigeon cytochrome c-specific, I-Ek-restricted T cell hybrid, which recognizes a determinant present within a 10-amino acid C-terminal fragment of the protein, it was previously demonstrated that peptides homologous to the peptide from pigeon cytochrome c, but which were not stimulatory, blocked the T cell response to pigeon cytochrome c as processed and presented by APC. In this report the ability of a series of fourteen, 20-amino acid overlapping peptides, representing the entire length of staphylococcal nuclease (Nase), were assessed for their ability to block the response of a pigeon cytochrome c-specific T cell hybrid to antigen-pulsed presenting cells. Only three Nase peptides blocked the I-Ek-restricted pigeon cytochrome c-specific T cell response. Two of these, Nase 61-80 and Nase 91-110, function as T cell antigens in the I-Ad and I-Ab-restricted response to Nase. The third blocking peptide, Nase 101-120, has not been shown to be a T cell antigen. Two other peptides, Nase 51-70 and Nase 81-100, which are recognized by Nase-specific T cells in the context of I-Ek, have no effect on the I-Ek-restricted cytochrome c-specific T cell response. None of these peptides block the higher affinity, heteroclitic response of pigeon cytochrome c-specific T cells to tobacco hornworm moth cytochrome c. Moreover, the response of an I-Ak-restricted T cell to ovalbumin was blocked by the I-Ek-restricted cytochrome c peptides from three different species. Thus, peptides with no obvious primary amino acid sequence homology, and which are not capable of being recognized in the context of the same Ia, compete with one another for the sites on the APC necessary for presentation of processed antigen to T cells. These results suggest that there are structures on the APC surface in addition to Ia, which are necessary for effective antigen presentation following processing. One suitable candidate for such a cell surface material is the recently identified peptide-binding protein, PBP72/74 (Lakey et al., Proc. Natl. Acad. Sci. USA 1987. 84: 1659).

Identification of a peptide binding protein that plays a role in antigen presentation

The helper T-cell response to globular proteins appears, in general, to require intracellular processing of the antigen, such that a peptide fragment containing the T-cell antigenic determinant is released and transported to and held on the surface of an Ia-expressing, antigen-presenting cell. However, the molecular details underlying these phenomena are largely unknown. The means by which antigenic peptides are anchored on the antigen-presenting cell surface was investigated. A cell surface protein is identified that was isolated by its ability to bind to a 24-amino acid peptide fragment of pigeon cytochrome c, residues 81-104, containing the major antigenic determinant for B10.A mouse T cells. This peptide binding protein, purified from [35S]methionine-labeled cells, appears as two discrete bands of approximately equal to 72 and 74 kDa after NaDodSO4/PAGE. The protein can be eluted from the peptide affinity column with equivalent concentrations of either the antigenic pigeon cytochrome c peptide or the corresponding nonantigenic peptide of mouse cytochrome c. However, it does not bind to the native cytochromes c, either of pigeon or mouse, and thus the protein appears to recognize some structure available only in the free peptides. This protein plays a role in antigen presentation as evidenced by the ability of rabbit antibodies raised against it to block the activation of an antigen-specific T-cell hybrid by antigen-presenting cells and pigeon cytochrome c. Its expression is not major histocompatibility complex-restricted in that the blocking activity of the antisera can be absorbed on spleen cells from mice of different haplotypes. This peptide binding protein can be isolated from a variety of cell types, including B cells, T cells, and fibroblasts. The anchoring of processed peptides on the cell surface by such a protein may play a role in antigen presentation--facilitating the interaction of antigenic peptides with Ia and/or the T-cell receptor.

Immunological self, nonself discrimination

The ability of immunodominant peptides derived from several antigen systems to compete with each other for T cell activation was studied. Only peptides restricted by a given transplantation antigen are mutually competitive. There is a correlation between haplotype restriction, ability to bind to the appropriate transplantation antigen, and ability to inhibit activation of other T cells restricted by the same transplantation antigen. An exception was noted in that a peptide derived from an antigen, bacteriophage lambda cI repressor, binds to the I-Ed molecule in a specific way, yet is not I-Ed-restricted. Comparison of the sequence of the repressor peptide with that of other peptides able to bind to (and be restricted by) I-Ed and a polymorphic region of the I-Ed molecule itself revealed a significant degree of homology. Thus, peptides restricted by a given class II molecule appear to be homologous to a portion of the class II molecule itself. The repressor-derived peptide is identical at several polymorphic residues at this site, and this may account for the failure of I-Ed to act as a restriction element. Comparison of antigenic peptide sequences with transplantation antigen sequences suggests a model that provides a basis for explaining self, nonself discrimination as well as alloreactivity.

A synthetic vaccine constructed by copolymerization of B and T cell determinants

Synthetic vaccines are based on the identification of short peptide sequences responsible for inducing a protective immune response. These sequences could contain B and/or T cell determinants. In this study, we have examined the recognition by B and T mouse lymphocytes of several synthetic peptides corresponding to regions of a bacterial and two viral proteins. These include a streptococcal S-34 peptide, H(99-121) and two other synthetic hepatitis B virus surface peptides. A lymph node proliferation assay was employed to detect T cell determinants. Limiting dilution analysis was used to estimate the frequency of clonal precursor B cells specific for an antigenic determinant. This study indicates that the synthetic hepatitis B virus surface peptides are recognized by B cells but not by T cells, whereas the S-34 peptide possesses both B and T epitopes. The copolymerization of the B determinant H(99-121) with S-34 has conferred immunogenicity to the H(99-121) peptide. After copolymerization, the synthetic hybrid molecule retained the S-34 T epitope and acquired a new determinant recognized by T cells. These results demonstrate that synthetic vaccines could be constructed by appropriate selection and organization of B and T determinants.