Selection pressure in alternative reading frames

Abstract

Overlapping genes are two protein-coding sequences sharing a significant part of the same DNA locus in different reading frames. Although in recent times an increasing number of examples have been found in bacteria the underlying mechanisms of their evolution are unknown. In this work we explore how selective pressure in a protein-coding sequence influences its overlapping genes in alternative reading frames. We model evolution using a time-continuous Markov process and derive the corresponding model for the remaining frames to quantify selection pressure and genetic noise. Our findings lead to the presumption that, once information is embedded in the reverse reading frame -2 (relative to the mother gene in +1) purifying selection in the protein-coding reading frame automatically protects the sequences in both frames. We also found that this coincides with the fact that the genetic noise measured using the conditional entropy is minimal in frame -2 under selection in the coding frame.

Figure 1. Transition Scheme.

Scheme of transitions in sequence direction on forward strand and in time direction.

Figure 2. Selection Pressure.

Estimation of nonsynonymous/synonymous rate ratio ω ^f for different parameter settings. In the left panel κ = 1.0, t = 1.0 and on the right panel we set κ = 5.0, t = 1.0. Protection of protein-coding frame +1 for ω<1 is directly coupled with a protection of reading frame −2.

Figure 3. Information Loss.

Conditional entropy for uniform input distribution over amino acids for different values of ω and κ = 1.0. On the left ω = 0.3, the protein-coding frame as well as frame −2 are protected, which results in a slower information loss than for the other reading frames. On the right ω = 3.0, we see the opposite scenario. At the black dotted line, half of the information is lost.

Figure 4. Sequence Similarity.

Mutual information for uniform input distribution over amino acids for different values of ω and κ = 1.0. On the left ω = 0.3, the amount of information transmitted over the channel is largest for the protected frames +1 and −2. On the right ω = 3.0, where those frames are not protected, the opposite holds.

Figure 5. Empirical Substitution Matrix.

Estimation of conditional entropy (left panel) and mutual information (right panel) for empirical codon substitution matrix P_ECM. A slower information loss for reading frames −2 is observed due to a protection of the protein-coding reading frame +1.