Analyzing single‐molecule manipulation experiments

Abstract

Single-molecule manipulation studies can provide quantitative information about the physical properties of complex biological molecules without ensemble artifacts obscuring the measurements. We demonstrate computational techniques which aim at more fully utilizing the wealth of information contained in noisy experimental time series. The “noise” comes from multiple sources, e.g. inherent thermal motion, instrument measurement error, etc. The primary focus of this article is a methodology that uses time domain based methods to extract the effective molecular friction from single-molecule pulling data. We studied molecules composed of 8 tandem repeat titin I27 domains, but the modeling approaches have applicability to other single-molecule mechanical studies. The merits and challenges associated with applying such a computational approach to existing single-molecule manipulation data are also discussed.

Rate limit of protein elastic response is tether dependent

“…2B. Our observations support the view that a tethered polypeptide samples its PMF with a diffusion coefficient of D eff ∼ 10 3 nm 2 ∕s, which is in surprisingly close agreement with previous measurements using tethered proteins (14)(15)(16)(17)(18).…”

P-Splines Using Derivative Information

“…At smaller length and time scales, these polymer models become more inaccurate, and in more complex biomolecules the dynamics are poorly quantitatively understood from a priori considerations. A semiparametric approach where the estimated local parameters have a physical interpretation shows promise in learning from time ordered single-molecule data in such situations [6, 7, 8, 10, 15]. It should be noted that purely nonparametric models [17, 18] can be difficult to reliably estimate (and check the statistical validity of) when a time-inhomogeneous driving term is present, as in the cases we report.…”

“…The inability to resolve all degrees of freedom motivates the use of inherently stochastic evolution rules. Note that “unresolved” ≠ “uninteresting”; the magnitude of the effective noise coefficients needs to be estimated and can relate to important molecular level events and can also change as a function of the resolved coordinate x [6, 8, 15, 23, 37]. However, the focus of this example is on the effective force (the local diffusion functions are constants whose value is fixed to the value of ${false(1\frac{1}{2}false)}^2$ for all components throughout).…”

“…The approach reported can also be modified to explicitly estimate/model “measurement noise” in cases where this noise can be modeled as a Gaussian. How to separate “thermal noise” from measurement noise in experimental single-molecule time series data is shown elsewhere [6, 8, 15]. In this article, the focus is on a benchmark all-atom molecular dynamics simulation of the gramicidin A ion channel [7].…”

“…However, other spline bases can be entertained, such as the B-spline basis as advocated when P-splines were introduced [11]. Smoothing splines can also be considered [21], but the ability of P-splines to parsimoniously represent complex nonlinear functions has appeal in longitudinal data [12] and functional data analysis [22] applications; these techniques show promise in providing a better quantitative understanding of batches of complex single-molecule time series [6, 15, 23]. We demonstrate how information about the (possibly correlated) noise processes can be utilized to improve function estimates using established generalized least squares (GLS) techniques [24] to modify the PuDI design matrix.…”