Decoupling of the PI3K Pathway via Mutation Necessitates Combinatorial Treatment in HER2+ Breast Cancer

We report here on experimental and theoretical efforts to determine how best to combine drugs that inhibit HER2 and AKT in HER2+ breast cancers. We accomplished this by measuring cellular and molecular responses to lapatinib and the AKT inhibitors (AKTi) GSK690693 and GSK2141795 in a panel of 22 HER2+ breast cancer cell lines carrying wild type or mutant PIK3CA. We observed that combinations of lapatinib plus AKTi were synergistic in HER2+/PIK3CAmut cell lines but not in HER2+/PIK3CAwt cell lines. We measured changes in phospho-protein levels in 15 cell lines after treatment with lapatinib, AKTi or lapatinib + AKTi to shed light on the underlying signaling dynamics. This revealed that p-S6RP levels were less well attenuated by lapatinib in HER2+/PIK3CAmut cells compared to HER2+/PIK3CAwt cells and that lapatinib + AKTi reduced p-S6RP levels to those achieved in HER2+/PIK3CAwt cells with lapatinib alone. We also found that that compensatory up-regulation of p-HER3 and p-HER2 is blunted in PIK3CAmut cells following lapatinib + AKTi treatment. Responses of HER2+ SKBR3 cells transfected with lentiviruses carrying control or PIK3CAmut sequences were similar to those observed in HER2+/PIK3CAmut cell lines but not in HER2+/PIK3CAwt cell lines. We used a nonlinear ordinary differential equation model to support the idea that PIK3CA mutations act as downstream activators of AKT that blunt lapatinib inhibition of downstream AKT signaling and that the effects of PIK3CA mutations can be countered by combining lapatinib with an AKTi. This combination does not confer substantial benefit beyond lapatinib in HER2+/PIK3CAwt cells.

Here we describe the dynamical model used to explore AKT pathway activation in PIK3CA mutant and wild-type cell lines, as outlined in Main Text and shown in

Model
We consider the signaling species shown in Fig 5A in Main Text, namely ERBB, AKT and S6. We assume that PIK3CA mutants differ from the wild-type case in having an ERBB independent route to AKT phosphorylation; otherwise we assume a unified dynamical model, both with respect to network topology and kinetic parameters. We do not make any assumption about the identity of the species mediating the mutant-specific AKT activation; to allow for the possibility that the relevant species are not included in the RPPA assay, in the statistical formulation below we treat the corresponding variable as a latent variable. Specifically, we assume a species "M" activates AKT independently of ERBB, as shown in Fig 5A in Main Text. Note also that although the link is shown as between M and AKT, we do not assume that phosphorylation is direct, but rather that it may occur through intermediate steps that are not explicitly described in the model. In the same way, the links from ERBB to AKT and from AKT to S6 are not intended to describe direct influences. All model parameters are estimated from RPPA time-course data, using a Bayesian formulation described below. Our model is presented graphically in Fig 5A in Main Text. In particular we do not model regulation of ERBB, which rapidly phosphorylates upon stimulation. We also assume that the fractions of phosphorylated protein are small relative to total protein, so that total protein levels may be used as a proxy for unphosphorylated protein levels. Then, conditional on the total protein levels X remaining constant, we describe the dynamics of phosphorylated species X * using Michaelis-Menten kinetics (Kholodenko 2006, Leskovac 2003, Steijaert 2010. We allow for phosphatase-mediated dephosphorylation, but do not model the dynamics of phosphatases themselves. Inhibitors (here, AKTi and Lapatinib) are modeled as reducing kinase activity of their targets. For simplicity we assume both inhibitors have negligible off-target effects. However inhibition is not assumed to be perfect (in the sense of completely removing kinase activity of the target); rather, a proportion 0 ≤ α ≤ 1 of the kinase activity is allowed to remain after intervention. Inhibitor data are modeled using indicator functions, as [p-AKT] → α I(AKTi) [p-AKT] for example, where I(AKTi) = 1 if the AKT inhibitor is used, otherwise I(AKTi) = 0.
It has been observed that p-AKT levels increase under treatment with AKTi; indeed Engelman (2009) writes "AKT catalytic site inhibitors might not block AKT phosphorylation, and might increase its phosphorylation through loss of negative-feedback regulation of PI3K". We therefore introduce a simple linear feedback term γ[p-AKT] into the model for p-AKT dynamics. This term is abrogated for experiments in which AKTi has been used, since then the kinase ability of AKT is blocked by the inhibitor, thereby removing the feedback. Note that we do not directly model the full mechanism underlying the feedback; rather the feedback term is intended to capture the overall dynamical influence on AKT phosphorylation. This term is indicated as a feedback edge in the network model (Fig 5A in Main Text).
Collecting together our modelling assumptions produces a kinetic description of phosphorylation dynamics:

Statistical inference
We use a Bayesian approach to carry out inference for the model described above, using RPPA time course data (as described in the Main Text) to fit the model. Bayesian inference requires prior probability distributions p(θ) for model parameters θ. This distribution is updated in light of observed data to produce a posterior distribution p(θ|data) from which conclusions may be drawn. Below we present our prior specification and computational approach for obtaining the posterior distribution.

Data and noise model
. Different experiments are characterized by different cell lines and different drug treatments. Total proteins levels X E (t) at time t were approximated from data Y E using linear interpolation, so that We denote by X * (t, x * ) the solution, conditional upon X E as above, to Eqns. 1,2,3 at time t, subject to the initial (t = 0) phosphoprotein concentrations X * = x * .
RPPA measurements are known only up to proportionality; we therefore normalized each species to have unit mean expression, where the average is taken across all experiments E. RPPA measurement error induces an approximately log-normal distribution for the observations, for example log(Y i E ) ∼ N (log(X i E ), σ 2 I) where typical signal-to-noise ratio is σ −1 ≈ 10. (Here and henceforth we define log(v) to be the vector with ith component log(v i ).)

Bayesian formulation
Write θ = (V , K, α, γ) for all unknown parameters. Following Xu et al. (2010) we assume all processes occur on observable time scales, motivating weakly informative gamma priors V i ∼ Γ(a, b), K i ∼ Γ(c, d) where a = 2, b = 1/2000, c = 2, d = 1/2 were chosen to give prior means V i = 1/1000 a.u./sec, K i = 1 a.u.. (Here the shape, scale parametrization is used.) For the interventional effect we take a beta distribution α i ∼ β(e, f ), where e = 2, f = 5 are chosen to give a prior drug efficacy of α i ≈ 0.3, meaning that 70% of kinase activity is abrogated as a result of the drug treatment. The effect γ is assigned γ ∼ Γ(a, b) since the effect on phosphorylation of AKT under treatment with AKTi is of a similar magnitude to that of p-ERBB inhibition. Initial phosphoprotein concentrations x * are assumed a priori to be drawn from the empirical distribution of the protein-specific data, or rather, from a log-normal distribution log N (µ, Σ) with mean and covariance µ, Σ, fit to this data.
Inference then proceeds based on the random variable Y * |Y , x * , θ, using the relevant conditional densities collected together below: The notation Γ(V ; a, b) indicates that each component V i of V is independently distributed as Γ(a, b); we use similar notation for the beta distribution. Markov chain Monte Carlo was used to sample from the posterior distribution. We exploited log-normal Metropolis-Hastings parameter proposals within a blocking strategy, using standard diagnostics to test convergence.

Prediction of inhibition effects
As shown in Fig 5B in Main Text, we predicted the effect of ERBB and/or AKT inhibition by considering the equilibrium level of S6 phosphorylation as a function of Lapatinib and AKTi efficiency. This was done using maximum a posteriori parameter values obtained after Bayesian inference as described above.

Sensitivity analysis
In order to ensure our results were not exquisitely sensitive to the actual data or to the Bayesian statistical formulation, we repeated the prediction procedure of  (Fig 1) in suggesting that further data are required for precise identification of model parameters.