Trends in Cancer
Volume 2, Issue 3, March 2016, Pages 144-158
Journal home page for Trends in Cancer

Review
Modeling Tumor Clonal Evolution for Drug Combinations Design

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Trends

Cancer is largely viewed as a clonal evolution process, and this view has implications on our understanding of tumor progression and occurrence of relapse.

Mathematical models from population genetics, evolutionary dynamics, and engineering are increasingly being used to study tumor dynamics during progression and in response to treatment.

Enabling technologies including next-generation sequencing are providing opportunities for high-resolution lineage tracing in clonal evolution experiments.

Mathematical models, combinatorial optimization, and engineering approaches are increasingly being used to complement experiments for rational design of drug combinations and drug scheduling.

Cancer is a clonal evolutionary process. This presents challenges for effective therapeutic intervention, given the constant selective pressure toward drug resistance. Mathematical modeling from population genetics, evolutionary dynamics, and engineering perspectives are being increasingly employed to study tumor progression, intratumoral heterogeneity, drug resistance, and rational drug scheduling and combinations design. In this review we discuss the promising opportunities that these interdisciplinary approaches hold for advances in cancer biology and treatment. We propose that quantitative modeling perspectives can complement emerging experimental technologies to facilitate enhanced understanding of disease progression and improved capabilities for therapeutic drug regimen designs.

Section snippets

Quantitative Approach To Study Tumor Evolution and Therapeutic Response

Recent data from tumor sequencing has increased attention on the broad relevance of intratumoral heterogeneity in cancer patients and their treatment. In light of these studies, the tumor biology field now more than ever regards cancer as an ongoing evolutionary process. As such, a systematic and comprehensive understanding of this malignancy and its dynamics will require capitalizing on quantitative methods from population genetics, evolution, and engineering. Several excellent reviews on

Tumor Clonal Evolution and Intratumoral Heterogeneity

The notion of cancer as a clonal evolutionary process dates to seminal work in 1976 by Nowell [13]. A key consequence of tumor clonal evolution is intratumoral heterogeneity – the founder clone develops successive alterations with fitness advantages subject to selection (see Glossary) forces (e.g., tumor progression, metastasis, and drug resistance). Heterogeneity in tumor cells across different regions was indeed observed by pathologists as early as the 1800s, based on cell morphology and

Quantitative Approaches to Modeling Clonal Evolution

Mathematical modeling of tumor development and metastasis has been the subject of comprehensive reviews periodically over the past decade 6, 29. Building on these, we will introduce here vital fundamental tools from population genetics [30] and evolutionary dynamics [31] as applied to cancer, and then move to emphasize a view of clonal evolution based on fitness landscapes and focus on relation to therapy. Mathematical studies of cancer began as early as the 1950s, from works by Nordling [32],

Fitness Landscapes

The mathematical models discussed thus far lack connection of genotype to phenotype, and of either or both to parameters characterizing ‘fitness’ of the population in a given environment (e.g., drug treatment condition). This can be accomplished via description of a fitness landscape (also known as adaptive landscape) 59, 60 – a mapping of a multidimensional genotype (and/or phenotype) space to its corresponding fitness. An idealized realization of this space may be seen in 3D (Figure 1A), with

Traversing the Fitness Landscape

Topology of landscapes is of particular importance because it provides information regarding evolutionary trajectories, predictability, or rate of adaptation. In particular, rugged landscapes (bearing multiple peaks and valleys) can occur as a result of sign epistasis, whereby the effects of a specific allele depend contextually on the genetic background at the other loci. This would cause particular paths along the fitness landscape to become inaccessible. Pathway inaccessibility in a rugged

Effects of Drug Treatment on Clonal Evolution

In parallel with the rising utility of NGS in studying intratumoral heterogeneity and tumor progression, analyses of matched biopsies of patients before and after drug treatment have also revealed extensive clonal dynamics. The mechanisms by which resistance/relapse occurs can be via (i) de novo mutations (e.g., genotoxic chemotherapy that induces mutagenesis), (ii) selection of a pre-existing resistant subclone with higher fitness, or (iii) tumor reduction and competitive release (whereby

Concluding Remarks

With our increased focus on viewing cancer through the evolutionary lens, we must necessarily equip ourselves with the quantitative tools from population genetics, evolutionary dynamics, and engineering to understand how cancer evolves and respond to treatment. We have presented here an overview of the quantitative approaches (Figure 2) that are becoming increasingly used in cancer research. Coupled with the enabling technology of high-throughput NGS, several themes are starting to emerge that

Acknowledgment

This work was supported by the Koch Institute Support (core) grant P30-CA14051 from the National Cancer Institute and the Integrative Cancer Biology Program grant U54-CA112967 (to M.T.H., D.A.L). B.Z. is supported by National Institutes of Health (NIH)/National Institute of General Medical Sciences (NIGMS) Interdepartmental Biotechnology Training Program 5T32GM008334.

Glossary

Control theory
studies the behavior of dynamical systems (e.g., electronics, mechanics, tumor population) in response to varying inputs, with the goal of developing ways to control the system and desired output responses.
Deterministic process
a deterministic process will always yield the same result given the same initial condition.
Epistasis
genetic interaction where the effect of one genetic alteration depends on the presence of one or more other alterations (genetic background).
Exponential growth

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