Non-canonical Activation of Akt in Serum-Stimulated Fibroblasts, Revealed by Comparative Modeling of Pathway Dynamics.

The dynamic behaviors of signaling pathways can provide clues to pathway mechanisms. In cancer cells, excessive phosphorylation and activation of the Akt pathway is responsible for cell survival advantages. In normal cells, serum stimulation causes brief peaks of extremely high Akt phosphorylation before reaching a moderate steady-state. Previous modeling assumed this peak and decline behavior (i.e., "overshoot") was due to receptor internalization. In this work, we modeled the dynamics of the overshoot as a tool for gaining insight into Akt pathway function. We built an ordinary differential equation (ODE) model describing pathway activation immediately upstream of Akt phosphorylation at Thr308 (Aktp308). The model was fit to experimental measurements of Aktp308, total Akt, and phosphatidylinositol (3,4,5)-trisphosphate (PIP3), from mouse embryonic fibroblasts with serum stimulation. The canonical Akt activation model (the null hypothesis) was unable to recapitulate the observed delay between the peak of PIP3 (at 2 minutes), and the peak of Aktp308 (at 30-60 minutes). From this we conclude that the peak and decline behavior of Aktp308 is not caused by PIP3 dynamics. Models for alternative hypotheses were constructed by allowing an arbitrary dynamic curve to perturb each of 5 steps of the pathway. All 5 of the alternative models could reproduce the observed delay. To distinguish among the alternatives, simulations suggested which species and timepoints would show strong differences. Time-series experiments with membrane fractionation and PI3K inhibition were performed, and incompatible hypotheses were excluded. We conclude that the peak and decline behavior of Aktp308 is caused by a non-canonical effect that retains Akt at the membrane, and not by receptor internalization. Furthermore, we provide a novel spline-based method for simulating the network implications of an unknown effect, and we demonstrate a process of hypothesis management for guiding efficient experiments.

SPEDRE: a web server for estimating rate parameters for cell signaling dynamics in data-rich environments.

Cell signaling pathways and metabolic networks are often modeled using ordinary differential equations (ODEs) to represent the production/consumption of molecular species over time. Regardless whether a model is built de novo or adapted from previous models, there is a need to estimate kinetic rate constants based on time-series experimental measurements of molecular abundance. For data-rich cases such as proteomic measurements of all species, spline-based parameter estimation algorithms have been developed to avoid solving all the ODEs explicitly. We report the development of a web server for a spline-based method. Systematic Parameter Estimation for Data-Rich Environments (SPEDRE) estimates reaction rates for biochemical networks. As input, it takes the connectivity of the network and the concentrations of the molecular species at discrete time points. SPEDRE is intended for large sparse networks, such as signaling cascades with many proteins but few reactions per protein. If data are available for all species in the network, it provides global coverage of the parameter space, at low resolution and with approximate accuracy. The output is an optimized value for each reaction rate parameter, accompanied by a range and bin plot. SPEDRE uses tools from COPASI for pre-processing and post-processing. SPEDRE is a free service at http://LTKLab.org/SPEDRE.

Systematic parameter estimation in data-rich environments for cell signalling dynamics.

MOTIVATION: Computational models of biological signalling networks, based on ordinary differential equations (ODEs), have generated many insights into cellular dynamics, but the model-building process typically requires estimating rate parameters based on experimentally observed concentrations. New proteomic methods can measure concentrations for all molecular species in a pathway; this creates a new opportunity to decompose the optimization of rate parameters. RESULTS: In contrast with conventional parameter estimation methods that minimize the disagreement between simulated and observed concentrations, the SPEDRE method fits spline curves through observed concentration points, estimates derivatives and then matches the derivatives to the production and consumption of each species. This reformulation of the problem permits an extreme decomposition of the high-dimensional optimization into a product of low-dimensional factors, each factor enforcing the equality of one ODE at one time slice. Coarsely discretized solutions to the factors can be computed systematically. Then the discrete solutions are combined using loopy belief propagation, and refined using local optimization. SPEDRE has unique asymptotic behaviour with runtime polynomial in the number of molecules and timepoints, but exponential in the degree of the biochemical network. SPEDRE performance is comparatively evaluated on a novel model of Akt activation dynamics including redox-mediated inactivation of PTEN (phosphatase and tensin homologue). AVAILABILITY AND IMPLEMENTATION: Web service, software and supplementary information are available at www.LtkLab.org/SPEDRE SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.