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.

Anisotropy of static electric permittivity and conductivity was measured for three groups of liquid crystals: (I) p-n-alkyl-p'-cyanobiphenyls (CnH2n+1-φ-φ-CN, n = 5,6,7,8), (II) p-p'-dialkylazoxybenzenes (CnH2n+1-φ-N(O) = N-φ-CnH2n+1, n = 5,6,7,8) and (III) p-alkyloxyphenyl-p'-alkoxybenzoates (CnH2n+1-O-φ-COO-φ-O-CmH2m+1, n = 8, m = 5; n = 8, m = 7; n = 10, m = 5; n = 11, m = 5). The nematic-smectic A phase transition for compounds of the I and II group manifests itself as a change of conductivity anisotropy sign due to a strong variation of the parallel component σ∥ only; for compounds of the III group both components of electric conductivity and permittivity change considerably.

Anisotropy of Static Electric Permittivity and Conductivity in Some Nematics and Smectics A

The nonlinear dielectric spectra of ${4\ensuremath{-}(trans\ensuremath{-}4}^{\ensuremath{'}}\ensuremath{-}n\ensuremath{-}\mathrm{h}\mathrm{e}\mathrm{x}\mathrm{y}\mathrm{l}\mathrm{c}\mathrm{y}\mathrm{c}\mathrm{l}\mathrm{o}\mathrm{h}\mathrm{e}\mathrm{x}\mathrm{y}\mathrm{l})\mathrm{i}\mathrm{s}\mathrm{o}\mathrm{t}\mathrm{h}\mathrm{i}\mathrm{o}\mathrm{c}\mathrm{y}\mathrm{a}\mathrm{n}\mathrm{a}\mathrm{t}\mathrm{o}\mathrm{b}\mathrm{e}\mathrm{n}\mathrm{z}\mathrm{e}\mathrm{n}\mathrm{e}$ $({\mathrm{C}}_{6}{\mathrm{H}}_{13}\mathrm{CyHx}\mathrm{}\mathrm{Ph}\mathrm{}\mathrm{NCS},$ 6CHBT) in benzene solutions were recorded in the whole concentration range up to an appearance of the two-phase isotropic and nematic region (0.82 mole fraction of 6CHBT, at $25\ifmmode^\circ\else\textdegree\fi{}\mathrm{C}).$ Two electric fields: (i) the field of high strength (110 kV/m) and low frequency (85 Hz) causing the dielectric nonlinearity, and (ii) the probing field of low strength and high frequency (100 kHz--3 GHz), were used. At about of 0.2 mole fraction of 6CHBT the nonlinear dielectric increment becomes positive. With increasing of 6CHBT concentration the dynamics of the increment shows a critical-like behavior, which can be interpreted in terms of the reorientation of the growing pseudonematic domains in the solutions studied.

Dynamics of the nonlinear dielectric properties of a nematogenic compound dissolved in a nonpolar medium.

Results presented give evidence of the existence of quasicritical, fluidlike behavior in the isotropic phase of 4-cyano-4-pentyl-biphenyl (5CB) for frequencies ranging from the static to the ionic-dominated [low-frequency (LF)] region. Despite the boost of dielectric permittivity on lowering the frequency below 1 kHz, values of the isotropic-nematic transition discontinuity (approximately 1.1 K) and the critical exponent alpha (approximately 0.5) remain constant. It is shown that the contribution from residual ionic impurities is a linear function of temperature in the critical, prenematic fluctuation-dominated region. The validity of the fluidlike and critical behavior for LF dielectric permittivity confirmed results of a derivative analysis of the experimental data: d(epsilon)/dT proportional to (T-T*)(-alpha), originally proposed for critical mixtures. Results of a preliminary test in the isotropic phase of 4-decyl-4'-isothiocyanatobiphenyl (10BT), on approaching the smectic-E phase, may indicate a general validity of results obtained.

Quasicritical behavior of the low-frequency dielectric permittivity in the isotropic phase of liquid crystalline materials.

The dielectric relaxation spectroscopy is used for studying the orientational molecular dynamics in the isotropic (I) and nematic (N) phases of two mesogenic liquids composed of the molecules of similar structure and length, but of an essentially different polarity:  n-heptylcyanobiphenyl, C7H15PhPhCN, 7CB (molecular dipole moment μ ≈ 5D) and 4-(trans-4‘-n-hexylcyclohexyl)isothiocyanatobenzene, C6H13CyHxPhNCS, 6CHBT (μ ≈ 2.5D); advantageously, the temperatures of the I−N phase transition for the two compounds are very close to each other (TNI = 316.6 ± 0.2 K). It is shown that regardless of the differences in polarity of 7CB and 6CHBT molecules and their abilities in dipolar aggregation, the values and temperature dependences of the relaxation time (corresponding to the rotational diffusion of the molecules around their short axis) are very close to each other, in both the isotropic and nematic phases of the liquids studied. Therefore, the data show that the dielectric relaxation processes occurring in di...

Contribution to understanding of the molecular dynamics in liquids.

The impedance spectroscopy studies performed for two strongly hydrogen-bonded liquid amides: N-methylpropionamide (NMP, CH(3)·NH·CO·C(2)H(5)) and N-ethylacetamide (NEA, C(2)H(5)·NH·CO·CH(3)) have shown that the two centers of the peptide linkage, -NH·CO-, active in the C=OH-N hydrogen bonds formation, exhibit quite different sensibilities to the steric screening effects. In contrast to the oxygen atom, a relatively small change (CH(3)- to C(2)H(5)-) in the screening of the hydrogen atom leads to an essential decrease of the degree of the amide self-association. As a consequence, both the static dielectric permittivity and the orientational entropy increment of NEA are essentially lower than those of NMP. However, it was found that the dynamic processes studied are only weakly influenced (in the case of dc conductivity, σ(DC)) or totally not influenced (the dielectric relaxation time, τ(D)) by the different degrees of NMP and NEA self-association. The experiment shows that for both the amides, the logσ(DC) vs. logτ(D) dependence is nonlinear and can be described with the fractional Stokes-Einstein-Debye relation, σ(DC)τ ≅ const, with the exponent s varying from about -0.8 to about -0.6 in the temperature range from 5 °C to 110 °C.

Jan Jadżyn

Papers

Anisotropy of Static Electric Permittivity and Conductivity in Some Nematics and Smectics A

Dynamics of the nonlinear dielectric properties of a nematogenic compound dissolved in a nonpolar medium.

Quasicritical behavior of the low-frequency dielectric permittivity in the isotropic phase of liquid crystalline materials.

Contribution to understanding of the molecular dynamics in liquids.

Fractional Stokes–Einstein–Debye relation and orientational entropy effects in strongly hydrogen-bonded liquid amides