SCF E3 Ligase Substrates Switch from CAN-D to Can-ubiquitylate

Liu et al. (2018) report a mathematical model predicting how the cellular repertoire of SCF E3 ligases is assembled by “adaptive exchange on demand,” with the limited pool of CUL1 scanning the vast sea of F-box proteins for those with substrates demanding ubiquitylation

Imaging geometry through dynamics: the observable representation

For many stochastic processes there is an underlying coordinate space, $V$, with the process moving from point to point in $V$ or on variables (such as spin configurations) defined with respect to $V$. There is a matrix of transition probabilities (whether between points in $V$ or between variables defined on $V$) and we focus on its ``slow'' eigenvectors, those with eigenvalues closest to that of the stationary eigenvector. These eigenvectors are the ``observables,'' and they can be used to recover geometrical features of $V$

Relative momentum for identical particles

Possible definitions for the relative momentum of identical particles are considered

A switch element in the autophagy E2 Atg3 mediates allosteric regulation across the lipidation cascade

Autophagy depends on the E2 enzyme, Atg3, functioning in a conserved E1-E2-E3 trienzyme cascade that catalyzes lipidation of Atg8-family ubiquitin-like proteins (UBLs). Molecular mechanisms underlying Atg8 lipidation remain poorly understood despite association of Atg3, the E1 Atg7, and the composite E3 Atg12-Atg5-Atg16 with pathologies including cancers, infections and neurodegeneration. Here, studying yeast enzymes, we report that an Atg3 element we term E123IR (E1, E2, and E3-interacting region) is an allosteric switch. NMR, biochemical, crystallographic and genetic data collectively indicate that in the absence of the enzymatic cascade, the Atg3(E123IR) makes intramolecular interactions restraining Atg3's catalytic loop, while E1 and E3 enzymes directly remove this brace to conformationally activate Atg3 and elicit Atg8 lipidation in vitro and in vivo. We propose that Atg3's E123IR protects the E2 similar to UBL thioester bond from wayward reactivity toward errant nucleophiles, while Atg8 lipidation cascade enzymes induce E2 active site remodeling through an unprecedented mechanism to drive autophagy

NEDD8 and ubiquitin ligation by cullin-RING E3 ligases

RING E3s comprise the largest family of ubiquitin (UB) and ubiquitin-like protein (UBL) ligases. RING E3s typically promote UB or UBL transfer from the active site of an associated E2 enzyme to a distally-recruited substrate. Many RING E3s – including the cullin-RING ligase family – are multifunctional, interacting with various E2s (or other E3s) to target distinct proteins, transfer different UBLs, or to initially modify substrates with UB or subsequently elongate UB chains. Here we consider recent structures of cullin-RING ligases, and their partner E2 enzymes, representing ligation reactions. The studies collectively reveal multimodal mechanisms – interactions between ancillary E2 or E3 domains, post-translational modifications, or auxiliary binding partners – directing cullin-RING E3-E2 enzyme active sites to modify their specific targets

Spectral properties of zero temperature dynamics in a model of a compacting granular column

The compacting of a column of grains has been studied using a one-dimensional Ising model with long range directed interactions in which down and up spins represent orientations of the grain having or not having an associated void. When the column is not shaken (zero 'temperature') the motion becomes highly constrained and under most circumstances we find that the generator of the stochastic dynamics assumes an unusual form: many eigenvalues become degenerate, but the associated multi-dimensional invariant spaces have but a single eigenvector. There is no spectral expansion and a Jordan form must be used. Many properties of the dynamics are established here analytically; some are not. General issues associated with the Jordan form are also taken up.Comment: 34 pages, 4 figures, 3 table

Sharing Polarization within Quantum Subspaces

Given an ensemble of n spins, at least some of which are partially polarized, we investigate the sharing of this polarization within a subspace of k spins. We assume that the sharing results in a pseudopure state, characterized by a single purity parameter which we call the bias. As a concrete example we consider ensembles of spin-1/2 nuclei in liquid-state nuclear magnetic resonance (NMR) systems. The shared bias levels are compared with some current entanglement bounds to determine whether the reduced subspaces can give rise to entangled states.Comment: 7 pages, 3 figure

Analysis of a three-component model phase diagram by Catastrophe Theory

We analyze the thermodynamical potential of a lattice gas model with three components and five parameters using the methods of Catastrophe Theory. We find the highest singularity, which has codimension five, and establish its transversality. Hence the corresponding seven-degree Landau potential, the canonical form Wigwam or $A_6$, constitutes the adequate starting point to study the overall phase diagram of this model.Comment: 16 pages, Latex file, submitted to Phys. Rev.

The Power of Duples (in Self-Assembly): It's Not So Hip To Be Square

In this paper we define the Dupled abstract Tile Assembly Model (DaTAM), which is a slight extension to the abstract Tile Assembly Model (aTAM) that allows for not only the standard square tiles, but also "duple" tiles which are rectangles pre-formed by the joining of two square tiles. We show that the addition of duples allows for powerful behaviors of self-assembling systems at temperature 1, meaning systems which exclude the requirement of cooperative binding by tiles (i.e., the requirement that a tile must be able to bind to at least 2 tiles in an existing assembly if it is to attach). Cooperative binding is conjectured to be required in the standard aTAM for Turing universal computation and the efficient self-assembly of shapes, but we show that in the DaTAM these behaviors can in fact be exhibited at temperature 1. We then show that the DaTAM doesn't provide asymptotic improvements over the aTAM in its ability to efficiently build thin rectangles. Finally, we present a series of results which prove that the temperature-2 aTAM and temperature-1 DaTAM have mutually exclusive powers. That is, each is able to self-assemble shapes that the other can't, and each has systems which cannot be simulated by the other. Beyond being of purely theoretical interest, these results have practical motivation as duples have already proven to be useful in laboratory implementations of DNA-based tiles

Reflections on Tiles (in Self-Assembly)

We define the Reflexive Tile Assembly Model (RTAM), which is obtained from the abstract Tile Assembly Model (aTAM) by allowing tiles to reflect across their horizontal and/or vertical axes. We show that the class of directed temperature-1 RTAM systems is not computationally universal, which is conjectured but unproven for the aTAM, and like the aTAM, the RTAM is computationally universal at temperature 2. We then show that at temperature 1, when starting from a single tile seed, the RTAM is capable of assembling n x n squares for n odd using only n tile types, but incapable of assembling n x n squares for n even. Moreover, we show that n is a lower bound on the number of tile types needed to assemble n x n squares for n odd in the temperature-1 RTAM. The conjectured lower bound for temperature-1 aTAM systems is 2n-1. Finally, we give preliminary results toward the classification of which finite connected shapes in Z^2 can be assembled (strictly or weakly) by a singly seeded (i.e. seed of size 1) RTAM system, including a complete classification of which finite connected shapes be strictly assembled by a "mismatch-free" singly seeded RTAM system.Comment: New results which classify the types of shapes which can self-assemble in the RTAM have been adde