Methodologies for Quantitative Systems Pharmacology (QSP) Models: Design and Estimation.

With the increased interest in the application of quantitative systems pharmacology (QSP) models within medicine research and development, there is an increasing need to formalize model development and verification aspects. In February 2016, a workshop was held at Roche Pharma Research and Early Development to focus discussions on two critical methodological aspects of QSP model development: optimal structural granularity and parameter estimation. We here report in a perspective article a summary of presentations and discussions.

Challenges and opportunities with modelling and simulation in drug discovery and drug development.

The benefits of modelling and simulation at the pre-clinical stage of drug development can be realized through formal and realistic integration of data on physicochemical properties, pharmacokinetics, pharmacodynamics, formulation and safety. Such data integration and the powerful combination of physiologically based pharmacokinetic (PBPK) with pharmacokinetic-pharmacodynamic relationship (PK/PD) models provides the basis for quantitative outputs allowing comparisons across compounds and resulting in improved decision-making during the selection process. Such PBPK/PD evaluations provide crucial information on the potency and safety of drug candidates in vivo and the bridging of the PK/PD concept established during the pre-clinical phase to clinical studies. Modelling and simulation is required to address a number of key questions at the various stages of the drug-discovery and -development process. Such questions include the following. (1) What is the expected human PK profile for potential clinical candidate(s)? (2) Is this profile and its associated PD adequate for the given indication? (3) What is the optimal dosing schedule with respect to safety and efficacy? (4) Is a food effect expected? (5) How can formulation be improved and what is the potential benefit? (6) What is the expected variability and uncertainty in the predictions?

Analysis of actin dynamics at the leading edge of crawling cells: implications for the shape of keratocyte lamellipodia.

Leading edge protrusion is one of the critical events in the cell motility cycle and it is believed to be driven by the assembly of the actin network. The concept of dendritic nucleation of actin filaments provides a basis for understanding the organization and dynamics of the actin network at the molecular level. At a larger scale, the dynamic geometry of the cell edge has been described in terms of the graded radial extension model, but this level of description has not yet been linked to the molecular dynamics. Here, we measure the graded distribution of actin filament density along the leading edge of fish epidermal keratocytes. We develop a mathematical model relating dendritic nucleation to the long-range actin distribution and the shape of the leading edge. In this model, a steady-state graded actin distribution evolves as a result of branching, growth and capping of actin filaments in a finite area of the leading edge. We model the shape of the leading edge as a product of the extension of the actin network, which depends on actin filament density. The feedback between the actin density and edge shape in the model results in a cell shape and an actin distribution similar to those experimentally observed. Thus, we explain the stability of the keratocyte shape in terms of the self-organization of the branching actin network.

Steps, kinetic anisotropy, and long-wavelength instabilities in directional solidification.

We consider the effect of anisotropic interface kinetics on long-wavelength instabilities during the directional solidification of a binary alloy having a vicinal interface. Linear theory predicts that a planar solidification front is stabilized under the effect of anisotropy as long as the segregation coefficient is small enough, whereas a novel instability appears at high rates of solidification. Furthermore, the neutral stability curve, indicating the values of the principal control parameter (here the morphological number) for which the growth rate of a sinusoidal perturbation of a given wavelength changes its sign, is shown to have up to three branches, two of them combining to form an isola for certain values of the control parameters. We identify conditions for which linear stability theory predicts the instability of the planar interface to long-wavelength traveling waves. A number of distinguished limits provide evolution equations that describe the resulting dynamical behavior of the crystal-melt interface and generalize previous work by Sivashinsky, Brattkus, and Davis and Riley and Davis. Bifurcation analysis and numerical computations for the derived evolution equations show that the anisotropy is able to promote the tendency to supercritical bifurcation, and also leads to the development of strongly preferred interface orientations for finite-amplitude deformations.