Bell's theorem as a signature of nonlocality: a classical counterexample

For a system composed of two particles Bell's theorem asserts that averages of physical quantities determined from local variables must conform to a family of inequalities. In this work we show that a classical model containing a local probabilistic interaction in the measurement process can lead to a violation of the Bell inequalities. We first introduce two-particle phase-space distributions in classical mechanics constructed to be the analogs of quantum mechanical angular momentum eigenstates. These distributions are then employed in four schemes characterized by different types of detectors measuring the angular momenta. When the model includes an interaction between the detector and the measured particle leading to ensemble dependencies, the relevant Bell inequalities are violated if total angular momentum is required to be conserved. The violation is explained by identifying assumptions made in the derivation of Bell's theorem that are not fulfilled by the model. These assumptions will be argued to be too restrictive to see in the violation of the Bell inequalities a faithful signature of nonlocality.Comment: Extended manuscript. Significant change

Optimality of mutation and selection in germinal centers

The population dynamics theory of B cells in a typical germinal center could play an important role in revealing how affinity maturation is achieved. However, the existing models encountered some conflicts with experiments. To resolve these conflicts, we present a coarse-grained model to calculate the B cell population development in affinity maturation, which allows a comprehensive analysis of its parameter space to look for optimal values of mutation rate, selection strength, and initial antibody-antigen binding level that maximize the affinity improvement. With these optimized parameters, the model is compatible with the experimental observations such as the ~100-fold affinity improvements, the number of mutations, the hypermutation rate, and the "all or none" phenomenon. Moreover, we study the reasons behind the optimal parameters. The optimal mutation rate, in agreement with the hypermutation rate in vivo, results from a tradeoff between accumulating enough beneficial mutations and avoiding too many deleterious or lethal mutations. The optimal selection strength evolves as a balance between the need for affinity improvement and the requirement to pass the population bottleneck. These findings point to the conclusion that germinal centers have been optimized by evolution to generate strong affinity antibodies effectively and rapidly. In addition, we study the enhancement of affinity improvement due to B cell migration between germinal centers. These results could enhance our understandings to the functions of germinal centers.Comment: 5 figures in main text, and 4 figures in Supplementary Informatio

High Affinity Antigen Recognition of the Dual Specific Variants of Herceptin Is Entropy-Driven in Spite of Structural Plasticity

The antigen-binding site of Herceptin, an anti-human Epidermal Growth Factor Receptor 2 (HER2) antibody, was engineered to add a second specificity toward Vascular Endothelial Growth Factor (VEGF) to create a high affinity two-in-one antibody bH1. Crystal structures of bH1 in complex with either antigen showed that, in comparison to Herceptin, this antibody exhibited greater conformational variability, also called “structural plasticity”. Here, we analyzed the biophysical and thermodynamic properties of the dual specific variants of Herceptin to understand how a single antibody binds two unrelated protein antigens. We showed that while bH1 and the affinity-improved bH1-44, in particular, maintained many properties of Herceptin including binding affinity, kinetics and the use of residues for antigen recognition, they differed in the binding thermodynamics. The interactions of bH1 and its variants with both antigens were characterized by large favorable entropy changes whereas the Herceptin/HER2 interaction involved a large favorable enthalpy change. By dissecting the total entropy change and the energy barrier for dual interaction, we determined that the significant structural plasticity of the bH1 antibodies demanded by the dual specificity did not translate into the expected increase of entropic penalty relative to Herceptin. Clearly, dual antigen recognition of the Herceptin variants involves divergent antibody conformations of nearly equivalent energetic states. Hence, increasing the structural plasticity of an antigen-binding site without increasing the entropic cost may play a role for antibodies to evolve multi-specificity. Our report represents the first comprehensive biophysical analysis of a high affinity dual specific antibody binding two unrelated protein antigens, furthering our understanding of the thermodynamics that drive the vast antigen recognition capacity of the antibody repertoire

High-Pressure Gel Loader for Capillary Array Electrophoresis Microchannel Plates

Microfabricated capillary array electrophoresis (μCAE) microchannel plates are the next generation of bioanalytical separation devices. To fully exploit the capabilities of μCAE devices, supporting technology such as robotic sample loading, gel loading, microplate washing, and data analysis must be developed. Here, we describe a device for loading gel into radial capillary array electrophoresis microplates and for plate washing and drying. The microplates are locked into a loading module, and high-pressure helium is used to drive aqueous separation media or wash solutions into the microchannels through fixtures connected to the central anode reservoir. Microplates are rapidly (30 s to 5 min) loaded with separation media, such as 3%–4.8% linear polyacrylamide or 0.7%–3.0% hydroxyethyl cellulose, for electrophoresis. The effective and rapid gel-filling and plate-cleaning methods together with short electrophoretic analysis times (2–30 min) make μCAE systems versatile and powerful nucleic acid analysis platforms