Biomolecular condensates undergirded by phase separations of proteins and nucleic acids serve crucial biological functions. To gain physical insights into their genetic basis, we study how liquid-liquid phase separation (LLPS) of intrinsically disordered proteins (IDPs) depends on their sequence charge patterns using a continuum Langevin chain model wherein each amino acid residue is represented by a single bead. Charge patterns are characterized by the "blockiness" measure κ and the "sequence charge decoration" (SCD) parameter. Consistent with random phase approximation (RPA) theory and lattice simulations, LLPS propensity as characterized by critical temperature T * cr increases with increasingly negative SCD for a set of sequences showing a positive correlation between κ and −SCD. Relative to RPA, the simulated sequence-dependent variation in T * cr is often-though not alwayssmaller, whereas the simulated critical volume fractions are higher. However, for a set of sequences exhibiting an anti-correlation between κ and −SCD, the simulated T * cr 's are quite insensitive to either parameters. Additionally, we find that blocky sequences that allow for strong electrostatic repulsion can lead to coexistence curves with upward concavity as stipulated by RPA, but the LLPS propensity of a strictly alternating charge sequence was likely overestimated by RPA and lattice models because interchain stabilization of this sequence requires spatial alignments that are difficult to achieve in real space. These results help delineate the utility and limitations of the charge pattern parameters and of RPA, pointing to further efforts necessary for rationalizing the newly observed subtleties.

No abstract

Intrinsically disordered proteins (IDPs) are important for biological functions. In contrast to folded proteins, molecular recognition among certain IDPs is "fuzzy" in that their binding and/or phase separation are stochastically governed by the interacting IDPs' amino acid sequences, while their assembled conformations remain largely disordered. To help elucidate a basic aspect of this fascinating yet poorly understood phenomenon, the binding of a homo or heterodimeric pair of polyampholytic IDPs is modeled statistical mechanically using cluster expansion. We find that the binding affinities of binary fuzzy complexes in the model correlate strongly with a newly derived simple "joint sequence charge decoration" parameter readily calculable from the pair of IDPs' sequence charge patterns. Predictions by our analytical theory are in essential agreement with coarse-grained explicit-chain simulations. This computationally efficient theoretical framework is expected to be broadly applicable to rationalizing and predicting sequence-specific IDP−IDP polyelectrostatic interactions.

Generative probabilistic modeling of biological sequences has widespread existing and potential use across biology and biomedicine, particularly given advances in high-throughput sequencing, synthesis and editing. However, we still lack methods with nucleotide resolution that are tractable at the scale of whole genomes and that can achieve high predictive accuracy either in theory or practice. In this article we propose a new generative sequence model, the Bayesian embedded autoregressive (BEAR) model, which uses a parametric autoregressive model to specify a conjugate prior over a nonparametric Bayesian Markov model. We explore, theoretically and empirically, applications of BEAR models to a variety of statistical problems including density estimation, robust parameter estimation, goodness-of-fit tests, and two-sample tests. We prove rigorous asymptotic consistency results including nonparametric posterior concentration rates. We scale inference in BEAR models to datasets containing tens of billions of nucleotides. On genomic, transcriptomic, and metagenomic sequence data we show that BEAR models provide large increases in predictive performance as compared to parametric autoregressive models, among other results. BEAR models offer a flexible and scalable framework, with theoretical guarantees, for building and critiquing generative models at the whole genome scale.

Generative probabilistic models of biological sequences have widespread existing and potential applications in analyzing, predicting and designing proteins, RNA and genomes. To test the predictions of such a model experimentally, the standard approach is to draw samples, and then synthesize each sample individually in the laboratory. However, often orders of magnitude more sequences can be experimentally assayed than can affordably be synthesized individually. In this article, we propose instead to use stochastic synthesis methods, such as mixed nucleotides or trimers. We describe a black-box algorithm for optimizing stochastic synthesis protocols to produce approximate samples from any target generative model. We establish theoretical bounds on the method’s performance, and validate it in simulation using held-out sequence-to-function predictors trained on real experimental data. We show that using optimized stochastic synthesis protocols in place of individual synthesis can increase the number of hits in protein engineering efforts by orders of magnitude, e.g. from zero to a thousand.

Understanding the consequences of mutation for molecular fitness and function is a fundamental problem in biology. Recently, generative probabilistic models have emerged as a powerful tool for estimating fitness from evolutionary sequence data, with accuracy sufficient to predict both laboratory measurements of function and disease risk in humans, and to design novel functional proteins. Existing techniques rest on an assumed relationship between density estimation and fitness estimation, a relationship that we interrogate in this article. We prove that fitness is not identifiable from observational sequence data alone, placing fundamental limits on our ability to disentangle fitness landscapes from phylogenetic history. We show on real datasets that perfect density estimation in the limit of infinite data would, with high confidence, result in poor fitness estimation; current models perform accurate fitness estimation because of, not despite, misspecification. Our results challenge the conventional wisdom that bigger models trained on bigger datasets will inevitably lead to better fitness estimation, and suggest novel estimation strategies going forward.