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The dynamics of biological processes are often modeled as systems of nonlinear ordinary differential equations (ODE). An important feature of nonlinear ODEs is that seemingly minor changes in initial conditions or parameters can lead to radically different behaviors. This is problematic because in general it is never possible to know/measure the precise state of any biological system due to measurement errors. The parameter synthesis problem is to identify sets of parameters (including initial conditions) for which a given system of nonlinear ODEs does not reach a given set of undesirable states. We present an efficient algorithm for solving this problem that combines sensitivity analysis with an efficient search over initial conditions. It scales to high-dimensional models and is exact if the given model is affine. We demonstrate our method on different models of the acute inflammatory response to bacterial infection, and identify initial conditions consistent with three biologically relevant outcomes.

Collective behavior involving distally separate regions in a protein is known to widely affect its function. In this paper, we present an online approach to study and characterize collective behavior in proteins as molecular dynamics simulations progress. Our representation of MD simulations as a stream of continuously evolving data allows us to succinctly capture spatial and temporal dependencies that may exist and analyze them efficiently using data mining techniques. By using multi-way analysis we identify (a) parts of the protein that are dynamically coupled, (b) constrained residues/ hinge sites that may potentially affect protein function and (c) time-points during the simulation where significant deviation in collective behavior occurred. We demonstrate the applicability of this method on two different protein simulations for barnase and cyclophilin A. For both these proteins we were able to identify constrained/ flexible regions, showing good agreement with experimental results and prior computational work. Similarly, for the two simulations, we were able to identify time windows where there were significant structural deviations. Of these time-windows, for both proteins, over 70% show collective displacements in two or more functionally relevant regions. Taken together, our results indicate that multi-way analysis techniques can be used to analyze protein dynamics and may be an attractive means to automatically track and monitor molecular dynamics simulations.

We introduce a model-based analysis technique for extracting and characterizing rhythmic expression profiles from genome-wide DNA microarray hybridization data. These patterns are clues to discovering rhythmic genes implicated in cell-cycle, circadian, and other biological processes. The algorithm, implemented in a program called RAGE (Rhythmic Analysis of Gene Expression), decouples the problems of estimating a pattern's periodicity and phase. Our algorithm is linear-time in frequency and phase resolution, an improvement over previous quadratic-time approaches. Unlike previous approaches, RAGE uses a true distance metric for measuring expression profile similarity, based on the Hausdorff distance. This results in better clustering of expression profiles for rhythmic analysis. The confidence of each frequency estimate is computed using Z-scores. We demonstrate that RAGE is superior to other techniques on synthetic and actual DNA microarray hybridization data. We also show how to replace the discretized phase search in our method with an exact (combinatorially precise) phase search, resulting in a faster algorithm with no complexity dependence on phase resolution.