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Monotonicity of fitness landscapes and mutation rate control.

ABSTRACT: A common view in evolutionary biology is that mutation rates are minimised. However, studies in combinatorial optimisation and search have shown a clear advantage of using variable mutation rates as a control parameter to optimise the performance of evolutionary algorithms. Much biological theory in this area is based on Ronald Fisher's work, who used Euclidean geometry to study the relation between mutation size and expected fitness of the offspring in infinite phenotypic spaces. Here we reconsider this theory based on the alternative geometry of discrete and finite spaces of DNA sequences. First, we consider the geometric case of fitness being isomorphic to distance from an optimum, and show how problems of optimal mutation rate control can be solved exactly or approximately depending on additional constraints of the problem. Then we consider the general case of fitness communicating only partial information about the distance. We define weak monotonicity of fitness landscapes and prove that this property holds in all landscapes that are continuous and open at the optimum. This theoretical result motivates our hypothesis that optimal mutation rate functions in such landscapes will increase when fitness decreases in some neighbourhood of an optimum, resembling the control functions derived in the geometric case. We test this hypothesis experimentally by analysing approximately optimal mutation rate control functions in 115 complete landscapes of binding scores between DNA sequences and transcription factors. Our findings support the hypothesis and find that the increase of mutation rate is more rapid in landscapes that are less monotonic (more rugged). We discuss the relevance of these findings to living organisms.

SUBMITTER: Belavkin RV

PROVIDER: S-EPMC5061859 | biostudies-other | 2016 Dec

REPOSITORIES: biostudies-other

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Monotonicity of fitness landscapes and mutation rate control.

Belavkin Roman V RV Channon Alastair A Aston Elizabeth E Aston John J Krašovec Rok R Knight Christopher G CG

Journal of mathematical biology 20160412 6-7

A common view in evolutionary biology is that mutation rates are minimised. However, studies in combinatorial optimisation and search have shown a clear advantage of using variable mutation rates as a control parameter to optimise the performance of evolutionary algorithms. Much biological theory in this area is based on Ronald Fisher's work, who used Euclidean geometry to study the relation between mutation size and expected fitness of the offspring in infinite phenotypic spaces. Here we recons ...[more]

PMID: 27072124

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Project description:BACKGROUND: Tumorigenesis requires multiple genetic changes. Mutator mutations are mutations that increase genomic instability, and according to the mutator hypothesis, accelerate tumorigenesis by facilitating oncogenic mutations. Alternatively, repeated lineage selection and expansion without increased mutation frequency may explain observed cancer incidence. Mutator lineages also risk increased deleterious mutations, leading to extinction, thus providing another counterargument to the mutator hypothesis. Both selection and extinction involve changes in lineage fitness, which may be represented as "trajectories" through a "fitness landscape" defined by genetics and environment. METHODOLOGY/PRINCIPAL FINDINGS: Here I systematically analyze the relative efficiency of tumorigenesis with and without mutator mutations by evaluating archetypal fitness trajectories using deterministic and stochastic mathematical models. I hypothesize that tumorigenic mechanisms occur clinically in proportion to their relative efficiency. This work quantifies the relative importance of mutator pathways as a function of experimentally measurable parameters, demonstrating that mutator pathways generally enhance efficiency of tumorigenesis. An optimal mutation rate for tumor evolution is derived, and shown to differ from that for species evolution. CONCLUSIONS/SIGNIFICANCE: The models address the major counterarguments to the mutator hypothesis, confirming that mutator mechanisms are generally more efficient routes to tumorigenesis than non-mutator mechanisms. Mutator mutations are more likely to occur early, and to occur when more oncogenic mutations are required to create a tumor. Mutator mutations likely occur in a minority of premalignant lesions, but these mutator premalignant lesions are disproportionately likely to develop into malignant tumors. Tumor heterogeneity due to mutator mutations may contribute to therapeutic resistance, and the degree of heterogeneity of tumors may need to be considered when therapeutic strategies are devised. The model explains and predicts important biological observations in bacterial and mouse systems, as well as clinical observations.

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Monotonicity of fitness landscapes and mutation rate control.

Publications

Monotonicity of fitness landscapes and mutation rate control.

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