Models from experiments: combinatorial drug perturbations of cancer cells

Abstract

We present a novel method for deriving network models from molecular profiles of perturbed cellular systems. The network models aim to predict quantitative outcomes of combinatorial perturbations, such as drug pair treatments or multiple genetic alterations. Mathematically, we represent the system by a set of nodes, representing molecular concentrations or cellular processes, a perturbation vector and an interaction matrix. After perturbation, the system evolves in time according to differential equations with built-in nonlinearity, similar to Hopfield networks, capable of representing epistasis and saturation effects. For a particular set of experiments, we derive the interaction matrix by minimizing a composite error function, aiming at accuracy of prediction and simplicity of network structure. To evaluate the predictive potential of the method, we performed 21 drug pair treatment experiments in a human breast cancer cell line (MCF7) with observation of phospho-proteins and cell cycle markers. The best derived network model rediscovered known interactions and contained interesting predictions. Possible applications include the discovery of regulatory interactions, the design of targeted combination therapies and the engineering of molecular biological networks.

Optimization of drug combinations using Feedback System Control

“…In these models, the system is treated as a black box, and it does not require a complete characterization of the biological networks 37,38 . (iii) Model-based combinations in which biological measurements are used to build explicit models of a target network using simulations 39,40 . This approach seems to be one of the most successful in multidrug design.…”

An S-System Parameter Estimation Method (SPEM) for Biological Networks

“…(2) To tackle the problem of identifying a unique solution, we use structure error (Kikuchi et al, 2003;Liu and Wang, 2008;Nelander et al, 2008) to force sparsity (Kikuchi et al, 2003) (by setting an adjustable threshold for the kinetic orders and forcing all kinetic orders whose absolute value is smaller than the threshold to be zero), thus also making it a closer match to biological systems. This approach has been applied to other algorithms (Liu and Wang, 2008), although here we continue to optimize the structure during the regression process.…”

Combining Targeted Therapies: Practical Issues to Consider at the Bench and Bedside

“…An example is the use of a synthetic lethality paradigm, wherein cells are treated with an initial drug and a siRNA library is used to define potential targets for synergistic combinations. Alternatively, one can limit the plethora of possible empirical combinations by mathematical modeling, such as through directed discovery algorithms [50,51] in which second generation combinations are built upon the results of a first set of testing, and so on.…”

“…Application of novel techniques in a comprehensive approach, revealing the interrelations among targets and the mechanisms of action underlying cancer (systems biology) [51,84], may lead to comprehensive diagnostic tools (systems pathology) [85] and specific combinations of drugs (cocktails of monoclonal antibodies, RNA therapeutics, or others) in what has been called the actualization of personalized medicine. We know that momentum in the era of targeted therapy will continue to accelerate, bringing new hope to our patients with cancer and their families.…”