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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.

Abstract:

The remarkable performance of overparameterized deep neural networks (DNNs) must arise from an interplay between network architecture, training algorithms, and structure in the data. To disentangle these three components for supervised learning, we apply a Bayesian picture based on the functions expressed by a DNN. The prior over functions is determined by the network architecture, which we vary by exploiting a transition between ordered and chaotic regimes. For Boolean function classification, we approximate the likelihood using the error spectrum of functions on data. Combining this with the prior yields an accurate prediction for the posterior, measured for DNNs trained with stochastic gradient descent. This analysis shows that structured data, together with a specific Occam’s razor-like inductive bias towards (Kolmogorov) simple functions that exactly counteracts the exponential growth of the number of functions with complexity, is a key to the success of DNNs.