Stochasticity in the Genotype-Phenotype Map: Implications for the Robustness and Persistence of Bet-Hedging

Abstract

Nongenetic variation in phenotypes, or bet-hedging, has been observed as a driver of drug resistance in both bacterial infections and cancers. Here, we study how bet-hedging emerges in genotype-phenotype (GP) mapping through a simple interaction model: a molecular switch. We use simple chemical reaction networks to implement stochastic switches that map gene products to phenotypes, and investigate the impact of structurally distinct mappings on the evolution of phenotypic heterogeneity. Bet-hedging naturally emerges within this model, and is robust to evolutionary loss through mutations to both the expression of individual genes, and to the network itself. This robustness explains an apparent paradox of bet-hedging-why does it persist in environments where natural selection necessarily acts to remove it? The structure of the underlying molecular mechanism, itself subject to selection, can slow the evolutionary loss of bet-hedging to ensure a survival mechanism against environmental catastrophes even when they are rare. Critically, these properties, taken together, have profound implications for the use of treatment-holidays to combat bet-hedging-driven resistant disease, as the efficacy of breaks from treatment will ultimately be determined by the structure of the GP mapping.KEYWORDS evolution; bet-hedging; genotype-phenotype map; bacterial persistence; drug resistance T REATMENT resistance in many diseases is driven by the pre-existence of resistant phenotypes within the population. Why such phenotypes coexist (with sensitive phenotypes), and persist in environments never exposed to drug treatment, remains a significant unanswered question. Phenotypic heterogeneity has been observed within isogenic populations of a number of organisms, and at many scales (Balázsi et al. 2011), from the unicellular-bacteria (Veening et al. 2008), fungi (Levy et al. 2012), or cancer cells (Gupta et al. 2011)-through insects (Danforth 1999Hopper 1999), plants (Childs et al. 2010), and even aspects of human development (Tonegawa 1983). Importantly, this intercellular variation has been observed even in homogeneous and constant environments, suggesting that aspects of organismal phenotype may be stochastically determined.In environments that fluctuate unpredictably, this phenomenon can serve as a survival mechanism by increasing the likelihood that at least some offspring are well-adapted to future environments. Thus, nongenetic, nonenvironmentallydriven variation in phenotypes has been termed bet-hedging, as a species diversifies the phenotypes within the population in order to "hedge its bets" against environmental change [see Seger (1987) for justification of this naming, and de Jong et al. (2011) for a discussion of what evolutionary phenomena can be considered bet-hedging]. Oscillatory environments are common in a range of ecological settings, including fluctuating climates, immune-pathogen interactions, or cyclic hypoxia within tumors, and the range of phenotypic traits that are thought to display stochastic determin...

Exploiting evolutionary steering to induce collateral drug sensitivity in cancer

“…For example, in a clonal cell line with no pre-existing resistance one would expect that all resistance dynamics are driven by drug tolerance followed by de novo resistance. This phenomenon is often described by bet-hedging dynamics 12 . This could be potentially studied with the presented platform, although one would expect different barcodes in different replicates, making the evolution highly stochastic.…”

“…Treatment resistance can also be polyclonal, with multiple distinct subclones harbouring different resistance mechanisms driving tumour progression, thus making resistance even harder to control 11 . In addition, drug-tolerant cancer cells or 'persistors' can survive and acquire de novo alterations that give rise to fully resistant subclones during or after treatment 12,13 . The emergence of pre-existing populations that prior to treatment are fitness neutral (or even deleterious) 14 and are positively selected by intervention can be recapitulated in the lab, as first demonstrated by the classic Luria-Delbruck experiment in bacteria 15 .…”

The contribution of evolutionary game theory to understanding and treating cancer

“…[36,113,114,119]. To be able to use the genotypic information obtained from ctDNA, we need to know the relationship between mutations and their phenotypic impact, i.e., the genotype-phenotype map [4,118]. To find out how to predict what genotype will eventually evolve to drive phenotypic resistance remains significant [55].…”

Persistence as an optimal hedging strategy

“…These strategies are akin to financial hedging, where diversifying an investment portfolio protects against economic uncertainty (3)(4)(5)(6). This similarity is widely acknowledged: parts of the biology and ecology literature refer to this phenomena as bet-hedging (2,5,(7)(8)(9). In this work, we introduce the concept of cellular hedging, where we explicitly model bacterial persistence using techniques from mathematical finance, including stochastic differential equations (SDEs) and stochastic optimal control theory.…”

“…Our goal is to develop a new framework for studying cellular hedging in response to environmental volatility by unifying the study of biological population dynamics with techniques financial mathematics. It is for this reason we use the term cellular hedging, instead of the term bet-hedging (2,5,(7)(8)(9). Despite the established importance of volatility in elucidating bacterial persistence, we find there is currently a scarcity of methods available to describe cellular hedging strategies under environmental volatility.…”