A Lyusternik–Graves theorem for the proximal point method

We consider a generalized version of the proximal point algorithm for solving the perturbed inclusion y∈T(x), where y is a perturbation element near 0 and T is a set-valued mapping acting from a Banach space X to a Banach space Y which is metrically regular around some point (xˉ,0) in its graph. We study the behavior of the convergent iterates generated by the algorithm and we prove that they inherit the regularity properties of T, and vice versa. We analyze the cases when the mapping T is metrically regular and strongly regular.Research of the first author was partially supported by Ministerio de Ciencia e Innovación (Spain), grant MTM2008-06695-C03-01 and program “Juan de la Cierva”. Research of the second author was partially supported by Contract EA4540 (France)

Cytomegalovirus (CMV) Epitope–Specific CD4 + T Cells Are Inflated in HIV + CMV + Subjects

Select CMV epitopes drive life-long CD8+ T cell memory inflation, but the extent of CD4 memory inflation is poorly studied. CD4+ T cells specific for human CMV (HCMV) are elevated in HIV+ HCMV+ subjects. To determine whether HCMV epitope–specific CD4+ T cell memory inflation occurs during HIV infection, we used HLA-DR7 (DRB1*07:01) tetramers loaded with the glycoprotein B DYSNTHSTRYV (DYS) epitope to characterize circulating CD4+ T cells in coinfected HLA-DR7+ long-term nonprogressor HIV subjects with undetectable HCMV plasma viremia. DYS-specific CD4+ T cells were inflated among these HIV+ subjects compared with those from an HIV− HCMV+ HLA-DR7+ cohort or with HLA-DR7–restricted CD4+ T cells from the HIV-coinfected cohort that were specific for epitopes of HCMV phosphoprotein-65, tetanus toxoid precursor, EBV nuclear Ag 2, or HIV gag protein. Inflated DYS-specific CD4+ T cells consisted of effector memory or effector memory–RA+ subsets with restricted TCRβ usage and nearly monoclonal CDR3 containing novel conserved amino acids. Expression of this near-monoclonal TCR in a Jurkat cell–transfection system validated fine DYS specificity. Inflated cells were polyfunctional, not senescent, and displayed high ex vivo levels of granzyme B, CX3CR1, CD38, or HLA-DR but less often coexpressed CD38+ and HLA-DR+. The inflation mechanism did not involve apoptosis suppression, increased proliferation, or HIV gag cross-reactivity. Instead, the findings suggest that intermittent or chronic expression of epitopes, such as DYS, drive inflation of activated CD4+ T cells that home to endothelial cells and have the potential to mediate cytotoxicity and vascular disease