Graphical models for inferring single molecule dynamics

<p>Abstract</p> <p>Background</p> <p>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)<it> versus</it> 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.</p> <p>Results</p> <p>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.</p> <p>Conclusions</p> <p>The results demonstrate the utility of graphical modeling for inference of dynamic processes in single molecule biophysics.</p

The Effect of Micrococcal Nuclease Digestion on Nucleosome Positioning Data

Eukaryotic genomes are packed into chromatin, whose basic repeating unit is the nucleosome. Nucleosome positioning is a widely researched area. A common experimental procedure to determine nucleosome positions involves the use of micrococcal nuclease (MNase). Here, we show that the cutting preference of MNase in combination with size selection generates a sequence-dependent bias in the resulting fragments. This strongly affects nucleosome positioning data and especially sequence-dependent models for nucleosome positioning. As a consequence we see a need to re-evaluate whether the DNA sequence is a major determinant of nucleosome positioning in vivo. More generally, our results show that data generated after MNase digestion of chromatin requires a matched control experiment in order to determine nucleosome positions

DNA interrogation by the CRISPR RNA-guided endonuclease Cas9

The clustered regularly interspaced short palindromic repeats (CRISPR)-associated enzyme Cas9 is an RNA-guided endonuclease that uses RNA-DNA base-pairing to target foreign DNA in bacteria. Cas9-guide RNA complexes are also effective genome engineering agents in animals and plants. Here we use single-molecule and bulk biochemical experiments to determine how Cas9-RNA interrogates DNA to find specific cleavage sites. We show that both binding and cleavage of DNA by Cas9-RNA require recognition of a short trinucleotide protospacer adjacent motif (PAM). Non-target DNA binding affinity scales with PAM density, and sequences fully complementary to the guide RNA but lacking a nearby PAM are ignored by Cas9-RNA. Competition assays provide evidence that DNA strand separation and RNA-DNA heteroduplex formation initiate at the PAM and proceed directionally towards the distal end of the target sequence. Furthermore, PAM interactions trigger Cas9 catalytic activity. These results reveal how Cas9 uses PAM recognition to quickly identify potential target sites while scanning large DNA molecules, and to regulate scission of double-stranded DNA