Simultaneous Inference of Cancer Pathways and Tumor Progression from Cross-Sectional Mutation Data

Abstract

Recent cancer sequencing studies provide a wealth of somatic mutation data from a large number of patients. One of the most intriguing and challenging questions arising from this data is to determine whether the temporal order of somatic mutations in a cancer follows any common progression. Since we usually obtain only one sample from a patient, such inferences are commonly made from cross-sectional data from different patients. This analysis is complicated by the extensive variation in the somatic mutations across different patients, variation that is reduced by examining combinations of mutations in various pathways. Thus far, methods to reconstruct tumor progression at the pathway level have restricted attention to known, a priori defined pathways.In this work we show how to simultaneously infer pathways and the temporal order of their mutations from cross-sectional data, leveraging on the exclusivity property of driver mutations within a pathway. We define the pathway linear progression model, and derive a combinatorial formulation for the problem of finding the optimal model from mutation data. We show that with enough samples the optimal solution to this problem uniquely identifies the correct model with high probability even when errors are present in the mutation data. We then formulate the problem as an integer linear program (ILP), which allows the analysis of datasets from recent studies with large numbers of samples. We use our algorithm to analyze somatic mutation data from three cancer studies, including two studies from The Cancer Genome Atlas (TCGA) on large number of samples on colorectal cancer and glioblastoma. The models reconstructed with our method capture most of the current knowledge of the progression of somatic mutations in these cancer types, while also providing new insights on the tumor progression at the pathway level.

Network-Based Method for Inferring Cancer Progression at the Pathway Level from Cross-Sectional Mutation Data

“…Vandin et al [20] introduced Pathway Linear Progression Model (PLPM) which was defined for an integer > 1 as an integer linear program problem of looking for * = ∈ ( ) ( , ), and showed that the problem is an NP-hard problem. To solve it more efficiently, we construct a weighted gene network based on exclusive degree between each pair of genes to simplify the relationships between the genes and to significantly reduce the computational complexity.…”

“…Second, how to detect driver pathways, which are frequently perturbed with a large number of tumor cells, and give rise to the product of tumorigenic properties, such as cell angiogenesis, proliferation or metastasis [1], [2], [3], [12], [13], [14], [15], [16], [17]. Third, how to determine temporal orders of the driver mutations in cancer patients [18], [19], [20], [21], [22]. The first question can usually be solved by comparing mutation frequencies across different individuals [6], [7], [8], [9], [10], [11].…”

“…However, it is almost impossible to obtain samples at multiple time-points from a single individual, therefore, it is difficult to answer the question about temporal progression and identify what mutations occur early in cancer progression [18], [19], [20], [21], [22]. One systematic approach to address the task is to identify mutually exclusive gene sets in cancer genomic data [1], [2], [3], [12], [13], [14], [15], [16], [23].…”

“…Several methods have been introduced to infer temporal progression of gene mutations from cross-sectional data [18], [19], [20], [25], [26], [27], [28]. Desper et al [25], [26] proposed a tree model inference algorithm based on the thought of maximum-weight which relates cancer progression to measurement on gains and losses of chromosomal regions in tumor cells.…”

“…The problem with these approaches is that cancers usually exhibit [2], [3], [12], [13], [14], [15], [16], [23] have indicated that driver mutations in the same pathway tend to be mutually exclusive, that is, most patients have no more than one mutation within the same pathway. Therefore, Vandin et al [20] introduced the exclusivity among mutations (genes) within the same pathway to infer cancer pathways and tumor progression from cross-sectional mutation data. They formulated the Pathway Linear Progression problem as an integer linear program.…”