Undulations in a weakly interacting mechanically generated molecular braid under tension

TL;DR

This paper models the behavior of weakly interacting molecular braids under tension, accounting for thermal fluctuations, steric effects, and external forces, to predict their geometric and mechanical properties.

Contribution

It introduces a comprehensive model that incorporates thermal, steric, and external forces to analyze the mechanics of weakly interacting molecular braids.

Findings

Predicted the external torque needed for specific braid turns.

Calculated end-to-end extension under pulling force.

Determined geometric parameters and lateral forces for the braid.

Abstract

We consider mechanically generated molecular braids composed of two molecules where long range interactions between them can be considered to be very weak. We describe a model that takes account of the thermal fluctuations of the braid, steric interactions between the molecules, and external mechanical forces. In this model, both sets of ends, of the two molecules, are considered to be separated by a fixed distance apart much larger than the radius of the braid. One set of ends are rotated to generate a braid of a certain number of pitches (or turns), while the other set remains fixed. This model may describe the situation in which the ends of each molecule are attached to a substrate and a magnetic bead; to the latter a pulling force and rotational torque can be applied. We discuss various aspects of our model. Most importantly, an expression for the free energy is given, from which equations, determining the various geometric parameters of the braid, can be obtained. By numerically solving these equations, we give predictions from the model for the external torque needed to produce a braid with a certain number of turns per bending persistence length, as well as the end to end extension of the two molecules for a given pulling force. Other geometric parameters, as well as the lateral force required to keep the ends of the two molecules apart, are also calculated.