The calculation of free‐energy differences is one of the main challenges in computational biology and biochemistry. Umbrella sampling, biased molecular dynamics (MD), is one of the methods that provide free energy along a reaction coordinate. Here, the method is derived in a historic overview and is compared with related methods like thermodynamic integration, slow growth, steered MD, or the Jarzynski‐based fast‐growth technique. In umbrella sampling, bias potentials along a (one‐ or more‐dimensional) reaction coordinate drive a system from one thermodynamic state to another (e.g., reactant and product). The intermediate steps are covered by a series of windows, at each of which an MD simulation is performed. The bias potentials can have any functional form. Often, harmonic potentials are used for their simplicity. From the sampled distribution of the system along the reaction coordinate, the change in free energy in each window can be calculated. The windows are then combined by methods like the weighted histogram analysis method or umbrella integration. If the bias potential is adapted to result in an even distribution between the end states, then this whole range can be spanned by one window (adaptive‐bias umbrella sampling). In this case, the free‐energy change is directly obtained from the bias. The sampling in each window can be improved by replica exchange methods; either by exchange between successive windows or by running additional simulations at higher temperatures. © 2011 John Wiley & Sons, Ltd. WIREs Comput Mol Sci 2011 1 932–942 DOI: 10.1002/wcms.66

Umbrella sampling: Umbrella sampling

We find that vibrational contributions to a solute’s free energy are in general insensitive to whether the solute vibrational frequencies are computed in the gas phase or in solution. In most cases, the difference is smaller than the intrinsic error in solvation free energies associated with the continuum approximation to solvation modeling, although care must be taken to avoid spurious results associated with limitations in the quantum-mechanical harmonic-oscillator approximation for very low-frequency molecular vibrations. We compute solute vibrational partition functions in aqueous and carbon tetrachloride solution and compare them to gas-phase molecular partition functions computed with the same level of theory and the same quasiharmonic approximation for the diverse and extensive set of molecules and ions included in the training set of the SMD continuum solvation model, and we find mean unsigned differences in vibrational contributions to the solute free energy of only about 0.2 kcal/mol. On the bas...

Use of Solution-Phase Vibrational Frequencies in Continuum Models for the Free Energy of Solvation

We review a selection of methods for performing enhanced sampling in molecular dynamics simulations. We consider methods based on collective variable biasing and on tempering, and offer both historical and contemporary perspectives. In collective-variable biasing, we first discuss methods stemming from thermodynamic integration that use mean force biasing, including the adaptive biasing force algorithm and temperature acceleration. We then turn to methods that use bias potentials, including umbrella sampling and metadynamics. We next consider parallel tempering and replica-exchange methods. We conclude with a brief presentation of some combination methods.

/pdf/enhanced-sampling-in-molecular-dynamics-using-metadynamics-47nyissgxy.pdf

Enhanced Sampling in Molecular Dynamics Using Metadynamics, Replica-Exchange, and Temperature-Acceleration

Free-energy calculations in the framework of classical molecular dynamics simulations are nowadays used in a wide range of research areas including solvation thermodynamics, molecular recognition, and protein folding. The basic components of a free-energy calculation, that is, a suitable model Hamiltonian, a sampling protocol, and an estimator for the free energy, are independent of the specific application. However, the attention that one has to pay to these components depends considerably on the specific application. Here, we review six different areas of application and discuss the relative importance of the three main components to provide the reader with an organigram and to make nonexperts aware of the many pitfalls present in free energy calculations.

/pdf/practical-aspects-of-free-energy-calculations-a-review-14nu617ukp.pdf

Practical Aspects of Free-Energy Calculations: A Review.

We review a selection of methods for performing enhanced sampling in 1 molecular dynamics simulations. We consider methods based on collective variable biasing 2

Enhanced sampling in molecular dynamics using metadynamics, replica-exchange, and temperature-acceleration

Most processes occurring in a system are determined by the relative free energy between two or more states because the free energy is a measure of the probability of finding the system in a given state When the two states of interest are connected by a pathway, usually called reaction coordinate, along which the free-energy profile is determined, this profile or potential of mean force (PMF) will also yield the relative free energy of the two states Twelve different methods to compute a PMF are reviewed and compared, with regard to their precision, for a system consisting of a pair of methane molecules in aqueous solution We analyze all combinations of the type of sampling (unbiased, umbrella-biased or constraint-biased), how to compute free energies (from density of states or force averaging) and the type of coordinate system (internal or Cartesian) used for the PMF degree of freedom The method of choice is constraint-bias simulation combined with force averaging for either an internal or a Cartesian PMF degree of freedom

A Comparison of Methods to Compute the Potential of Mean Force

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A Comparison of Methods to Compute the Potential of Mean Force