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. 2016 Dec;204(4):1523-1539.
doi: 10.1534/genetics.116.193474. Epub 2016 Oct 21.

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

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Free PMC article

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

Daniel Nichol et al. Genetics. .
Free PMC article

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: bacterial persistence; bet-hedging; drug resistance; evolution; genotype–phenotype map.

Figures

Figure 1
Figure 1
Schematic representation of the CRN model for determining phenotypes from genotypes. The gene expression profiles (g) are assumed to be fixed for each genotype, and the dynamics of expression from the biological genotype (green dashed leftmost box) are ignored. These modeling assumptions allow us to explore the implications of network-intrinsic noise (purple dashed centered box) independently of gene-intrinsic noise.
Figure 2
Figure 2
Invasion probabilities for a single mutant with genotype corresponding to a probability p2 of producing phenotype A into a resident population with probability p1. The probabilities are calculated from Equations 6 and 7 with parameters wA=2.0, wB=1.01. Note that deleterious and neutral mutations cannot fix under our model of invasion dynamics; hence, invasion in the case p2p1 (above the antidiagonal of the plot) is impossible.
Figure 3
Figure 3
Example molecular switches as GP maps. Each column shows the characteristics of one of the four switches (DC, DCx, DCy, and AM) introduced in the main text. The first row shows the name, CRN structure, and precise definition of each switch. The second row shows stochastic trajectories of the number of molecule x in the system for four different simulations of each switch. The starting condition in all simulations is x=y=30, (b=0 for the AM network). Note that all of the switches are able to resolve to either of the stable conditions, x=60 or x=0, which correspond to the phenotypes A and B, respectively. Row three shows contour plots displaying the probability of switching to phenotype A for each possible initial condition with 0<x0,y060 and x0+y00 (b=0 for the AM switch). Contour lines show subspaces of genotype space of equal hedging probability for hedges equal to 0.1,0.2,,0.9.
Figure 4
Figure 4
The model for simulating treatment holidays. (A) The overall model consists of first determining a post-treatment holiday genotype, g, and then simulating drug treatment on a population with bet-hedging determined by that genotype. (B) The expected postholiday genotype is determined from the invasion probabilities π(g), which are, in turn, dependent on the molecular switch. (C) A stochastic death–birth process is used to determine an extinction time, text.
Figure 5
Figure 5
Redundancy results in bet-hedging that is robust to mutation. (A) Redundancy in the CRN implementing the DC switch maintains molecular switching when chemical species are deleted. Marked in red is the switching probability for initial conditions (20,30,30,20) before deletion (0), after the deletion of x (1), and after the deletion of x and y (2). Contour lines show initial conditions of equal switching behavior. (B) Redundancy in the CRN implementing the AM molecular switch. Switching is maintained if the species x, y and b are removed in any order. We omit the case where y is removed before x due to symmetry. (C) A molecular switch that can reduce to either AM or DC when specific reactions are inhibited.
Figure 6
Figure 6
GP mapping determines the dynamics of invasion. (A) The relationship between population genotype, x0, and average population fitness for each molecular switch. (B) Invasion probabilities for a new genotype x0+1 into a resident population of genotype x0. (C) Invasion probabilities for resident and invader genotypes.
Figure 7
Figure 7
Convergence dynamics through genotype and probability space for the GP maps defined by DC, DCx, DCy, and AM; 30 stochastic realizations of the evolutionary simulation through both genotype and probability space are shown for (A) the DCy switch, (B) the DC switch, (C) the DCx switch, and (D) the AM switch. Due to the rapid initial change in hedging probability for the DCx switch, the convergence dynamics are also shown on a restricted scale. As the probability of phenotype B rapidly approaches zero in the AM switch simulation but never converges, the dynamics are shown on a logarithmic scale. The expected convergence time for the DCy switch is marked in green, for the DC switch is marked in red, and for the DCx switch is marked in blue.
Figure 8
Figure 8
Treatment dynamics for populations endowed with the different switching networks after differing timescales of treatment holidays for a cytotoxic drug regime. Each histogram shows the distribution of extinction times over 2000 simulations of treatment in an individual-based model. The switch used as the GP map is shown as the column heading. The genotype and associated probability of phenotype A (shown inset to each subfigure) are determined by an evolutionary simulation of a treatment holiday for a timescale, measured in mutational events, determined by the row. The gray background (top row) indicates that no extinction occurred within the simulated 20,000 hr of treatment. The blue background indicates extinction times longer than a timeframe viable for an antibiotic treatment (240 hr), a green background (or inset star) indicates extinction times within this time frame.

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References

    1. Adkins S., Shabbir A., 2014. Biology, ecology and management of the invasive parthenium weed (Parthenium hysterophorus L.). Pest Manag. Sci. 70: 1023–1029. - PubMed
    1. Alto B. W., Lampman R. L., Kesavaraju B., Muturi E. J., 2013. Pesticide-induced release from competition among competing Aedes aegypti and Aedes albopictus (Diptera: Culicidae). J. Med. Entomol. 50: 1240–1249. - PubMed
    1. Angluin D., Aspnes J., Eisenstat D., 2008. A simple population protocol for fast robust approximate majority. Distrib. Comput. 21: 87–102.
    1. Balaban N. Q., Merrin J., Chait R., Kowalik L., Leibler S., 2004. Bacterial persistence as a phenotypic switch. Science 305: 1622–1625. - PubMed
    1. Balázsi G., van Oudenaarden A., Collins J. J., 2011. Cellular decision making and biological noise: from microbes to mammals. Cell 144: 910–925. - PMC - PubMed

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