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.

Experimental studies of the dielectric properties in the nematic and isotropic phases of 4-cyanophenyl-4′-n-octylbenzoate (8CPB) have been performed in the frequency range from 50 kHz to 100 MHz. The relaxation process related to the rotation around the short molecular axis has been analysed. The results obtained have revealed that in the vicinity of the I-N phase transition, the molecular subdiffusional rotation process occurs. It is connected with the pretransitional effects which are observed both in the static and dynamic dielectric measurements. On the basis of the temperature dependence of the relaxation time in the nematic and isotropic phases, the orientational order parameter 〈P2〉 has been determined. The values of 〈P2〉 obtained in this way have been compared with those evaluated from the measurements of the polarized electronic absorption of the dichroic dye, dissolved as guest probe in the mesogenic host.

Dielectric and orientational properties of nematogenic 4-n-octyl(4′-cyanophenyl)benzoate

This paper presents the results of the viscosity measurements performed for the isotropic phase of the homologous series of mesogenic 4-(trans-4-n-alkylcyclohexyl)isothiocyanatobenzenes (CnH2n+1−CyHxPhNCS, nCHBT) for n = 0 to n = 12.

http://www.electronicsandbooks.com/eab1/manual/Magazine/J/Journal%20of%20Chemical%20&%20Engineering%20Data/44-47/je000105h.pdf

Viscosity of the Homologous Series of 4-(trans-4-n-Alkylcyclohexyl)isothiocyanatobenzenes

The application of an external magnetic field on the magnetic fluids induces needle like structuralization of magnetic particles. The influence of this aggregation of magnetic particles in an external magnetic field H on the magneto-dielectric behaviour and dielectric breakdown strength of a transformer oil based magnetic fluids was measured. The observed decrease of dielectric breakdown strength (for H = 0 and H ⊥ E) vs. distance between electrodes is found to be in agreement with a theory of semi-classical bond percolation for a non-linear composite material. In situation when E ∥ H oscillations of dielectric breakdown strength were observed that are associated with a size effect probably.

Dielectric breakdown strength in magnetic fluids

Abstract The results o f a dielectric relaxation study (in the frequency region from about 1 kHz to 1 GHz) of the liquid crystalline title com pound (C3H7-Cyhx-Ph-NCS , 3-CHBT) in the isotropic and the nematic phase (measurements with electric field parallel to alignment) are presented. The spectra of both phases can be described by two relaxation processes of Debye-type, possibly related to rotation around the long and short molecular axes.

Dielectric Relaxation in Nematic and Isotropic Phases of 4-(trans-4'-n-Propylcyclohexyl) isothiocyanatobenzene

The static dielectric constants and the optical birefringence for four members of the homologous series of bicyclo[2,2,2]octane derivatives with -NCS terminal group (pentyl to octyl) have been measured as a function of temperature. From the dielectric anisotropy, the optical birefringence as well as the polarized absorption spectra of the dichroic dye dissolved in the liquid crystalline host the order parameter has been determined. The results obtained by using various experimental methods have been compared with those calculated from the Maier-Saupe mean field theory. It has been found that the order parameter for the successive homologues shows alternation similar to that exhibited for the nematic-isotropic transition temperature.

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Jan Jadżyn

Papers

Dielectric and orientational properties of nematogenic 4-n-octyl(4′-cyanophenyl)benzoate

Viscosity of the Homologous Series of 4-(trans-4-n-Alkylcyclohexyl)isothiocyanatobenzenes

Dielectric breakdown strength in magnetic fluids

Dielectric Relaxation in Nematic and Isotropic Phases of 4-(trans-4'-n-Propylcyclohexyl) isothiocyanatobenzene

Dielectric and Optical Studies of Homologous Series of Bicyclo[2,2,2]octane Derivatives with -NCS Terminal Group