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We consider an M/M/1 queue with the special feature that the speed of the server alternates between two constant values S[sub L] and S[sub H] > S[sub L]. The high-speed periods are exponentially distributed, and the low-speed periods have a regularly varying distribution. We obtain explicit asymptotics for the tail of the workload distribution. The two cases in which the offered traffic load is smaller respectively larger than the low service speed are shown to result in completely different asymptotics. [ABSTRACT FROM AUTHOR]

The engineering of catalytic function in antibodies requires precise information on their structure. Here, results are presented that show how the antibody domain structure affects its functionality. The previously designed organophosphate-metabolizing reactibody A17 has been re-engineered by replacing its constant κ light chain by the λ chain (A17λ), and the X-ray structure of A17λ has been determined at 1.95 Å resolution. It was found that compared with A17κ the active centre of A17λ is displaced, stabilized and made more rigid owing to interdomain interactions involving the CDR loops from the VL and VH domains. These VL/VH domains also have lower mobility, as deduced from the atomic displacement parameters of the crystal structure. The antibody elbow angle is decreased to 126° compared with 138° in A17κ. These structural differences account for the subtle changes in catalytic efficiency and thermodynamic parameters determined with two organophosphate ligands, as well as in the affinity for peptide substrates selected from a combinatorial cyclic peptide library, between the A17κ and A17λ variants. The data presented will be of interest and relevance to researchers dealing with the design of antibodies with tailor-made functions.

Igs offer a versatile template for combinatorial and rational design approaches to the de novo creation of catalytically active proteins. We have used a covalent capture selection strategy to identify biocatalysts from within a human semisynthetic antibody variable fragment library that uses a nucleophilic mechanism. Specific phosphonylation at a single tyrosine within the variable light-chain framework was confirmed in a recombinant IgG construct. High-resolution crystallographic structures of unmodified and phosphonylated Fabs display a 15-Å-deep two-chamber cavity at the interface of variable light (V(L)) and variable heavy (V(H)) fragments having a nucleophilic tyrosine at the base of the site. The depth and structure of the pocket are atypical of antibodies in general but can be compared qualitatively with the catalytic site of cholinesterases. A structurally disordered heavy chain complementary determining region 3 loop, constituting a wall of the cleft, is stabilized after covalent modification by hydrogen bonding to the phosphonate tropinol moiety. These features and presteady state kinetics analysis indicate that an induced fit mechanism operates in this reaction. Mutations of residues located in this stabilized loop do not interfere with direct contacts to the organophosphate ligand but can interrogate second shell interactions, because the H3 loop has a conformation adjusted for binding. Kinetic and thermodynamic parameters along with computational docking support the active site model, including plasticity and simple catalytic components. Although relatively uncomplicated, this catalytic machinery displays both stereo- and chemical selectivity. The organophosphate pesticide paraoxon is hydrolyzed by covalent catalysis with rate-limiting dephosphorylation. This reactibody is, therefore, a kinetically selected protein template that has enzyme-like catalytic attributes.

Expression of recombinant antibodies in mammalian cells is one of key problems in immunobiotechnology. Alternatively, expression of a broad panel of antibodies and of their fragments may be effectively done in yeast cells. We obtained expression strains of the methylotrophic beast Pichia pastoris producing single chain human catalytic antibody A17 (A.17scFv), Fab-fragment (A.17Fab) and full-size light chain (A.17Lch). These antibodies were characterized in terms of functional activity. The capacity to specifically bind and transform organophosphorus compounds has been demonstrated for A.17scFv and A.17Fab. The loss of activity of the antibody light chain when expressed alone indicates that the active site is formed by both heavy and light chains of the antibody. We determined the reversible constant Kd and the first order constant (k2) of the reaction of the covalent modification of A.17scFv and A.17Fab by irreversible inhibitor of the serine proteases p-nitrophenyl 8-methyl-8-azobicyclo[3.2.1]phosphonate (Phosphonate X). Calculated values indicate that activity of the antibodies expressed in yeast is similar to the full-size antibody A17 and single chain antibody A.17 expressed in CHO and E. coli cells respectively.

This is a mathematical study of the interactions between non-linear feedback (density dependence) and uncorrelated random noise in the dynamics of unstructured populations. The stochastic non-linear dynamics are generally complex, even when the deterministic skeleton possesses a stable equilibrium. There are three critical factors of the stochastic non-linear dynamics; whether the intrinsic population growth rate (lambda) is smaller than, equal to, or greater than 1; the pattern of density dependence at very low and very high densities; and whether the noise distribution has exponential moments or not. If lambda < 1, the population process is generally transient with escape towards extinction. When lambda > or = 1, our quantitative analysis of stochastic non-linear dynamics focuses on characterizing the time spent by the population at very low density (rarity), or at high abundance (commonness), or in extreme states (rarity or commonness). When lambda >1 and density dependence is strong at high density, the population process is recurrent: any range of density is reached (almost surely) in finite time. The law of time to escape from extremes has a heavy, polynomial tail that we compute precisely, which contrasts with the thin tail of the laws of rarity and commonness. Thus, even when lambda is close to one, the population will persistently experience wide fluctuations between states of rarity and commonness. When lambda = 1 and density dependence is weak at low density, rarity follows a universal power law with exponent -3/2. We provide some mathematical support for the numerical conjecture [Ferriere, R., Cazelles, B., 1999. Universal power laws govern intermittent rarity in communities of interacting species. Ecology 80, 1505-1521.] that the -3/2 power law generally approximates the law of rarity of 'weakly invading' species with lambda values close to one. Some preliminary results for the dynamics of multispecific systems are presented.