Evolution on distributive lattices

Beerenwinkel, Niko; Eriksson, Nicholas; Sturmfels, Bernd

doi:10.1016/j.jtbi.2006.03.013

Cited by 35 publications

(58 citation statements)

References 27 publications

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“…More general methods that include convergence describe the model in terms of probabilistic directed acyclic graphs, or Bayesian networks (Hjelm et al, 2006;Gerstung et al, 2009;Beerenwinkel and Sullivant, 2009;Beerenwinkel et al, 2006Beerenwinkel et al, , 2007Gerstung et al, 2011;Sakoparnig and Beerenwinkel, 2012;Shahrabi Farahani and Lagergren, 2013). These methods impose different restrictions on the model to limit the search space and to represent possible features of cancer progression.…”

Section: Previous Workmentioning

confidence: 99%

“…A number of methods for inferring temporal progression of mutations from cross-sectional data have been introduced (Desper et al, 2000(Desper et al, , 1999Beerenwinkel et al, 2005a,b;Rahnenführer et al, 2005;Tofigh et al, 2011;Hjelm et al, 2006;Gerstung et al, 2009;Beerenwinkel and Sullivant, 2009;Beerenwinkel et al, 2006Beerenwinkel et al, , 2007Gerstung et al, 2011;Sakoparnig and Beerenwinkel, 2012;Shahrabi Farahani and Lagergren, 2013) (see section 1.1). These methods consider models of increasing complexity for cancer progression: trees, mixtures of trees, and Bayesian network models with different constraints.…”

Section: Introduction Cmentioning

confidence: 99%

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

Raphael

Vandin

2014

Lecture Notes in Computer Science

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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.

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Section: Previous Workmentioning

confidence: 99%

Section: Introduction Cmentioning

confidence: 99%

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

Raphael

Vandin

2014

Lecture Notes in Computer Science

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“…(Perelson, 1999) and evolution, e.g. (Beerenwinkel et al, 2006) are based on the assumption of constant drug concentrations. Our results highlight the importance of drug pharmacokinetics, in the case of zidovudine on the delay of viral DNA chain completion.…”

Section: Discussionmentioning

confidence: 99%

Pharmacokinetic–pharmacodynamic relationship of NRTIs and its connection to viral escape: An example based on zidovudine

Kleist¹,

Huisinga²

2009

European Journal of Pharmaceutical Sciences

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In HIV disease, the mechanisms of drug-resistance are only poorly understood. Incomplete suppression of HIV by antiretroviral agents is suspected to be a main reason. The objective of this in silico study is to elucidate the pharmacokinetic origins of incomplete viral suppression, exemplified for zidovudine (AZT) as a representative of the key class of nucleoside reverse transcriptase inhibitors (NRTIs). AZT, like other NRTIs, exerts its main action through its intracellular triphoshate (AZT-TP) by competition with natural thymidine triphosphate. We developed a physiologically based pharmacokinetic (PBPK) model describing the intracellular pharmacokinetics of AZT anabolites and subsequently established the pharmacokinetic-pharmacodynamic relationship. The PBPK model has been validated against clinical data of different dosing schemes. We reduced the PBPK model to derive a simple threecompartment model for AZT and AZT-TP that can readily be used in population analysis of clinical trials. A novel machanistic, and for NRTIs generic effect model has been developed that incorporates the primary effect of AZT-TP and potential secondary effect of zidovudine monophosphate. The proposed models were used to analyze the efficacy and potential toxicity of different dosing schemes for AZT. Based on the mechanism of action of NRTIs, we found that drug heterogeneities due to temporal fluctuations can create a major window of unsuppressed viral replication. For AZT, this window was most pronounced for a 600mg/once daily dosing scheme, in which insufficient viral suppression was observed for almost half the dosing period.

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“…The parameters µ of the NI-CBN model were generated by drawing uniform random numbers r i , i = 1,...,|E | − 1, from the interval (−1,3), sorting them as −1 = r 0 < r 1 < ···< r |E |−1 < r |E | = 3, and setting µ g = r |g| . This defines a graded fitness landscape, i.e., the fitness (or phenotype) depends only on the number of mutations (Beerenwinkel et al, 2006). The runtime for fitting each model was between one minute and two hours on a standard PC.…”

Section: Simulation Studymentioning

confidence: 99%

“…Several statistical models have been proposed for this purpose, including Bayesian networks (Klingler and Brutlag, 1994, Deforche, Silander, Camacho, Grossman, Soares, Laethem, Kantor, Moreau, and Va n d a m m e , 2006, Poon, Lewis, Pond, and Frost, 2007) and dependency networks (Carlson, Brumme, Rousseau, Brumme, Matthews, Kadie, Mullins, Walker, Harrigan, Goulder, and Heckerman, 2008). Order constraints represent a specific type of dependency and a specialized Bayesian network model, called conjuctive Bayesian network (CBN), has been proposed that uses a partial order to represent these constraints (Beerenwinkel, Eriksson, and Sturmfels, 2006, Beerenwinkel and Sullivant, 2009, Gerstung, Baudis, Moch, and Beerenwinkel, 2009.…”

Section: Introductionmentioning

confidence: 99%

Learning Monotonic Genotype-Phenotype Maps

Beerenwinkel

Knupfer

Tresch³

2011

Statistical Applications in Genetics and Molecular Biology

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Evolutionary escape of pathogens from the selective pressure of immune responses and from medical interventions is driven by the accumulation of mutations. We introduce a statistical model for jointly estimating the dynamics and dependencies among genetic alterations and the associated phenotypic changes. The model integrates conjunctive Bayesian networks, which define a partial order on the occurrences of genetic events, with isotonic regression. The resulting genotypephenotype map is non-decreasing in the lattice of genotypes. It describes evolutionary escape as a directed process following a phenotypic gradient, such as a monotonic fitness landscape. We present efficient algorithms for parameter estimation and model selection. The model is validated using simulated data and applied to HIV drug resistance data. We find that the effect of many resistance mutations is non-linear and depends on the genetic background in which they occur.

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Evolution on distributive lattices

Cited by 35 publications

References 27 publications

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

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

Pharmacokinetic–pharmacodynamic relationship of NRTIs and its connection to viral escape: An example based on zidovudine

Learning Monotonic Genotype-Phenotype Maps

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