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Abstract:

Ruggedness—the prevalence of fitness peaks—and navigability—the existence of fitness-increasing paths to a target—are key factors affecting evolution on fitness landscapes. Here, we analyze these properties in landscapes that inherit biophysically grounded genotype–phenotype (GP) maps. By assuming a random phenotype-fitness assignment as a baseline, the structure of the GP maps is included without imposing further fitness correlations. We show analytically that the expected ruggedness can be predicted from two quantities: the sizes of neutral components (NCs)—mutationally connected genotype sets with the same phenotype—and their evolvabilities, defined as the number of distinct phenotypes among the NC’s mutational neighbors. Other features—such as robustness—influence ruggedness only indirectly via correlations with evolvability. Numerical results across diverse GP maps confirm that NC size and evolvability alone suffice to predict both the mean prevalence and heights of peaks. These calculations also provide new insights: Under random phenotype-fitness assignment, peaks arising from high-evolvability NCs have higher expected fitness than those from low-evolvability NCs. Thus, when evolvability correlates positively with NC size, the formation of large low-fitness peaks is impeded. We further derive an approximate scaling law for the minimal average evolvability required for navigability. Our framework applies broadly across GP maps, providing general insight into when and why fitness landscapes are expected to be rugged or navigable.

Abstract:

By linking genetic sequences to phenotypic traits, genotype-phenotype maps represent a key layer in biological organization. Their structure modulates the effects of genetic mutations which can contribute to shaping evolutionary outcomes. Recent work based on algorithmic information theory introduced an upper bound on the likelihood of a random genetic mutation causing a transition between two phenotypes, using only the conditional complexity between them. Here we evaluate how well this bound works for a range of genotype-phenotype maps, including a differential equation model for circadian rhythm, a matrix-multiplication model of gene regulatory networks, a developmental model of tooth morphologies for ringed seals, a polyomino-tile shape model of biological self-assembly, and the hydrophobic/polar (HP) lattice protein model. By assessing three levels of predictive performance, we find that the bound provides meaningful estimates of phenotype transition probabilities across these complex systems. These results suggest that transition probabilities can be predicted to some degree directly from the phenotypes themselves, without needing detailed knowledge of the underlying genotype-phenotype map.

Abstract:

DNA–RNA hybrid strand displacement underpins the function of many natural and engineered systems. Understanding and controlling factors affecting DNA–RNA strand displacement reactions is necessary to enable control of processes such as CRISPR-Cas9 gene editing. By combining multiscale modeling with strand displacement experiments, we show that the distribution of bases within the displacement domain has a very strong effect on reaction kinetics, a feature unique to DNA–RNA hybrid strand displacement. Merely by redistributing bases within a displacement domain of fixed base composition, we are able to design sequences whose reaction rates span more than four orders of magnitude. We extensively characterize this effect in reactions involving the invasion of dsDNA by an RNA strand, as well as the invasion of a hybrid duplex by a DNA strand. In all-DNA strand displacement reactions, we find a predictable but relatively weak sequence dependence, confirming that DNA–RNA strand displacement permits far more thermodynamic and kinetic control than its all-DNA counterpart. We show that oxNA, a recently introduced coarse-grained model of DNA–RNA hybrids, can reproduce trends in experimentally observed reaction rates. We also develop a simple kinetic model for predicting strand displacement rates. On the basis of these results, we argue that base distribution effects may play an important role in natural R-loop formation and in the function of the guide RNAs that direct CRISPR-Cas systems.