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The problem of reconstructing and identifying intracellular protein signalingand biochemical networks is of critical importance in biology today. We soughtto develop a mathematical approach to this problem using, as a test case, oneof the most well-studied and clinically important signaling networks in biologytoday, the epidermal growth factor receptor (EGFR) driven signaling cascade.More specifically, we suggest a method, augmented sparse reconstruction, forthe identification of links among nodes of ordinary differential equation (ODE)networks from a small set of trajectories with different initial conditions.Our method builds a system of representation by using a collection of integralsof all given trajectories and by attenuating block of terms in therepresentation itself. The system of representation is then augmented withrandom vectors, and minimization of the 1-norm is used to find sparserepresentations for the dynamical interactions of each node. Augmentation byrandom vectors is crucial, since sparsity alone is not able to handle the largeerror-in-variables in the representation. Augmented sparse reconstructionallows to consider potentially very large spaces of models and it is able todetect with high accuracy the few relevant links among nodes, even whenmoderate noise is added to the measured trajectories. After showing theperformance of our method on a model of the EGFR protein network, we sketchbriefly the potential future therapeutic applications of this approach.

Augmented Sparse Reconstruction of Protein Signaling Networks