Integrin activation - the importance of a positive feedback

Integrins mediate cell adhesion and are essential receptors for the development and functioning of multicellular organisms. Integrin activation is known to require both ligand and talin binding and to correlate with cluster formation but the activation mechanism and precise roles of these processes are not yet resolved. Here mathematical modeling, with known experimental parameters, is used to show that the binding of a stabilizing factor, such as talin, is alone insufficient to enable ligand-dependent integrin activation for all observed conditions; an additional positive feedback is required.Comment: in press in Bulletin of Mathematical Biolog

Quantifier elimination by lazy model enumeration

We propose a quantifier elimination scheme based on nested lazy model enumeration through SMT-solving, and projections. This scheme may be applied to any logic that fulfills certain conditions; we illustrate it for linear real arithmetic. The quantifier elimination problem for linear real arithmetic is doubly exponential in the worst case, and so is our method. We have implemented it and benchmarked it against other methods from the literature

Determining the optimal size of small molecule mixtures for high throughput NMR screening

High-throughput screening (HTS) using NMR spectroscopy has become a common component of the drug discovery effort and is widely used throughout the pharmaceutical industry. NMR provides additional information about the nature of small molecule-protein interactions compared to traditional HTS methods. In order to achieve comparable efficiency, small molecules are often screened as mixtures in NMR-based assays. Nevertheless, an analysis of the efficiency of mixtures and a corresponding determination of the optimum mixture size (OMS) that minimizes the amount of material and instrumentation time required for an NMR screen has been lacking. A model for calculating OMS based on the application of the hypergeometric distribution function to determine the probability of a \u27hit\u27 for various mixture sizes and hit rates is presented. An alternative method for the deconvolution of large screening mixtures is also discussed. These methods have been applied in a high-throughput NMR screening assay using a small, directed library