Choice Of Collective Variables Research Articles

Application of Machine Learning Algorithms to Metadynamics for the Elucidation of the Binding Modes and Free Energy Landscape of Drug/Target Interactions: a Case Study.

In the context of drug discovery, computational methods were able to accelerate the challenging process of designing and optimizing a new drug candidate. Amongst the possible atomistic simulation approaches, metadynamics (metaD) has proven very powerful. However, the choice of collective variables (CVs) is not trivial for complex systems. To automate the process of CVs identification, we apply here two different machine learning (ML) algorithms, namely DeepLDA and Autoencoder, to the metaD simulation of a well-researched drug/target complex, constituted by a pharmacologically relevant non-canonical DNA secondary structure (G-quadruplex) and a metallodrug acting as its stabilizer, as well as solvent molecules.

Chasing collective variables using temporal data-driven strategies.

The convergence of free-energy calculations based on importance sampling depends heavily on the choice of collective variables (CVs), which in principle, should include the slow degrees of freedom of the biological processes to be investigated. Autoencoders (AEs), as emerging data-driven dimension reduction tools, have been utilised for discovering CVs. AEs, however, are often treated as black boxes, and what AEs actually encode during training, and whether the latent variables from encoders are suitable as CVs for further free-energy calculations remains unknown. In this contribution, we review AEs and their time-series-based variants, including time-lagged AEs (TAEs) and modified TAEs, as well as the closely related model variational approach for Markov processes networks (VAMPnets). We then show through numerical examples that AEs learn the high-variance modes instead of the slow modes. In stark contrast, time series-based models are able to capture the slow modes. Moreover, both modified TAEs with extensions from slow feature analysis and the state-free reversible VAMPnets (SRVs) can yield orthogonal multidimensional CVs. As an illustration, we employ SRVs to discover the CVs of the isomerizations of N-acetyl-N'-methylalanylamide and trialanine by iterative learning with trajectories from biased simulations. Last, through numerical experiments with anisotropic diffusion, we investigate the potential relationship of time-series-based models and committor probabilities.

Collective variable discovery in the age of machine learning: reality, hype and everything in between.

Understanding the kinetics and thermodynamics profile of biomolecules is necessary to understand their functional roles which has a major impact in mechanism driven drug discovery. Molecular dynamics simulation has been routinely used to understand conformational dynamics and molecular recognition in biomolecules. Statistical analysis of high-dimensional spatiotemporal data generated from molecular dynamics simulation requires identification of a few low-dimensional variables which can describe the essential dynamics of a system without significant loss of information. In physical chemistry, these low-dimensional variables are often called collective variables. Collective variables are used to generate reduced representations of free energy surfaces and calculate transition probabilities between different metastable basins. However the choice of collective variables is not trivial for complex systems. Collective variables range from geometric criteria such as distances and dihedral angles to abstract ones such as weighted linear combinations of multiple geometric variables. The advent of machine learning algorithms led to increasing use of abstract collective variables to represent biomolecular dynamics. In this review, I will highlight several nuances of commonly used collective variables ranging from geometric to abstract ones. Further, I will put forward some cases where machine learning based collective variables were used to describe simple systems which in principle could have been described by geometric ones. Finally, I will put forward my thoughts on artificial general intelligence and how it can be used to discover and predict collective variables from spatiotemporal data generated by molecular dynamics simulations.

Orthogonal order parameters to model the reaction coordinate of an enzyme catalyzed reaction

The choice of suitable collective variables in formulating an optimal reaction coordinate is a challenging task for activated transitions between a pair of stable states especially when dealing with biochemical changes such as enzyme catalyzed reactions. A detailed benchmarking study is carried out on the choice of collective variables that can distinguish between the stable states unambiguously. We specifically address the issue if these variables may be directly used to model the optimal reaction coordinate, or if it would be better to use their orthogonalized counterparts. The proposed computational scheme is applied to the rate determining intramolecular proton transfer step in the enzyme human carbonic anhydrase II. The optimum reaction coordinate is determined with and without orthogonalization of the collective variables pertinent to a key conformational fluctuation and the actual proton transfer step at the active site of the enzyme. Suitability of the predicted reaction coordinates in different processes is examined in terms of the free energy profile projected along the reaction coordinate, the rate constant of transition and the underlying molecular mechanism of barrier crossing. Our results indicate that a better agreement with earlier simulation and experimental data is obtained when the orthogonalized collective variables are used to model the reaction coordinate.

Predictive collective variable discovery with deep Bayesian models.

Extending spatio-temporal scale limitations of models for complex atomistic systems considered in biochemistry and materials science necessitates the development of enhanced sampling methods. The potential acceleration in exploring the configurational space by enhanced sampling methods depends on the choice of collective variables (CVs). In this work, we formulate the discovery of CVs as a Bayesian inference problem and consider the CVs as hidden generators of the full-atomistic trajectory. The ability to generate samples of the fine-scale atomistic configurations using limited training data allows us to compute estimates of observables as well as our probabilistic confidence on them. The methodology is based on emerging methodological advances in machine learning and variational inference. The discovered CVs are related to physicochemical properties which are essential for understanding mechanisms especially in unexplored complex systems. We provide a quantitative assessment of the CVs in terms of their predictive ability for alanine dipeptide (ALA-2) and ALA-15 peptide.

A variational conformational dynamics approach to the selection of collective variables in metadynamics.

In this paper, we combine two powerful computational techniques, well-tempered metadynamics and time-lagged independent component analysis. The aim is to develop a new tool for studying rare events and exploring complex free energy landscapes. Metadynamics is a well-established and widely used enhanced sampling method whose efficiency depends on an appropriate choice of collective variables. Often the initial choice is not optimal leading to slow convergence. However by analyzing the dynamics generated in one such run with a time-lagged independent component analysis and the techniques recently developed in the area of conformational dynamics, we obtain much more efficient collective variables that are also better capable of illuminating the physics of the system. We demonstrate the power of this approach in two paradigmatic examples.

METAGUI 3: A graphical user interface for choosing the collective variables in molecular dynamics simulations

Molecular dynamics (MD) simulations allow the exploration of the phase space of biopolymers through the integration of equations of motion of their constituent atoms. The analysis of MD trajectories often relies on the choice of collective variables (CVs) along which the dynamics of the system is projected. We developed a graphical user interface (GUI) for facilitating the interactive choice of the appropriate CVs. The GUI allows: defining interactively new CVs; partitioning the configurations into microstates characterized by similar values of the CVs; calculating the free energies of the microstates for both unbiased and biased (metadynamics) simulations; clustering the microstates in kinetic basins; visualizing the free energy landscape as a function of a subset of the CVs used for the analysis. A simple mouse click allows one to quickly inspect structures corresponding to specific points in the landscape.Program summaryProgram Title: METAGUI 3Program Files doi:http://dx.doi.org/10.17632/wyxjndwkbp.1Licensing provisions: GPLv3Programming language: Tcl/Tk, FortranJournal reference of previous version: METAGUI [1]Does the new version supersede the previous version?: NoNature of problem: Choose the appropriate collective variables for describing the thermodynamics and kinetics of a biomolecular system through biased and unbiased molecular dynamics.Solution method: Provide an environment to compute and visualize free energy surfaces as a function of collective variables, interactively defined.Additional comments: METAGUI 3 is not a standalone program but a plugin that provides analysis features within VMD (version 1.9.2 or higher). [1]X. Biarnés, F. Pietrucci, F. Marinelli, A. Laio, METAGUI. A VMD interface for analyzing metadynamics and molecular dynamics simulations, Computer Physics Communications 183 (2012) 203–211.

Molecular recognition of DNA by ligands: Roughness and complexity of the free energy profile

Understanding the molecular mechanism by which probes and chemotherapeutic agents bind to nucleic acids is a fundamental issue in modern drug design. From a computational perspective, valuable insights are gained by the estimation of free energy landscapes as a function of some collective variables (CVs), which are associated with the molecular recognition event. Unfortunately the choice of CVs is highly non-trivial because of DNA's high flexibility and the presence of multiple association-dissociation events at different locations and/or sliding within the grooves. Here we have applied a modified version of Locally-Scaled Diffusion Map (LSDMap), a nonlinear dimensionality reduction technique for decoupling multiple-timescale dynamics in macromolecular systems, to a metadynamics-based free energy landscape calculated using a set of intuitive CVs. We investigated the binding of the organic drug anthramycin to a DNA 14-mer duplex. By performing an extensive set of metadynamics simulations, we observed sliding of anthramycin along the full-length DNA minor groove, as well as several detachments from multiple sites, including the one identified by X-ray crystallography. As in the case of equilibrium processes, the LSDMap analysis is able to extract the most relevant collective motions, which are associated with the slow processes within the system, i.e., ligand diffusion along the minor groove and dissociation from it. Thus, LSDMap in combination with metadynamics (and possibly every equivalent method) emerges as a powerful method to describe the energetics of ligand binding to DNA without resorting to intuitive ad hoc reaction coordinates.