Parametrizations of elliptic curves by Shimura curves and by classical modular curves

Fix an isogeny class

Complementary intrastrand base pairing during initiation of Herpes simplex virus type 1 DNA replication

The herpes simplex virus type 1 origin of DNA replication, oriS, contains three copies of the recognition sequence for the viral initiator protein, origin binding protein (OBP), arranged in two palindromes. The central box I forms a short palindrome with box III and a long palindrome with box II. Single-stranded oriS adopts a conformation, oriS*, that is tightly bound by OBP. Here we demonstrate that OBP binds to a box III–box I hairpin with a 3′ single-stranded tail in oriS*. Mutations designed to destabilize the hairpin abolish the binding of OBP to oriS*. The same mutations also inhibit DNA replication. Second site complementary mutations restore binding of OBP to oriS* as well as the ability of mutated oriS to support DNA replication. OriS* is also an efficient activator of the hydrolysis of ATP by OBP. Sequence analyses show that a box III–box I palindrome is an evolutionarily conserved feature of origins of DNA replication from human, equine, bovine, and gallid alpha herpes viruses. We propose that oriS facilitates initiation of DNA synthesis in two steps and that OBP exhibits exquisite specificity for the different conformations oriS adopts at these stages. Our model suggests that distance-dependent cooperative binding of OBP to boxes I and II in duplex DNA is succeeded by specific recognition of a box III–box I hairpin in partially unwound DNA.

Computation of Surface Electrical Potentials of Plant Cell Membranes : Correspondence to Published Zeta Potentials from Diverse Plant Sources

A Gouy-Chapman-Stern model has been developed for the computation of surface electrical potential (ψ0) of plant cell membranes in response to ionic solutes. The present model is a modification of an earlier version developed to compute the sorption of ions by wheat (Triticum aestivum L. cv Scout 66) root plasma membranes. A single set of model parameters generates values for ψ0 that correlate highly with published ζ potentials of protoplasts and plasma membrane vesicles from diverse plant sources. The model assumes ion binding to a negatively charged site (R− = 0.3074 μmol m−2) and to a neutral site (P0 = 2.4 μmol m−2) according to the reactions R− + IΖ ⇌ RIΖ−1 and P0 + IΖ ⇌ PIΖ, where IΖ represents an ion of charge Ζ. Binding constants for the negative site are 21,500 m−1 for H+, 20,000 m−1 for Al3+, 2,200 m−1 for La3+, 30 m−1 for Ca2+ and Mg2+, and 1 m−1 for Na+ and K+. Binding constants for the neutral site are 1/180 the value for binding to the negative site. Ion activities at the membrane surface, computed on the basis of ψ0, appear to determine many aspects of plant-mineral interactions, including mineral nutrition and the induction and alleviation of mineral toxicities, according to previous and ongoing studies. A computer program with instructions for the computation of ψ0, ion binding, ion concentrations, and ion activities at membrane surfaces may be requested from the authors.

The evolution of emergent computation.

A simple evolutionary process can discover sophisticated methods for emergent information processing in decentralized spatially extended systems. The mechanisms underlying the resulting emergent computation are explicated by a technique for analyzing particle-based logic embedded in pattern-forming systems. Understanding how globally coordinated computation can emerge in evolution is relevant both for the scientific understanding of natural information processing and for engineering new forms of parallel computing systems.

Rapid local synchronization of action potentials: toward computation with coupled integrate-and-fire neurons.

The collective behavior of interconnected spiking nerve cells is investigated. It is shown that a variety of model systems exhibit the same short-time behavior and rapidly converge to (approximately) periodic firing patterns with locally synchronized action potentials. The dynamics of one model can be described by a downhill motion on an abstract energy landscape. Since an energy landscape makes it possible to understand and program computation done by an attractor network, the results will extend our understanding of collective computation from models based on a firing-rate description to biologically more realistic systems with integrate-and-fire neurons.