Proposed coupled-oscillator model for <i>C. crescentus</i> cell cycle control.

<p>(<b>A</b>) Interactions between core cell cycle regulatory module and cell division module. Cell division module is represented as looped connections of protein expression and interaction events. This closed loop is established by both protein interaction causalities and temporally connected events. The color scheme is the same as <b>Figure S9</b> in <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002778#pcbi.1002778.s001" target="_blank">Text S1</a>. The interactions are schematized in the lower panel. (<b>B</b>) Derived coupling function . See <b><a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002778#pcbi.1002778.s001" target="_blank">Text S1</a></b> for details. (<b>C</b>) Reverse-calculated PRC overlapped with experimental PRC data for 15-min pulses. (<b>D</b>) Comparison between experimental PRC data for 10-min pulses and calculated PRC based on the coupling function in (<b>B</b>) derived from 15-min-pulse data. See <b><a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002778#pcbi.1002778.s001" target="_blank">Text S1</a></b> for details.</p

<i>C. crescentus</i> cells can be phase locked.

<p>(<b>A</b>) Phase locking a population of single cells. The upper panel shows the cell growth trajectory overlapped with the external inducer pulse train (<b><a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002778#pcbi.1002778.s001" target="_blank">Text S1</a></b>). The inserts are magnified views from 0 to 260 min and from 520 to 780 min. The lower panel shows the divisions of single cells (261 cells at pulse start) that were monitored for over 20 hrs. The timing of division events for individual cells are plotted (black dots) along lines parallel to the Time axis. Cells are arranged along the vertical axis according to their phases prior to the first perturbation (i.e., the diagonal line immediately before time zero). Inducer profile along experimental time is indicated in red, where high and low xylose levels are 0.03% (w/v) and 0.00009% (w/v) respectively. (<b>B</b>) Phase difference distribution. Phase difference (in minutes) between the internal cell cycle oscillator and external oscillator is analyzed. The distributions of phase difference after 2^nd and 10^th pulses are shown. (<b>C</b>) Quantification of phase evolution and division synchrony. The distributions in (b) are used to quantify the mean phase difference and synchronization. Both quantities are plotted with respect to the number of pulses delivered.</p

Schematic for phase locking the stalked <i>C. crescentus</i> cell division cycle by periodically perturbing <i>ctrA</i> expression.

<p>(<b>A</b>) <i>C. crescentus</i> stalked cell cycle is driven by oscillating concentration of the master regulator protein, CtrA. The cell cycle begins with low CtrA concentration, allowing initiation of chromosome replication. CtrA levels then rise gradually, accompanied by cell growth and division. Cytoplasmic compartmentalization at the pre-divisional stage triggers the rapid proteolysis of CtrA, initiating another round of stalked cell division. (<b>B</b>) Schematic of phase locking. (Left) The expression of exogenous <i>ctrA</i> (in a mutant lacking endogenous <i>ctrA</i>) is controlled by a periodic inducer pulse train which oscillates between two discrete levels (Low and High), which then phase locks the dividing stalked cells on the surface of a microfludic flow channel (lower micrograph) as schematized on the right.</p

The phase is more readily delayed than advanced.

<p>(<b>A</b>) Quantification of synchronization index under various external pulse profiles. The synchronization index ranges from zero to one as the population varies from asynchronous to synchronous. The synchronization indices (less the initial value) from the eighth to twelfth pulses are plotted for a variety of external periods ranging from 56 min to 89 min (converted to frequency) with 10 min and 15 min pulses (left vertical axis). The horizontal bars (right vertical axis) indicate the range for 1∶1 phase locking of a noise-free cell cycle oscillator (Arnold Tongues). Such frequency ranges are inferred from the phase resetting curves in (a) and (b). is the intrinsic frequency. (<b>B</b>) Phase resetting curve (PRC) for 15 min pulses. The data (open circles) are fitted with a real trigonometric polynomial of degree three (solid line) to ensure periodicity. (<b>C</b>) Schematics for perturbations on CtrA oscillation by a single elevated <i>ctrA</i> expression pulse at two possible time points. (<b>D</b>) Comparison between experimental and simulated 15-min-pulse PRCs based on the model of Li and Tyson <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002778#pcbi.1002778-Li1" target="_blank">[19]</a>.</p

Refining Disordered Peptide Ensembles with Computational Amide I Spectroscopy: Application to Elastin-Like Peptides

The characterization of intrinsically disordered protein (IDP) ensembles is complicated both by inherent heterogeneity and by the fact that many common experimental techniques function poorly when applied to IDPs. For this reason, the development of alternative structural tools for probing IDP ensembles has attracted considerable attention. Here we describe our recent work in developing experimental and computational tools for characterizing IDP ensembles using Amide I (backbone carbonyl stretch) vibrational spectroscopy. In this approach, the infrared (IR) absorption frequencies of isotope-labeled amide bonds probe their local electrostatic environments and structures. Empirical frequency maps allow us to use this spectroscopic data as a direct experimental test of atomistic structural models. We apply these methods to a family of short elastin-like peptides (ELPs), fragments of the elastin protein based around the Pro-Gly turn motif characteristic of the elastomeric segments of the full protein. Using a maximum entropy analysis that applies constraints from experimental spectra to weighting predicted spectra from molecular dynamics (MD) ensembles, we find that peptides with Ala or Val side chains preceding the Pro-Gly turn unit exhibit a stronger tendency toward extended structures than do Gly-Pro-Gly motifs, suggesting an important role for steric interactions in tuning the molecular properties of elastin

Improved Statistical Methods Enable Greater Sensitivity in Rhythm Detection for Genome-Wide Data

<div><p>Robust methods for identifying patterns of expression in genome-wide data are important for generating hypotheses regarding gene function. To this end, several analytic methods have been developed for detecting periodic patterns. We improve one such method, JTK_CYCLE, by explicitly calculating the null distribution such that it accounts for multiple hypothesis testing and by including non-sinusoidal reference waveforms. We term this method empirical JTK_CYCLE with asymmetry search, and we compare its performance to JTK_CYCLE with Bonferroni and Benjamini-Hochberg multiple hypothesis testing correction, as well as to five other methods: cyclohedron test, address reduction, stable persistence, ANOVA, and F24. We find that ANOVA, F24, and JTK_CYCLE consistently outperform the other three methods when data are limited and noisy; empirical JTK_CYCLE with asymmetry search gives the greatest sensitivity while controlling for the false discovery rate. Our analysis also provides insight into experimental design and we find that, for a fixed number of samples, better sensitivity and specificity are achieved with higher numbers of replicates than with higher sampling density. Application of the methods to detecting circadian rhythms in a metadataset of microarrays that quantify time-dependent gene expression in whole heads of Drosophila melanogaster reveals annotations that are enriched among genes with highly asymmetric waveforms. These include a wide range of oxidation reduction and metabolic genes, as well as genes with transcripts that have multiple splice forms.</p></div

Z-score normalization allows combining of time series from different datasets into smooth time series.

<p><i>Pdp1</i> gene expression from metadata before (A) and after (B) Z-score normalization. Light gray crosses indicate individual replicates, and the black curve is the mean.</p

Empirical <b>p</b>-values are uniformly distributed for the null model of JTK_CYCLE.

<p><i>P</i>-values versus their ranks from lowest (most significant) to highest (least significant) for JTK_CYCLE testing phases at 2 h intervals (green line) or phases and asymmetries at 2 h intervals (blue line) with time series consisting of Gaussian noise. Unbiased estimates should follow the black line (see text). (A) “Initial” <i>p</i>-values from JTK_CYCLE with multiple hypothesis testing underestimate the true <i>p</i>-values. (B) The Bonferroni correction results in <i>p</i>-values that are too high (less significant). (C) The Benjamini-Hochberg correction performs better than the Bonferroni correction but still results in <i>p</i>-values that are generally too high. (D) Empirical <i>p</i>-values that we calculate by permutation are close to uniformly distributed, as desired; their correspondence to the null model improves as the number of hypotheses tested increases.</p

Higher numbers of replicates provide greater sensitivity compared to increased density of time points for the same number of samples.

<p>Results shown are AUROC values for sine and ramp simulated data with 50% noise (see <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1004094#pcbi.1004094.s004" target="_blank">S4 Fig</a>. for additional waveforms and sample numbers). “Points” refers to the number of time points per period (“Points 12” refers to 12 points per period) and “Replicates” refers to the number of replicates per time series (“Replicates 2” refers to 2 samples per time point). Together, “Points 12 Replicates 2” refers to a time series that consists of 12 time points per period with 2 replicates per time point. Abbreviations are the same as in <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1004094#pcbi.1004094.g004" target="_blank">Fig. 4</a>.</p

AUROCs for simulated data with 50% noise (standard deviation of Gaussian noise as a percent of amplitude).

<p>An AUROC value of 1 represents perfect discrimination between rhythmic and arrhythmic time series, and a value of 0.5 corresponds to random guessing. In each panel, the number of replicates increases from 1 to 4 replicates from left to right, and the number of sampled points per period is indicated by color. AUROC for single-replicate ANOVA (for which the method is undefined) is set at 0.5 exactly. Imp: impulse waveform, Cyclo: cyclohedron test, Address: address reduction, Stable: stable persistence, JTK: original JTK_CYCLE with Bonferroni correction, JTK_BH: JTK_CYCLE with Benjamini-Hochberg correction with symmetric triangle reference, eJTK: empirical JTK_CYCLE with symmetric triangle reference, JTK_BH_aby2: JTK_CYCLE with Benjamini-Hochberg correction and triangle references with asymmetries from 2 to 22 h by 2 h, eJTK_aby2: empirical JTK_CYCLE with triangle references with asymmetries from 2 to 22 h by 2 h.</p