Modeling metastatic progression from cross-sectional cancer genomics data.

MOTIVATION: Metastasis formation is a hallmark of cancer lethality. Yet, metastases are generally unobservable during their early stages of dissemination and spread to distant organs. Genomic datasets of matched primary tumors and metastases may offer insights into the underpinnings and the dynamics of metastasis formation. RESULTS: We present metMHN, a cancer progression model designed to deduce the joint progression of primary tumors and metastases using cross-sectional cancer genomics data. The model elucidates the statistical dependencies among genomic events, the formation of metastasis, and the clinical emergence of both primary tumors and their metastatic counterparts. metMHN enables the chronological reconstruction of mutational sequences and facilitates estimation of the timing of metastatic seeding. In a study of nearly 5000 lung adenocarcinomas, metMHN pinpointed TP53 and EGFR as mediators of metastasis formation. Furthermore, the study revealed that post-seeding adaptation is predominantly influenced by frequent copy number alterations. AVAILABILITY AND IMPLEMENTATION: All datasets and code are available on GitHub at https://github.com/cbg-ethz/metMHN.

Low-rank tensor methods for Markov chains with applications to tumor progression models.

Cancer progression can be described by continuous-time Markov chains whose state space grows exponentially in the number of somatic mutations. The age of a tumor at diagnosis is typically unknown. Therefore, the quantity of interest is the time-marginal distribution over all possible genotypes of tumors, defined as the transient distribution integrated over an exponentially distributed observation time. It can be obtained as the solution of a large linear system. However, the sheer size of this system renders classical solvers infeasible. We consider Markov chains whose transition rates are separable functions, allowing for an efficient low-rank tensor representation of the linear system's operator. Thus we can reduce the computational complexity from exponential to linear. We derive a convergent iterative method using low-rank formats whose result satisfies the normalization constraint of a distribution. We also perform numerical experiments illustrating that the marginal distribution is well approximated with low rank.

Modelling cancer progression using Mutual Hazard Networks.

MOTIVATION: Cancer progresses by accumulating genomic events, such as mutations and copy number alterations, whose chronological order is key to understanding the disease but difficult to observe. Instead, cancer progression models use co-occurrence patterns in cross-sectional data to infer epistatic interactions between events and thereby uncover their most likely order of occurrence. State-of-the-art progression models, however, are limited by mathematical tractability and only allow events to interact in directed acyclic graphs, to promote but not inhibit subsequent events, or to be mutually exclusive in distinct groups that cannot overlap. RESULTS: Here we propose Mutual Hazard Networks (MHN), a new Machine Learning algorithm to infer cyclic progression models from cross-sectional data. MHN model events by their spontaneous rate of fixation and by multiplicative effects they exert on the rates of successive events. MHN compared favourably to acyclic models in cross-validated model fit on four datasets tested. In application to the glioblastoma dataset from The Cancer Genome Atlas, MHN proposed a novel interaction in line with consecutive biopsies: IDH1 mutations are early events that promote subsequent fixation of TP53 mutations. AVAILABILITY AND IMPLEMENTATION: Implementation and data are available at https://github.com/RudiSchill/MHN. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

Scale-Invariant Biomarker Discovery in Urine and Plasma Metabolite Fingerprints.

Metabolomics data is typically scaled to a common reference like a constant volume of body fluid, a constant creatinine level, or a constant area under the spectrum. Such scaling of the data, however, may affect the selection of biomarkers and the biological interpretation of results in unforeseen ways. Here, we studied how both the outcome of hypothesis tests for differential metabolite concentration and the screening for multivariate metabolite signatures are affected by the choice of scale. To overcome this problem for metabolite signatures and to establish a scale-invariant biomarker discovery algorithm, we extended linear zero-sum regression to the logistic regression framework and showed in two applications to 1H NMR-based metabolomics data how this approach overcomes the scaling problem. Logistic zero-sum regression is available as an R package as well as a high-performance computing implementation that can be downloaded at https://github.com/rehbergT/zeroSum .

Approximation formula for complex spacing ratios in the Ginibre ensemble.

Recently, Sá, Ribeiro, and Prosen [Phys. Rev. X 10, 021019 (2020)10.1103/PhysRevX.10.021019] introduced complex spacing ratios to analyze eigenvalue correlations in non-Hermitian systems. At present there are no analytical results for the probability distribution of these ratios in the limit of large system size. We derive an approximation formula for the Ginibre universality class of random matrix theory which converges exponentially fast to the limit of infinite matrix size. We also give results for moments of the distribution in this limit.

Loss-Function Learning for Digital Tissue Deconvolution.

The gene expression profile of a tissue averages the expression profiles of all cells in this tissue. Digital tissue deconvolution addresses the following inverse problem: given the expression profile y of a tissue, what is the cellular composition c of that tissue? If X is a matrix whose columns are reference profiles of individual cell types, the composition c can be computed by minimizing ℒ ( y - X c ) for a given loss function ℒ . Current methods use predefined all-purpose loss functions. They successfully quantify the dominating cells of a tissue, while often falling short in detecting small cell populations. In this study we use training data to learn the loss function ℒ along with the composition c . This allows us to adapt to application-specific requirements such as focusing on small cell populations or distinguishing phenotypically similar cell populations. Our method quantifies large cell fractions as accurately as existing methods and significantly improves the detection of small cell populations and the distinction of similar cell types.

DTD: An R Package for Digital Tissue Deconvolution.

Digital tissue deconvolution (DTD) estimates the cellular composition of a tissue from its bulk gene-expression profile. For this, DTD approximates the bulk as a mixture of cell-specific expression profiles. Different tissues have different cellular compositions, with cells in different activation states, and embedded in different environments. Consequently, DTD can profit from tailoring the deconvolution model to a specific tissue context. Loss-function learning adapts DTD to a specific tissue context, such as the deconvolution of blood, or a specific type of tumor tissue. We provide software for loss-function learning, for its validation and visualization, and for applying the DTD models to new data.

Principles of Systems Biology, No. 31.

This month: selected work from the 2018 RECOMB meeting, organized by Ecole Polytechnique and held last April in Paris.

Wigner surmise for mixed symmetry classes in random matrix theory.

We consider the nearest-neighbor spacing distributions of mixed random matrix ensembles interpolating between different symmetry classes or between integrable and nonintegrable systems. We derive analytical formulas for the spacing distributions of 2×2 or 4×4 matrices and show numerically that they provide very good approximations for those of random matrices with large dimension. This generalizes the Wigner surmise, which is valid for pure ensembles that are recovered as limits of the mixed ensembles. We show how the coupling parameters of small and large matrices must be matched depending on the local eigenvalue density.

Overlap Dirac operator at nonzero chemical potential and random matrix theory.

We show how to introduce a quark chemical potential in the overlap Dirac operator. The resulting operator satisfies a Ginsparg-Wilson relation and has exact zero modes. It is no longer gamma5 Hermitian, but its nonreal eigenvalues still occur in pairs. We compute the spectral density of the operator on the lattice and show that, for small eigenvalues, the data agree with analytical predictions of non-Hermitian chiral random matrix theory for both trivial and nontrivial topology. We also explain an observed change in the number of zero modes as a function of chemical potential.

QCD dirac operator at nonzero chemical potential: lattice data and matrix model.

Recently, a non-Hermitian chiral random matrix model was proposed to describe the eigenvalues of the QCD Dirac operator at nonzero chemical potential. This matrix model can be constructed from QCD by mapping it to an equivalent matrix model which has the same symmetries as QCD with chemical potential. Its microscopic spectral correlations are conjectured to be identical to those of the QCD Dirac operator. We investigate this conjecture by comparing large ensembles of Dirac eigenvalues in quenched SU(3) lattice QCD at a nonzero chemical potential to the analytical predictions of the matrix model. Excellent agreement is found in the two regimes of weak and strong non-Hermiticity, for several different lattice volumes.