Coarse master equation from Bayesian analysis of replica molecular dynamics simulations

We use Bayesian inference to derive the rate coefficients of a coarse master equation from molecular dynamics simulations. Results from multiple short simulation trajectories are used to estimate propagators. A likelihood function constructed as a product of the propagators provides a posterior distribution of the free coefficients in the rate matrix determining the Markovian master equation. Extensions to non-Markovian dynamics are discussed, using the trajectory "paths" as observations. The Markovian approach is illustrated for the filling and emptying transitions of short carbon nanotubes dissolved in water. We show that accurate thermodynamic and kinetic properties, such as free energy surfaces and kinetic rate coefficients, can be computed from coarse master equations obtained through Bayesian inference.     

Coarse nonlinear dynamics and metastability of filling-emptying transitions: water in carbon nanotubes

Using a coarse-grained molecular dynamics (CMD) approach we study the apparent nonlinear dynamics of water molecules filling or emptying carbon nanotubes as a function of system parameters. Different levels of the pore hydrophobicity give rise to tubes that are empty, water-filled, or fluctuate between these two long-lived metastable states. The corresponding coarse-grained free-energy surfaces and their hysteretic parameter dependence are explored by linking MD to continuum fixed point and bifurcation algorithms. The results are validated through equilibrium MD simulations.     

Excitonic effects in molecular crystals built up by small organic molecules

The excitonic effects of biphenyl and 2,2′-bithiophene are investigated within an ab initio framework. For this purpose the Bethe–Salpeter equation for the two-particle Greens function is solved. Therefrom the imaginary part of the dielectric function is derived, which includes the electron–hole interaction in the absorption process. It turns out that these organic molecular crystals, which are built by small molecules, give rise to sizeable exciton binding-energies, which are between 0.7 and 0.8 eV. To study the influence of the intermolecular interaction, the exciton binding energy of crystalline biphenyl is calculated as a function of pressure. The decrease of both, the band gap and the exciton binding energy, results in a slight red-shift of the lowest optically active singlet exciton.     

Allene-alkyne cross-coupling for stereoselective synthesis of substituted 1,4-dienes and cross-conjugated trienes

Titanium-mediated cross-coupling of allenic alcohols with alkynes has been investigated. Divergent reaction pathways were discovered that provide either stereodefined 1,4-dienes or substituted cross-conjugated trienes. In short, allene substitution plays a critical role in the determination of reaction pathway.     

A family of angle-moments proportional to r-n,n = 1,2,…, in free space

The moments M_n(r) ≡ 1/2 ∝^2π₀ dθ sinⁿ θ I(r,θ) of the intensity I(r, θ) in free space surrounding a spherical object emitting radiation with an arbitrary directional dependence are shown to be exactly proportional to r^-(n+1), n = 0, 1,….     

Kinetics and mechanism of proton transport across membrane nanopores

We use computer simulations to study the kinetics and mechanism of proton passage through a narrow-pore carbon-nanotube membrane separating reservoirs of liquid water. Free energy and rate constant calculations show that protons move across the membrane diffusively along single-file chains of hydrogen-bonded water molecules. Proton passage through the membrane is opposed by a high barrier in the effective potential, reflecting the large electrostatic penalty for desolvation and reminiscent of charge exclusion in biological water channels. At neutral pH, we estimate a translocation rate of about 1 proton per hour and tube.     

Layering and position-dependent diffusive dynamics of confined fluids

We study the diffusive dynamics of a hard-sphere fluid confined between parallel smooth hard walls. The position-dependent diffusion coefficient normal to the walls is larger in regions of high local packing density. High density regions also have the largest available volume, consistent with the fast local diffusivity. Indeed, local and global diffusivities as a function of the Widom insertion probability approximately collapse onto a master curve. Parallel and average normal diffusivities are strongly coupled at high densities and deviate from bulk fluid behavior.     

Atomistic insights into rhodopsin activation from a dynamic model

Rhodopsin, the light sensitive receptor responsible for blue-green vision, serves as a prototypical G protein-coupled receptor (GPCR). Upon light absorption, it undergoes a series of conformational changes that lead to the active form, metarhodopsin II (META II), initiating a signaling cascade through binding to the G protein transducin (G(t)). Here, we first develop a structural model of META II by applying experimental distance restraints to the structure of lumi-rhodopsin (LUMI), an earlier intermediate. The restraints are imposed by using a combination of biased molecular dynamics simulations and perturbations to an elastic network model. We characterize the motions of the transmembrane helices in the LUMI-to-META II transition and the rearrangement of interhelical hydrogen bonds. We then simulate rhodopsin activation in a dynamic model to study the path leading from LUMI to our META II model for wild-type rhodopsin and a series of mutants. The simulations show a strong correlation between the transition dynamics and the pharmacological phenotypes of the mutants. These results help identify the molecular mechanisms of activation in both wild type and mutant rhodopsin. While static models can provide insights into the mechanisms of ligand recognition and predict ligand affinity, a dynamic model of activation could be applicable to study the pharmacology of other GPCRs and their ligands, offering a key to predictions of basal activity and ligand efficacy.     

Protein folding kinetics under force from molecular simulation

Despite a large number of studies on the mechanical unfolding of proteins, there are still relatively few successful attempts to refold proteins in the presence of a stretching force. We explore refolding kinetics under force using simulations of a coarse-grained model of ubiquitin. The effects of force on the folding kinetics can be fitted by a one-dimensional Kramers theory of diffusive barrier crossing, resulting in physically meaningful parameters for the height and location of the folding activation barrier. By comparing parameters obtained from pulling in different directions, we find that the unfolded state plays a dominant role in the refolding kinetics. Our findings explain why refolding becomes very slow at even moderate pulling forces and suggest how it could be practically observed in experiments at higher forces.