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.

This paper presents the results of measurements of the static and dynamic electric permittivity, the shear viscosity of a freely flowing sample, and the splay and bend elastic constants for 1-(4-trans -propylcyclohexyl)-2-(4-cyanophenyl)ethane (C3H7-CyHx-CH2CH2-Ph-C=N) (3CCPE). The static permittivity of the isotropic phase shows pre-nematic critical behaviour which is discussed in the frame of the fluid-like model of Mukherjee. From the temperature dependence of the dielectric relaxation time (corresponding to the molecular rotation around the short axis) and the shear viscosity, the strength of the nematic potential and the effective length of the 3CCPE molecule (in the isotropic phase), were estimated. The splay and bend elastic constants were determined from the voltage dependence of the capacitance of a planar nematic cell.

Dielectric, viscous and elastic properties of nematogenic 1-(4- trans -propylcyclohexyl)-2-(4-cyanophenyl)ethane

https://www.szfki.hu/~eber/EN_Publist_files/PhysProc9_41_2010.pdf

Structural transitions in nematic liquid crystals doped with magnetite functionalized single walled carbon nanotubes

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Dielectric, Viscous, and Elastic Properties of Mesogenic 4-n-Hexyloxy-4'-Cyanobiphenyl

Linear and nonlinear dipolar relaxation of 4,4′-n-hexylcyanobiphenyl

Abstract Static and dynamic investigations of the dielectric properties of the liquid crystal 1-(4-isothio-cyanatophenyl)-2-(4-hexyl-bicyclo[2,2,2]octane-1)ethane in the nematic and isotropic phases have been carried out in the frequency region from 1 kHz to 1 GHz. Two relaxation processes, described by the Debye functions, have been observed not only in the isotropic but also in the nematic phase, when the measurements of the electric permittivity vs. frequency have been made parallel to the orientation axis of liquid crystal. These processes are related to the rotation of the permanent dipole moment around two main molecular axes. The height of the potential barrier which hinders the rotation of the liquid crystal molecule around the short axis in the ordered nematic phase and the order parameter of the liquid crystal investigated have been estimated on the basis of the relaxation time values in the nematic and isotropic phases.

Jan Jadżyn

Papers

Dielectric, viscous and elastic properties of nematogenic 1-(4- trans -propylcyclohexyl)-2-(4-cyanophenyl)ethane

Structural transitions in nematic liquid crystals doped with magnetite functionalized single walled carbon nanotubes

Dielectric, Viscous, and Elastic Properties of Mesogenic 4-n-Hexyloxy-4'-Cyanobiphenyl

Linear and nonlinear dipolar relaxation of 4,4′-n-hexylcyanobiphenyl

Dielectric Behaviour of 1-(4-Isothiocyanatophenyl)-2-(4-hexyl- bicyclo[2,2,2]octane-1)ethane in Nematic and Isotropic Phases