Moving frames and prolongations of real algebraic actions

We prove that every real algebraic action on a smooth real algebraic variety has a prolongation with a "moving frame"

Phosphoryl Transfer Step in the C-terminal Src Kinase Controls Src Recognition

All members of the Src family of nonreceptor protein tyrosine kinases are phosphorylated and subsequently down-regulated by the C-terminal Src kinase, Csk. Although the recognition of Src protein substrates is essential for a diverse set of signaling events linked to cellular growth and differentiation, the factors controlling this critical protein-protein interaction are not well known. To understand how Csk recognizes Src, the chemical/physical events that modulate apparent substrate affinity and turnover were investigated. Src is phosphorylated in a biphasic manner in rapid quench flow experiments, suggesting that the phosphoryl transfer step is fast and highly favorable and does not limit overall turnover. As opposed to other kinase-substrate pairs, turnover is not limited by the physical release of ADP based on stopped-flow fluorescence and catalytic trapping experiments, suggesting that other steps control net phosphorylation. The Kd for Src is considerably larger than the Km based on single turnover kinetic and equilibrium sedimentation experiments. Taken together, the data are consistent with a mechanism whereby Csk achieves a low Km for the substrate Src, not by stabilizing protein-protein interactions but rather by facilitating a fast phosphoryl transfer step. In this manner, the phosphoryl transfer step functions as a chemical clamp facilitating substrate recognition

Dynamics on Lorentz manifolds

Within the general framework of the dynamics of "large" groups on geometric spaces, the focus is on the types of groups that can act in complicated ways on Lorentz manifolds, and on the structure of the resulting manifolds and actions. This particular area of dynamics is an active one, and not all the results are in their final form. However, at this point, a great deal can be said about the particular Lie groups that come up in this context. It is impressive that, even assuming very weak recurrence of the action, the list of possible groups is quite restricted. For the most complicated of th

Smooth Counterexamples to Frame Bundle Freeness

We provide counterexamples to P. Olver’s freeness conjecture for C ∞ actions. In fact, we show that a counterexample exists for any connected real Lie group with noncompact center, as well as for the additive group of the integers