^{1}

^{*}

^{†}

^{2}

^{3}

^{4}

^{*}

^{†}

^{1}

^{2}

^{3}

^{4}

Edited by: Valentina Tozzini, Nanosciences Institute, National Research Council, Italy

Reviewed by: Sebastien Fiorucci, University of Nice Sophia Antipolis, France; Matteo Tiberti, Danish Cancer Society Research Centre (DCRC), Denmark

This article was submitted to Biological Modeling and Simulation, a section of the journal Frontiers in Molecular Biosciences

†These authors have contributed equally to this work

This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) and the copyright owner(s) are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.

In this perspective, we discuss where and how accounting for electronic many-body polarization affects the accuracy of classical molecular dynamics simulations of biomolecules. While the effects of electronic polarization are highly pronounced for molecules with an opposite total charge, they are also non-negligible for interactions with overall neutral molecules. For instance, neglecting these effects in important biomolecules like amino acids and phospholipids affects the structure of proteins and membranes having a large impact on interpreting experimental data as well as building coarse grained models. With the combined advances in theory, algorithms and computational power it is currently realistic to perform simulations with explicit polarizable dipoles on systems with relevant sizes and complexity. Alternatively, the effects of electronic polarization can also be included at zero additional computational cost compared to standard fixed-charge force fields using the electronic continuum correction, as was recently demonstrated for several classes of biomolecules.

In molecular dynamics simulations, the interactions between molecules are described with approximate potentials known as force fields that mimic the true Born-Oppenheimer energy hypersurface. Among these methods, pairwise additive potentials are very popular for modeling biomolecules such as proteins, lipids or nucleic acids (Ponder and Case,

The limited predictive accuracy of non-polarizable force fields led the molecular modeling community to develop new generation “polarizable” force fields (Gresh et al.,

Secondary structure of proteins is to a large extent determined by an intricate network of hydrogen bonds. The description of hydrogen bonds in standard force fields, however, does not contain important contributions, e.g., from polarization and partially covalent character (Babin et al.,

Membrane proteins form a large part of cellular proteome and are in direct contact with amphiphilic cellular membranes, which influence their structure and activity (Lee,

This could make an impression that the currently available non-polarizable lipid force fields provide comparable accuracy to the models with explicit polarization at a fraction of the computational cost. While the non-polarizable models yield accurate results in many cases (Lucas et al.,

In general, the structure of divalent cations complexes that are widespread in biosystems is traditionally problematic in non-polarizable simulations (Kohagen et al., ^{2+} and Mg^{2+} (Piquemal et al.,

The necessity of polarizability and screening in modeling lipid bilayers has been an issue from the very beginning of computational modeling of model membranes. The first pioneering works on phospholipid bilayers document the need of including polarizability and extra screening in the development of the first models, which was achieved at that time through an empirical scaling factor for the partial atomic charges of the phospholipids (Egberts et al.,

Electronic continuum correction is a very efficient alternative to otherwise computationally demanding explicit modeling of electronic polarization (Bedrov et al.,

In ECC all particles are assumed to have equal polarizabilities and the electric field and electron density within each particle is homogenous (Leontyev and Stuchebrukhov, _{el}, as _{el} is close to 2 for a wide variety of biologically relevant environments meaning that even interfaces like biological membranes do not give rise to large gradients. Despite the coarseness of the approximations, the effects of electronic polarization are described sufficiently well for a variety of biologically relevant molecules in a condensed phase (Duboué-Dijon et al.,

The common implementation of ECC via charge rescaling profoundly resembles an empirical scaling factor, which, obviously, reduces the interaction of charged molecules. From both the derived ECC theory (Leontyev and Stuchebrukhov,

The accuracy of the implicit methods including ECC is limited and gradually becomes inadequate in cases, which do not adhere to the assumed approximations. For instance, the complex electronic structure of Zn^{2+} makes it difficult to capture the ion pairing of zinc chloride with ECC unless specific ad hoc interaction terms between the ions are introduced (Duboué-Dijon et al.,

The AMOEBA force field with explicit polarizable dipoles correctly reproduces water structure around Zn^{2+} in bulk solution and its free energy of hydration, however, it still does not capture the fine details of zinc chloride ion pairing. The reason for that is that Zn^{2+} exhibits considerably large charge transfer effects prefiguring what is happening with transition metals where back-donation effects become important (Gresh et al.,

Such effects also exist with variable magnitude in biomolecular simulations, and resorting to more accurate methods employing physics even beyond explicit polarization will be likely required for predictive accuracy in many cases, e.g., metalloproteins, which shall be interesting playgrounds for such modeling (Gresh et al.,

This being said the question remains: is there any practically achievable perspective application of such advanced models to meaningfully large simulations of biologically relevant systems?—Certainly yes. If the use of polarizable models has been doomed by their computational cost for years, things have dramatically improved. In terms of computational requirements, the approaches utilizing Drude particles (Lopes et al.,

This situation has gradually changed in recent years. First, in link with the improved multi-timestep integration, the key mathematical problem of solving the point dipole equations using iterative methods was alleviated using new non-iterative approaches such as the Truncated Conjugate Gradient (TCG-1) (Aviat et al.,

Overall, methodology has made a key progress and will continue in this direction for all types of polarizable force fields as the accessible computer power quickly increases reducing therefore the computational gap with additive potentials. Whereas specialized highly accurate water potentials based on many-body expansions emerge such as MBPOL (Riera et al.,

In summary, we have presented several important classes and case studies of biomolecules, where including polarizability is an important factor for the simulation accuracy. Cytosolic environment in cells is mostly composed of water solutions of ions, for which polarizability is necessary for the accurate description of the solvated structure of ions, their pairing and interaction with other biomolecules (Piquemal et al.,

The representation of electronic polarization in classical MD simulations can vary largely with Drude and induced point dipoles approaches on one side and continuum approximations on the other (Cieplak et al.,

Biomolecules in the real world cannot turn off their polarizability. Hence, molecular dynamics simulations, which aim to give a realistic, robust, and predictive results, cannot afford to neglect this important contribution to the electrostatic interaction. Currently, polarizable force fields for a large variety of biomolecules and simulation codes implementing polarizability exist and are readily available to solve various biophysical problems (Wu et al.,

All datasets generated for this study are included in the article/supplementary material.

All authors listed have made a substantial, direct and intellectual contribution to the work, and approved it for publication.

The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

We thank the organizers of the CECAM workshop 2019 Multiscale Modeling from Macromolecules to Cell: Opportunities and Challenges of Biomolecular Simulations for their kind invitation to this special research topic.

^{*}: a molecular electronic density-based force field for molecular dynamics simulations