p-adic L functions and trivial zeroes

The following is adapted from the notes for the lecture. It announces results and conjectures about values of the p-adic L function of the symmetric square of an elliptic curve.

Does a neuroimmune interaction contribute to the genesis of painful peripheral neuropathies?

Painful peripheral neuropathies are precipitated by nerve injury from disease or trauma. All such injuries will be accompanied by an inflammatory reaction, a neuritis, that will mobilize the immune system. The role of the inflammation itself is difficult to determine in the presence of structural damage to the nerve. A method has been devised to produce a focal neuritis in the rat sciatic nerve that involves no more than trivial structural damage to the nerve. This experimental focal neuritis produces neuropathic pain sensations (heat- and mechano-hyperalgesia, and cold- and mechano-allodynia) in the ipsilateral hind paw. The abnormal pain sensations begin in 1–2 days and last for 4–6 days, with a subsequent return to normal. These results suggest that there is a neuroimmune interaction that occurs at the outset of nerve injury (and perhaps episodically over time in slow developing conditions like diabetic neuropathy) that produces neuropathic pain. The short duration of the phenomena suggest that they may prime the system for more slowly developing mechanisms of abnormal pain (e.g., ectopic discharge in axotomized primary afferent neurons) that underlie the chronic phase of painful neuropathy.

Protein-protein interaction: a genetic selection for compensating mutations at the barnase-barstar interface.

Barnase and barstar are trivial names of the extracellular RNase and its intracellular inhibitor produced by Bacillus amyloliquefaciens. Inhibition involves the formation of a very tight one-to-one complex of the two proteins. With the crystallographic solution of the structure of the barnase-barstar complex and the development of methods for measuring the free energy of binding, the pair can be used to study protein-protein recognition in detail. In this report, we describe the isolation of suppressor mutations in barstar that compensate for the loss in interaction energy caused by a mutation in barnase. Our suppressor search is based on in vivo selection for barstar variants that are able to protect host cells against the RNAse activity of those barnase mutants not properly inhibited by wild-type barstar. This approach utilizes a plasmid system in which barnase expression is tightly controlled to keep the mutant barnase gene silent. When expression of barnase is turned on, failure to form a complex between the mutant barnase and barstar has a lethal effect on host cells unless overcome by substitution of the wild-type barstar by a functional suppressor derivative. A set of barstar suppressors has been identified for barnase mutants with substitutions in two amino acid positions (residues 102 and 59), which are critically involved in both RNase activity and barstar binding. The mutations selected as suppressors could not have been predicted on the basis of the known protein structures. The single barstar mutation with the highest information content for inhibition of barnase (H102K) has the substitution Y30W. The reduction in binding caused by the R59E mutation in barnase can be partly reversed by changing Glu-76 of barstar, which forms a salt bridge with the Arg-59 in the wild-type complex, to arginine, thus completing an interchange of the two charges.