Steps and Bumps: Precision Extraction of Discrete States of Molecular Machines

Abstract

We report statistical time-series analysis tools providing improvements in the rapid, precision extraction of discrete state dynamics from time traces of experimental observations of molecular machines. By building physical knowledge and statistical innovations into analysis tools, we provide techniques for estimating discrete state transitions buried in highly correlated molecular noise. We demonstrate the effectiveness of our approach on simulated and real examples of steplike rotation of the bacterial flagellar motor and the F1-ATPase enzyme. We show that our method can clearly identify molecular steps, periodicities and cascaded processes that are too weak for existing algorithms to detect, and can do so much faster than existing algorithms. Our techniques represent a step in the direction toward automated analysis of high-sample-rate, molecular-machine dynamics. Modular, open-source software that implements these techniques is provided.

An abrupt weakening of the subpolar gyre as trigger of Little Ice Age-type episodes

“…Two remarkably different behaviors can nevertheless be identified in the Past1000s: whereas the SPG weakens progressively at an almost constant rate throughout the entire last millennium in R1 and R2 (with trends of the order of −0.10 Sv/century), the SPG in R3 shows a rapid shift from a strong to a weak state around 1600. An algorithm for discrete level identification (Little et al 2011) allows an objective characterization of the shift: it occurs in about two decades, accounts for a weakening of 0.72 Sv, and separates two stationary states, each covering at least 250 years (Fig. 1a, horizontal solid lines for Past1000-R3, and Fig.…”

“…Horizontal dash-dotted and dashed lines respectively account for the 25th-75th and 5th-95th percentiles of the SPG strength in PiControl. Horizontal solid lines are the discrete levels extracted following the algorithm described in Little et al (2011). b Annual globally averaged values of the reconstructed TSI (black line, in W/m 2 ) (Vieira et al 2011) and the simulated volcanic forcing, shown as net adiative flux anomalies, long plus short waves (LW + SW, in W/m 2 ), at the top of the atmosphere with respect to the climatological mean.…”

Energy-based scheme for reconstruction of piecewise constant signals observed in the movement of molecular machines

“…Due to the stochastic nature of enzymatic stepping the number of steps is often not known a priori. Therefore, different step finding algorithms have been developed [17][18][19][20].One class of algorithms determine steps from single molecule data based on statistical hypothesis testing in a moving window. A prominent example is the so called t-test, which is based on the Student's t-test [18].…”

“…Thus, if steps are hidden in noise such algorithms behave as efficient filter-functions, and accurate step-detection requires an additional second stage on the filtered, i.e. denoised data [20].Here, we present a novel two stage approach, termed Energy Based Stepfinding (EBS), where both stages are based on the minimisation of energy functions. In a first stage, we denoise the signal with a highly efficient and fast optimization algorithm.…”

“…In fact, TVDN with this λ h performs often very well in tracing the actual signal even under noisy conditions. Consequently, if TVDN is used as first stage, the choice of the regularization parameter is very important and can significantly influence the performance of further steps.Previously, TVDN has been applied in a step detection algorithm of the rotary flagella motor movement [20,27]. The method to determine the parameter λ developed here could be directly applied to this problem thus increasing the accuracy of the denoising scheme.…”