Enhanced Sampling

A history-dependent method that discourages revisiting previously explored regions of the free energy surface by depositing Gaussian-shaped bias potentials along selected collective variables (CVs).

• Well-Tempered Metadynamics (WTMetaD): Scales the Gaussian height down as bias accumulates, ensuring asymptotic convergence to the true free energy.
• Multiple-Walker Metadynamics: Parallel replicas share a common bias potential, dramatically accelerating exploration.
• Commonly used to study protein-ligand unbinding, crystal nucleation, and conformational changes.

A foundational method that divides the reaction coordinate into discrete windows and applies a harmonic restraining potential to sample each window independently.

• The overlapping biased distributions are recombined using the Weighted Histogram Analysis Method (WHAM) or Multistate Bennett Acceptance Ratio (MBAR).
• Provides rigorous free energy profiles along a predefined reaction coordinate.
• Remains the gold standard for calculating ion channel permeation free energies and lipid bilayer partitioning.

Also known as parallel tempering, REMD runs multiple non-interacting replicas of the system at different temperatures and periodically attempts to swap configurations between adjacent replicas according to a Metropolis criterion.

• Enables the system to escape kinetic traps by diffusing through temperature space.
• Temperature-REMD is the most common variant; Hamiltonian-REMD scales specific interaction terms instead of temperature.
• Particularly effective for protein folding and peptide aggregation studies where enthalpic barriers are high.

A method that modifies the potential energy landscape by adding a boost potential when the system's potential energy falls below a threshold, effectively raising the energy of local minima.

• Does not require predefined collective variables, making it useful for blind exploration.
• Gaussian Accelerated MD (GaMD): An improved variant that adds a harmonic boost potential, enabling accurate reweighting to recover the original free energy landscape.
• Widely applied to GPCR activation and kinase domain motions.

Applies an external, time-dependent force to guide the system along a specified direction, mimicking atomic force microscopy (AFM) pulling experiments.

• The Jarzynski equality can be used to reconstruct the equilibrium free energy profile from multiple non-equilibrium pulling trajectories.
• Constant-force and constant-velocity pulling protocols are both common.
• Frequently used to study ligand dissociation pathways, protein unfolding, and mechanosensitive channel gating.

A method that continuously estimates the average force acting along a collective variable and applies an equal and opposite biasing force to cancel it, resulting in a uniform, diffusive sampling along the CV.

• The negative integral of the average force directly yields the potential of mean force (PMF).
• Extended-system ABF (eABF) couples the CV to a fictitious particle, improving stability and convergence.
• Ideal for mapping free energy landscapes along torsional angles and distance-based reaction coordinates.

A low-dimensional function $s(\vec{R})$ of atomic coordinates that describes the slow, essential degrees of freedom governing a rare event. The choice of CV is the single most critical decision in enhanced sampling.

• Examples: Distance between two atoms, radius of gyration, number of hydrogen bonds, dihedral angles
• Good CVs: Capture the bottleneck of the transition and discriminate between all relevant metastable states
• Poor CVs: Lead to hysteresis and failed sampling despite computational effort