Arginine mutation alters binding of a human monoclonal antibody to antigens linked to systemic lupus erythematosus and the antiphospholipid syndrome

Objective: Previous studies have shown the importance of somatic mutations and arginine residues in the complementarity-determining regions (CDRs) of pathogenic anti-double-stranded DNA (anti-dsDNA) antibodies in human and murine lupus, and in studies of murine antibodies, a role of mutations at position 53 in VH CDR2 has been demonstrated. We previously demonstrated in vitro expression and mutagenesis of the human IgG1 monoclonal antibody B3. The present study was undertaken to investigate, using this expression system, the importance of the arginine residue at position 53 (R53) in B3 VH. Methods: R53 was altered, by site-directed mutagenesis, to serine, asparagine, or lysine, to create 3 expressed variants of VH. In addition, the germline sequence of the VH3-23 gene (from which B3 VH is derived) was expressed either with or without arginine at position 53. These 5 new heavy chains, as well as wild-type B3 VH, were expressed with 4 different light chains, and the resulting antibodies were assessed for their ability to bind to nucleosomes, -actinin, cardiolipin, ovalbumin, 2-glycoprotein I (2GPI), and the N-terminal domain of 2GPI (domain I), using direct binding assays. Results: The presence of R53 was essential but not sufficient for binding to dsDNA and nucleosomes. Conversely, the presence of R53 reduced binding to -actinin, ovalbumin, 2GPI, and domain I of 2GPI. The combination B3 (R53S) VH/B3 VL bound human, but not bovine, 2GPI. Conclusion: The fact that the R53S substitution significantly alters binding of B3 to different clinically relevant antigens, but that the alteration is in opposite directions depending on the antigen, implies that this arginine residue plays a critical role in the affinity maturation of antibody B3

Partner symmetries of the complex Monge-Ampere equation yield hyper-Kahler metrics without continuous symmetries

We extend the Mason-Newman Lax pair for the elliptic complex Monge-Amp\`ere equation so that this equation itself emerges as an algebraic consequence. We regard the function in the extended Lax equations as a complex potential. We identify the real and imaginary parts of the potential, which we call partner symmetries, with the translational and dilatational symmetry characteristics respectively. Then we choose the dilatational symmetry characteristic as the new unknown replacing the K\"ahler potential which directly leads to a Legendre transformation and to a set of linear equations satisfied by a single real potential. This enables us to construct non-invariant solutions of the Legendre transform of the complex Monge-Amp\`ere equation and obtain hyper-K\"ahler metrics with anti-self-dual Riemann curvature 2-form that admit no Killing vectors.Comment: submitted to J. Phys.

Partner symmetries and non-invariant solutions of four-dimensional heavenly equations

We extend our method of partner symmetries to the hyperbolic complex Monge-Amp\`ere equation and the second heavenly equation of Pleba\~nski. We show the existence of partner symmetries and derive the relations between them for both equations. For certain simple choices of partner symmetries the resulting differential constraints together with the original heavenly equations are transformed to systems of linear equations by an appropriate Legendre transformation. The solutions of these linear equations are generically non-invariant. As a consequence we obtain explicitly new classes of heavenly metrics without Killing vectors.Comment: 20 pages, 1 table, corrected typo

Multi-Hamiltonian structure of Plebanski's second heavenly equation

We show that Plebanski's second heavenly equation, when written as a first-order nonlinear evolutionary system, admits multi-Hamiltonian structure. Therefore by Magri's theorem it is a completely integrable system. Thus it is an example of a completely integrable system in four dimensions

Milk Urea Content and δ13C as Potential Tool for Differentiation of Milk from Organic and Conventional Low- and High-Input Farming Systems

The influence of farming type (conventional or organic) and production system (low-and high-input) on various quality characteristics of milk have been in the focus of studies over the last decade. The aim of this work was to evaluate the impact of different dairy management and production systems on carbon stable isotopes ratio (δ13C) and milk urea content. The samples of raw milk were collected each two weeks at certified organic high-input and low-input farms, conventional high-input and low-input farms in late indoor period and outdoor period. Data analysis showed clear difference between milk from organic high- and low-input farms with non-overlapping range between -22.90 ‰ and -24.70‰ for δ13С in protein fraction (equal 1.80‰) and between -25.90‰ and -28.20‰ (equal 2.30‰) for δ13С in fat fraction independently from season factor, as for Δδ13С (protein-fat) values in milk from high-input (1.50-3.00‰) and low-input (3.20-6.30‰) organic farms. Analysis of correlation between δ13С in protein fraction and milk urea content values showed that during late indoor period the most significant difference was detected between milk from organic low-input and conventional high-input farms (5.85‰ for δ13С in protein fraction and 4.65 mg/100 g of milk urea content). During outdoor period, the non-overlapping range was established for low-input and high-input organic farms (3.40‰ for δ13С in protein fraction and 10.77 mg/100 g of milk urea content). Results of δ13С values in fat and protein milk fractions, as combination of δ13С in protein fraction and milk urea content could be a potential tool for the distinguish of milk from different farming types, based on different feed composition

Superconductor-Insulator Transition in a Capacitively Coupled Dissipative Environment

We present results on disordered amorphous films which are expected to undergo a field-tuned Superconductor-Insulator Transition.The addition of a parallel ground plane in proximity to the film changes the character of the transition.Although the screening effects expected from "dirty-boson" theories are not evident,there is evidence that the ground plane couples a certain type of dissipation into the system,causing a dissipation-induced phase transition.The dissipation due to the phase transition couples similarly into quantum phase transition systems such as superconductor-insulator transitions and Josephson junction arrays.Comment: 4 pages, 4 figure

Genus Two Partition and Correlation Functions for Fermionic Vertex Operator Superalgebras I

We define the partition and $n$-point correlation functions for a vertex operator superalgebra on a genus two Riemann surface formed by sewing two tori together. For the free fermion vertex operator superalgebra we obtain a closed formula for the genus two continuous orbifold partition function in terms of an infinite dimensional determinant with entries arising from torus Szeg\"o kernels. We prove that the partition function is holomorphic in the sewing parameters on a given suitable domain and describe its modular properties. Using the bosonized formalism, a new genus two Jacobi product identity is described for the Riemann theta series. We compute and discuss the modular properties of the generating function for all $n$-point functions in terms of a genus two Szeg\"o kernel determinant. We also show that the Virasoro vector one point function satisfies a genus two Ward identity.Comment: A number of typos have been corrected, 39 pages. To appear in Commun. Math. Phy

Localized Breathing Modes in Granular Crystals with Defects

We investigate nonlinear localized modes at light-mass impurities in a one-dimensional, strongly-compressed chain of beads under Hertzian contacts. Focusing on the case of one or two such "defects", we analyze the problem's linear limit to identify the system eigenfrequencies and the linear defect modes. We then examine the bifurcation of nonlinear defect modes from their linear counterparts and study their linear stability in detail. We identify intriguing differences between the case of impurities in contact and ones that are not in contact. We find that the former bears similarities to the single defect case, whereas the latter features symmetry-breaking bifurcations with interesting static and dynamic implications

What Does an Exemplary Middle School Mathematics Teacher Look Like? The Use of a Professional Development Rubric

A School University Research Network (SURN) committee composed of current mathematics teachers, central office math supervisors, building administrators, mathematicians, and mathematics educators researched numerous sources regarding best practices in mathematics instruction. The resulting professional development rubric synthesizes their findings and can serve a professional development role by providing teachers and administrators with a tool to develop clarity and consensus on best mathematics instructional practices, and how these practices are implemented in the classroom. It is also being used as a tool for cooperating teachers in their supervision of student teachers and as a reflective method for self-evaluation

Multiple Reggeon Exchange from Summing QCD Feynman Diagrams

Multiple reggeon exchange supplies subleading logs that may be used to restore unitarity to the Low-Nussinov Pomeron, provided it can be proven that the sum of Feynman diagrams to all orders gives rise to such multiple regge exchanges. This question cannot be easily tackled in the usual way except for very low-order diagrams, on account of delicate cancellations present in the sum which necessitate individual Feynman diagrams to be computed to subleading orders. Moreover, it is not clear that sums of high-order Feynman diagrams with complicated criss-crossing of lines can lead to factorization implied by the multi-regge scenario. Both of these difficulties can be overcome by using the recently developed nonabelian cut diagrams. We are then able to show that the sum of $s$-channel-ladder diagrams to all orders does lead to such multiple reggeon exchanges.Comment: uu-encoded latex file with 11 postscript figures (20 pages