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Pancreatic Ductal Adenocarcinoma is among the leading causes of cancer related deaths globally due to its extreme difficulty to detect and treat. Recently, research focus has shifted to analyzing the microenvironment of pancreatic cancer to better understand its key molecular mechanisms. This microenvironment can be represented with a multi-scale model consisting of pancreatic cancer cells (PCCs), pancreatic stellate cells (PSCs), as well as cytokines and growth factors which are responsible for intercellular communication between the PCCs and PSCs. We have built a stochastic Boolean network (BN) model, validated by literature and clinical data, in which we probed for intervention strategies that force this gene regulatory network (GRN) from a diseased state to a healthy state. To do so, we implemented methods from phenotype control theory to determine a procedure for regulating specific genes within the microenvironment. We identify target genes and molecules such that the application of their control drives the GRN to the desired state by suppression (or expression) and disruption of specific signaling pathways that will eventually lead to the eradication of the cancer cells. After applying well studied control methods such as stable motifs, feedback vertex set, and computational algebra, we discovered that each produces a different set of control targets that are not necessarily minimal nor unique. Yet, we were able to gain more insight about the performance of each process and the overlap of targets discovered. Nearly every control set contains cytokines, KRas, and HER2/neu which suggests they are key players in the system’s dynamics. To that end, this model can be used to produce further insight into the complex biological system of pancreatic cancer with hopes of finding new potential targets.

Many processes in biology and medicine have been modeled using Markov decision processes which provides a rich algorithmic theory for model analysis and optimal control. An optimal control problem for stochastic discrete systems consists of deriving a control policy that dictates how the system will move from one state to another such that the probability of reaching a desired state is maximized. In this paper, we focus on the class of Markov decision processes that is obtained by considering stochastic Boolean networks equipped with control actions. Here, we study the effect of changes in model parameters on optimal control policies. Specifically, we conducted a sensitivity analysis on optimal control policies for a Boolean model of the T-cell large granular lymphocyte (\textit{T-LGL}). For this model, we quantified how the choice of propensity parameters impacts the effectiveness of the optimal policy and then we provide thresholds at which the effectiveness is guaranteed. We also examined the effect on the optimal control policies of the level of noise that is usually added for simulations. Finally, we studied the effect on changes in the propensity parameters on the time to absorption and the mixing time for a Boolean model of the Repressilator.

Pancreatic Ductal Adenocarcinoma (PDAC) is widely known for its poor prognosis because it is often diagnosed when the cancer is in a later stage. We built a model to analyze the microenvironment of pancreatic cancer in order to better understand the interplay between pancreatic cancer, stellate cells, and their signaling cytokines. Specifically, we have used our model to study the impact of inducing four common mutations: KRAS, TP53, SMAD4, and CDKN2A. After implementing the various mutation combinations, we used our stochastic simulator to derive aggressiveness scores based on simulated attractor probabilities and long-term trajectory approximations. These aggression scores were then corroborated with clinical data. Moreover, we found sets of control targets that are effective among common mutations. These control sets contain nodes within both the pancreatic cancer cell and the pancreatic stellate cell, including PIP3, RAF, PIK3 and BAX in pancreatic cancer cell as well as ERK and PIK3 pancreatic stellate cell. Many of these nodes were found to be differentially expressed among pancreatic cancer patients in the TCGA database. Furthermore, literature suggests that many of these nodes can be targeted by drugs currently in circulation. The results herein help provide a proof of concept in the path towards personalized medicine through a means of mathematical systems biology. All data and code used for running simulations, statistical analysis, and plotting is available on a GitHub repository at https://github.com/drplaugher/PCC_Mutations .