Structural aspects of antibody-antigen interaction revealed through small random peptide libraries

Summary Two small random peptide libraries, one composed of 4550 dodecapeptides and one of 8000 tripeptides, were synthesized in newly developed credit-card format miniPEPSCAN cards (miniPEPSCAN libraries). Each peptide was synthesized in a discrete well (455 peptides/card). The two miniPEPSCAN libraries were screened with three different monoclonal antibodies (Mabs). Two other random peptide libraries, expressed on the wall of bacteria (recombinant libraries) and composed of 10⁷ hexa- and octapeptides, were screened with the same three Mabs. The aim of this study was to compare the amino acid sequence of peptides selected from small and large pools of random peptides and, in this way, investigate the potential of small random peptide libraries. The screening of the two miniPEPSCAN libraries resulted in the identification of a surprisingly large number of antibody-binding peptides, while the screening of the large recombinant libraries, using the same Mabs, resulted in the identification of only a small number of peptides. The large number of peptides derived from the small random peptide libraries allowed the determination of consensus sequences. These consensus sequences could be related to small linear and nonlinear parts of the respective epitopes. The small number of peptides derived from the large random peptide libraries could only be related to linear epitopes that were previously mapped using small libraries of overlapping peptides covering the antigenic protein. Thus, with respect to the cost and speed of identifying peptides that resemble linear and nonlinear parts of epitopes, small diversity libraries based on synthetic peptides appear to be superior to large diversity libraries based on expression systems.Abbreviations ABTS 2,2-azino-di-3-ethylbenzthiazoline sulfonate - EGF epidermal growth factor - Mab monoclonal antibody - OD_ccd optical density obtained using CCD camera - RAMPO rabbit-antimouse peroxidase - SDS sodium dodecylsulfate - TGEV transmissible gastroenteritis virus     

Real analysis related to the Monge-Ampère equation

In this paper we consider a family of convex sets in , , , , satisfying certain axioms of affine invariance, and a Borel measure satisfying a doubling condition with respect to the family The axioms are modelled on the properties of the solutions of the real Monge-Ampère equation. The purpose of the paper is to show a variant of the Calderón-Zygmund decomposition in terms of the members of This is achieved by showing first a Besicovitch-type covering lemma for the family and then using the doubling property of the measure The decomposition is motivated by the study of the properties of the linearized Monge-Ampère equation. We show certain applications to maximal functions, and we prove a John and Nirenberg-type inequality for functions with bounded mean oscillation with respect to

     

On a class of functions with equal infima over a domain and its boundary

In this paper, we present a class of functions:f:X such that inf _xX f(x)= , whereX is a nonempty, finitely compact and convex set in a vector space andB _x ={xX: y aff(X){x:[x, y]X={x}. Our main tool is a recent minimax theorem by Ricceri (Ref. 1).     

Coupling of the GB set property for ergodic averages

Let (Y,,,T) be an ergodic dynamical system. LetA be an nonempty subset ofL ²() such that , whereA=sup{||sȒt||₂ ,s, tA} andN(A, u) is the smallest number ofL ²()-open balls of radiusu, centered inA, enough to coverA. Let . We prove as a consequence of a more general result, thatC(A) is aGB subset ofL ²().     

A “Multiplicative Coboundary” theorem for some sequences of random matrices

Schmidt(¹⁰) showed that if the family of distributions of the partial sums of a strictly stationary random sequence is tight, then that random sequence is a coboundary. Here an analog of that result is proved for some sequences of random matrices, with partial sums replaced by matrix products.     

Weak separation properties for self-similar sets

We develop a theory for self-similar sets in that fulfil the weak separation property of Lau and Ngai, which is weaker than the open set condition of Hutchinson.

     

HYPERFINITE TRANSVERSAL THEORY. II

We continue the investigation of validity of Hall's theorem in the case of the Loeb space of an internal, uniformly distributed, hyperfinite measure space initiated in1992 by the author. Some new classes of graphs are introduced for which the measure theoretic version of Hall's theorem still holds.

     

Realization of fixed point sets

Letf:XX be a selfmap of a compact connected polyhedron, andA a nonempty closed subset ofX. In this paper, we shall deal with the question whether or not there is a mapg:XX homotopic tof such that the fixed point set Fixg ofg equalsA. We introduce a necessary condition for the existence of such a mapg. It is shown that this condition is easy to check, and hence some sufficient conditions are obtained.Partially supported by the Natural Science Foundation of Liaoning University.     

Quantitative stability of variational systems: III.ε-approximate solutions

We prove that the-optimal solutions of convex optimization problems are Lipschitz continuous with respect to data perturbations when these are measured in terms of the epi-distance. A similar property is obtained for the distance between the level sets of extended real valued functions. We also show that these properties imply that the-subgradient mapping is Lipschitz continuous.Research supported in part by the National Science Foundation and the Air Force Office of Scientific Research.     

Electronic structure of BeH2

Nonorthogonal single‐configuration and multiconfiguration ab initio calculations are carried out on the BeH₂ molecule in its equilibrium (D_∞h) geometry, using a highly optimized even‐tempered Slater‐type orbital (STO) basis set. The results are used as a basis for a discussion of the electronic structure of the molecule in modern‐VB terms. A value of R_e = 1.329 Å is obtained. Values are also obtained for the symmetric‐stretch harmonic frequency (2053 cm^?1), electric quadrupole moment (?5.60 Buckingham), and nuclear quadrupole coupling constants (?3.59 MHz for ⁹Be and 0.0915 MHz for ²H). © 2005 Wiley Periodicals, Inc. Int J Quantum Chem, 2006