Publications

Over the past decade, the Rosetta biomolecular modeling suite has informed diverse biological questions and engineering challenges ranging from interpretation of low-resolution structural data to design of nanomaterials, protein therapeutics, and vaccines. Central to Rosetta’s success is the energy function: a model parametrized from small-molecule and X-ray crystal structure data used to approximate the energy associated with each biomolecule conformation. This paper describes the mathematical models and physical concepts that underlie the latest Rosetta energy function, called the Rosetta Energy Function 2015 (REF15). Applying these concepts, we explain how to use Rosetta energies to identify and analyze the features of biomolecular models. Finally, we discuss the latest advances in the energy function that extend its capabilities from soluble proteins to also include membrane proteins, peptides containing noncanonical amino acids, small molecules, carbohydrates, nucleic acids, and other macromolecules.

We study the relaxation dynamics of photocarriers in the paramagnetic Mott insulating phase of the half-filled two-band Hubbard model. Using nonequilibrium dynamical mean-field theory, we excite charge carriers across the Mott gap by a short hopping modulation, and simulate the evolution of the photodoped population within the Hubbard bands. We observe an ultrafast charge-carrier relaxation driven by the emission of local spin excitations with an inverse relaxation time proportional to the Hund's coupling. The photodoping generates additional side-bands in the spectral function, and for strong Hund's coupling, the photodoped population also splits into several resonances. The dynamics of the local many-body states reveals two effects, thermal blocking and kinetic freezing, which manifest themselves when the Hund's coupling becomes of the order of the temperature or the bandwidth, respectively. These effects, which are absent in the single-band Hubbard model, should be relevant for the interpretation of experiments on correlated materials with multiple active orbitals. In particular, the features revealed in the nonequilibrium energy distribution of the photocarriers are experimentally accessible, and provide information on the role of the Hund's coupling in these materials.

Standard approaches to Bayesian parameter inference in large-scale structure assume a Gaussian functional form (chi-squared form) for the likelihood. This assumption, in detail, cannot be correct. Likelihood free inferences such as approximate Bayesian computation (ABC) relax these restrictions and make inference possible without making any assumptions on the likelihood. Instead ABC relies on a forward generative model of the data and a metric for measuring the distance between the model and data. In this work, we demonstrate that ABC is feasible for LSS parameter inference by using it to constrain parameters of the halo occupation distribution (HOD) model for populating dark matter haloes with galaxies. Using specific implementation of ABC supplemented with population Monte Carlo importance sampling, a generative forward model using HOD and a distance metric based on galaxy number density, two-point correlation function and galaxy group multiplicity function, we constrain the HOD parameters of mock observation generated from selected ‘true' HOD parameters. The parameter constraints we obtain from ABC are consistent with the ‘true' HOD parameters, demonstrating that ABC can be reliably used for parameter inference in LSS. Furthermore, we compare our ABC constraints to constraints we obtain using a pseudo-likelihood function of Gaussian form with MCMC and find consistent HOD parameter constraints. Ultimately, our results suggest that ABC can and should be applied in parameter inference for LSS analyses.

The instant invention provides methods and related compositions for identifying polypeptides with improved stability and/or enzymatic activity in comparison to native forms, wherein the identified polypeptides comprise one or more non-natural amino acids. In certain embodiments, the present invention relates to novel phosphotriesterase enzymes comprising one or more non-natural amino acids. In a particular embodiment, the instant invention provides novel phosphotriesterase enzymes with greater stability and/or enhanced activity in comparison to native forms of the enzyme. The present invention also relates to compositions comprising novel phophotriesterase enzymes, such as prophylactics, decontaminants, animal feedstocks, and assay kits.

Given sparse or low-quality radial-velocity measurements of a star, there are often many qualitatively different stellar or exoplanet companion orbit models that are consistent with the data. The consequent multimodality of the likelihood function leads to extremely challenging search, optimization, and MCMC posterior sampling over the orbital parameters. Here we create a custom Monte Carlo sampler for sparse or noisy radial-velocity measurements of two-body systems that can produce posterior samples for orbital parameters even when the likelihood function is poorly behaved. The six standard orbital parameters for a binary system can be split into four non-linear parameters (period, eccentricity, argument of pericenter, phase) and two linear parameters (velocity amplitude, barycenter velocity). We capitalize on this by building a sampling method in which we densely sample the prior pdf in the non-linear parameters and perform rejection sampling using a likelihood function marginalized over the linear parameters. With sparse or uninformative data, the sampling obtained by this rejection sampling is generally multimodal and dense. With informative data, the sampling becomes effectively unimodal but too sparse: in these cases we follow the rejection sampling with standard MCMC. The method produces correct samplings in orbital parameters for data that include as few as three epochs. The Joker can therefore be used to produce proper samplings of multimodal pdfs, which are still informative and can be used in hierarchical (population) modeling. We give some examples that show how the posterior pdf depends sensitively on the number and time coverage of the observations and their uncertainties.

Modeling self-organization of neural networks for unsupervised learning using Hebbian and anti-Hebbian plasticity has a long history in neuroscience. Yet, derivations of single-layer networks with such local learning rules from principled optimization objectives became possible only recently, with the introduction of similarity matching objectives. What explains the success of similarity matching objectives in deriving neural networks with local learning rules? Here, using dimensionality reduction as an example, we introduce several variable substitutions that illuminate the success of similarity matching. We show that the full network objective may be optimized separately for each synapse using local learning rules both in the offline and online settings. We formalize the long-standing intuition of the rivalry between Hebbian and anti-Hebbian rules by formulating a min-max optimization problem. We introduce a novel dimensionality reduction objective using fractional matrix exponents. To illustrate the generality of our approach, we apply it to a novel formulation of dimensionality reduction combined with whitening. We confirm numerically that the networks with learning rules derived from principled objectives perform better than those with heuristic learning rules.

We present a hierarchical probabilistic model for improving geometric stellar distance estimates using color--magnitude information. This is achieved with a data driven model of the color--magnitude diagram, not relying on stellar models but instead on the relative abundances of stars in color--magnitude cells, which are inferred from very noisy magnitudes and parallaxes. While the resulting noise-deconvolved color--magnitude diagram can be useful for a range of applications, we focus on deriving improved stellar distance estimates relying on both parallax and photometric information. We demonstrate the efficiency of this approach on the 1.4 million stars of the Gaia TGAS sample that also have APASS magnitudes. Our hierarchical model has 4~million parameters in total, most of which are marginalized out numerically or analytically. We find that distance estimates are significantly improved for the noisiest parallaxes and densest regions of the color--magnitude diagram. In particular, the average distance signal-to-noise ratio and uncertainty improve by 19~percent and 36~percent, respectively, with 8~percent of the objects improving in SNR by a factor greater than 2. This computationally efficient approach fully accounts for both parallax and photometric noise, and is a first step towards a full hierarchical probabilistic model of the Gaia data.

The proper positioning of mitotic spindle in the single-cell Caenorhabditis elegans embryo is achieved initially by the migration and rotation of the pronuclear complex (PNC) and its two associated astral microtubules (MTs). Pronuclear migration produces global cytoplasmic flows that couple the mechanics of all microtubules, the PNC, and the cell periphery with each other through their hydrodynamic interactions (HIs). We present the first computational study that explicitly accounts for detailed HIs between the cytoskeletal components and demonstrate the key consequences of HIs on the mechanics of pronuclear migration. First we show that, because of HIs between the MTs, the cytoplasm-filled astral MTs behave like a porous medium with its permeability decreasing with increasing the number of MTs. We then directly study the dynamics of PNC migration under various force-transduction models, including the pushing or pulling of MTs at the cortex, and the pulling of MTs by cytoplasmically-bound force generators. While achieving proper position and orientation on reasonable time-scales does not uniquely choose a model, we find that each model produces a different signature in its induced cytoplasmic flow. We suggest then that cytoplasmic flows can be used to differentiate between mechanisms.

Cerebellar granule cells, which constitute half the brain's neurons, supply Purkinje cells with contextual information necessary for motor learning, but how they encode this information is unknown. Here we show, using two-photon microscopy to track neural activity over multiple days of cerebellum-dependent eyeblink conditioning in mice, that granule cell populations acquire a dense representation of the anticipatory eyelid movement. Initially, granule cells responded to neutral visual and somatosensory stimuli as well as periorbital airpuffs used for training. As learning progressed, two-thirds of monitored granule cells acquired a conditional response whose timing matched or preceded the learned eyelid movements. Granule cell activity covaried trial by trial to form a redundant code. Many granule cells were also active during movements of nearby body structures. Thus, a predictive signal about the upcoming movement is widely available at the input stage of the cerebellar cortex, as required by forward models of cerebellar control.

Differential binding of transcription factors (TFs) at cis-regulatory loci drives the differentiation and function of diverse cellular lineages. Understanding the regulatory interactions that underlie cell fate decisions requires characterizing TF binding sites (TFBS) across multiple cell types and conditions. Techniques, e.g. ChIP-Seq can reveal genome-wide patterns of TF binding, but typically requires laborious and costly experiments for each TF-cell-type (TFCT) condition of interest. Chromosomal accessibility assays can connect accessible chromatin in one cell type to many TFs through sequence motif mapping. Such methods, however, rarely take into account that the genomic context preferred by each factor differs from TF to TF, and from cell type to cell type. To address the differences in TF behaviors, we developed Mocap, a method that integrates chromatin accessibility, motif scores, TF footprints, CpG/GC content, evolutionary conservation and other factors in an ensemble of TFCT-specific classifiers. We show that integration of genomic features, such as CpG islands improves TFBS prediction in some TFCT. Further, we describe a method for mapping new TFCT, for which no ChIP-seq data exists, onto our ensemble of classifiers and show that our cross-sample TFBS prediction method outperforms several previously described methods.