Publications

One of the most demanding tasks in astronomical image processing---in terms of precision---is the centroiding of stars. Upcoming large surveys are going to take images of billions of point sources, including many faint stars, with short exposure times. Real-time estimation of the centroids of stars is crucial for real-time PSF estimation, and maximal precision is required for measurements of proper motion. The fundamental Cram\'{e}r-Rao lower bound sets a limit on the root-mean-squared-error achievable by optimal estimators. In this work, we aim to compare the performance of various centroiding methods, in terms of saturating the bound, when they are applied to relatively low signal-to-noise ratio unsaturated stars assuming zero-mean constant Gaussian noise. In order to make this comparison, we present the ratio of the root-mean-squared-errors of these estimators to their corresponding Cram\'{e}r-Rao bound as a function of the signal-to-noise ratio and the full-width at half-maximum of faint stars. We discuss two general circumstances in centroiding of faint stars: (i) when we have a good estimate of the PSF, (ii) when we do not know the PSF. In the case that we know the PSF, we show that a fast polynomial centroiding after smoothing the image by the PSF can be as efficient as the maximum-likelihood estimator at saturating the bound. In the case that we do not know the PSF, we demonstrate that although polynomial centroiding is not as optimal as PSF profile fitting, it comes very close to saturating the Cram\'{e}r-Rao lower bound in a wide range of conditions. We also show that the moment-based method of center-of-light never comes close to saturating the bound, and thus it does not deliver reliable estimates of centroids.

We introduce a fast algorithm for computing volume potentials - that is, the convolution of a translation invariant, free-space Green's function with a compactly supported source distribution defined on a uniform grid. The algorithm relies on regularizing the Fourier transform of the Green's function by cutting off the interaction in physical space beyond the domain of interest. This permits the straightforward application of trapezoidal quadrature and the standard FFT, with superalgebraic convergence for smooth data. Moreover, the method can be interpreted as employing a Nystrom discretization of the corresponding integral operator, with matrix entries which can be obtained explicitly and rapidly. This is of use in the design of preconditioners or fast direct solvers for a variety of volume integral equations. The method proposed permits the computation of any derivative of the potential, at the cost of an additional FFT.

We generated a global genetic interaction network for Saccharomyces cerevisiae, constructing more than 23 million double mutants, identifying about 550,000 negative and about 350,000 positive genetic interactions. This comprehensive network maps genetic interactions for essential gene pairs, highlighting essential genes as densely connected hubs. Genetic interaction profiles enabled assembly of a hierarchical model of cell function, including modules corresponding to protein complexes and pathways, biological processes, and cellular compartments. Negative interactions connected functionally related genes, mapped core bioprocesses, and identified pleiotropic genes, whereas positive interactions often mapped general regulatory connections among gene pairs, rather than shared functionality. The global network illustrates how coherent sets of genetic interactions connect protein complex and pathway modules to map a functional wiring diagram of the cell.

We present new integral representations in two dimensions for the elastance problem in electrostatics and the mobility problem in Stokes flow. These representations lead to resonance-free Fredholm integral equations of the second kind and well conditioned linear systems upon discretization. By coupling our integral equations with high order quadrature and fast multipole acceleration, large-scale problems can be solved with only modest computing resources. We also discuss some applications of these boundary value problems in applied physics.

Environmental Gene Regulatory Influence Networks (EGRINs) coordinate the timing and rate of gene expression in response to environmental signals. EGRINs encompass many layers of regulation, which culminate in changes in accumulated transcript levels. Here, we inferred EGRINs for the response of five tropical Asian rice (Oryza sativa) cultivars to high temperatures, water deficit, and agricultural field conditions by systematically integrating time series transcriptome data, patterns of nucleosome-free chromatin, and the occurrence of known cis-regulatory elements. First, we identified 5,447 putative target genes for 445 transcription factors (TFs) by connecting TFs with genes harboring known cis-regulatory motifs in nucleosome-free regions proximal to their transcriptional start sites. We then used network component analysis to estimate the regulatory activity for each TF based on the expression of its putative target genes. Finally, we inferred an EGRIN using the estimated TFA as the regulator. The EGRINs include regulatory interactions between 4,052 target genes regulated by 113 TFs. We resolved distinct regulatory roles for members of the heat shock factor family, including a putative regulatory connection between abiotic stress and the circadian clock. TFA estimation using network component analysis is an effective way of incorporating multiple genome-scale measurements into network inference.

Background
A major bottleneck in our understanding of the molecular underpinnings of life is the assignment of function to proteins. While molecular experiments provide the most reliable annotation of proteins, their relatively low throughput and restricted purview have led to an increasing role for computational function prediction. However, assessing methods for protein function prediction and tracking progress in the field remain challenging.

Results
We conducted the second critical assessment of functional annotation (CAFA), a timed challenge to assess computational methods that automatically assign protein function. We evaluated 126 methods from 56 research groups for their ability to predict biological functions using Gene Ontology and gene-disease associations using Human Phenotype Ontology on a set of 3681 proteins from 18 species. CAFA2 featured expanded analysis compared with CAFA1, with regards to data set size, variety, and assessment metrics. To review progress in the field, the analysis compared the best methods from CAFA1 to those of CAFA2.

Conclusions
The top-performing methods in CAFA2 outperformed those from CAFA1. This increased accuracy can be attributed to a combination of the growing number of experimental annotations and improved methods for function prediction. The assessment also revealed that the definition of top-performing algorithms is ontology specific, that different performance metrics can be used to probe the nature of accurate predictions, and the relative diversity of predictions in the biological process and human phenotype ontologies. While there was methodological improvement between CAFA1 and CAFA2, the interpretation of results and usefulness of individual methods remain context-dependent.

Poly-proline type II (PPII) helical PXXP motifs are the recognition elements for a variety of protein–protein interactions that are critical for cellular signaling. Despite development of protocols for locking peptides into α-helical and β-strand conformations, there remains a lack of analogous methods for generating mimics of PPII helical structures. We describe herein a strategy to enforce PPII helical secondary structure in the 19-residue TrpPlexus miniature protein. Through sequence variation, we showed that a network of cation–π interactions could drive the formation of PPII helical conformations for both peptide and N-substituted glycine peptoid residues. The achievement of chemically diverse PPII helical scaffolds provides a new route towards discovering peptidomimetic inhibitors of protein–protein interactions mediated by PXXP motifs.

Protein secondary structures serve as geometrically constrained scaffolds for the display of key interacting residues at protein interfaces. Given the critical role of secondary structures in protein folding and the dependence of folding propensities on backbone dihedrals, secondary structure is expected to influence the identity of residues that are important for complex formation. Counter to this expectation, we find that a narrow set of residues dominates the binding energy in protein–protein complexes independent of backbone conformation. This finding suggests that the binding epitope may instead be substantially influenced by the side-chain conformations adopted. We analyzed side-chain conformational preferences in residues that contribute significantly to binding. This analysis suggests that preferred rotamers contribute directly to specificity in protein complex formation and provides guidelines for peptidomimetic inhibitor design.

We give a principled approach for the selection of a boundary integral, retarded potential representation for the solution of scattering problems for the wave equation in an exterior domain.

Locomotion in an organism is a consequence of the coupled interaction between brain, body and environment. Motivated by qualitative observations and quantitative perturbations of crawling in Drosophila melanogaster larvae, we construct a minimal integrative mathematical model for its locomotion. Our model couples the excitation-inhibition circuits in the nervous system to force production in the muscles and body movement in a frictional environment, thence linking neural dynamics to body mechanics via sensory feedback in a heterogeneous environment. Our results explain the basic observed phenomenology of crawling with and without proprioception, and elucidate the stabilizing role that proprioception plays in producing a robust crawling phenotype in the presence of biological perturbations. More generally, our approach allows us to make testable predictions on the effect of changing body-environment interactions on crawling, and serves as a step in the development of hierarchical models linking cellular processes to behavior.