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A method for calculating the free energy difference between two structurally defined conformational states of a chemical system is developed. A path is defined using a previously reported collective variable that interpolates between two or more conformations, and a restraint is introduced in order to keep the system close to the path. The evolution of the system along the path, which typically presents a high free energy barrier, is generated using enhanced sampling schemes. Although the formulation of the method in terms of a path is quite general, an important advance in this work is the demonstration that prior knowledge of the path is, in fact, not needed and that the free energy difference can be obtained using a simplified definition of the path collective variable that only involves the endpoints. We first validate this method on cyclohexane isomerization. The method is then tested for an extensive conformational change in a realistic molecular system by calculating the free energy difference between the α-helix and β-hairpin conformations of deca-alanine in solution. Finally, the method is applied to a biologically relevant system to calculate the free energy difference of an observed and a hypothetical conformation of an antigenic peptide bound to a major histocompatibility complex. [ABSTRACT FROM AUTHOR]

Enhanced sampling techniques that target a set of collective variables and that use molecular dynamics as the driving engine have seen widespread application in the computational molecular sciences as a means to explore the free-energy landscapes of complex systems. The use of molecular dynamics as the fundamental driver of the sampling requires the introduction of a time step whose magnitude is limited by the fastest motions in a system. While standard multiple time-stepping methods allow larger time steps to be employed for the slower and computationally more expensive forces, the maximum achievable increase in time step is limited by resonance phenomena, which inextricably couple fast and slow motions. Recently, we introduced deterministic and stochastic resonance-free multiple time step algorithms for molecular dynamics that solve this resonance problem and allow ten- to twenty-fold gains in the large time step compared to standard multiple time step algorithms [P. Minary et al., Phys. Rev. Lett. 93, 150201 (2004); B. Leimkuhler et al., Mol. Phys. 111, 3579-3594 (2013)]. These methods are based on the imposition of isokinetic constraints that couple the physical system to Nosé-Hoover chains or Nos'e-Hoover Langevin schemes. In this paper, we show how to adapt these methods for collective variable-based enhanced sampling techniques, specifically adiabatic free-energy dynamics/temperature-accelerated molecular dynamics, unified free-energy dynamics, and by extension, metadynamics, thus allowing simulations employing these methods to employ similarly very large time steps. The combination of resonance-free multiple time step integrators with free-energy-based enhanced sampling significantly improves the efficiency of conformational exploration. [ABSTRACT FROM AUTHOR]

Adiabatic free energy dynamics (AFED) was introduced by Rosso et al. [J. Chem. Phys.2002, 116, 4389] for computing free energy profiles quickly and accurately using a dynamical adiabatic separation between a set of collective variables or reaction coordinates and the remaining degrees of freedom of a system. This approach has been shown to lead to a significant gain in efficiency versus traditional methods such as umbrella sampling, thermodynamic integration, and free energy perturbation for generating one-dimensional free energy profiles. More importantly, AFED is able to generate multidimensional free energy surfaces efficiently via full sweeps of the surface that rapidly map out the locations of the free energy minima. The most significant drawback to the AFED approach is the need to transform the coordinates into a generalized coordinate system that explicitly contains the collective variables of interest. Recently, Maragliano and Vanden-Eijnden built upon the AFED approach by introducing a set of extended phase-space variables, to which the adiabatic decoupling and high temperature are applied [Chem. Phys. Lett.2006, 426, 168]. In this scheme, which the authors termed "temperature accelerated molecular dynamics" or TAMD, the need for explicit coordinate transformations is circumvented. The ability of AFED and TAMD to generate free energy surfaces efficiently depends on the thermostatting mechanism employed, since both approaches are inherently nonequilibrium due to the adiabatic decoupling. Indeed, Maragliano and Vanden-Eijnden did not report any direct generation of free energy surfaces within the overdamped Langevin dynamics employed by these authors. Here, we show that by formulating TAMD in a manner that is closer to the original AFED approach, including the generalized Gaussian moment thermostat (GGMT) and multiple time-scale integration, multidimensional free energy surfaces for complex systems can be generated directly from the probability distribution function of the extended phase-space variables. The new TAMD formulation, which we term driven AFED or d-AFED, is applied to compare the conformational preferences of small peptides both in gas phase and in solution for three force fields. The results show that d-AFED/TAMD accurately and efficiently generates free energy surfaces in two collective variables useful for characterizing the conformations, namely, the radius of gyration, RG, and number of hydrogen bonds, NH. [ABSTRACT FROM AUTHOR]

We correct an error in our original paper. Calculations originally reported for the alanine tripeptide were performed using the earlier driven adiabatic free energy dynamics (d-AFED) approach rather than the new unified free energy dynamics (UFED) scheme. When UFED is applied to this system, the rate of convergence of the free energy surface improves significantly over that originally reported for d-AFED. [ABSTRACT FROM AUTHOR]

The quality of classical biomolecularsimulations is inevitably limited by two problems: the accuracy ofthe force field used and the comprehensiveness of configuration spacesampling. In this work we tackle the sampling problem by carryingout driven adiabatic free energy dynamics to obtain converged freeenergy surfaces of dipeptides in the gas phase and in solution usingselected dihedral angles as collective variables. To calculate populationsof conformational macrostates observed in experiment, we introducea fuzzy clustering algorithm in collective-variable space, which delineatesmacrostates without prior definition of arbitrary boundaries. Withthis approach, we calculate the conformational preferences of smallpeptides with six biomolecular force fields chosen from among themost recent and widely used. We assess the accuracy of each forcefield against recently published Raman or IR–UV spectroscopymeasurements of conformer populations for the dipeptides in solutionor in the gas phase. [ABSTRACT FROM AUTHOR]

The generation of free energy landscapes corresponding to conformational equilibria in complex molecular systems remains a significant computational challenge. Adding to this challenge is the need to represent, store, and manipulate the often high-dimensional surfaces that result from rare-event sampling approaches employed to compute them. In this Letter, we propose the use of artificial neural networks as a solution to these issues. Using specific examples, we discuss network training using enhanced-sampling methods and the use of the networks in the calculation of ensemble averages. [ABSTRACT FROM AUTHOR]