Khanh N. Dinh Lab

The finite state projection (FSP) method has enabled us to solve the chemical master equation of some biological models that were considered out of reach not long ago. Since the original FSP method, much effort has gone into transforming it into an adaptive time-stepping algorithm as well as studying its accuracy. Some of the improvements include the multiple time interval FSP, the sliding windows, and most notably the Krylov-FSP approach. Our goal in this tutorial is to give the reader an overview of the current methods that build on the FSP.

Recent years have seen considerable work on inference about cancer evolution from mutations identified in cancer samples. Much of the modeling work has been based on classical models of population genetics, generalized to accommodate time-varying cell population size. Reverse-time, genealogical views of such models, commonly known as coalescents, have been used to infer aspects of the past of growing populations. Another approach is to use branching processes, the simplest scenario being the classical linear birth-death process. Inference from evolutionary models of DNA often exploits summary statistics of the sequence data, a common one being the so-called Site Frequency Spectrum (SFS). In a bulk tumor sequencing experiment, we can estimate for each site at which a novel somatic point mutation has arisen, the proportion of cells that carry that mutation. These numbers are then grouped into collections of sites which have similar mutant fractions. We examine how the SFS based on birth-death processes differs from those based on the coalescent model. This may stem from the different sampling mechanisms in the two approaches. However, we also show that despite this, they are quantitatively comparable for the range of parameters typical for tumor cell populations. We also present a model of tumor evolution with selective sweeps, and demonstrate how it may help in understanding the history of a tumor as well as the influence of data pre-processing. We illustrate the theory with applications to several examples from The Cancer Genome Atlas tumors.

Approximate Bayesian Computation (ABC) is a popular inference method when likelihoods are hard to come by. Practical bottlenecks of ABC applications include selecting statistics that summarize the data without losing too much information or introducing uncertainty, and choosing distance functions and tolerance thresholds that balance accuracy and computational efficiency. Recent studies have shown that ABC methods using random forest (RF) methodology perform well while circumventing many of ABC’s drawbacks. However, RF construction is computationally expensive for large numbers of trees and model simulations, and there can be high uncertainty in the posterior if the prior distribution is uninformative. Here we further adapt random forests to the ABC setting in two ways. The first exploits distributional random forests to provide a direct method for inferring the joint posterior distribution of parameters of interest, while the second describes a sequential Monte Carlo approach which updates the prior distribution iteratively to focus on the most likely regions in the parameter space. We show that the new methods can accurately infer posterior distributions for a wide range of deterministic and stochastic models in different scientific areas.

Cancer development is characterized by chromosomal instability, manifesting in frequent occurrences of different genomic alteration mechanisms ranging in extent and impact. Mathematical modeling can help evaluate the role of each mutational process during tumor progression, however existing frameworks can only capture certain aspects of chromosomal instability (CIN). We present CINner, a mathematical framework for modeling genomic diversity and selection during tumor evolution. The main advantage of CINner is its flexibility to incorporate many genomic events that directly impact cellular fitness, from driver gene mutations to copy number alterations (CNAs), including focal amplifications and deletions, missegregations and whole-genome duplication (WGD). We apply CINner to find chromosome-arm selection parameters that drive tumorigenesis in the absence of WGD in chromosomally unstable cancer types from the Pan-Cancer Analysis of Whole Genomes (PCAWG, n=718). We found that the selection parameters predict WGD prevalence among different chromosomally unstable tumors, hinting that the selective advantage of WGD cells hinges on their tolerance for aneuploidy and escape from nullisomy. Analysis of inference results using CINner across cancer types in The Cancer Genome Atlas (n=8207) further reveals that the inferred selection parameters reflect the bias between tumor suppressor genes and oncogenes on specific genomic regions. Direct application of CINner to model the WGD proportion and fraction of genome altered (FGA) in PCAWG uncovers the increase in CNA probabilities associated with WGD in each cancer type. CINner can also be utilized to study chromosomally stable cancer types, by applying a selection model based on driver gene mutations and focal amplifications or deletions (chronic lymphocytic leukemia in PCAWG, n=95). Finally, we used CINner to analyze the impact of CNA probabilities, chromosome selection parameters, tumor growth dynamics and population size on cancer fitness and heterogeneity. We expect that CINner will provide a powerful modeling tool for the oncology community to quantify the impact of newly uncovered genomic alteration mechanisms on shaping tumor progression and adaptation.

Recent evidence shows that despite considerable effort, currently available algorithms for estimating intra-tumor heterogeneity (ITH) remain limited. We developed DECODE (Deciphering Cancer Origin from DNA Evolution), a novel mutation clustering method that incorporates the impact of sample-specific sequencing coverage and mutation calling biases. On synthetic data, DECODE outperformed existing methods across multiple clonality metrics and accurately detected and characterized the neutral tail in the site frequency spectrum (SFS), which encodes the tumor’s ongoing expansion mode. In acute myeloid leukemia, accounting for the neutral tail enabled DECODE to yield more parsimonious clonal decompositions that align more closely with known subclonal dynamics that drive relapse. Applied to data from The Cancer Genome Atlas, DECODE not only detected a neutral SFS tail in most samples across tumor types but also uncovered a clinically meaningful link between ITH and survival in low-grade glioma. By jointly inferring clonality and expansion mode, DECODE provides two complementary and prognostically relevant readouts of tumor evolution from single tumor genomic samples.