Crooks equation for steered molecular dynamics using a Nosé-Hoover thermostat

The Crooks equation [Eq. (10) in J. Stat. Phys. 90, 1481 (1998)], originally derived for microscopically reversible Markovian systems, relates the work done on a system during an irreversible transformation to the free energy difference between the final and the initial state of the transformation. In the present work we provide a theoretical proof of the Crooks equation in the context of constant volume, constant temperature steered molecular dynamics simulations of systems thermostated by means of the Nosé-Hoover method (and its variant using a chain of thermostats). As a numerical test we use the folding and unfolding processes of decaalanine in vacuo at finite temperature. We show that the distribution of the irreversible work for the folding process is markedly non-Gaussian thereby implying, according to Crooks equation, that also the work distribution of the unfolding process must be inherently non-Gaussian. The clearly asymmetric behavior of the forward and backward irreversible work distributions is a signature of a non-Markovian regime for the folding/unfolding of decaalanine.     

Geometric preferences in iron(II) and zinc(II) model complexes of peptide deformylase

A combination of experimental and theoretical studies on (N,S(thiolate))M(II)-formate complexes (M = Fe, Zn) suggests a rationale for the metal ion dependence of peptide deformylase.     

Thioether sulfur oxygenation from O2 or H2O2 reactivity of copper complexes with tridentate N2Sthioether ligands

To model thioether-copper coordination chemistry including oxidative reactivity, such as occurs in the copper monooxygenases peptidylglycine -hydroxylating monooxygenase (PHM) and dopamine beta-hydroxylase (DbetaH), we have synthesized new tridentate N2S ligands LSEP and LSBz [LSEP = methyl(2-phenethylsulfanylpropyl)(2-pyridin-2-ylethyl)amine; LSBz = (2-benzylsulfanylpropyl)methyl(2-pyridin-2-ylethyl)amine)]. Both copper(I) and copper(II) complexes have been prepared, and their respective O2 and H2O2 chemistry has been studied. Under mild conditions, oxygenation of [(LSEP)CuI]+ (1a) and [(LSBz)CuI]+ (2a) leads to ligand sulfoxidation, thus exhibiting copper monooxygenase activity. A copper(II) complex of this sulfoxide ligand product, [(LSOEP)CuII(CH3OH)(OClO3)2], has been structurally characterized, demonstrating Cu-Osulfoxide ligation. The X-ray structure of [(LSEP)CuII(H2O)(OClO3)]+ (1b) and its solution UV-visible spectral properties [S-CuII LMCT band at 365 nm (MeCN solvent); epsilon = 4285 M-1 cm-1] indicate the thioether sulfur atom is bound to the cupric ion in both the solid (CuII-S distance: 2.31 A) and solution states. Reaction of 1b with H2O2 leads to sulfonation via the sulfoxide; excess hydrogen peroxide gives mostly sulfone product. These results may provide some insight into recent reports concerning protein methionine oxidation, showing the potential importance of copper-mediated oxidation processes in certain biological settings.     

Effects of coherence on the degree of polarization in a young interference pattern

Recent predictions concerning the relationship between the degree of polarization at a typical point of a Young interference pattern and the degree of coherence of the electromagnetic field at the pinholes are tested by a simple experiment. In particular, it is shown that light that is completely unpolarized at the pinholes can become partially polarized across the fringe pattern.     

Inverse statistical problems: from the inverse Ising problem to data science

Inverse problems in statistical physics are motivated by the challenges of ‘big data’ in different fields, in particular high-throughput experiments in biology. In inverse problems, the usual procedure of statistical physics needs to be reversed: Instead of calculating observables on the basis of model parameters, we seek to infer parameters of a model based on observations. In this review, we focus on the inverse Ising problem and closely related problems, namely how to infer the coupling strengths between spins given observed spin correlations, magnetizations, or other data. We review applications of the inverse Ising problem, including the reconstruction of neural connections, protein structure determination, and the inference of gene regulatory networks. For the inverse Ising problem in equilibrium, a number of controlled and uncontrolled approximate solutions have been developed in the statistical mechanics community. A particularly strong method, pseudolikelihood, stems from statistics. We also review the inverse Ising problem in the non-equilibrium case, where the model parameters must be reconstructed based on non-equilibrium statistics.     

Analysis of Nonlinear Poro-Elastic and Poro-Visco-Elastic Models

We consider the initial and boundary value problem for a system of partial differential equations describing the motion of a fluid–solid mixture under the assumption of full saturation. The ability of the fluid phase to flow within the solid skeleton is described by the permeability tensor, which is assumed here to be a multiple of the identity and to depend nonlinearly on the volumetric solid strain. In particular, we study the problem of the existence of weak solutions in bounded domains, accounting for non-zero volumetric and boundary forcing terms. We investigate the influence of viscoelasticity on the solution functional setting and on the regularity requirements for the forcing terms. The theoretical analysis shows that different time regularity requirements are needed for the volumetric source of linear momentum and the boundary source of traction depending on whether or not viscoelasticity is present. The theoretical results are further investigated via numerical simulations based on a novel dual mixed hybridized finite element discretization. When the data are sufficiently regular, the simulations show that the solutions satisfy the energy estimates predicted by the theoretical analysis. Interestingly, the simulations also show that, in the purely elastic case, the Darcy velocity and the related fluid energy might become unbounded if indeed the data do not enjoy the time regularity required by the theory.     

Morse Index and Linear Stability of the Lagrangian Circular Orbit in a Three-Body-Type Problem Via Index Theory

It is well known that the linear stability of the Lagrangian elliptic solutions in the classical planar three-body problem depends on a mass parameter β and on the eccentricity e of the orbit. We consider only the circular case (e = 0) but under the action of a broader family of singular potentials: α-homogeneous potentials, for \(\alpha \in (0, 2)\), and the logarithmic one. It turns out indeed that the Lagrangian circular orbit persists also in this more general setting. We discover a region of linear stability expressed in terms of the homogeneity parameter α and the mass parameter β, then we compute the Morse index of this orbit and of its iterates and we find that the boundary of the stability region is the envelope of a family of curves on which the Morse indices of the iterates jump. In order to conduct our analysis we rely on a Maslov-type index theory devised and developed by Y. Long, X. Hu and S. Sun; a key role is played by an appropriate index theorem and by some precise computations of suitable Maslov-type indices.     

Gold-catalyzed 1,2-/1,2-bis-acetoxy migration of 1,4-bis-propargyl acetates: a mechanistic study

The late transition metal catalyzed rearrangement of propargyl acetates offers an interesting platform for the development of synthetically useful transformations. We have recently shown that gold complexes can catalyze a highly selective tandem 1,2-/1,2-bis-acetoxy migration in 1,4-bis-propargyl acetates to form 2,3-bis-acetoxy-1,3-dienes. In this way, (1Z,3Z)- or (1Z,3E)- and (1E,3Z)-1,3-dienes could be obtained in a stereocontrolled manner depending on the electronic and steric features of the ancillary ligand bound to gold and the substituents at the propargylic positions. In this work, we report an experimental study on the scope of this transformation, plus a detailed theoretical examination of the reaction mechanism, which has revealed the key features responsible for the reaction stereoselectivity. Synthetic applications towards the one-pot synthesis of quinoxaline heterocycles and tandem Diels-Alder processes have also been devised.     

Easy separation of Δ and Λ isomers of highly luminescent [Ir(III)]-cyclometalated complexes based on chiral phenol-oxazoline ancillary ligands

A new class of neutral cyclometalated iridium(III) complexes with enantiomerically pure C(1)-symmetric phenol-oxazolines (3a,b) have been synthetized in high yields and fully characterized. Resolution of the corresponding Δ(R) and Λ(R) or Δ(S) and Λ(S) isomers was easily achieved by conventional flash chromatography. The corresponding Δ and Λ helicities have been confirmed by CD spectroscopy and X-ray crystallography. Regarding the absorption and luminescence properties with unpolarized light, no significant difference between Δ and Λ isomers has been observed. A strong blue luminescence is observed for deaerated solutions of complexes 5a and 5b in CH(3)CN.