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.

/pdf/the-restaurant-at-the-end-of-the-random-walk-recent-1w7yr3snyb.pdf

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.

Dielectric relaxation of N,N′-diethylurea in non-polar media

Dielectric polarization and non-linear dielectric effects in pivalonitrile solutions

Dielectric measurements on the antiferroelectric smectic C (SmCPA) and isotropic (I) phases of a substance formed by bent‐shaped molecules were performed in the frequency range from 0.1 Hz to 0.1 GHz. Three absorption ranges, corresponding to a slow collective process, the reorientation of the molecular core around the long axes and the fast dynamics of the terminal groups, were detected in the SmCPA phase, whereas only two ranges, related to the two last processes, appear in the isotropic state. At the I–SmCPA phase transition the process of molecular reorientation around the long axes changes stepwise with respect to the absorption band intensity and the relaxation time, while the activation energy remains practically unchanged. The activation energy for the dynamics of the terminal groups increases at the I–SmCPA transition.

Broadband dielectric investigations on a compound consisting of bent‐shaped molecules

Studies of the dielectric relaxation were made for the isotropic and nematic phases of 4-(trans-4'-n-heptylcyclohexyl)isothiocyanatobenzene, (C/sub 7/H/sub 15/-C/sub y/H/sub x/-Ph-N=C=S) (7CHBT) in the frequency range from 100 kHz to 1 GHz. In the nematic phase two relaxation processes were recorded for the dielectric permittivity component measured parallel to the molecular orientation (director n/spl I.oarr/) and three relaxation processes for the perpendicular permittivity component. The elementary contributions to the total dielectric absorption are found to be of the Debye-type. The strength of the nematic potential and the nematic order parameter as a function of temperature were estimated. The results obtained were compared with the predictions of the Maier-Saupe theory.

Determination of the order parameter of 4-(trans-4'-n-heptyl-cyclohexyl)isothiocyanato-benzene by means of dielectric relaxation spectroscopy

The paper presents the results of the measurements of the dielectric relaxation of nematic 6-CHBT performed for differentvalues ofthe angle between the directions of the macroscopic orientation of the sample (director n) and the probing electricfield E. Analysis ofthe evolution ofthe relaxation spectrum from 4(o) (E n) to i(o) (E I n) allowed one to explainthe inconsistency in the molecular interpretation ofthe spectra A model of the molecular dynamics in the oriented nematicsis proposed.Keywords: dielectric relaxation, neniatic, molecular dynamics 1. INTRODUCTION Studies of the dielectric relaxation in nematic liquid crystals are of a special interest and importance. The possibilityof control of the molecular orientation in the whole nematic sample by an electric I magnetic field or by an appropriatepreparation of the electrodes surface, gives an exceptional opportunity for studies of the molecular dynamics in correlation to the directions of the principal axes of the nematogenic molecule. One could expect that in such advantageous

Jan Jadżyn

Papers

Dielectric relaxation of N,N′-diethylurea in non-polar media

Dielectric polarization and non-linear dielectric effects in pivalonitrile solutions

Broadband dielectric investigations on a compound consisting of bent‐shaped molecules

Determination of the order parameter of 4-(trans-4'-n-heptyl-cyclohexyl)isothiocyanato-benzene by means of dielectric relaxation spectroscopy

Molecular model of the dielectric relaxation in nematic liquid crystals