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A critical step in data analysis for many different types of experiments is the identification of features with theoretically defined shapes in N-dimensional datasets; examples of this process include finding peaks in multi-dimensional molecular spectra or emitters in fluorescence microscopy images. Identifying such features involves determining if the overall shape of the data is consistent with an expected shape, however, it is generally unclear how to quantitatively make this determination. In practice, many analysis methods employ subjective, heuristic approaches, which complicates the validation of any ensuing results - especially as the amount and dimensionality of the data increase. Here, we present a probabilistic solution to this problem by using Bayes' rule to calculate the probability that the data has any one of several potential shapes. This probabilistic approach may be used to objectively compare how well different theories describe a dataset, identify changes between datasets, and detect features within data using a corollary method called Bayesian Inference-based Template Search (BITS); several proof-of-principle examples are provided. Altogether, this mathematical framework serves as an automated 'engine' capable of computationally executing analysis decisions currently made by visual inspection across the sciences., Comment: 35 pages (24 Manuscript, 11 Supporting Materials), 4 Figures

During the initiation stage of protein synthesis, a ribosomal initiation complex (IC) is assembled on a messenger RNA (mRNA) template. In bacteria, the speed and accuracy of this assembly process are regulated by the complementary activities of three essential initiation factors (IFs). Selection of an authentic N-formylmethionyl-transfer RNA (fMet-tRNA\textsuperscript{fMet}) and the canonical, triplet-nucleotide mRNA start codon are crucial events during assembly of a canonical, ribosomal 70S IC. Mis-initiation due to the aberrant selection of an elongator tRNA or a non-canonical start codon are rare events that result in the assembly of a pseudo 70S IC or a non-canonical 70S IC, respectively. Here, we have developed a theoretical model for the stochastic kinetics of canonical-, pseudo-, and non-canonical 70S IC assembly that includes all of the major steps of the IC assembly process that have been observed and characterized in ensemble kinetic-, single-molecule kinetic-, and structural studies of the fidelity of translation initiation. Specifically, we use the rates of the individual steps in the IC assembly process and the formalism of first-passage times to derive exact analytical expressions for the probability distributions for the assembly of canonical-, pseudo- and non-canonical 70S ICs. In order to illustrate the power of this analytical approach, we compare the theoretically predicted first-passage time distributions with the corresponding computer simulation data. We also compare the mean times required for completion of these assemblies with experimental estimates. In addition to generating new, testable hypotheses, our theoretical model can also be easily extended as new experimental 70S IC assembly data become available, thereby providing a versatile tool for interpreting these data and developing advanced models of the mechanism and regulation of translation initiation., Comment: Comments are welcome

At equilibrium, thermodynamic and kinetic information can be extracted from biomolecular energy landscapes by many techniques. However, while static, ensemble techniques yield thermodynamic data, often only dynamic, single-molecule techniques can yield the kinetic data that describes transition-state energy barriers. Here we present a generalized framework based upon dwell-time distributions that can be used to connect such static, ensemble techniques with dynamic, single-molecule techniques, and thus characterize energy landscapes to greater resolutions. We demonstrate the utility of this framework by applying it to cryogenic electron microscopy (cryo-EM) and single-molecule fluorescence resonance energy transfer (smFRET) studies of the bacterial ribosomal pre-translocation complex. Among other benefits, application of this framework to these data explains why two transient, intermediate conformations of the pre-translocation complex, which are observed in a cryo-EM study, may not be observed in several smFRET studies., Comment: 43 pages, including 6 figures

We address the problem of analyzing sets of noisy time-varying signals that all report on the same process but confound straightforward analyses due to complex inter-signal heterogeneities and measurement artifacts. In particular we consider single-molecule experiments which indirectly measure the distinct steps in a biomolecular process via observations of noisy time-dependent signals such as a fluorescence intensity or bead position. Straightforward hidden Markov model (HMM) analyses attempt to characterize such processes in terms of a set of conformational states, the transitions that can occur between these states, and the associated rates at which those transitions occur; but require ad-hoc post-processing steps to combine multiple signals. Here we develop a hierarchically coupled HMM that allows experimentalists to deal with inter-signal variability in a principled and automatic way. Our approach is a generalized expectation maximization hyperparameter point estimation procedure with variational Bayes at the level of individual time series that learns an single interpretable representation of the overall data generating process., Comment: 9 pages, 5 figures

Background: The recent explosion of experimental techniques in single molecule biophysics has generated a variety of novel time series data requiring equally novel computational tools for analysis and inference. This article describes in general terms how graphical modeling may be used to learn from biophysical time series data using the variational Bayesian expectation maximization algorithm (VBEM). The discussion is illustrated by the example of single-molecule fluorescence resonance energy transfer (smFRET) versus time data, where the smFRET time series is modeled as a hidden Markov model (HMM) with Gaussian observables. A detailed description of smFRET is provided as well. Results: The VBEM algorithm returns the model's evidence and an approximating posterior parameter distribution given the data. The former provides a metric for model selection via maximum evidence (ME), and the latter a description of the model's parameters learned from the data. ME/VBEM provide several advantages over the more commonly used approach of maximum likelihood (ML) optimized by the expectation maximization (EM) algorithm, the most important being a natural form of model selection and a well-posed (non-divergent) optimization problem. Conclusions: The results demonstrate the utility of graphical modeling for inference of dynamic processes in single molecule biophysics., Comment: 22 pages, 5 figures; Journal special issue for workshop papers from "New Problems and Methods in Computational Biology" A workshop at the Twenty-Third Annual Conference on Neural Information Processing Systems (NIPS 2009) Whistler, BC, Canada, December 11 or 12, 2009. (cf. http://videolectures.net/nipsworkshops09_computational_biology/)

Determining the mechanism by which transfer RNAs (tRNAs) rapidly and precisely transit through the ribosomal A, P and E sites during translation remains a major goal in the study of protein synthesis. Here, we report the real-time dynamics of the L1 stalk, a structural element of the large ribosomal subunit that is implicated in directing tRNA movements during translation. Within pre-translocation ribosomal complexes, the L1 stalk exists in a dynamic equilibrium between open and closed conformations. Binding of elongation factor G (EF-G) shifts this equilibrium towards the closed conformation through one of at least two distinct kinetic mechanisms, where the identity of the P-site tRNA dictates the kinetic route that is taken. Within post-translocation complexes, L1 stalk dynamics are dependent on the presence and identity of the E-site tRNA. Collectively, our data demonstrate that EF-G and the L1 stalk allosterically collaborate to direct tRNA translocation from the P to the E sites, and suggest a model for the release of E-site tRNA.

Time series data provided by single-molecule Forster resonance energy transfer (sm-FRET) experiments offer the opportunity to infer not only model parameters describing molecular complexes, e.g. rate constants, but also information about the model itself, e.g. the number of conformational states. Resolving whether or how many of such states exist requires a careful approach to the problem of model selection, here meaning discriminating among models with differing numbers of states. The most straightforward approach to model selection generalizes the common idea of maximum likelihood-selecting the most likely parameter values-to maximum evidence: selecting the most likely model. In either case, such inference presents a tremendous computational challenge, which we here address by exploiting an approximation technique termed variational Bayes. We demonstrate how this technique can be applied to temporal data such as smFRET time series; show superior statistical consistency relative to the maximum likelihood approach; and illustrate how model selection in such probabilistic or generative modeling can facilitate analysis of closely related temporal data currently prevalent in biophysics. Source code used in this analysis, including a graphical user interface, is available open source via http://vbFRET.sourceforge.net