Simulating ion channel activation mechanisms using swarms of trajectories

Atomic-level studies of protein activity represent a significant challenge as a result of the complexity of conformational changes occurring on wide-ranging timescales, often greatly exceeding that of even the longest simulations. A prime example is the elucidation of protein allosteric mechanisms, where localized perturbations transmit throughout a large macromolecule to generate a response signal. For example, the conversion of chemical to electrical signals during synaptic neurotransmission in the brain is achieved by specialized membrane proteins called pentameric ligand-gated ion channels. Here, the binding of a neurotransmitter results in a global conformational change to open an ion-conducting pore across the nerve cell membrane. X-ray crystallography has produced static structures of the open and closed states of the proton-gated GLIC pentameric ligand-gated ion channel protein, allowing for atomistic simulations that can uncover changes related to activation. We discuss a range of enhanced sampling approaches that could be used to explore activation mechanisms. In particular, we describe recent application of an atomistic string method, based on Roux's “swarms of trajectories” approach, to elucidate the sequence and interdependence of conformational changes during activation. We illustrate how this can be combined with transition analysis and Brownian dynamics to extract thermodynamic and kinetic information, leading to understanding of what controls ion channel function. © 2019 Wiley Periodicals, Inc.     

Super‐ and Ferroelastic Organic Semiconductors for Ultraflexible Single‐Crystal Electronics

Like silicon, single crystals of organic semiconductors are pursued to attain intrinsic charge transport properties. However, they are intolerant to mechanical deformation, impeding their application in flexible electronic devices. Such contradictory properties, namely exceptional molecular ordering and mechanical flexibility, are unified in this work. We found that bis(triisopropylsilylethynyl)pentacene (TIPS‐P) crystals can undergo mechanically induced structural transitions to exhibit superelasticity and ferroelasticity. These properties arise from cooperative and correlated molecular displacements and rotations in response to mechanical stress. By utilizing a bending‐induced ferroelastic transition of TIPS‐P, flexible single‐crystal electronic devices were obtained that can tolerate strains (?) of more than 13 % while maintaining the charge carrier mobility of unstrained crystals (μ>0.7 μ₀). Our work will pave the way for high‐performance ultraflexible single‐crystal organic electronics for sensors, memories, and robotic applications.     

Isotopy Stable Dynamics Relative to Compact Invariant Sets

Let f be an orientation-preserving homeomorphism of a compactorientable manifold. Sufficient conditions are given for thepersistence of a collection of periodic points under isotopyof f relative to a compact invariant set A. Two main applicationsare described. In the first, A is the closure of a single discreteorbit of f, and f has a Smale horseshoe, all of whose periodicorbits persist; in the second, A is a minimal invariant Cantorset obtained as the limit of a sequence of nested periodic orbits,all of which are shown to persist under isotopy relative toA. 1991 Mathematics Subject Classification: 58F20, 58F15.     

Molecular structure and mass spectrum of dicarbonylbis(tetraphenylcyclobutadiene)molybdenum

The crystal structure on dicarbonylbis(tetraphenylcyclobutadiene)molybdenum has been determined from three-dimensional X-ray data collected by counter methods. The structure consists of monomeric units with each Mo atom bonded to two carbonyl and two Ph₄C₄ groups. Excluding phenyl substituents, the local symmetry about Mo is very nearly C_2υ. Both cyclobutadiene (CBD) groups are asymmetrically bonded to Mo, and the spread in Mo—C(CBD) distances (2.26 to 2.38 Å;) is significantly larger than that found with other structures containing substituted cyclobutadiene groups. The carbonyl groups show several short intramolecular C?C contacts with the cyclobutadiene C atoms (2.68 to 3.03 Å;) and with each other (2.63 Å;). They appear to be wedged between the Ph₄C₄ groups and to be responsible for the asymmetric bonding of the cyclobutadiene groups. The mass spectrum, which shows the characteristic fragmentation pattern of cyclobutadienemetal complexes, suggests a relatively high thermal stability for the title compound. Crystallographic data are as follows: space group P2₁/n; unit cell a 20.15(2), b 18.82(3), c 11.03(1) Å;, β 91.59(6)°; V 4181 Å;³; d_calc for Z = 4 is 1.380 and d_obs is 1.365(7) g/cm³. A total of 1659 reflections with F² ≥ 2σ were used to refine the structure to final values of R_F = 0.063 and R_wF = 0.041.     

Neuromagnetic brain responses to words from semantic sub- and supercategories

Background  

We explored spatio-temporal patterns of cortical activity evoked by written words from super-ordinate and sub-ordinate semantic categories and hoped to find a differential cortical and/or temporal distribution of the brain response depending on the level of the categories. Twenty-three subjects saw 360 words belonging to six sub-ordinate categories (mammals, birds, fish, fruit, flowers, trees) within two super-ordinate categories (fauna, flora). Visually evoked magnetic fields were determined from whole-head (148-sensor) magnetoencephalography and analyzed in the source space (Minimum Norm Estimate).     

The role of isomorphism in synthetic analysis. Pruning the search tree by finding disjoint isomorphic substructures

Isomorphism is an equivalence relation that is less stringent than identity (equality), and it is useful for synthetic analysis, since it allows one to find reflexive routes for targets even when they do not have an element of symmetry.     

Pruning theory and Thurston’s classification of surface homeomorphisms

Two dynamical deformation theories are presented – one for surface homeomorphisms, called pruning, and another for graph endomorphisms, called kneading– both giving conditions under which all of the dynamics in an open set can be destroyed, while leaving the dynamics unchanged elsewhere. The theories are related to each other and to Thurston’s classification of surface homeomorphisms up to isotopy. Received February 20, 2000 / final version received February 26, 2001?Published online May 29, 2001     

Counterexamples to Additivity of Minimum Output p-Rényi Entropy for p Close to 0

Complementing recent progress on the additivity conjecture of quantum information theory, showing that the minimum output p-Rényi entropies of channels are not generally additive for p > 1, we demonstrate here by a careful random selection argument that also at p = 0, and consequently for sufficiently small p, there exist counterexamples. An explicit construction of two channels from 4 to 3 dimensions is given, which have non-multiplicative minimum output rank; for this pair of channels, numerics strongly suggest that the p-Rényi entropy is non-additive for all p ≲ 0.11. We conjecture however that violations of additivity exist for all p < 1.