Abstract kinetic equations with positive collision operators

We consider "forward-backward" parabolic equations in the abstract form $Jd \psi / d x + L \psi = 0$, $0< x < \tau \leq \infty$, where $J$ and $L$ are operators in a Hilbert space $H$ such that $J=J^*=J^{-1}$, $L=L^* \geq 0$, and $\ker L = 0$. The following theorem is proved: if the operator $B=JL$ is similar to a self-adjoint operator, then associated half-range boundary problems have unique solutions. We apply this theorem to corresponding nonhomogeneous equations, to the time-independent Fokker-Plank equation $\mu \frac {\partial \psi}{\partial x} (x,\mu) = b(\mu) \frac {\partial^2 \psi}{\partial \mu^2} (x, \mu)$, $0<x<\tau$, $\mu \in \R$, as well as to other parabolic equations of the "forward-backward" type. The abstract kinetic equation $T d \psi/dx = - A \psi (x) + f(x)$, where $T=T^*$ is injective and $A$ satisfies a certain positivity assumption, is considered also.Comment: 20 pages, LaTeX2e, version 2, references have been added, changes in the introductio

Role of phosphorylation in p53 acetylation and PAb421 epitope recognition in baculoviral and mammalian expressed proteins

Post-translational modifications, such as phosphorylation and acetylation of the tumour suppressor protein p53, elicit important effects on the function and the stability of the resultant protein. However, as phosphorylation and acetylation are dynamic events subject to complex controls, elucidating the relationships between phosphorylation and acetylation is difficult. In the present study we sought to address this problem by comparing full-length wild-type p53 with full-length p53 proteins mutated at specific phosphorylation targets. Recombinant murine p53 proteins were expressed in insect cells (using the baculoviral expression vector system) and in a mammalian in vitro transcription/translation reticulocyte lysate system. In p53 proteins derived from baculoviral expression vectors, S37A (but not S37D) was found to abrogate phosphorylation at S15. Lysine 382 (K382) is constitutively acetylated and was shown to form part of the epitope recognized by PAb421. Lysine 373 (K373) was only acetylated following substitutions at S315 (S315A or S315D) or at S378 (S378A). Importantly, in baculoviral expressed proteins, PAb421 reactivity was independent of K373 acetylation status, indicating that acetylation at K382 specifically determines the PAb421 epitope