More for less: predicting and maximizing genomic variant discovery via Bayesian nonparametrics

While the cost of sequencing genomes has decreased dramatically in recent years, this expense often remains non-trivial. Under a fixed budget, scientists face a natural trade-off between quantity and quality: spending resources to sequence a greater number of genomes or spending resources to sequence genomes with increased accuracy. Our goal is to find the optimal allocation of resources between quantity and quality. Optimizing resource allocation promises to reveal as many new variations in the genome as possible. In this paper, we introduce a Bayesian nonparametric methodology to predict the number of new variants in a follow-up study based on a pilot study. When experimental conditions are kept constant between the pilot and follow-up, we find that our prediction is competitive with the best existing methods. Unlike current methods, though, our new method allows practitioners to change experimental conditions between the pilot and the follow-up. We demonstrate how this distinction allows our method to be used for more realistic predictions and for optimal allocation of a fixed budget between quality and quantity.

Enumerating High Numbers of Fluorophores from Photobleaching Experiments: a Bayesian Nonparametrics Approach

Determining the number of biomolecules within a small, diffraction-limited spot, is key to understanding intermolecular interactions that form the basis of all of information processing relevant to life. To enumerate the number of biomolecules within such a small region of interest (ROI), it is possible to illuminate an ROI containing a collection of fluorescently labeled biomolecules and observe the ROI’s brightness over time. As most fluorescent labels (fluorophores) are initially in a fluorescently active state, the brightness diminishes in a step-like pattern as fluorophores photobleach one at a time. Naively, by counting steps, one could determine the number of fluorophores present. However, this analysis is complicated by photon shot noise, camera noise that amplifies intrinsic photon shot noise and fluorophore photophysics (i.e., states with variable emission visited by fluorophores). Current state of the art can typically enumerate as many as 20 fluorophores reliably. Yet in many biophysics problems, fluorophore numbers can vastly exceed 20 within an ROI. For this reason, we develop a method to learn the number of fluorophores alongside other parameters required to achieve high counts simultaneously and self-consistently (e.g., fluorophore photophysical rate parameters and camera parameters). As the number of fluorophores is initially unknown and may be very large, and as not all fluorophores may initially be emitting photons, we cannot rely on a traditional (parametric) Bayesian framework. As such, to achieve our goal of exceeding the state of the art by a factor of about 5, we must abandon the parametric Bayesian paradigm and invoke novel tools within Bayesian nonparametrics never previously used in step counting by photobleaching.

Direct Photon-by-photon Analysis of Time-Resolved Pulsed Excitation Data using Bayesian Nonparametrics

Lifetimes of chemical species are typically estimated, across each illuminated spot of a sample, by either fitting time correlated single photon counting (TCSPC) decay histograms or, more recently, through phasor analysis from time-resolved photon arrivals. While both methods yield lifetimes in a computationally efficient manner, the performance of both methods is limited by the choices made when fitting a TCSPC histogram. In addition, phasor analysis also requires setting the number of chemical species by hand before lifetimes can be determined. Yet the number of species itself is encoded in the photon arrival times collected for each illuminated spot and need not be set by hand a priori. Here we propose a direct photo-by-photon analysis of data drawn from pulsed excitation experiments to infer, simultaneously and self-consistently, the number of species and their associated lifetimes from as little as a few thousand photons for two species. We do so by leveraging new mathematical tools within the Bayesian nonparametric (BNP) paradigm that we have previously exploited in the analysis of single photon arrivals from single spot confocal microscopy. We benchmark our method on simulated as well as experimental data for one, two, three, and four species with data sets from both immobilized and freely diffusing molecules at the level of one illuminated spot.SUMMARYPhoton arrivals obtained from fluorescence experiments encode not only the lifetimes of chemical species but also the number of chemical species involved in the experiment. Traditional methods of analysis, such as phasor methods and methods relying on maximum likelihood or (parametric) Bayesian analysis of photon arrivals or photon arrival histograms of TCSPC data, must first ascertain the number of chemical species separately and, once specified, determine their associated lifetimes. Here we develop a method to learn the number of fluorescence species and their associated lifetimes simultaneously. We achieve this by exploiting Bayesian nonparametrics. We benchmark our approach on both simulated and experimental data for one species and mixtures of two to four species.