One of the challenges of the modern photonics is to develop all-optical devices enabling increased speed and energy efficiency for transmitting and processing information on an optical chip. It is believed that the recently suggested ParityTime (PT) symmetric photonic systems with alternating regions of gain and loss can bring novel functionalities. In such systems, losses are as important as gain and, depending on the structural parameters, gain compensates losses. Generally, PT systems demonstrate nontrivial non-conservative wave interactions and phase transitions, which can be employed for signal filtering and switching, opening new prospects for active control of light. In this review, we discuss a broad range of problems involving nonlinear PT-symmetric photonic systems with an intensitydependent refractive index. Nonlinearity in such PT symmetric systems provides a basis for many effects such as the formation of localized modes, nonlinearly-induced PT-symmetry breaking, and all-optical switching. Nonlinear PT-symmetric systems can serve as powerful building blocks for the development of novel photonic devices targeting an active light control.

Autoantibody-mediated tissue destruction is among the main features of organ-specific autoimmunity. This report describes ''an antibody enzyme'' (abzyme) contribution to the site-specific degradation of a neural antigen. We detected proteolytic activity toward myelin basic protein (MBP) in the fraction of antibodies purified from the sera of humans with multiple sclerosis (MS) and mice with induced experimental allergic encephalomyelitis. Chromatography and zymography data demonstrated that the proteolytic activity of this preparation was exclusively associated with the antibodies. No activity was found in the IgG fraction of healthy donors. The human and murine abzymes efficiently cleaved MBP but not other protein substrates tested. The sites of MBP cleavage determined by mass spectrometry were localized within immunodominant regions of MBP. The abzymes could also cleave recombinant substrates containing encephalytogenic MBP 85-101 peptide. An established MS therapeutic Copaxone appeared to be a specific abzyme inhibitor. Thus, the discovered epitope-specific antibodymediated degradation of MBP suggests a mechanistic explanation of the slow development of neurodegeneration associated with MS.

Dynamics of a chain of interacting parity-time-invariant nonlinear dimers is investigated. A dimer is built as a pair of coupled elements with equal gain and loss. A relation between stationary soliton solutions of the model and solitons of the discrete nonlinear Schrödinger (DNLS) equation is demonstrated. Approximate solutions for solitons whose width is large in comparison to the lattice spacing are derived, using a continuum counterpart of the discrete equations. These solitons are mobile, featuring nearly elastic collisions. Stationary solutions for narrow solitons, which are immobile due to the pinning by the effective Peierls-Nabarro potential, are constructed numerically, starting from the anticontinuum limit. The solitons with the amplitude exceeding a certain critical value suffer an instability leading to blowup, which is a specific feature of the nonlinear parity-time-symmetric chain, making it dynamically different from DNLS lattices. A qualitative explanation of this feature is proposed. The instability threshold drops with the increase of the gain-loss coefficient, but it does not depend on the lattice coupling constant, nor on the soliton's velocity.

The pathologic role of autoantibodies in autoimmune disease is widely accepted. Recently, we reported that anti-myelin basic protein (MBP) serum Abs from multiple sclerosis (MS) patients exhibit proteolytic activity toward the autoantigen. The aim of this study is to determine MBP epitopes specific for the autoantibodies in MS and compare these data with those from other neuronal disorders (OND), leading to the generation of new diagnostic and prognostic criteria. We constructed a MBP-derived recombinant “epitope library” covering the entire molecule. We used ELISA and PAGE/surface-enhanced laser desorption/ionization mass spectroscopy assays to define the epitope binding/cleaving activities of autoantibodies isolated from the sera of 26 MS patients, 22 OND patients, and 11 healthy individuals. The levels of autoantibodies to MBP fragments 48–70 and 85–170 as well as to whole MBP and myelin oligodendrocyte glycoprotein molecules were significantly higher in the sera of MS patients than in those of healthy donors. In contrast, selective reactivity to the two MBP fragments 43–68 and 146–170 distinguished the OND and MS patients. Patients with MS (77% of progressive and 85% of relapsing-remitting) but only 9% of patients with OND and no healthy donors were positive for catalysis, showing pronounced epitope specificity to the encephalitogenic MBP peptide 81–103. This peptide retained its substrate properties when flanked with two fluorescent proteins, providing a novel fluorescent resonance energy transfer approach for MS studies. Thus, anti-MBP autoantibody-mediated, epitope-specific binding and cleavage may be regarded as a specific characteristic of MS compared with OND and healthy donors and may serve as an additional biomarker of disease progression.

DNA-hydrolyzing activity of IgG autoantibodies from sera of patients with various types of lymphoproliferative diseases was investigated. The association of DNA-hydrolyzing activity with the antibody (Ab) fraction has been proved by newly developed affinity-capture assay. Study of abzyme incidence in blood tumors and systemic lupus erythematosis (SLE) revealed linkage of anti-DNA Ab catalysts to mature B-cell tumors, and increased probability of DNA-abzymes formation on the background of autoimmune manifestations. These data suggest possible similarity between mechanisms of abzyme formation in SLE and B-cell lymphomas. A new mechanism of formation of DNA-specific catalytic Abs has been proposed based on the increased crossreactivity of polyclonal DNA-abzymes to DNA-depleted nuclear matrix proteins. The possibility of the abzyme production as Ab to the energetically destabilized ground state of the antigen has been discussed. Preliminary results were obtained that indicate the complement-independent cytotoxicity of anti-DNA autoantibodies isolated from blood of patients with SLE and chronic lymphocytic leukemia.

We show that the parity-time (PT ) symmetric coupled optical waveguides with gain and loss support localised oscillatory structures similar to the breathers of the classical φ 4 model. The power carried by the PT -breather oscillates periodically, switching back and forth between the waveguides, so that the gain and loss are compensated on the average. The breathers are found to coexist with solitons and be prevalent in the products of the soliton collisions. We demonstrate that the evolution of the small-amplitude breather's envelope is governed by a system of two coupled nonlinear Schrödinger equations, and employ this Hamiltonian system to show that the smallamplitude PT -breathers are stable.

We study the scattering of linear and nonlinear waves in a long waveguide array with a parity-time (PT)symmetric defect created by two waveguides with balanced gain and loss. We present exact solutions for the scattering of linear waves on such a defect, and then demonstrate numerically that the linear theory can describe, with a good accuracy, the soliton scattering in the case of weak nonlinearity. We reveal that the reflected and transmitted linear and nonlinear waves can be amplified substantially after interaction with the PT-symmetric defect thus allowing an active control of the wave scattering in the array.

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