Step Detection in Single-Molecule Real Time Trajectories Embedded in Correlated Noise

Single-molecule real time trajectories are embedded in high noise. To extract kinetic or dynamic information of the molecules from these trajectories often requires idealization of the data in steps and dwells. One major premise behind the existing single-molecule data analysis algorithms is the Gaussian ‘white’ noise, which displays no correlation in time and whose amplitude is independent on data sampling frequency. This so-called ‘white’ noise is widely assumed but its validity has not been critically evaluated. We show that correlated noise exists in single-molecule real time trajectories collected from optical tweezers. The assumption of white noise during analysis of these data can lead to serious over- or underestimation of the number of steps depending on the algorithms employed. We present a statistical method that quantitatively evaluates the structure of the underlying noise, takes the noise structure into account, and identifies steps and dwells in a single-molecule trajectory. Unlike existing data analysis algorithms, this method uses Generalized Least Squares (GLS) to detect steps and dwells. Under the GLS framework, the optimal number of steps is chosen using model selection criteria such as Bayesian Information Criterion (BIC). Comparison with existing step detection algorithms showed that this GLS method can detect step locations with highest accuracy in the presence of correlated noise. Because this method is automated, and directly works with high bandwidth data without pre-filtering or assumption of Gaussian noise, it may be broadly useful for analysis of single-molecule real time trajectories

RNA Unwinding by NS3 Helicase: A Statistical Approach

The study of double-stranded RNA unwinding by helicases is a problem of basic scientific interest. One such example is provided by studies on the hepatitis C virus (HCV) NS3 helicase using single molecule mechanical experiments. HCV currently infects nearly 3% of the world population and NS3 is a protein essential for viral genome replication. The objective of this study is to model the RNA unwinding mechanism based on previously published data and study its characteristics and their dependence on force, ATP and NS3 protein concentration. In this work, RNA unwinding by NS3 helicase is hypothesized to occur in a series of discrete steps and the steps themselves occurring in accordance with an underlying point process. A point process driven change point model is employed to model the RNA unwinding mechanism. The results are in large agreement with findings in previous studies. A gamma distribution based renewal process was found to model well the point process that drives the unwinding mechanism. The analysis suggests that the periods of constant extension observed during NS3 activity can indeed be classified into pauses and subpauses and that each depend on the ATP concentration. The step size is independent of external factors and seems to have a median value of 11.37 base pairs. The steps themselves are composed of a number of substeps with an average of about 4 substeps per step and an average substep size of about 3.7 base pairs. An interesting finding pertains to the stepping velocity. Our analysis indicates that stepping velocity may be of two kinds- a low and a high velocity

Seven-Year Neurodevelopmental Scores and Prenatal Exposure to Chlorpyrifos, a Common Agricultural Pesticide

Background: In a longitudinal birth cohort study of inner-city mothers and children (Columbia Center for Children’s Environmental Health), we have previously reported that prenatal exposure to chlorpyrifos (CPF) was associated with neurodevelopmental problems at 3 years of age

Prenatal and postnatal bisphenol A exposure and asthma development among inner-city children

Background Bisphenol A (BPA) is used widely to manufacture food container linings. Mouse models suggest exposure to BPA might increase allergic inflammation. Objectives We hypothesized that BPA exposure, as assessed based on urinary BPA concentrations, would be associated with increased odds of wheeze and asthma and increased fraction of exhaled nitric oxide (Feno) values in children. Methods The Columbia Center for Children's Environmental Health recruited pregnant women for a prospective birth cohort study (n = 568). Mothers during the third trimester and children at ages 3, 5, and 7 years provided spot urine samples. Total urinary BPA concentrations were measured by using online solid-phase extraction, high-performance liquid chromatography, isotope-dilution tandem mass spectrometry. Wheeze in the last 12 months was measured by using questionnaires at ages 5, 6, and 7 years. Asthma was determined by a physician once between ages 5 and 12 years. Feno values were measured at ages 7 to 11 years. Results Prenatal urinary BPA concentrations were associated inversely with wheeze at age 5 years (odds ratio [OR], 0.7; 95% CI, 0.5-0.9; P = .02). Urinary BPA concentrations at age 3 years were associated positively with wheeze at ages 5 years (OR, 1.4; 95% CI, 1.1-1.8; P = .02) and 6 years (OR, 1.4; 95% CI, 1.0-1.9; P = .03). BPA concentrations at age 7 years were associated with wheeze at age 7 years (OR, 1.4; 95% CI, 1.0-1.9; P = .04) and Feno values (β = 0.1; 95% CI, 0.02-0.2; P = .02). BPA concentrations at ages 3, 5, and 7 years were associated with asthma (OR, 1.5 [95% CI, 1.1-2.0], P = .005; OR, 1.4 [95% CI, 1.0-1.9], P = .03; and OR, 1.5 [95% CI, 1.0-2.1], P = .04, respectively). Conclusions This is the first report of an association between postnatal urinary BPA concentrations and asthma in children

Schematic of the RNA unwinding process.

<p> represents the mean level of the steps and represents the jump locations. is the inter-jump interval.</p

Histogram and Boxplots of estimated Stepping velocities.

<p>Histogram and Boxplots of estimated Stepping velocities.</p

Jump Intervals - Gamma QQ Plot.

<p>The dots indicate the observed data and the red line indicates the reference line. NS3 and ATP concentrations are labeled above the plot.</p

Pause - Subpause estimate across ATP concentration.

<p>Pause - Subpause estimate across ATP concentration.</p

Residuals from fit.

<p>Residual plot, QQ-plot of residuals, the autocorrelation function (ACF) and the partial autocorrelation (PACF) plots of the residuals. The red dots indicate the points with zero weights and the blue dots non-zero weights.</p