A network modeling approach to elucidate drug resistance mechanisms and predict combinatorial drug treatments in breast cancer

Abstract

Background: Mechanistic models of within-cell signal transduction networks can explain how these networks integrate internal and external inputs to give rise to the appropriate cellular response. These models can be fruitfully used in cancer cells, whose aberrant decision-making regarding their survival or death, proliferation or quiescence can be connected to errors in the state of nodes or edges of the signal transduction network. Results: Here we present a comprehensive network, and discrete dynamic model, of signal transduction in breast cancer based on the literature of ER+, HER2+, and PIK3CA-mutant breast cancers. The network model recapitulates known resistance mechanisms to PI3K inhibitors and suggests other possibilities for resistance. The model also reveals known and novel combinatorial interventions that are more effective than PI3K inhibition alone. Conclusions: The use of a logic-based, discrete dynamic model enables the identification of results that are mainly due to the organization of the signaling network, and those that also depend on the kinetics of individual events. Network-based models such as this will play an increasing role in the rational design of high-order therapeutic combinations.

Control of Intracellular Molecular Networks Using Algebraic Methods

“…, ι −1 n (x n )) is a fixed point of F. In particular, we can now "extend" the discrete dynamical system F to a discrete dynamical system F : F n → F n without changing the dynamics of the original system. 7.2 An approach for deriving a polynomial dynamical system from a mixed-state dynamical system A common approach to representing mixed-state dynamical systems is to give Boolean expressions for when a certain node will attain a given value based on the state of the other nodes [56,37]. For example, in the signaling network model presented in [37], the rule for representing how E2F3 attains values 1 or 2 are shown in Table 4.…”

“…We note that there are several published control methods that do not rely on the PDS representation of discrete models, such as Stable Motifs [55], Feedback Vertex Sets [57], Minimal Hitting Sets [49,25], and several others [36,26,35,14,56]. Our method provides a flexible control framework that, for instance, allows for the identification of controllers for creating new (desired) steady states, a feature that other methods do not allow.…”

“…As our method uses polynomial algebra over a finite field, all network nodes need to take values in a common finite field, in particular, all nodes need to have the same number of possible values. In many published models, however, different nodes take on different numbers of states, and this number generally does not allow the imposition of a finite field structure (for which the number is required to be a power of a prime number); see, e.g., [37,56]. As part of the algorithm in this manuscript, we present a method to convert models with a general number of mixed discrete states into a model that satisfies the computational algebra requirements, without changing the model's steady states, and which is not equivalent to the well-known reduction to a Boolean network that adds new nodes to the network, as done in [56].…”

Exact calculation of stationary solution and parameter sensitivity analysis of stochastic continuous time Boolean models

“…Besides the calculation of the stationary solution for an individual set of parameters and initial conditions, ExaStoLog contains 16 other functions to visualize the results and to perform parameter sensitivity analysis Model nodes (dynamic) STG (Mb, density) calculation time Traynard et al (2016) 13 (12) 1.4Mb, 7e-4 0.35-0.6 sec Zañudo et al (2017) 20 (16) 237Mb, 7e-6 0.4-3 sec Cohen et al (2015) 20 (18) 297Mb, 8e-6 2.5-25sec Sahin et al (2009) 20 (19) 318Mb, 9e-6 2-19 sec Table 1: Boolean models analyzed in manuscript. Calculation time is for a single solution of one set of initial conditions and parameters, on a CENTOS computer with 8 cores (Intel(R) Xeon(R) CPU X5472 3.00GHz), without parallelization.…”

“…Because of the exact nature of the calculation, it is guaranteed to find all states of the stationary solutions and their probability values after convergence, eliminating the issue of choosing a sufficient amount of time and number of sample trajectories to reach convergence and all attractors of a model. We perform parameter sensitivity analysis and visualization of solutions and their dependence on parameters on a number of published Boolean models (Traynard et al, 2016;Zañudo et al, 2017;Sahin et al, 2009;Cohen et al, 2015) to explore how sensitive these models are to variations in transition rates.…”