Inferring the diameter of a biopolymer from its stretching response

Abstract

We investigate the stretching response of a thick polymer model by means of extensive stochastic simulations. The computational results are synthesized in an analytic expression that characterizes how the force versus elongation curve depends on the polymer structural parameters: its thickness and granularity (spacing of the monomers). The expression is used to analyze experimental data for the stretching of various different types of biopolymers: polypeptides, polysaccharides, and nucleic acids. Besides recovering elastic parameters (such as the persistence length) that are consistent with those obtained from standard entropic models, the approach allows us to extract viable estimates for the polymers diameter and granularity. This shows that the basic structural polymer features have such a profound impact on the elastic behavior that they can be recovered with the sole input of stretching measurements.

FIGURE 1

(a) Pictorial sketch of a discrete TC with thickness Δ and granularity a (here, Δ = 4a). The finite thickness introduces steric constraints that forbid configurations where the chain self-intersects. (b) These constraints (which, e.g., for the chain of ellipsoids, may be implemented only with heavy computational expenditure) are more conveniently treated within the three-body prescription of the TC model. Within this approach, the centerline of a viable configuration is such that the radii, r_ijk, of the circles going through any triplet of points, i, j, k, on the curve are not smaller than Δ.

FIGURE 2

(a) Elongation versus force (expressed in units of k_BT/a) for a chain of thickness Δ/a = 1. Data points are presented in the (log(1 – x), log(f)) plane to highlight the WLC- and FJC-like regimes found at moderate and high forces. (b) Illustration of the low-force crossover from the Hookean regime, to the Pincus one, for a chain of thickness Δ/a = 1 and N = 1200 beads.

FIGURE 3

Typical fit of the PEVK stretching data through the TC model. The particular fit yields a contour length L_c = 147.6 ± 0.3 nm, a thickness Δ = 0.34 ± 0.01 nm, and a granularity a = 0.45 ± 0.02 nm. For this set, the WLC provides a fit with a analogous to that of the TC and yields L_c = 148.1 ± 0.1 nm and

FIGURE 4

Fit of the cellulose stretching data through the TC model. The fit was carried out using forces up to 300 pN and yielded a contour length L_c = 82.35 ± 0.02 nm, a thickness Δ = 0.54 ± 0.02 nm, and a granularity a = 1.02 ± 0.01 nm.

FIGURE 5

Fit of dsDNA stretching measurements through the TC model. Forces up to 10 pN were used.