Quantum and Quantum-inspired Methods forde novoDiscovery of Altered Cancer Pathways

Abstract

The combinatorial calculations for de novo discovery of altered pathways in cancer cohorts involve both coverage (i.e. recurrence) and mutual exclusivity, and solving mutual exclusivity problems is NP-hard for classical computers. Advances in quantum computing systems and our classical, quantum-inspired algorithm GAMA (Graver Augmented Multi-seed Algorithm) motivated us to revisit methods for identifying altered pathways. Using different types of quantum and classical algorithms, we report novel formulations of the problem that are tailored to these new computational models. Our formulations require fewer binary variables than available methods, and offer a tuning parameter that allows a trade-off between coverage and exclusivity; varying this parameter returns a variety of solutions. We illustrate our formulations and methods with TCGA mutation data for Acute Myeloid Leukemia (AML). Both the D-Wave quantum annealing solver and the classical GAMA solver returned altered pathways that are known to be important in AML, with different tuning parameter values returning alternative altered pathways. Our reduced-variable algorithm and QUBO problem formulations demonstrate how quantum annealing-based binary optimization solvers can be used now in cancer genomics.

The Topology of Mutated Driver Pathways

“…Our topological journey departs from the (well trodden) path that recognized that signaling or regulatory pathways can be viewed as independent sets (modulo some notion of tolerance) in a matrix with rows as patients and columns as genes, which is used in determining new pathways via different computational methods (see our companion paper [1] and previous works [21,22,5,18,10]). Our key insight is that these pathways (however discovered), when grouped together, define a simplicial complex which is, pictorially, a polytope with faces given by those pathways.…”

“…We have applied our approach to two mutation data (formulations and algorithms are available in [1]): Acute myeloid leukemia [14] and Glioblastoma multiforme [13]. For both data, we have computed the assignment tumor → pathways through persistent pathway complexes (thus, declared robust output).…”

“…Sample ID Pathways Cyto 0 0, 1,2,6,8,11,12,13,15,16,18,19,23,24,25,27,28,29,30,31,33,35,40,41,42,51,52 , 53 Good 1 0, 1, 2 , 7, 8, 11, 12, 13, 14, 17, 18, 20, 21, 22, 23, 30, 33, 36, 37, 40, 53 , 54 Good 2 0, 1, 2, 3 , 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 16, 17, 18, 19, 20, 21, 22, 23, 26, 36, 41, 43, 44, 45, 46, 47, 48, 50 , 58 Good 3 0, 1, 2, 3 , 5, 6, 7, 8, 9, 11, 12, 13, 14, 16, 17, 18, 20, 21, 22, 26, 36, 41, 43, 44, 45, 47, 48, 50 , 58 Good 4 0, 1, 2, 3 , 5, 6, 8, 10, 11, 12, 13, 15, 16, 18, 19, 23, 24, 25, 27, 28, 29, 30, 31, 33, 35, 40, 41, 42, 43, 44, 45, 46, 50, 51, 52, 53, 57, 58, 63 , 64 Good 5 0, 1, 2 , 4, 6, 8, 10, 11, 12, 13, 15, 16, 18, 19, 23, 24, 25, 27, 28, 29, 30, 31, 33, 35, 40, 41, 42, 51, 52 , 53 Good 6 0, 1, 2, 3 , 5, 6, 7, 8, 9, 11, 12, 13, 14, 15, 16, 17, 18, 20, 21, 22, 26, 27, 30, 31, 33, 36, 37, 41, 43, 44, 45, 47, 48, 50, 51, 53, 57, 58, 61 , 64 Good 7 0, 1, 2, 3 , 5, 6, 7, 8, 9, 10, 11, 12, 13, 14,...…”

“…Since the advent of DNA sequencing technologies, our understanding has progressed enormously and resulted in useful therapies. 1 Notwithstanding the above, cancer morbidity is still very high and our understanding is still incomplete. Certainly, finding more relevant pathways will be helpful.…”

“…We also believe that to start building a house it is not enough to simply accumulate more stones faster. To that end, 1 Current advances include the introduction of a single anti-cancer agents, which simply bind with growth factor receptors stopping abnormal cell proliferations. For instance, in the context of breast cancer, Herceptin antibody stops cells abnormal proliferation signals by binding with the excess of growth factor receptors on the cell surface caused by point mutations in the gene Her2.…”