Towards a new age of virtual ADME/TOX and multidimensional drug discovery

With the continual pressure to ensure follow-up molecules to billiondollar blockbuster drugs, there is a hurdle in profitability and growth forpharmaceutical companies in the next decades. With each success and failurewe increasingly appreciate that a key to the success of synthesized moleculesthrough the research and development process is the possession of drug-likeproperties. These properties include an adequate bioactivity as well as adequatesolubility, an ability to cross critical membranes (intestinal and sometimesblood-brain barrier), reasonable metabolic stability and of course safety inhumans. Dependent on the therapeutic area being investigated it might also bedesirable to avoid certain enzymes or transporters to circumvent potentialdrug-drug interactions. It may also be important to limit the induction ofthese same proteins that can result in further toxicities. We have clearlymoved the assessment of in vitro absorption, distribution, metabolism, excretionand toxicity (ADME/TOX) parameters much earlier in the discovery organizationthan a decade ago with the inclusion of higher throughput systems. We are alsonow faced with huge amounts of ADME/TOX data for each molecule that needinterpretation and also provide a valuable resource for generating predictivecomputational models for future drug discovery. The present review aims toshow what tools exist today for visualizing and modeling ADME/TOX data, what toolsneed to be developed, and how both the present and future tools are valuable for virtualfiltering using ADME/TOX and bioactivity properties in parallel as a viable addition topresent practices.     

Representation of a Smooth Isometric Deformation of a Planar Material Region into a Curved Surface

We consider the problem of characterizing the smooth, isometric deformations of a planar material region identified with an open, connected subset \({\mathcal{D}}\) of two-dimensional Euclidean point space \(\mathbb{E}^{2}\) into a surface \({\mathcal{S}}\) in three-dimensional Euclidean point space \(\mathbb{E}^{3}\). To be isometric, such a deformation must preserve the length of every possible arc of material points on \({\mathcal{D}}\). Characterizing the curves of zero principal curvature of \({\mathcal{S}}\) is of major importance. After establishing this characterization, we introduce a special curvilinear coordinate system in \(\mathbb{E}^{2}\), based upon an à priori chosen pre-image form of the curves of zero principal curvature in \({\mathcal{D}}\), and use that coordinate system to construct the most general isometric deformation of \({\mathcal{D}}\) to a smooth surface \({\mathcal{S}}\). A necessary and sufficient condition for the deformation to be isometric is noted and alternative representations are given. Expressions for the curvature tensor and potentially nonvanishing principal curvature of \({\mathcal{S}}\) are derived. A general cylindrical deformation is developed and two examples of circular cylindrical and spiral cylindrical form are constructed. A strategy for determining any smooth isometric deformation is outlined and that strategy is employed to determine the general isometric deformation of a rectangular material strip to a ribbon on a conical surface. Finally, it is shown that the representation established here is equivalent to an alternative previously established by Chen, Fosdick and Fried (J. Elast. 119:335–350, 2015).     

Nonaqueous capillary electrophoresis method for the enantiomeric purity determination of S-timolol using heptakis(2,3-di-O-methyl-6-O-sulfo)-beta-cyclodextrin: validation using the accuracy profile strategy and estimation of uncertainty

Nonaqueous capillary electrophoresis (NACE) was successfully applied to the enantiomeric purity determination of S-timolol maleate using heptakis(2,3-di-O-methyl-6-O-sulfo)-beta-cyclodextrin (HDMS-beta-CD) as chiral selector. With a background electrolyte made up of a methanolic solution of 0.75 M formic acid, 30 mM potassium camphorsulfonate and containing 30 mM HDMS-beta-CD, the determination of 0.1% of R-timolol in S-timolol could be performed with an enantiomeric resolution of 8.5. Pyridoxine was selected as internal standard. The NACE method was then fully validated by applying a novel strategy using accuracy profiles. It is based on beta-expectation tolerance intervals for the total measurement error which includes trueness and intermediate precision. The uncertainty of measurements derived from beta-expectation tolerance intervals was estimated at each concentration level of the validation standards. To confirm the suitability of the developed and validated method, several real samples of S-timolol maleate containing R-timolol maleate at different concentrations were analysed and the results were compared to those obtained by liquid chromatography.     

LC method for the determination of R-timolol in S-timolol maleate: Validation of its ability to quantify and uncertainty assessment

This article presents the validation results of a chiral liquid chromatographic (LC) method previously developed for the quantitative determination of R-timolol in S-timolol maleate samples. A novel validation strategy based on the accuracy profiles was used to select the most appropriate regression model, to assess the method accuracy within well defined acceptance limits and to determine the limits of quantitation as well as the concentration range.The validation phase was completed by the investigation of the risk profiles of various acceptable regression models in order to ensure the risk of obtaining the future measurements outside the acceptance limits fixed a priori.On the other hand, the present paper also shows how data used in this validation approach can be used to estimate the measurement uncertainty. The uncertainty derived from β-expectation tolerance interval (), which is equal to the uncertainty of measurements as well as the expanded uncertainty (U_x) using a coverage factor k = 2 was estimated. The uncertainty estimates obtained from validation data were finally compared with those obtained from interlaboratory and robustness studies.     

Energetic and spectral properties of triple photon downconversion in a phase-matched KTiOPO4 crystal

We measured the spectrum and energy of infrared triple photons generated in a phase-matched KTiOPO4 crystal pumped by picosecond beams at 532 and 1662 nm. The experimental data are in good agreement with our model, taking into account the spectral linewidths of the incident beams as well as a parasitic Kerr effect.     

A deconvolution enhancement of the Navier–Stokes-αβ model

A deconvolution enhancement of the Navier–Stokes-αβ model for turbulent flow is introduced. The energy and energy-dissipation rate for the enhanced model are derived. It is also shown that the consistency error, relative to the Navier–Stokes equations, and the microscale of the enhanced model are less than those of the Navier–Stokes-αβ model. The proposed model is used to simulate the Taylor–Green vortex problem and results show a qualitatively improved representation of the mean-square vorticity when compared to the Navier–Stokes-αβ model. Numerical studies of the energy spectrum and the alignment between the vorticity and the eigenvectors of the stretching tensor for three-dimensional turbulent flows with Re = 200 are used to explore the utility of the model. A benchmark problem of a two-dimensional channel flow over a step for Re = 600 also indicates that this model can be applied to more general flows than those involving periodic boundary conditions.     

Observation of a non-adiabatic geometric phase for elastic waves

We report the experimental observation of a geometric phase for elastic waves in a waveguide with helical shape. The setup reproduces the experiment by Tomita and Chiao [A. Tomita, R.Y. Chiao, Phys. Rev. Lett. 57 (1986) 937–940, 2471] that showed first evidence of a Berry phase, a geometric phase for adiabatic time evolution, in optics. Experimental evidence of a non-adiabatic geometric phase has been reported in quantum mechanics. We have performed an experiment to observe the polarization transport of classical elastic waves. In a waveguide, these waves are polarized and dispersive. Whereas the wavelength is of the same order of magnitude as the helix’s radius, no frequency dependent correction is necessary to account for the theoretical prediction. This shows that in this regime, the geometric phase results directly from geometry and not from a correction to an adiabatic phase.     

A continuum mechanical theory for turbulence: a generalized Navier–Stokes-<Emphasis Type="Italic">α</Emphasis> equation with boundary conditions

We develop a continuum-mechanical formulation and generalization of the Navier–Stokes-α equation based on a recently developed framework for fluid-dynamical theories involving higher-order gradient dependencies. Our flow equation involves two length scales α and β. The first of these enters the theory through the specific free-energy α ²|D|², where D is the symmetric part of the gradient of the filtered velocity, and contributes a dispersive term to the flow equation. The remaining scale is associated with a dissipative hyperstress which depends linearly on the gradient of the filtered vorticity and which contributes a viscous term, with coefficient proportional to β ², to the flow equation. In contrast to Lagrangian averaging, our formulation delivers boundary conditions and a complete structure based on thermodynamics applied to an isothermal system. For a fixed surface without slip, the standard no-slip condition is augmented by a wall-eddy condition involving another length scale ℓ characteristic of eddies shed at the boundary and referred to as the wall-eddy length. As an application, we consider the classical problem of turbulent flow in a plane, rectangular channel of gap 2h with fixed, impermeable, slip-free walls and make comparisons with results obtained from direct numerical simulations. We find that α/β ~ Re ^0.470 and ℓ/h ~ Re ^−0.772, where Re is the Reynolds number. The first result, which arises as a consequence of identifying the specific free-energy with the specific turbulent kinetic energy, indicates that the choice β = α required to reduce our flow equation to the Navier–Stokes-α equation is likely to be problematic. The second result evinces the classical scaling relation η/L ~ Re ^−3/4 for the ratio of the Kolmogorov microscale η to the integral length scale L.