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Highly Similar Average Collateral Effect of Synonymous Mutations Across Alternative Reading Frames: A Potential Role In Evolvability

Stefan Wichmann

Stefan Wichmann

Technical University of MunichMunich, Germany
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Wichmann, Stefan
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Zachary Ardern

Zachary Ardern

  • Technical University of MunichMunich, Germany
  • Wellcome Sanger InstituteCambridge, United Kingdom
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Ardern, Zachary
  
Mar 17, 2023
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Article Category: Review
Published Online: Mar 17, 2023
Page range: 1 - 11
DOI: https://doi.org/10.2478/biocosmos-2023-0001
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© 2023 Stefan Wichmann et al., published by Sciendo
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Figure 1.

(A) The five alternative reading frames, named according to a shortened form of the schema used in Wei and Zhang (42). In this schema s = sense, a = antisense, and the number represents the codon position of the alternative frame that corresponds to position 1 in the reference frame; the relevant codon position numbers are underlined here. (B) Example of “collateral effects” in alternative frames following synonymous mutations in the reference frame. Variants at the nucleotide level and changes in amino acids encoded by alternative reading frames are shown in red and light yellow; the original amino acids encoded in the alternative frames are shown in blue.
(A) The five alternative reading frames, named according to a shortened form of the schema used in Wei and Zhang (42). In this schema s = sense, a = antisense, and the number represents the codon position of the alternative frame that corresponds to position 1 in the reference frame; the relevant codon position numbers are underlined here. (B) Example of “collateral effects” in alternative frames following synonymous mutations in the reference frame. Variants at the nucleotide level and changes in amino acids encoded by alternative reading frames are shown in red and light yellow; the original amino acids encoded in the alternative frames are shown in blue.

Figure 2.

(A) In this 2D representation of the model, sequence space is represented with circles corresponding to fitness peaks, and an initial distribution of sequences is represented as colored points. Each fitness peak is a symmetric cone with radius 0.2 in a normalized sequence space of size 1 x 1. The top right peak’s fitness value (height, H) is 160 and the lower left peak has H = 40. (B) Illustration of conservative and explorative mutations in the model—the most likely direction of conservative mutations is affected by whether the sequence (the point particle) is situated within a peak, while explorative mutations are not, and the magnitude of the conservative mutation step size is smaller than the magnitude of explorative mutation step size (i.e., se > sc).
(A) In this 2D representation of the model, sequence space is represented with circles corresponding to fitness peaks, and an initial distribution of sequences is represented as colored points. Each fitness peak is a symmetric cone with radius 0.2 in a normalized sequence space of size 1 x 1. The top right peak’s fitness value (height, H) is 160 and the lower left peak has H = 40. (B) Illustration of conservative and explorative mutations in the model—the most likely direction of conservative mutations is affected by whether the sequence (the point particle) is situated within a peak, while explorative mutations are not, and the magnitude of the conservative mutation step size is smaller than the magnitude of explorative mutation step size (i.e., se > sc).

Figure 3.

The standard deviation σD of mutation effect values (Dc) across all alternative frames calculated for 107 alternative codes. The position of the standard genetic code among the alternative code set is shown with the vertical red line (only 0.77% of other “block” codes have equivalent consistency across frames). This style of figure is standard in the code optimality literature.
The standard deviation σD of mutation effect values (Dc) across all alternative frames calculated for 107 alternative codes. The position of the standard genetic code among the alternative code set is shown with the vertical red line (only 0.77% of other “block” codes have equivalent consistency across frames). This style of figure is standard in the code optimality literature.

Figure 4.

The proportion P of all sequences in one of the two peaks or outside any peak across 8 × 105 mutation steps. The data was created from 100 sequences, sc = 0.001 and se = 0.01. A: With an approximately optimal value of pc = 0.9 most sequences eventually end up in the higher peak (H=160) with some stochastic fluctuations. B: When fewer mutations are conservative (pc = 0.78), sequences accumulate in the higher peak faster, but with larger stochastic fluctuations, and the population as a whole does not reach high fitness. The effect of other parameter values is shown in Figure 5.
The proportion P of all sequences in one of the two peaks or outside any peak across 8 × 105 mutation steps. The data was created from 100 sequences, sc = 0.001 and se = 0.01. A: With an approximately optimal value of pc = 0.9 most sequences eventually end up in the higher peak (H=160) with some stochastic fluctuations. B: When fewer mutations are conservative (pc = 0.78), sequences accumulate in the higher peak faster, but with larger stochastic fluctuations, and the population as a whole does not reach high fitness. The effect of other parameter values is shown in Figure 5.

Figure 5.

The average fitness value of 100 sequences after 8 × 105 mutations for different values of conservative mutation probability pc and explorative mutation step size se. The conservative mutation step size is fixed to sc = 0. 001. Fitness expectation values fall into three regions. In (I), sequences are retained in both peaks, in (II), sequences are restricted to the higher peak, and in (III), sequences are not retained in either peak. If we keep the average mutation effect size at a constant value (black line) we find almost the same functional relation between pc and se as that describing region (II) which optimizes the expected fitness.
The average fitness value of 100 sequences after 8 × 105 mutations for different values of conservative mutation probability pc and explorative mutation step size se. The conservative mutation step size is fixed to sc = 0. 001. Fitness expectation values fall into three regions. In (I), sequences are retained in both peaks, in (II), sequences are restricted to the higher peak, and in (III), sequences are not retained in either peak. If we keep the average mutation effect size at a constant value (black line) we find almost the same functional relation between pc and se as that describing region (II) which optimizes the expected fitness.

Summarized properties of the two types of evolutionary “step” within the model_

Mutation type Step size Biased toward higher fitness? Probability of this mutation
conservative sc Yes, if within a peak pc
explorative se No 1-pc
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