We present a method for determining the free-energy dependence on a selected number of collective variables using an adaptive bias. The formalism provides a unified description which has metadynamics and canonical sampling as limiting cases. Convergence and errors can be rigorously and easily controlled. The parameters of the simulation can be tuned so as to focus the computational effort only on the physically relevant regions of the order parameter space. The algorithm is tested on the reconstruction of an alanine dipeptide free-energy landscape.

Well-tempered metadynamics: a smoothly converging and tunable free-energy method.

Combined quantum-mechanics/molecular-mechanics (QM/MM) approaches have become the method of choice for modeling reactions in biomolecular systems. Quantum-mechanical (QM) methods are required for describing chemical reactions and other electronic processes, such as charge transfer or electronic excitation. However, QM methods are restricted to systems of up to a few hundred atoms. However, the size and conformational complexity of biopolymers calls for methods capable of treating up to several 100,000 atoms and allowing for simulations over time scales of tens of nanoseconds. This is achieved by highly efficient, force-field-based molecular mechanics (MM) methods. Thus to model large biomolecules the logical approach is to combine the two techniques and to use a QM method for the chemically active region (e.g., substrates and co-factors in an enzymatic reaction) and an MM treatment for the surroundings (e.g., protein and solvent). The resulting schemes are commonly referred to as combined or hybrid QM/MM methods. They enable the modeling of reactive biomolecular systems at a reasonable computational effort while providing the necessary accuracy.

QM/MM Methods for Biomolecular Systems

Eukaryotic genomes are packaged into nucleosome particles that occlude the DNA from interacting with most DNA binding proteins. Nucleosomes have higher affinity for particular DNA sequences, reflecting the ability of the sequence to bend sharply, as required by the nucleosome structure. However, it is not known whether these sequence preferences have a significant influence on nucleosome position in vivo, and thus regulate the access of other proteins to DNA. Here we isolated nucleosome-bound sequences at high resolution from yeast and used these sequences in a new computational approach to construct and validate experimentally a nucleosome–DNA interaction model, and to predict the genome-wide organization of nucleosomes. Our results demonstrate that genomes encode an intrinsic nucleosome organization and that this intrinsic organization can explain ∼50% of the in vivo nucleosome positions. This nucleosome positioning code may facilitate specific chromosome functions including transcription factor binding, transcription initiation, and even remodelling of the nucleosomes themselves.

http://absimage.aps.org/image/MAR08/MWS_MAR08-2008-020581.pdf

The Genomic Code for Nucleosome Positioning

Metadynamics is a powerful algorithm that can be used both for reconstructing the free energy and for accelerating rare events in systems described by complex Hamiltonians, at the classical or at the quantum level. In the algorithm the normal evolution of the system is biased by a history-dependent potential constructed as a sum of Gaussians centered along the trajectory followed by a suitably chosen set of collective variables. The sum of Gaussians is exploited for reconstructing iteratively an estimator of the free energy and forcing the system to escape from local minima. This review is intended to provide a comprehensive description of the algorithm, with a focus on the practical aspects that need to be addressed when one attempts to apply metadynamics to a new system: (i) the choice of the appropriate set of collective variables; (ii) the optimal choice of the metadynamics parameters and (iii) how to control the error and ensure convergence of the algorithm.

http://iopscience.iop.org/article/10.1088/0034-4885/71/12/126601/pdf

Metadynamics: a method to simulate rare events and reconstruct the free energy in biophysics, chemistry and material science

CP2K is an open source electronic structure and molecular dynamics software package to perform atomistic simulations of solid-state, liquid, molecular, and biological systems. It is especially aimed at massively parallel and linear-scaling electronic structure methods and state-of-the-art ab initio molecular dynamics simulations. Excellent performance for electronic structure calculations is achieved using novel algorithms implemented for modern high-performance computing systems. This review revisits the main capabilities of CP2K to perform efficient and accurate electronic structure simulations. The emphasis is put on density functional theory and multiple post–Hartree–Fock methods using the Gaussian and plane wave approach and its augmented all-electron extension.

/pdf/cp2k-an-electronic-structure-and-molecular-dynamics-software-4domuefs67.pdf

CP2K: An electronic structure and molecular dynamics software package - Quickstep: Efficient and accurate electronic structure calculations

A new molecular dynamics method for calculating free energy profiles for rare events is presented. The new method is based on the creation of an adiabatic separation between a reaction coordinate subspace and the remaining degrees of freedom within a molecular dynamics run. This is achieved by associating with the reaction coordinate(s) a high temperature and large mass, thereby allowing the activated process to occur while permitting the remaining degrees of freedom to respond adiabatically. In this limit, by applying a formal multiple time scale Liouville operator factorization, it can be rigorously shown that the free energy profile is obtained directly from the probability distribution of the reaction coordinate subspace and, therefore, no unbiasing of the configuration space or postprocessing of the output data is required. The new method is applied to a variety of model problems including a two-dimensional free energy surface and its performance tested against free energy calculations using the “blue moon ensemble” approach. The comparison shows that free energy profiles can be calculated with greater ease and efficiency using the new method.

On the use of the adiabatic molecular dynamics technique in the calculation of free energy profiles

The methodology of ab initio molecular dynamics, wherein finite-temperature dynamical trajectories are generated by using forces computed "on the fly" from electronic structure calculations, has had a profound influence in modern theoretical research. Ab initio molecular dynamics allows chemical processes in condensed phases to be studied in an accurate and unbiased manner, leading to new paradigms in the elucidation of microscopic mechanisms, rationalization of experimental data, and testable predictions of new phenomena. The purpose of this work is to give a brief introduction to the technique and to review several important recent developments in the field. Several illustrative examples showing the power of the technique have been chosen. Perspectives on future directions in the field also will be given.

https://www.pnas.org/content/pnas/102/19/6654.full.pdf

Ab initio molecular dynamics: Concepts, recent developments, and future trends

Tuning Cytokine Receptor Signaling by Re-orienting Dimer Geometry with Surrogate Ligands.

https://www.cs.ox.ac.uk/people/peter.minary/csb/publications/Publication_20_Peter_Minary.pdf

Modeling nucleic acids.

Although molecular dynamics methods are commonly used to drive biomolecular simulations, the technique provides insufficient sampling to impact studies of the 200-300 residue proteins of greatest interest. One severe limitation of molecular dynamics is that the integrators are restricted by resonance phenomena to small time steps $(\ensuremath{\Delta}tl8\text{ }\text{ }\mathrm{f}\mathrm{s})$ much slower then the time scales of important structural and solvent rearrangements. Here, a novel set of equations of motion and a reversible, resonance-free, integrator are designed which permit step sizes on the order of 100 fs to be used.

Peter Minary

Papers

On the use of the adiabatic molecular dynamics technique in the calculation of free energy profiles

Ab initio molecular dynamics: Concepts, recent developments, and future trends

Tuning Cytokine Receptor Signaling by Re-orienting Dimer Geometry with Surrogate Ligands.

Modeling nucleic acids.

Long time molecular dynamics for enhanced conformational sampling in biomolecular systems