Developing Consistent Molecular Dynamics Force Fields for Biological Chromophores via Force Matching

From Chemical Drawing to Electronic Properties of Semiconducting Polymers in Bulk: A Tool for Chemical Discovery

A quantum chemistry (QC)/molecular dynamics (MD) scheme is developed to calculate electronic properties of semiconducting polymers in three steps: (i) constructing the polymer force field through a unified workflow, (ii) equilibrating polymer models, and (iii) calculating electronic structure properties (e.g., density of states and localization length) from the equilibrated models by QC approaches. Notably, as the second step of this scheme is generally the most time-consuming one, we introduce an alternative method to compute thermally averaged electronic properties in bulk, based on the simulation of a polymer chain in the solution of its repeat units, which is shown to reproduce the microstructure of polymer chains and their electrostatic effect (successfully tested for five benchmark polymers) 10 times faster than state-of-the-art methods. In fact, this scheme offers a consistent and speedy way of estimating electronic properties of polymers from their chemical drawings, thus ensuring the availability of a homogeneous set of simulations to derive structure-property relationships and material design principles. As an example, we show how the electrostatic effect of the polymer chain environment can disturb the localized electronic states at the band tails and how this effect is more significant in the case of diketopyrrolopyrrole polymers as compared to indacenodithiophene and dithiopheneindenofluorene ones.

Identification of Residues Potentially Involved in Optical Shifts in the Water-Soluble Chlorophyll a-Binding Protein through Molecular Dynamics Simulations

Reversible light and thermally induced spectral shifts are universally observed in a wide variety of pigment-protein complexes at temperatures ranging from cryogenic to ambient. In this paper, we employed large-scale molecular dynamics (MD) simulations of a prototypical pigment-protein complex to better understand these shifts at a molecular scale. Although multiple mechanisms have been proposed over the years, no verification of these proposals via MD simulations has thus far been performed; our work represents the first step in this direction. From simulations of the water-soluble chlorophyll-binding protein complex, we determined that rearrangements of long hydrogen bonds were unlikely to be the origin of the multiwell landscape features necessary to explain observed spectral shifts. We also assessed small motions of amino acid residues and identified side chain rotations of some of these residues as likely candidates for the origin of relevant multiwell landscape features. The protein free-energy landscapes associated with side chain rotations feature energy barriers of around 1100-1600 cm-1, in agreement with optical spectroscopy results, with the most promising residue type associated with experimental signatures being serine, which possesses a symmetric triple-well landscape and moment of inertia of a relevant magnitude.

Reparameterization of Non-Bonded Parameters for Copper Ions in Plastocyanin: An Adaptive Force Matching Study

Molecular mechanics rely on existing experimental and theoretical inputs to confidently calculate the trajectories of molecular systems. These calculations, however, are often hindered by missing force field parameters. A notable subject of this problem is metal centers of proteins. This study parameterized, through an adaptive force matching (AFM) workflow, the copper cofactor of plastocyanin in its two oxidation states. New 12-6 Lennard-Jones (LJ) parameters and atomic partial charges were generated to complete the non-bonded description of the copper site. Our models show uniform distorted tetrahedral structures for reduced plastocyanin, Cu(I), and oxidized plastocyanin, Cu(II). These structures align with the QM/MM MD results and existing crystallography studies. TD-DFT calculations, meanwhile, showed that conformations with elongated axial Cu-SMet and shortened equatorial Cu-SCys bonds retain the experimental UV-Vis profile of blue copper (BC) proteins, thus signifying the importance of Cu-S interactions on BC proteins' unique spectroscopic properties.

Recent progress in atomistic modeling of light-harvesting complexes: a mini review

In this mini review, we focus on recent advances in the atomistic modeling of biological light-harvesting (LH) complexes. Because of their size and sophisticated electronic structures, multiscale methods are required to investigate the dynamical and spectroscopic properties of such complexes. The excitation energies, in this context also known as site energies, excitonic couplings, and spectral densities are key quantities which usually need to be extracted to be able to determine the exciton dynamics and spectroscopic properties. The recently developed multiscale approach based on the numerically efficient density functional tight-binding framework followed by excited state calculations has been shown to be superior to the scheme based on pure classical molecular dynamics simulations. The enhanced approach, which improves the description of the internal vibrational dynamics of the pigment molecules, yields spectral densities in good agreement with the experimental counterparts for various bacterial and plant LH systems. Here, we provide a brief overview of those results and described the theoretical foundation of the multiscale protocol.

Accurate Quantum-Mechanically Derived Force-Fields through a Fragment-Based Approach: Balancing Specificity and Transferability in the Prediction of Self-Assembly in Soft Matter

The wide range of time/length scales covered by self-assembly in soft matter makes molecular dynamics (MD) the ideal candidate for simulating such a supramolecular phenomenon at an atomistic level. However, the reliability of MD outcomes heavily relies on the accuracy of the adopted force-field (FF). The spontaneous re-ordering in liquid crystalline materials stands as a clear example of such collective self-assembling processes, driven by a subtle and delicate balance between supramolecular interactions and single-molecule flexibility. General-purpose transferable FFs often dramatically fail to reproduce such complex phenomena, for example, the error on the transition temperatures being larger than 100 K. Conversely, quantum-mechanically derived force-fields (QMD-FFs), specifically tailored for the target system, were recently shown (J. Phys. Chem. Lett.2022,13, 243) to allow for the required accuracy as they not only well reproduced transition temperatures but also yielded a quantitative agreement with the experiment on a wealth of structural, dynamic, and thermodynamic properties. The main drawback of this strategy stands in the computational burden connected to the numerous quantum mechanical (QM) calculations usually required for a target-specific parameterization, which has undoubtedly hampered the routine application of QMD-FFs. In this work, we propose a fragment-based strategy to extend the applicability of QMD-FFs, in which the amount of QM calculations is significantly reduced, being a single-molecule-optimized geometry and its Hessian matrix the only QM information required. To validate this route, a new FF is assembled for a large mesogen, exploiting the parameters obtained for two smaller liquid crystalline molecules, in this and previous work. Lengthy MD simulations are carried out with the new transferred QMD-FF, observing again a spontaneous re-orientation in the correct range of temperatures, with good agreement with the available experimental measures. The present results strongly suggest that a partial transfer of QMD-FF parameters can be invoked without a significant loss of accuracy, thus paving the way to exploit the method's intrinsic predictive capabilities in the simulation of novel soft materials.

Computational development of a phase-sensitive membrane raft probe

Derivatives of the widely used 1,6-diphenyl-1,3,5-hexatriene molecular probe have been considered using a multiscale approach involving spin-flip time-dependent density functional theory, classical molecular dynamics and hybrid quantum mechanics/molecular mechanics. We identify a potential probe of membrane phase (i.e. to preferentially detect liquid-ordered regions of lipid bilayers), which exhibits restricted access to a conical intersection in the liquid-ordered phase but is freely accessible in less ordered molecular environments. The characteristics of this probe also mark it as a candidate for an aggregation induced emission fluorophore.

Molecular Dynamics with Constrained Nuclear Electronic Orbital Density Functional Theory: Accurate Vibrational Spectra from Efficient Incorporation of Nuclear Quantum Effects

Nuclear quantum effects play a crucial role in many chemical and biological systems involving hydrogen atoms yet are difficult to include in practical molecular simulations. In this paper, we combine our recently developed methods of constrained nuclear-electronic orbital density functional theory (cNEO-DFT) and constrained minimized energy surface molecular dynamics (CMES-MD) to create a new method for accurately and efficiently describing nuclear quantum effects in molecular simulations. By use of this new method, dubbed cNEO-MD, the vibrational spectra of a set of small molecules are calculated and compared with those from conventional ab initio molecular dynamics (AIMD) as well as from experiments. With the same formal scaling, cNEO-MD greatly outperforms AIMD in describing the vibrational modes with significant hydrogen motion characters, demonstrating the promise of cNEO-MD for simulating chemical and biological systems with significant nuclear quantum effects.

Q-Force: Quantum Mechanically Augmented Molecular Force Fields

The quality of molecular dynamics simulations strongly depends on the accuracy of the underlying force fields (FFs) that determine all intra- and intermolecular interactions of the system. Commonly, transferable FF parameters are determined based on a representative set of small molecules. However, such an approach sacrifices accuracy in favor of generality. In this work, an open-source and automated toolkit named Q-Force is presented, which augments these transferable FFs with molecule-specific bonded parameters and atomic charges that are derived from quantum mechanical (QM) calculations. The molecular fragmentation procedure allows treatment of large molecules (>200 atoms) with a low computational cost. The generated Q-Force FFs can be used at the same computational cost as transferable FFs, but with improved accuracy: We demonstrate this for the vibrational properties on a set of small molecules and for the potential energy surface on a complex molecule (186 atoms) with photovoltaic applications. Overall, the accuracy, user-friendliness, and minimal computational overhead of the Q-Force protocol make it widely applicable for atomistic molecular dynamics simulations.

Automated Parameterization of Quantum Mechanically Derived Force Fields for Soft Materials and Complex Fluids: Development and Validation

The reliability of molecular dynamics (MD) simulations in predicting macroscopic properties of complex fluids and soft materials, such as liquid crystals, colloidal suspensions, or polymers, relies on the accuracy of the adopted force field (FF). We present an automated protocol to derive specific and accurate FFs, fully based on ab initio quantum mechanical (QM) data. The integration of the Joyce and Picky procedures, recently proposed by our group to provide an accurate description of simple liquids, is here extended to larger molecules, capable of exhibiting more complex fluid phases. While the standard Joyce protocol is employed to parameterize the intramolecular FF term, a new automated procedure is here proposed to handle the computational cost of the QM calculations required for the parameterization of the intermolecular FF term. The latter is thus obtained by integrating the old Picky procedure with a fragmentation reconstruction method (FRM) that allows for a reliable, yet computationally feasible sampling of the intermolecular energy surface at the QM level. The whole FF parameterization protocol is tested on a benchmark liquid crystal, and the performances of the resulting quantum mechanically derived (QMD) FF were compared with those delivered by a general-purpose, transferable one, and by the third, "hybrid" FF, where only the bonded terms were refined against QM data. Lengthy atomistic MD simulations are carried out with each FF on extended 5CB systems in both isotropic and nematic phases, eventually validating the proposed protocol by comparing the resulting macroscopic properties with other computational models and with experiments. The QMD-FF yields the best performances, reproducing both phases in the correct range of temperatures and well describing their structure, dynamics, and thermodynamic properties, thus providing a clear protocol that may be explored to predict such properties on other complex fluids or soft materials.

Quantum and semiclassical dynamical studies of nonadiabatic processes in solution: achievements and perspectives

We concisely review the main methodological approaches to model nonadiabatic dynamics in isotropic solutions and their applications. Three general classes of models are identified as the most used to include solvent effects in the simulations. The first model describes the solvent as a set of harmonic collective modes coupled to the solute degrees of freedom, and the second as a continuum, while the third explicitly includes solvent molecules in the calculations. The issues related to the use of these models in semiclassical and quantum dynamical simulations are discussed, as well as the main limitations and perspectives of each approach.

ParaMol: A Package for Automatic Parameterization of Molecular Mechanics Force Fields

The ensemble of structures generated by molecular mechanics (MM) simulations is determined by the functional form of the force field employed and its parameterization. For a given functional form, the quality of the parameterization is crucial and will determine how accurately we can compute observable properties from simulations. While accurate force field parameterizations are available for biomolecules, such as proteins or DNA, the parameterization of new molecules, such as drug candidates, is particularly challenging as these may involve functional groups and interactions for which accurate parameters may not be available. Here, in an effort to address this problem, we present ParaMol, a Python package that has a special focus on the parameterization of bonded and nonbonded terms of druglike molecules by fitting to ab initio data. We demonstrate the software by deriving bonded terms' parameters of three widely known drug molecules, viz. aspirin, caffeine, and a norfloxacin analogue, for which we show that, within the constraints of the functional form, the methodologies implemented in ParaMol are able to derive near-ideal parameters. Additionally, we illustrate the best practices to follow when employing specific parameterization routes. We also determine the sensitivity of different fitting data sets, such as relaxed dihedral scans and configurational ensembles, to the parameterization procedure, and discuss the features of the various weighting methods available to weight configurations. Owing to ParaMol's capabilities, we propose that this software can be introduced as a routine step in the protocol normally employed to parameterize druglike molecules for MM simulations.

Normal mode analysis of spectral density of FMO trimers: Intra- and intermonomer energy transfer

The intermolecular contribution to the spectral density of the exciton-vibrational coupling of the homotrimeric Fenna-Matthews-Olson (FMO) light-harvesting protein of green sulfur bacteria P. aestuarii is analyzed by combining a normal mode analysis of the protein with the charge density coupling method for the calculation of local transition energies of the pigments. Correlations in site energy fluctuations across the whole FMO trimer are found at low vibrational frequencies. Including, additionally, the high-frequency intrapigment part of the spectral density, extracted from line-narrowing spectra, we study intra- and intermonomer exciton transfer. Whereas the intrapigment part of the spectral density is important for fast intramonomer exciton relaxation, the intermolecular contributions (due to pigment-environment coupling) determine the intermonomer exciton transfer. Neither the variations of the local Huang-Rhys factors nor the correlations in site energy fluctuations have a critical influence on energy transfer. At room temperature, the intermonomer transfer in the FMO protein occurs on a 10 ps time scale, whereas intramonomer exciton equilibration is roughly two orders of magnitude faster. At cryogenic temperatures, intermonomer transfer limits the lifetimes of the lowest exciton band. The lifetimes are found to increase between 20 ps in the center of this band up to 100 ps toward lower energies, which is in very good agreement with the estimates from hole burning data. Interestingly, exciton delocalization in the FMO monomers is found to slow down intermonomer energy transfer, at both physiological and cryogenic temperatures.

DFTB/MM Molecular Dynamics Simulations of the FMO Light-Harvesting Complex

Because of the size of light-harvesting complexes and the involvement of electronic degrees of freedom, computationally these systems need to be treated with a combined quantum-classical description. To this end, Born-Oppenheimer molecular dynamics simulations have been employed in a quantum mechanics/molecular mechanics (QM/MM) fashion for the ground state followed by excitation energy calculations again in a QM/MM scheme for the Fenna-Matthews-Olson (FMO) complex. The self-consistent-charge density functional tight-binding (DFTB) method electrostatically coupled to a classical description of the environment was applied to perform the ground-state dynamics. Subsequently, long-range-corrected time-dependent DFTB calculations were performed to determine the excitation energy fluctuations of the individual bacteriochlorophyll a molecules. The spectral densities obtained using this approach show an excellent agreement with experimental findings. In addition, the fluctuating site energies and couplings were used to estimate the exciton transfer dynamics.

Automated parameterization of quantum-mechanically derived force-fields including explicit sigma holes: A pathway to energetic and structural features of halogen bonds in gas and condensed phase

In classical molecular dynamics, general purpose atomistic force-fields (FFs) often deliver inaccurate results when dealing with halogen bonds (XBs), notwithstanding their crucial role in many fields of science, ranging from material design to drug development. Given the large dimensions of the systems of interest, it would be therefore desirable to increase the FF accuracy maintaining the simplicity of the standard Lennard-Jones (LJ) plus point charge description to avoid an excessive computational cost. A simple yet effective strategy consists in introducing a number of virtual sites able to mimic the so-called "explicit σ-hole." In this work, we present an automated FF parameterization strategy based on a global optimization of both LJ and charge parameters with respect to accurate quantum mechanical data, purposely computed for the system under investigation. As a test case, we report on two homologue series, characterized either by weak or strong XBs, namely, the di-halogenated methanes and the mono-, di-, and tri-substituted acetonitriles, taking into consideration Cl, Br, and I substituents. The resulting quantum mechanically derived FFs are validated for each compound in the gas and in the condensed phase by comparing them to general purpose and specific FFs without virtual sites and to highly accurate reference quantum mechanical data. The results strongly support the adoption of the specific FFs with virtual sites, which overcome the other investigated models in representing both gas phase energetics and the structural patterns of the liquid phase structure related to the presence of XBs.

On the arrangement of chromophores in light harvesting complexes: chance versus design

We used a homogeneous computational approach to derive the excitonic Hamiltonian for five light harvesting complexes containing only one type of chromophore and compare them in terms of statistical descriptors. We then studied the approximate exciton dynamics for the five complexes introducing a measure, the (averaged and time-dependent) inverse participation ratio, that enables the comparison between very diverse complexes on the same ground. We find that the global dynamics are very similar across the set of systems despite the variety of geometric structures of the complexes. In particular, the dynamics of four out of five light harvesting complexes are barely distinguishable with a small variation from the norm seen only for the Fenna-Matthews-Olson complex. We use the information from the realistic Hamiltonians to build a reduced model system that shows how the global dynamics are ultimately dominated by a single parameter, the degree of localization of the excitonic Hamiltonian eigenstates. Considering the physically plausible range of system parameters, the reduced model explains why the dynamics are so similar across most light harvesting complexes containing a single type of chromophore regardless of the detailed pattern of the inter-chromophore excitonic coupling.

Quantum Chemical Modeling of the Photoinduced Activity of Multichromophoric Biosystems

Multichromophoric biosystems represent a broad family with very diverse members, ranging from light-harvesting pigment-protein complexes to nucleic acids. The former are designed to capture, harvest, efficiently transport, and transform energy from sunlight for photosynthesis, while the latter should dissipate the absorbed radiation as quickly as possible to prevent photodamages and corruption of the carried genetic information. Because of the unique electronic and structural characteristics, the modeling of their photoinduced activity is a real challenge. Numerous approaches have been devised building on the theoretical development achieved for single chromophores and on model Hamiltonians that capture the essential features of the system. Still, a question remains: is a general strategy for the accurate modeling of multichromophoric systems possible? By using a quantum chemical point of view, here we review the advancements developed so far highlighting differences and similarities with the single chromophore treatment. Finally, we outline the important limitations and challenges that still need to be tackled to reach a complete and accurate picture of their photoinduced properties and dynamics.

How the dyes affect folding of small proteins in single-molecule FRET experiments: A simulation study

A key question in the application of the single-molecule Förster resonance energy transfer (smFRET) technique to study protein folding is how the dyes affect the protein behavior. Understanding of these effects is particularly important for small proteins, for which the dyes, along with their linkers, can be comparable in size (mass) with the protein. Using a coarse-grained model, we simulated folding of BBL protein and two of its FRET constructs. The obtained results suggest that even for small proteins, such as the 45-residue BBL, the appearance of the excluded volume in the protein conformation space due to the presence of dyes does not change the overall picture of folding. At the same time, some deviations from folding of the original protein are observed, in particular, the FRET constructs fold considerably slower than the original protein because the protein collapse in the initial state of folding is slowed down due to the protein loading with relatively massive dyes.

Computational Characterization of a Cholesterol-Based Molecular Rotor in Lipid Membranes

Biophysical properties of cellular membranes critically depend on their content of cholesterol and its interaction with various other lipid species. Cholesterol-dependent friction at the nanoscale can be studied with molecular rotors, whose quantum yield depends on rotational dynamics of functional groups during their excited state lifetime. Here, we present a detailed computational analysis of a phenyl-BODIPY-linked cholesterol based molecular rotor in direct comparison with the well-known TopFluor-cholesterol. We describe a new parametrization strategy of force field parameters for the BODIPY moiety and carry out extensive molecular dynamics simulations of the probe in membranes in the absence or presence of cholesterol. Our study quantifies the extent of membrane perturbation by these probes, analyzes their tilting resistance in the bilayer and derives dynamic properties directly related to the rotor propensity. We show that phenyl-BODIPY-cholesterol bears potential as a cholesterol-dependent molecular rotor to report about microviscosity of sterol-containing model and cell membranes.