Radical pair substitution in chemically induced dynamic nuclear polarization. Co-operative effects

The problem of radical pair substitution in Chemically Induced Dynamic Nuclear Polarization is reconsidered. The singlet—triplet evolution in the radical pairs is described in a continuous fashion, assuming non-disturbance of the electron spin state during the scavenging reaction. The CIDNP effect of the recombination product of the secondary pair is demonstrated to result from the “co-operative effect” of singlet—triplet evolution in both the primary and the secondary pair. The hypothetical one proton case, in which the primary pair has different g-factors and a zero hyperfine interaction, and the secondary pair equal g-factors and a non-zero hyperfine interaction is treated qualitatively. Some examples are discussed in which older models lead to a faulty interpretation of experimental results.     

Annealed Scaling for a Charged Polymer

This paper studies an undirected polymer chain living on the one-dimensional integer lattice and carrying i.i.d. random charges. Each self-intersection of the polymer chain contributes to the interaction Hamiltonian an energy that is equal to the product of the charges of the two monomers that meet. The joint probability distribution for the polymer chain and the charges is given by the Gibbs distribution associated with the interaction Hamiltonian. The focus is on the annealed free energy per monomer in the limit as the length of the polymer chain tends to infinity. We derive a spectral representation for the free energy and use this to prove that there is a critical curve in the parameter plane of charge bias versus inverse temperature separating a ballistic phase from a subballistic phase. We show that the phase transition is first order. We prove large deviation principles for the laws of the empirical speed and the empirical charge, and derive a spectral representation for the associated rate functions. Interestingly, in both phases both rate functions exhibit flat pieces, which correspond to an inhomogeneous strategy for the polymer to realise a large deviation. The large deviation principles in turn lead to laws of large numbers and central limit theorems. We identify the scaling behaviour of the critical curve for small and for large charge bias. In addition, we identify the scaling behaviour of the free energy for small charge bias and small inverse temperature. Both are linked to an associated Sturm-Liouville eigenvalue problem. A key tool in our analysis is the Ray-Knight formula for the local times of the one-dimensional simple random walk. This formula is exploited to derive a closed form expression for the generating function of the annealed partition function, and for several related quantities. This expression in turn serves as the starting point for the derivation of the spectral representation for the free energy, and for the scaling theorems. What happens for the quenched free energy per monomer remains open. We state two modest results and raise a few questions.     

A directly labeled TR-FRET assay for monitoring phosphoinositide-3-kinase activity

Phosphoinositide 3-kinases (PI3Ks) comprise a family of kinases that transfer the terminal phosphate of adenosine triphosphate to phosphoinositides at the 3-hydroxyl of the inositol ring to form phosphoinositide (3,4,5) triphosphate (PIP3). The PI3Ks have been shown to play key roles in cell growth, motility, morphology, and survival and thus are of interest as targets in anti-inflammatory and anti-oncogenic drug development. To facilitate identification of novel and selective inhibitors of PI3Ks, we have developed a TR-FRET assay that uses directly labeled reagents. The assay makes use of the high affinity binding of phosphoinositides to a Pleckstrin homology (PH) domain in the general receptor for phosphoinositides 1 (Grp1) protein. It monitors PIP3 produced from the enzymatic reaction by measuring its competition with Bodipy-FL-labeled PIP3 for binding to Terbium chelate-labeled Grp1. By using directly labeled reagents, this assay configuration offers higher sensitivity and faster binding/dissociation kinetics than existing non-radioactive assays, which are critical for competitive assay formats. The assay is homogenous, robust (Z' = 0.88), and simple and, thus, compatible with high throughput screening (HTS) processes.     

Random walk in a high density dynamic random environment

The goal of this note is to prove a law of large numbers for the empirical speed of a green particle that performs a random walk on top of a field of red particles which themselves perform independent simple random walks on Z^d${\mathbb{Z}}^d$, d≥1$d\ge 1$. The red particles jump at rate 1 and are in a Poisson equilibrium with density μ$\mu$. The green particle also jumps at rate 1, but uses different transition kernels p^′$p^{\prime }$ and p^″$p^{″}$ depending on whether it sees a red particle or not. It is shown that, in the limit as μ→∞$\mu \to \infty$, the speed of the green particle tends to the average jump under p^′$p^{\prime }$. This result is far from surprising, but it is non-trivial to prove. The proof that is given in this note is based on techniques that were developed in Kesten and Sidoravicius (2005) to deal with spread-of-infection models. The main difficulty is that, due to particle conservation, space–time correlations in the field of red particles decay slowly. This places the problem in a class of random walks in dynamic random environments for which scaling laws are hard to obtain.     

Random walks in a random field of decaying traps

We study random walks on ^d (d 1) containing traps subject to decay. The initial trap distribution is random. In the course of time, traps decay independently according to a given lifetime distribution. We derive a necessary and sufficient condition under which the walk eventually gets trapped with probability 1. We prove bounds and asymptotic estimates for the survival probability as a function of time and for the average trapping time. These are compared with some well-known results for nondecaying traps.     

Copolymer with Pinning: Variational Characterization of the Phase Diagram

This paper studies a polymer chain in the vicinity of a linear interface separating two immiscible solvents. The polymer consists of random monomer types, while the interface carries random charges. Both the monomer types and the charges are given by i.i.d. sequences of random variables. The configurations of the polymer are directed paths that can make i.i.d. excursions of finite length above and below the interface. The Hamiltonian has two parts: a monomer-solvent interaction (“copolymer”) and a monomer-interface interaction (“pinning”). The quenched and the annealed version of the model each undergo a transition from a localized phase (where the polymer stays close to the interface) to a delocalized phase (where the polymer wanders away from the interface). We exploit the approach developed in Bolthausen et al. (arXiv:1110.1315v1); Cheliotis and den Hollander (arXiv:1005.3661v1) to derive variational formulas for the quenched and the annealed free energy per monomer. These variational formulas are analyzed to obtain detailed information on the critical curves separating the two phases and on the typical behavior of the polymer in each of the two phases. Our main results settle a number of open questions.