(570g) A Global Sensitivity Approach for the Analysis of Intracellular PI3K/AKT Signaling Pathway During Definitive Endoderm Induction of Human Embryonic Stem Cells

Introduction: Differentiation of human embryonic stem cells (hESCs) to the definitive endoderm lineage is an important step towards important functional cell types of the pancreas and liver. In vitrodifferentiation efforts are directed towards the activation of cellular signaling pathways which are active during embryonic development in vertebrates. As an important step in the chemical induction of definitive endoderm, modulation of the growth factor mediated PI3K/AKT pathway has been implicated in the control of the outcome of other pathways by making early fate decisions between the maintenance of pluripotency and initiation of differentiation [1]. Specifically, PI3K/AKT pathway suppresses the differentiation signals and sustains the undifferentiated state, while inhibition of the pathway results in up-regulation of Smad and Wnt signaling pathways [2]. Mathematical models can help in the formulation of informative experiments to identify the precise role of these interactions and the conditions under which the cell commits to a particular fate. However, by nature, stem cell systems exhibit intricate signaling pathways; and with the added uncertainty in physical parameters, mechanistic models are either incomplete or difficult to build. One possible solution to construct predictable models is to perform sensitivity analysis on models validated in other cellular contexts and identify regions of interest relating to an experimentally observed output. Given the multivariate nature of the problem, such a sensitivity analysis has to be global in approach to capture the nonlinear interactions between the system parameters.  The goal of our study was the use of global sensitivity analysis to design experiments to analyze the role of PI3K/AKT pathway following the induction of hESCs towards definitive endoderm.

Methods: IGF mediated activation of the PI3K/AKT pathway was analyzed using the model developed by Sedaghat et al [3]. The model encompasses receptor binding dynamics followed by activation of intracellular signaling cascade resulting in the phosphorylation of a key node in the pathway, i.e. AKT. The activation of Akt has been correlated to various phenotypic outcomes of the cell related to survival, differentiation, stemness, migration etc. We based our global sensitivity analysis on random sampling high dimensional model representation (RS-HDMR) developed by Rabitz et al [4]. The technique constructs a meta-model of the original signaling pathway and by using orthogonal function decomposition techniques, evaluates the well-known Sobol’ sensitivity indices of the  system input parameters to the model output. The advantage of using RS-HDMR lies in the reduction in number of random samples required (~10³ - 10⁴) to estimate the sensitivity indices as compared to computationally expensive brute-force Monte Carlo methods (> 10⁶). Through our analysis, we identified key rate parameters to which the phospho-Akt concentrations are sensitive to, in the presence and absence of feedback mechanisms. Our analysis revealed interesting behaviors of phopho-Akt and its functional dependence on the various system parameters. This knowledge was used to design an in vitro strategy to inhibit the PI3K/AKT pathway and study the phospho-Akt protein dynamics during the initial stages of differentiating hESCs.

Results: According to our sensitivity analysis, PTEN (phosphatase and tensin homolog), which is a negative regulator of the PI3K/AKT pathway and parameters associated with receptor activation were the most sensitive parameters in the absence of feedback. However, with feedback, the in silico phopho-Akt population segregated into high phospho-Akt and low phospho-Akt regions. RS-HDMR in each of these regions revealed differences in sensitive parameters, particularly to negative feedback loops which inhibit the ability of tyrosine phosphorylated IRS (Insulin receptor substrate) to complex with PI3K and activate downstream Akt. Interestingly, even after PI3K inhibition, our experiments showed increase in phospho-Akt in the initial stages of differentiation and Smad activation and it hints towards a possible cross-talk with other pathways like Smad and Wnt involved in differentiation which maintain higher phopho-Akt levels by modulation of the likely sensitive parameters. 

Conclusion: RS-HDMR with polynomial approximation was successful in identifying the most sensitive parameters in the insulin signaling pathway and compared well to the brute-force Monte Carlo estimates. Although different variants of RS-HDMR exist, our analysis proves that even simple orthonormal polynomial approximations can give accurate ranking of the sensitive parameters and often, such a ranking is what we seek to prioritize experimental resources to reducing the uncertainty of the sensitive inputs. Our integrated mathematical and experimental approach was successful in explaining the important parameters affecting the PI3K/AKT pathway in differentiating hESCs.

References

1.         McLean AB, D'Amour KA, Jones KL, Krishnamoorthy M, Kulik MJ, Reynolds DM, Sheppard AM, Liu H, Xu Y, Baetge EE: Activin A efficiently specifies definitive endoderm from human embryonic stem cells only when phosphatidylinositol 3-kinase signaling is suppressed. Stem Cells 2007, 25:29-38.

2.         Singh AM, Reynolds D, Cliff T, Ohtsuka S, Mattheyses AL, Sun Y, Menendez L, Kulik M, Dalton S: Signaling Network Crosstalk in Human Pluripotent Cells: A Smad2/3-Regulated Switch that Controls the Balance between Self-Renewal and Differentiation. Cell Stem Cell 2012, 10:312-326.

3.         Sedaghat AR, Sherman A, Quon MJ: A mathematical model of metabolic insulin signaling pathways. American Journal of Physiology-Endocrinology and Metabolism 2002, 283:E1084-E1101.

4.         Li G, Rosenthal C, Rabitz H: High dimensional model representations. The Journal of Physical Chemistry A 2001, 105:7765-7777.