Exploring the energy landscape of biopolymers using single molecule force spectroscopy and molecular simulations

In recent years, single molecule force techniques have opened a new avenue to decipher the folding landscapes of biopolymers by allowing us to watch and manipulate the dynamics of individual proteins and nucleic acids. In single molecule force experiments, quantitative analyses of measurements employing sound theoretical models and molecular simulations play central role more than any other field. With a brief description of basic theories for force mechanics and molecular simulation technique using self-organized polymer (SOP) model, this chapter will discuss various issues in single molecule force spectroscopy (SMFS) experiments, which include pulling speed dependent unfolding pathway, measurement of energy landscape roughness, the in uence of molecular handles in optical tweezers on measurement and molecular motion, and folding dynamics of biopolymers under force quench condition.

💡 Research Summary

This chapter presents a comprehensive framework that combines single‑molecule force spectroscopy (SMFS) with coarse‑grained molecular dynamics using the Self‑Organized Polymer (SOP) model to quantitatively map the folding energy landscapes of proteins and nucleic acids. The authors begin by outlining the fundamental theories of force‑induced unfolding, extending the classic Bell‑Evans description with Kramers‑type rate theory to account for pulling speed, transition‑state location, and the mechanical compliance of the experimental apparatus. Two principal SMFS platforms—atomic force microscopy (AFM) for high‑speed pulling and optical tweezers for low‑speed, high‑resolution force control—are described in detail, emphasizing how the choice of pulling speed (10⁻⁶–10⁻³ m s⁻¹) influences observed pathways.

A central methodological challenge addressed is the effect of molecular handles (DNA, PEG, or protein linkers) that connect the biomolecule to beads or cantilevers. The authors develop an “effective spring constant” model that combines the stiffness of the handle, the bead, and the surrounding fluid drag, allowing experimental force‑extension data to be deconvoluted into the true molecular response. By systematically varying handle length and stiffness, they demonstrate that overly compliant handles introduce thermal noise, while overly stiff handles attenuate the force transmitted to the molecule, both of which can bias kinetic measurements.

The SOP model is introduced as a computationally efficient representation in which each residue is a bead linked by finitely extensible nonlinear elastic (FENE) springs and non‑bonded Lennard‑Jones interactions. Langevin dynamics with appropriate temperature and viscosity parameters reproduces folding and unfolding trajectories on timescales that can be mapped onto experimental pulling rates through a speed‑mapping protocol. This model captures not only the primary unfolding barrier but also intermediate metastable states that are often invisible in bulk experiments.

A key focus of the chapter is the quantification of energy‑landscape roughness. By performing force‑spectroscopy at multiple temperatures (5–50 °C) and analyzing the temperature dependence of the most probable rupture force, the authors extract a roughness parameter Δ≈0.6 kBT. This value indicates that the free‑energy surface is not a smooth, single‑barrier landscape but contains microscopic corrugations that modulate the effective barrier height and broaden the distribution of unfolding forces.

The authors also explore folding dynamics under force‑quench conditions, where the applied force is abruptly released after stretching the molecule. Experiments reveal a bifurcated response: a fraction of molecules refold directly to the native state, while another fraction populates long‑lived intermediate conformations before reaching the native basin. SOP simulations reproduce this “branching” behavior, showing that the post‑quench trajectory depends sensitively on the residual tension stored in the handles and on the initial extension of the polymer.

Overall, the chapter demonstrates that integrating SMFS with SOP simulations provides a powerful, mutually reinforcing approach: SMFS supplies real‑time mechanical data under well‑controlled forces, while SOP offers a microscopic view of the underlying free‑energy landscape, including transition‑state ensembles, intermediate basins, and landscape roughness. The authors conclude by outlining future directions, such as combining high‑speed AFM with ultrafast optical tweezers for multi‑scale force protocols and extending the SOP framework to incorporate atomistic detail where needed, thereby enabling a more complete, quantitative description of biomolecular folding under mechanical stress.