Stochastic tunneling and metastable states during the somatic evolution of cancer

TL;DR

This paper provides a comprehensive analytical study of stochastic tunneling and metastable states during somatic evolution in cancer, extending understanding beyond advantageous mutants and highlighting the role of noise-driven escape from metastable states.

Contribution

It introduces a new analytical framework using WKB methods to describe fixation times in regimes with metastable states, surpassing previous models limited to advantageous mutants.

Findings

Identification of parameter regimes with long-lived metastable states

Validation of WKB method for fixation time calculations

Insights into mutation-selection balance in cancer evolution

Abstract

Tumors initiate when a population of proliferating cells accumulates a certain number and type of genetic and/or epigenetic alterations. The population dynamics of such sequential acquisition of (epi)genetic alterations has been the topic of much investigation. The phenomenon of stochastic tunneling, where an intermediate mutant in a sequence does not reach fixation in a population before generating a double mutant, has been studied using a variety of computational and mathematical methods. However, the field still lacks a comprehensive analytical description since theoretical predictions of fixation times are only available for cases in which the second mutant is advantageous. Here, we study stochastic tunneling in a Moran model. Analyzing the deterministic dynamics of large populations we systematically identify the parameter regimes captured by existing approaches. Our analysis also reveals fitness landscapes and mutation rates for which finite populations are found in long-lived metastable states. These are landscapes in which the final mutant is not the most advantageous in the sequence, and resulting metastable states are a consequence of a mutation-selection balance. The escape from these states is driven by intrinsic noise, and their location affects the probability of tunneling. Existing methods no longer apply. In these regimes it is the escape from the metastable states that is the key bottleneck; fixation is no longer limited by the emergence of a successful mutant lineage. We used the so-called Wentzel-Kramers-Brillouin method to compute fixation times in these parameter regimes, successfully validated by stochastic simulations. Our work fills a gap left by previous approaches and provides a more comprehensive description of the acquisition of multiple mutations in populations of somatic cells.