An engineered IN-1 Fab fragment with improved affinity for the Nogo-A axonal growth inhibitor permits immunochemical detection and shows enhanced neutralizing activity

The myelin axonal growth inhibitor NI-220/250 (Nogo-A) has attracted considerable attention in elucidating the mechanisms that account for the lack of plasticity in the adult central nervous system. The cognate monoclonal antibody IN-1, which was obtained prior to the molecular characterization of its Nogo-A antigen, has played a crucial role in this respect. However, this murine IgM/κ antibody does not only provide an inappropriate format for in vivo studies, its low antigen affinity has also hampered the thorough structure-function analysis of its neutralizing effect toward the Nogo-A inhibitor on a molecular basis. We describe here the affinity maturation of a bacterially produced functional IN-1 Fab fragment via protein engineering. A soluble fragment of Nogo-A derived from the central exon 3 of its gene, which was prepared by secretion into the periplasm of Escherichia coli, served as a target in these experiments. After repeated cycles of site-directed random mutagenesis and screening, the mutant II.1.8 of the IN-1 Fab fragment was obtained, carrying five side chain substitutions within CDR-L3. Its dissociation constant for the complex with the recombinant Nogo-A fragment was determined in surface plasmon resonance measurements as approximately 1 μM. The affinity of the unmutated IN-1 Fab fragment was 8-fold lower. The engineered Fab fragment appeared to be well suited for the specific detection of Nogo-A in immunochemical assays and for the histochemical staining of myelin-rich tissue sections. Most importantly, its concentration-dependent neutralizing effect on the Nogo-A inhibitory activity was significantly enhanced in cell culture. This study confirms Nogo-A to be the antigen of the IN-1 antibody and it demonstrates increased potential of the engineered Fab fragment as a reagent for promoting axonal regeneration in viv

The resonance spectrum of the cusp map in the space of analytic functions

We prove that the Frobenius--Perron operator $U$ of the cusp map $F:[-1,1]\to[-1,1]$, $F(x)=1-2\sqrt{|x|}$ (which is an approximation of the Poincar\'e section of the Lorenz attractor) has no analytic eigenfunctions corresponding to eigenvalues different from 0 and 1. We also prove that for any $q\in(0,1)$ the spectrum of $U$ in the Hardy space in the disk \{z\in\C:|z-q|<1+q\} is the union of the segment $[0,1]$ and some finite or countably infinite set of isolated eigenvalues of finite multiplicity.Comment: Submitted to JMP; The description of the spectrum in some Hardy spaces is adde

Asymptotics of the Farey Fraction Spin Chain Free Energy at the Critical Point

We consider the Farey fraction spin chain in an external field $h$. Using ideas from dynamical systems and functional analysis, we show that the free energy $f$ in the vicinity of the second-order phase transition is given, exactly, by $$f \sim \frac t{\log t}-\frac1{2} \frac{h^2}t \quad \text{for} \quad h^2\ll t \ll 1 .$$ Here $t=\lambda_{G}\log(2)(1-\frac{\beta}{\beta_c})$ is a reduced temperature, so that the deviation from the critical point is scaled by the Lyapunov exponent of the Gauss map, $\lambda_G$. It follows that $\lambda_G$ determines the amplitude of both the specific heat and susceptibility singularities. To our knowledge, there is only one other microscopically defined interacting model for which the free energy near a phase transition is known as a function of two variables. Our results confirm what was found previously with a cluster approximation, and show that a clustering mechanism is in fact responsible for the transition. However, the results disagree in part with a renormalisation group treatment

Complete spectral data for analytic Anosov maps of the torus

Using analytic properties of Blaschke factors we construct a family of analytic hyperbolic diffeomorphisms of the torus for which the spectral properties of the associated transfer operator acting on a suitable Hilbert space can be computed explicitly. As a result, we obtain explicit expressions for the decay of correlations of analytic observables without resorting to any kind of perturbation argument.Comment: 19 pages, 4 figure

Neuropathology of 16p13.11 Deletion in Epilepsy

16p13.11 genomic copy number variants are implicated in several neuropsychiatric disorders, such as schizophrenia, autism, mental retardation, ADHD and epilepsy. The mechanisms leading to the diverse clinical manifestations of deletions and duplications at this locus are unknown. Most studies favour NDE1 as the leading disease-causing candidate gene at 16p13.11. In epilepsy at least, the deletion does not appear to unmask recessive-acting mutations in NDE1, with haploinsufficiency and genetic modifiers being prime candidate disease mechanisms. NDE1 encodes a protein critical to cell positioning during cortical development. As a first step, it is important to determine whether 16p13.11 copy number change translates to detectable brain structural alteration. We undertook detailed neuropathology on surgically resected brain tissue of two patients with intractable mesial temporal lobe epilepsy (MTLE), who had the same heterozygous NDE1-containing 800 kb 16p13.11 deletion, using routine histological stains and immunohistochemical markers against a range of layer-specific, white matter, neural precursor and migratory cell proteins, and NDE1 itself. Surgical temporal lobectomy samples from a MTLE case known not to have a deletion in NDE1 and three non-epilepsy cases were included as disease controls. We found that apart from a 3 mm hamartia in the temporal cortex of one MTLE case with NDE1 deletion and known hippocampal sclerosis in the other case, cortical lamination and cytoarchitecture were normal, with no differences between cases with deletion and disease controls. How 16p13.11 copy changes lead to a variety of brain diseases remains unclear, but at least in epilepsy, it would not seem to be through structural abnormality or dyslamination as judged by microscopy or immunohistochemistry. The need to integrate additional data with genetic findings to determine their significance will become more pressing as genetic technologies generate increasingly rich datasets. Detailed examination of brain tissue, where available, will be an important part of this process in neurogenetic disease specifically