Logarithms and sectorial projections for elliptic boundary problems

On a compact manifold with boundary, consider the realization B of an elliptic, possibly pseudodifferential, boundary value problem having a spectral cut (a ray free of eigenvalues), say R_-. In the first part of the paper we define and discuss in detail the operator log B; its residue (generalizing the Wodzicki residue) is essentially proportional to the zeta function value at zero, zeta(B,0), and it enters in an important way in studies of composed zeta functions zeta(A,B,s)=Tr(AB^{-s}) (pursued elsewhere). There is a similar definition of the operator log_theta B, when the spectral cut is at a general angle theta. When B has spectral cuts at two angles theta < phi, one can define the sectorial projection Pi_{theta,phi}(B) whose range contains the generalized eigenspaces for eigenvalues with argument in ] theta, phi [; this is studied in the last part of the paper. The operator Pi_{theta,phi}(B) is shown to be proportional to the difference between log_theta B and log_phi B, having slightly better symbol properties than they have. We show by examples that it belongs to the Boutet de Monvel calculus in many special cases, but lies outside the calculus in general.Comment: 27 pages, minor adjustments and correction of typos. To appear in Math. Scan

Two new types of assays to determine protein concentrations in biological fluids using mass spectrometry of intact proteins with cystatin C in spinal fluid as an example

There is no reference method that is generally acknowledged to be unbiased for the determination of the concentration of any protein in biological fluids. This is probably because mass spectrometry (MS) methods acknowledged as reference methods for determination of low molecular mass substances in biological fluids, e.g. creatinine, have been difficult to adapt for proteins. Here we suggest two tentative MS methods, which might be used as reference methods for the determination of protein concentrations in biological fluids. One is based upon the addition to the fluid of a non-proteome reference protein, very similar to the one to be measured, and analyzing the ratio between the corresponding peaks in a selected ion monitoring (SIM) chromatogram. We call this method LC-MS-NPRP (NPRP, Non-Proteome Reference Protein). The other method is based upon the classical standard addition assay for low molecular mass substances. The results of these assays for cystatin C in spinal fluid were compared to those obtained by an immunoassay. Both methods indicated lower concentration than the immunoassay. This was found to be due to the presence of a significant fraction of monohydroxylated cystatin C in spinal fluid. It turned out that the sum of the unhydroxylated and hydroxylated cystatin C concentrations, determined by either of the two MS methods, were close to the results obtained by the immunoassay. These MS-based methods analyze intact proteins and therefore seem more suitable for the determination of protein concentrations in biological fluids than other MS-based methods requiring proteolytic degradation with its inherent lack of precision

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Reduction in glomerular pore size is not restricted to pregnant women. Evidence for a new syndrome: 'Shrunken pore syndrome'.

The plasma levels of cystatin C, β2-microglobulin, beta-trace protein, retinol binding protein (RBP) and creatinine were determined in plasma samples from 111 randomly selected patients with eGFRcystatin C ≤ 60% of eGFRcreatinine and from 55 control patients with 0.9eGFRcreatinine ≤ eGFRcystatin C ≤ 1.1eGFRcreatinine (eGFRcystatin C ≈ eGFRcreatinine). The concentration ratios of cystatin C/creatinine, β2-microglobulin/creatinine, beta-trace protein/creatinine and RBP/creatinine were significantly higher in patients with eGFRcystatin C ≤ 60% of eGFRcreatinine than in patients with eGFRcystatin C ≈ eGFRcreatinine. When the patients were divided into three groups with different estimated GFR intervals (≤ 40, 40-60 and ≥ 60 mL/min/1.73m(2)) the concentration ratios of cystatin C/creatinine, β2-microglobulin/creatinine, and beta-trace protein/creatinine were significantly higher in patients with eGFRcystatin C ≤ 60% of eGFRcreatinine than in patients with eGFRcystatin C ≈ eGFRcreatinine for all GFR intervals. Similar results were obtained when the population without pregnant women was studied as well as the subpopulations of men or of non-pregnant women. Populations of pre-eclamptic women and pregnant women in the third trimester display similar results. Since the production of these four proteins with sizes similar to that of cystatin C is not co-regulated, the most likely explanation for the simultaneous increase of their creatinine-ratios in patients with eGFRcystatin C ≤ 60% of eGFRcreatinine is that their elimination by glomerular filtration is decreased. We suggest that this is due to a reduction in pore diameter of the glomerular membrane and propose the designation 'Shrunken pore syndrome' for this pathophysiological state

High throughput testing of drug library substances and monoclonal antibodies for capacity to reduce formation of cystatin C dimers to identify candidates for treatment of hereditary cystatin C amyloid angiopathy.

Objective. To establish a high-throughput system for testing the ability of drugs or monoclonal antibodies to reduce the in vitro formation of cystatin C dimers to identify substances potentially useful for treatment of patients with hereditary cystatin C amyloid angiopathy (HCCAA). Methods. Various combinations of incubation temperature, time period, guanidinium chloride concentration and concentration of cystatin C monomers were tested in low-volume formats to induce dimer formation of recombinant cystatin C. The extent of dimerization was analysed by gel filtration chromatography and agarose gel electrophoresis. Results. A high-throughput system based upon agarose gel electrophoresis was developed and used to test 1040 drugs in a clinical drug library for their capacity to reduce cystatin C dimer formation in vitro. Seventeen substances reducing dimer formation by more than 30% were identified. A similar system for testing the capacity of monoclonal antibodies against cystatin C to reduce the in vitro formation of cystatin C dimers was also developed and used to test a panel of 12 monoclonal antibodies. Seven antibodies reducing dimer formation by more than 30% were identified and the two most potent, Cyst28 and HCC3, reduced dimerization by 75 and 60%, respectively. Conclusion. We constructed a simple high-throughput system for testing the capacity of drugs and monoclonal antibodies to reduce the in vitro formation of cystatin C dimers and several candidates for treatment of HCCAA could be identified

Cystatin C influences the autoimmune but not inflammatory response to cartilage type II collagen leading to chronic arthritis development

Introduction: Collagen-induced arthritis (CIA) is a mouse model for rheumatoid arthritis (RA) and is induced after immunization with type II collagen (CII). CIA, like RA, is an autoimmune disease leading to destruction of cartilage and joints, and both the priming and inflammatory phases have been suggested to be dependent on proteases. In particular, the cysteine proteases have been proposed to be detrimental to the arthritic process and even immunomodulatory. A natural inhibitor of cysteine proteases is cystatin C. Methods: Cystatin C-deficient, sufficient and heterozygous mice were tested for onset, incidence and severity of CIA. The effect of cystatin C-deficiency was further dissected by testing the inflammatory effector phase of CIA; that is, collagen antibody-induced arthritis model and priming phase, that is, T cell response both in vivo and in vitro. In addition, in order to determine the importance of T cells and antigen-presenting cells (APCs), these cell populations were separated and in vitro T cell responses determined in a mixed co-culture system. Finally, flow cytometry was used in order to further characterize cell populations in cystatin C-deficient mice. Results: Here, we show that mice lacking cystatin C, develop arthritis at a higher incidence and an earlier onset than wild-type controls. Interestingly, when the inflammatory phase of CIA was examined independently from immune priming then cystatin C-deficiency did not enhance the arthritis profile. However, in line with the enhanced CIA, there was an increased T cell and B cell response as delayed-type hypersensitivity reaction and anti-CII antibody titers were elevated in the cystatin C-deficient mice after immunization. In addition, the ex vivo naive APCs from cystatin C-deficient mice had a greater capacity to stimulate T cells. Interestingly, dendritic cells had a more activated phenotype in naive cystatin C-deficient mice. Conclusions: The lack of cystatin C enhances CIA and primarily affects in vivo priming of the immune system. Although the mechanism of this is still unknown, we show evidence for a more activated APC compartment, which would elevate the autoimmune response towards CII, thus resulting in an enhanced development of chronic arthritis

Certification of Cystatin C in the Human Serum Reference Material ERM-DA471/IFCC - Certified Reference Material ERM®-DA471/IFCC

The production of ERM-DA471/IFCC, certified for the mass concentration of cystatin C, is described. Serum was produced from blood collected in 2 collection centres according to a procedure ensuring that it was obtained from healthy donors, and that the lipid content of the serum was low. The serum was processed, spiked with recombinant cystatin C, and lyophilised. It was verified that the material is homogenous and stable. The material was characterised using a pure protein primary reference preparation (PRP) as calibrant. The PRP was prepared from recombinant cystatin C, and its concentration determined by dry mass determination. The characterisation of ERM-DA471/IFCC was performed by particle enhanced immuno-nephelometry, particle enhanced immuno-turbidimetry and enzyme amplified single radial immuno-diffusion. The certified cystatin C mass concentration in ERM-DA471/IFCC, if reconstituted according to the specified procedure, is 5.48 mg/L, the expanded uncertainty (k = 2) is 0.15 mg/L.JRC.DG.D.2-Reference material