Fractional dynamics has experienced a firm upswing during the past few years, having been forged into a mature framework in the theory of stochastic processes. A large number of research papers developing fractional dynamics further, or applying it to various systems have appeared since our first review article on the fractional Fokker–Planck equation (Metzler R and Klafter J 2000a, Phys. Rep. 339 1–77). It therefore appears timely to put these new works in a cohesive perspective. In this review we cover both the theoretical modelling of sub- and superdiffusive processes, placing emphasis on superdiffusion, and the discussion of applications such as the correct formulation of boundary value problems to obtain the first passage time density function. We also discuss extensively the occurrence of anomalous dynamics in various fields ranging from nanoscale over biological to geophysical and environmental systems.

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The restaurant at the end of the random walk: recent developments in the description of anomalous transport by fractional dynamics

Molecular recognition in biological systems relies on the existence of specific attractive interactions between two partner molecules. Structure-based drug design seeks to identify and optimize such interactions between ligands and their host molecules, typically proteins, given their three-dimensional structures. This optimization process requires knowledge about interaction geometries and approximate affinity contributions of attractive interactions that can be gleaned from crystal structure and associated affinity data.

Here we compile and review the literature on molecular interactions as it pertains to medicinal chemistry through a combination of careful statistical analysis of the large body of publicly available X-ray structure data and experimental and theoretical studies of specific model systems. We attempt to extract key messages of practical value and complement references with our own searches of the CSDa,(1) and PDB databases.(2) The focus is on direct contacts between ligand and protein functional groups, and we restrict ourselves to those interactions that are most frequent in medicinal chemistry applications. Examples from supramolecular chemistry and quantum mechanical or molecular mechanics calculations are cited where they illustrate a specific point. The application of automated design processes is not covered nor is design of physicochemical properties of molecules such as permeability or solubility.

Throughout this article, we wish to raise the readers’ awareness that formulating rules for molecular interactions is only possible within certain boundaries. The combination of 3D structure analysis with binding free energies does not yield a complete understanding of the energetic contributions of individual interactions. The reasons for this are widely known but not always fully appreciated. While it would be desirable to associate observed interactions with energy terms, we have to accept that molecular interactions behave in a highly nonadditive fashion.3,4 The same interaction may be worth different amounts of free energy in different contexts, and it is very hard to find an objective frame of reference for an interaction, since any change of a molecular structure will have multiple effects. One can easily fall victim to confirmation bias, focusing on what one has observed before and building causal relationships on too few observations. In reality, the multiplicity of interactions present in a single protein−ligand complex is a compromise of attractive and repulsive interactions that is almost impossible to deconvolute. By focusing on observed interactions, one neglects a large part of the thermodynamic cycle represented by a binding free energy: solvation processes, long-range interactions, conformational changes. Also, crystal structure coordinates give misleadingly static views of interactions. In reality a macromolecular complex is not characterized by a single structure but by an ensemble of structures. Changes in the degrees of freedom of both partners during the binding event have a large impact on binding free energy.

The text is organized in the following way. The first section treats general aspects of molecular design: enthalpic and entropic components of binding free energy, flexibility, solvation, and the treatment of individual water molecules, as well as repulsive interactions. The second half of the article is devoted to specific types of interactions, beginning with hydrogen bonds, moving on to weaker polar interactions, and ending with lipophilic interactions between aliphatic and aromatic systems. We show many examples of structure−activity relationships; these are meant as helpful illustrations but individually can never confirm a rule.

http://pubs.acs.org/doi/pdf/10.1021/jm100112j

A Medicinal Chemist’s Guide to Molecular Interactions

An intriguing problem in condensed matter physics is understanding the glass transition, in particular the dynamics in the equilibrium liquid close to vitrification Recent advances have been made by using hydrostatic pressure as an experimental variable These results are reviewed, with an emphasis in the insight provided into the mechanisms underlying the relaxation properties of glass-forming liquids and polymers

https://iopscience.iop.org/article/10.1088/0034-4885/68/6/R03/pdf

Supercooled dynamics of glass-forming liquids and polymers under hydrostatic pressure

https://orbilu.uni.lu/bitstream/10993/20503/1/Lagerwall%20%26%20Scalia%202012.pdf

A new era for liquid crystal research: Applications of liquid crystals in soft matter nano-, bio- and microtechnology

This Review covers the recent developments (2005-2015) in the design, synthesis, characterization, and application of thermotropic ionic liquid crystals. It was designed to give a comprehensive overview of the "state-of-the-art" in the field. The discussion is focused on low molar mass and dendrimeric thermotropic ionic mesogens, as well as selected metal-containing compounds (metallomesogens), but some references to polymeric and/or lyotropic ionic liquid crystals and particularly to ionic liquids will also be provided. Although zwitterionic and mesoionic mesogens are also treated to some extent, emphasis will be directed toward liquid-crystalline materials consisting of organic cations and organic/inorganic anions that are not covalently bound but interact via electrostatic and other noncovalent interactions.

Ionic Liquid Crystals: Versatile Materials.

Abstract The static and dynamic dielectric properties o f the title system are reported for a concentration series from about 8 mmol/1 up to 2.3 mol/I at 20 °C. The apparent moment (4.2 D , extrapolated to infinite dilution) decreases with increasing concentration, the relaxation time increases proportional to viscosity, that is, somewhat steeper than usually observed. Com parison with other molecules suggests that these features are mainly due to the high dipole moment rather than being specifically related to the prolate shape o f the molecule. The broadening o f the spectrum toward the high frequency side, on the other hand, may be due to the molecular shape.

Dielectric Properties of 4-Cyanobiphenyl in 1,4-Dioxane Solution

Long-range orientational order of four nematogenic liquid crystals has been determined on the basis of the optical birefringence, the dielectric anisotropy, and the polarized absorption spectra of the dichroic dye dissolved in the liquid crystalline host. The values of the order parameters obtained by using various experimental methods have been compared with those obtained from the Maier-Saupe mean field theory.

Molecular order in some nematics determined from optical and dielectric investigations

The problem of the nonlinear ac dielectric response in polyelectrolytes is carried out by considering these electrically charged systems acted on by a strong dc bias electric field superimposed on a weak ac field. An infinite set of coupled (translation-rotation) kinetic equations is derived, and by using a perturbation procedure, we establish a new expression for the complex dielectric increment of an assembly of nonpolar rodlike macroions surrounded by small counterions. By considering the stationary regime, we show that the electric polarization of the nonpolar macroion is given by calculating the expectation value of P1(cos ϑ)H1(x), where P1 and H1 stand for the first Legendre and Hermite polynomials, respectively. The results so obtained provide new relaxation features, which are presented in the form of analytic expressions and illustrated by Cole-Cole-like diagrams and three-dimensional dispersion and absorption plots in order to show the influence of the coupling parameter a measuring the importan...

Nonlinear harmonic components in dielectric relaxation of polyelectrolytes

In this work we describe the magnetic Freedericksz transition in HABbased (4,4′-di-n-heptylazoxybenzene) ferronematics. The ferronematic samples were prepared with two different volume concentrations of magnetic particles φ1 = 2 × 10−5 and φ2 = 2 × 10−4. The liquid crystal HAB is nematic at the temperatures from ≈ 53◦C to 70◦C and smectic A at the temperatures under 53◦C. The anisotropy of dielectric permitivity of HAB liquid crystal is positive in nematic phase and negative in smectic A phase. The magnetic Fredericksz transition was studied in nematic phase at temperature 60◦C.

The Anchoring Energy of Liquid Crystal Molecules to Magnetic Particles in HAB-Based Ferronematics

Studies of the nonlinear dipolar relaxation in the frequency range from 1 MHz to 3 GHz have been carried out for diluted solutions of 4,4'-n-hexylcyanobiphenyl and 4-(trans-4'-n- hexylcyclohexyl)isothiocyanatobenzene in benzene at 25 degrees C. The nonlinear dielectric effect has been measured with a weak alternating field superimposed on a strong quasi-static bias field of the amplitude of 1.1 X 107 V/m. The nonlinear relaxation spectrum has been interpreted in terms of the theory proposed by Coffey et al.© (1999) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.

Jan Jadżyn

Papers

Dielectric Properties of 4-Cyanobiphenyl in 1,4-Dioxane Solution

Molecular order in some nematics determined from optical and dielectric investigations

Nonlinear harmonic components in dielectric relaxation of polyelectrolytes

The Anchoring Energy of Liquid Crystal Molecules to Magnetic Particles in HAB-Based Ferronematics

Nonlinear dielectric relaxation in dipolar systems