A chirality-based metrics for free-energy calculations in biomolecular systems

Simulation workflows to predict the circular dichroism and circularly polarized luminescence of chiral materials

Chiral materials are attracting considerable interest in various fields in view of their unique properties and optical activity. Indeed, the peculiar features of chiral materials to absorb and emit circularly polarized light enable their use in an extensive range of applications. Motivated by the interest in boosting the development of chiral materials characterized by enhanced chiroptical properties such as circular dichroism (CD) and circular polarized luminescence (CPL), we herein illustrate in this tutorial how theoretical simulations can be used for the predictions and interpretations of chiroptical data and for the identification of chiral geometries. We are focusing on computational frameworks that can be used to investigate the theoretical aspects of chiral materials' photophysical and conformational characteristics. We will then illustrate ab initio methods based on density functional theory (DFT) and its time-dependent extension (TD-DFT) to simulate CD and CPL signals, and we will exemplify a variety of enhanced sampling techniques useful for an adequate sampling of the configurational space for chiral systems.

Unsupervised Data-Driven Reconstruction of Molecular Motifs in Simple to Complex Dynamic Micelles

The reshuffling mobility of molecular building blocks in self-assembled micelles is a key determinant of many their interesting properties, from emerging morphologies and surface compartmentalization, to dynamic reconfigurability and stimuli-responsiveness. However, the microscopic details of such complex structural dynamics are typically nontrivial to elucidate, especially in multicomponent assemblies. Here we show a machine-learning approach that allows us to reconstruct the structural and dynamic complexity of mono- and bicomponent surfactant micelles from high-dimensional data extracted from equilibrium molecular dynamics simulations. Unsupervised clustering of smooth overlap of atomic position (SOAP) data enables us to identify, in a set of multicomponent surfactant micelles, the dominant local molecular environments that emerge within them and to retrace their dynamics, in terms of exchange probabilities and transition pathways of the constituent building blocks. Tested on a variety of micelles differing in size and in the chemical nature of the constitutive self-assembling units, this approach effectively recognizes the molecular motifs populating them in an exquisitely agnostic and unsupervised way, and allows correlating them to their composition in terms of constitutive surfactant species.

Physics-Inspired Structural Representations for Molecules and Materials

The first step in the construction of a regression model or a data-driven analysis, aiming to predict or elucidate the relationship between the atomic-scale structure of matter and its properties, involves transforming the Cartesian coordinates of the atoms into a suitable representation. The development of atomic-scale representations has played, and continues to play, a central role in the success of machine-learning methods for chemistry and materials science. This review summarizes the current understanding of the nature and characteristics of the most commonly used structural and chemical descriptions of atomistic structures, highlighting the deep underlying connections between different frameworks and the ideas that lead to computationally efficient and universally applicable models. It emphasizes the link between properties, structures, their physical chemistry, and their mathematical description, provides examples of recent applications to a diverse set of chemical and materials science problems, and outlines the open questions and the most promising research directions in the field.

Learning how planarization can affect dichroic patterns in polyfluorenes

The circular dichroism spectra of a single chain of polyfluorene was predicted for a p-twisted helix conformation and local planarized polymer sections in the presence and in the absence of thermal vibrations. Under thermal vibrations at 300 K, the planarized section of polyfluorene affords a red-shifted positive dichroic band between 446 and 456 nm, preserving a degree of chirality. The S1 ← S0 excitation energy decreases from 3.29 eV, for the p-twisted helix to 2.77 or 2.71 eV, for planarized sections with one or two coplanar twists, respectively. Thermal vibrations and intramolecular rotations eventually affect the circular dichroism spectrum patterns, where planarized bent conformers induce a positive band towards 450 nm.

Synergistic Approach of Ultrafast Spectroscopy and Molecular Simulations in the Characterization of Intramolecular Charge Transfer in Push-Pull Molecules

The comprehensive characterization of Intramolecular Charge Transfer (ICT) stemming in push-pull molecules with a delocalized π-system of electrons is noteworthy for a bespoke design of organic materials, spanning widespread applications from photovoltaics to nanomedicine imaging devices. Photo-induced ICT is characterized by structural reorganizations, which allows the molecule to adapt to the new electronic density distribution. Herein, we discuss recent photophysical advances combined with recent progresses in the computational chemistry of photoactive molecular ensembles. We focus the discussion on femtosecond Transient Absorption Spectroscopy (TAS) enabling us to follow the transition from a Locally Excited (LE) state to the ICT and to understand how the environment polarity influences radiative and non-radiative decay mechanisms. In many cases, the charge transfer transition is accompanied by structural rearrangements, such as the twisting or molecule planarization. The possibility of an accurate prediction of the charge-transfer occurring in complex molecules and molecular materials represents an enormous advantage in guiding new molecular and materials design. We briefly report on recent advances in ultrafast multidimensional spectroscopy, in particular, Two-Dimensional Electronic Spectroscopy (2DES), in unraveling the ICT nature of push-pull molecular systems. A theoretical description at the atomistic level of photo-induced molecular transitions can predict with reasonable accuracy the properties of photoactive molecules. In this framework, the review includes a discussion on the advances from simulation and modeling, which have provided, over the years, significant information on photoexcitation, emission, charge-transport, and decay pathways. Density Functional Theory (DFT) coupled with the Time-Dependent (TD) framework can describe electronic properties and dynamics for a limited system size. More recently, Machine Learning (ML) or deep learning approaches, as well as free-energy simulations containing excited state potentials, can speed up the calculations with transferable accuracy to more complex molecules with extended system size. A perspective on combining ultrafast spectroscopy with molecular simulations is foreseen for optimizing the design of photoactive compounds with tunable properties.

Unsupervised machine learning in atomistic simulations, between predictions and understanding

Automated analyses of the outcome of a simulation have been an important part of atomistic modeling since the early days, addressing the need of linking the behavior of individual atoms and the collective properties that are usually the final quantity of interest. Methods such as clustering and dimensionality reduction have been used to provide a simplified, coarse-grained representation of the structure and dynamics of complex systems from proteins to nanoparticles. In recent years, the rise of machine learning has led to an even more widespread use of these algorithms in atomistic modeling and to consider different classification and inference techniques as part of a coherent toolbox of data-driven approaches. This perspective briefly reviews some of the unsupervised machine-learning methods-that are geared toward classification and coarse-graining of molecular simulations-seen in relation to the fundamental mathematical concepts that underlie all machine-learning techniques. It discusses the importance of using concise yet complete representations of atomic structures as the starting point of the analyses and highlights the risk of introducing preconceived biases when using machine learning to rationalize and understand structure-property relations. Supervised machine-learning techniques that explicitly attempt to predict the properties of a material given its structure are less susceptible to such biases. Current developments in the field suggest that using these two classes of approaches side-by-side and in a fully integrated mode, while keeping in mind the relations between the data analysis framework and the fundamental physical principles, will be key to realizing the full potential of machine learning to help understand the behavior of complex molecules and materials.

Defining an Optimal Metric for the Path Collective Variables

Path Collective Variables (PCVs) are a set of path-like variables that have been successfully used to investigate complex chemical and biological processes and compute their associated free energy surfaces and kinetics. Their current implementation relies on general, but at times inefficient, metrics (such as RMSD or DRMSD) to evaluate the distance between the instantaneous conformational state during the simulation and the reference coordinates defining the path. In this work, we present a new algorithm to construct optimal PCVs metrics as linear combinations of different CVs weighted through a spectral gap optimization procedure. The method was tested first on a simple model, trialanine peptide, in vacuo and then on a more complex path of an anticancer inhibitor binding to its pharmacological target. We also compared the results to those obtained with other path-based algorithms. We find that not only our proposed approach is able to automatically select relevant CVs for the PCVs metric but also that the resulting PCVs allow for reconstructing the associated free energy very efficiently. What is more, at difference with other path-based methods, our algorithm is able to explore nonlocally the reaction path space.

A Versatile Computational Strategy To Characterize the Free-Energy Landscape of Excited States in Oligofluorenes

The π-rich rings of conjugated polymers and molecular rotors shape their typical properties, allowing a variety of chemical and photoresponsive phenomena. Herein, we present a computational method in the framework of classical simulations to estimate the free-energy gap between ground and excited states of oligofluorenes, which is a class of molecular rotors widely used in optoelectronic devices, because of the inner torsional rotation triggered by light irradiation. We devised multiple sets of free-energy simulations in combination with free-energy perturbation theory to predict the free-energy gap between the ground state and the first excited state. The computed excitation energies show good agreement with experiments. The approach presented herein allows one to achieve comprehensive sampling of the conformational landscape and accurate estimates of the excited state free-energy landscapes at the same time.

Free-energy predictions and absorption spectra calculations for supramolecular nanocarriers and their photoactive cargo

We reconstructed the free-energy landscape for supramolecular nanoparticles of amphiphilic methacrylated-based co-polymers. Their self-assembly in aqueous solution and encapsulation of borondipyrromethene (BODIPY) derivatives were enforced through atomistic free-energy simulations. The BODIPY binding modes detected in each of the free-energy basins were validated through a comparison of theoretical absorption spectra, calculated at the TD-DFT level, to their experimental counterparts. The nanoparticle distribution is controlled within a thermodynamic regime, with free-energy barriers approaching 8 kcal mol^-1, enabling the existence of different-sized nanoparticles in aqueous solution at room temperature. Two types of supramolecular morphologies were identified. One is compact and spherical in shape and the other is large and donut-like, with the former more stable than the latter by 4 kcal mol^-1. The morphology of the supramolecular host affects the binding mode of the BODIPY guests. Stacked BODIPY aggregates are encapsulated in the spherical nanocarriers, whereas isolated chromophores associate with the donut-shaped assemblies.

Dataset of the AAC2 conformations in the c-, intermediate- and m-states obtained from free-energy simulations

The data reported herein are related to the article entitled: "The switching mechanism of the mitochondrial ADP/ATP carrier explored by free-energy landscapes" (Pietropaolo et al., 2016) [1]. We report the coordinates of the ADP/ATP carrier (AAC2) in the presence and absence of adenine and guanine nucleotides in the c-, intermediate- and m-states obtained from the free-energy simulations and corresponding to the free-energy minima.

The switching mechanism of the mitochondrial ADP/ATP carrier explored by free-energy landscapes

The ADP/ATP carrier (AAC) of mitochondria has been an early example for elucidating the transport mechanism alternating between the external (c-) and internal (m-) states (M. Klingenberg, Biochim. Biophys. Acta 1778 (2008) 1978-2021). An atomic resolution crystal structure of AAC is available only for the c-state featuring a three repeat transmembrane domain structure. Modeling of transport mechanism remained hypothetical for want of an atomic structure of the m-state. Previous molecular dynamics studies simulated the binding of ADP or ATP to the AAC remaining in the c-state. Here, a full description of the AAC switching from the c- to the m-state is reported using well-tempered metadynamics simulations. Free-energy landscapes of the entire translocation from the c- to the m-state, based on the gyration radii of the c- and m-gates and of the center of mass, were generated. The simulations revealed three free-energy basins attributed to the c-, intermediate- and m-states separated by activation barriers. These simulations were performed with the empty and with the ADP- and ATP-loaded AAC as well as with the poorly transported AMP and guanine nucleotides, showing in the free energy landscapes that ADP and ATP lowered the activation free-energy barriers more than the other substrates. Upon binding AMP and guanine nucleotides a deeper free-energy level stabilized the intermediate-state of the AAC2 hampering the transition to the m-state. The structures of the substrate binding sites in the different states are described producing a full picture of the translocation events in the AAC.

Effect of Different Z-Inducers on the Stabilization of Z Portion in BZ-DNA Sequence: Correlation Between Experimental and Simulation Data

In this study we show the outstanding agreement between simulation and experimental data concerning the efficient stabilization effect by NaCl of Z conformation. We demonstrate by circular dichroism (CD) experiments that Na(+) not only is able to induce a B to Z form transition in a short (GC)3 alternated portion of a sequence having 17 basis, but also is the best stabilizer in comparison with other Z inducers used (spermine and NiCl2). This result was confirmed by free energy calculations.

Predicting the switchable screw sense in fluorene-based polymers

A chirality-switching free-energy landscape was reconstructed on a 43-mer of poly(9,9-dioctylfluoren-2,7-diyl) (PDOF). The simulations were conducted on amorphous silica surface as well as in the vacuum phase for a single chain or for a group of sixteen chains. The achiral-to-chiral transition occurs only on amorphous silica (activation free-energy 35 kcal mol(-1) ), where the enantiomeric (homochiral) basins are detected. This was supported by the experiments where effective chirality induction to PDOF using circularly polarized light (CPL) was attained only for a film deposited on a quartz glass and not for a solution or a suspension. These results indicate that interactions of PDOF with amorphous silica play a crucial role in chirality switching. Importance of chain assembling was also indicated. Theoretical ECD spectra of the enantiomeric basins containing a 51 helix reproduce the experimental spectra.

Molecular mechanism of polyacrylate helix sense switching across its free energy landscape

Helical polymers with switchable screw sense are versatile frameworks for chiral functional materials. In this work, we reconstructed the free energy landscape of helical poly(2,7-bis(4-tert-butylphenyl)fluoren-9-yl acrylate) [poly(BBPFA)], as its racemization is selectively driven by light without any rearrangement of chemical bonds. The chirality inversion was enforced by atomistic free energy simulations using chirality indices as reaction coordinates. The free energy landscape reproduced the experimental electronic circular dichroism spectra. We propose that the chirality inversion of poly(BBPFA) proceeds from a left-handed 31 helix via multistate free energy pathways to reach the right-handed 31 helix. The inversion is triggered by the rotation of biphenyl units with an activation barrier of 38 kcal/mol. To the best of our knowledge, this is the first report on the chiral inversion mechanism of a helical polymer determined in a quantitative way in the framework of atomistic free energy simulations.

Computational study of synthetic agonist ligands of ionotropic glutamate receptors

Neurological glutamate receptors are among the most important and intensely studied protein ligand binding systems in humans. They are crucial for the functioning of the central nervous system and involved in a variety of pathologies. Apart from the neurotransmitter glutamate, several artificial, agonistic and antagonistic ligands are known. Of particular interest here are novel photoswitchable agonists that would open the field of optogenetics to glutamate receptors. The receptor proteins are complex, membrane-bound multidomain oligomers that undergo large scale functional conformational changes, making detailed studies of their atomic structure challenging. Therefore, a thorough understanding of the microscopic details of ligand binding and receptor activation remains elusive in many cases. This topic has been successfully addressed by theoretical studies in the past and in this paper, we present extensive molecular dynamics simulation and free energy calculation results on the binding of AMPA and an AMPA derivative, which is the basis for designing light-sensitive ligands. We provide a two-step model for ligand binding domain activation and predict binding free energies for novel compounds in good agreement to experimental observations.

Exploring metal-driven stereoselectivity of glycopeptides by free-energy calculations

A formalism to quantify the chemical stereoselectivity, based on free energy of binding calculations, is here discussed. It is used to explain the stereoselectivity of two diastereoisomeric frameworks, comprising the dimer of a copper(II)-peptide core of L- and D-carnosine, respectively, each bound to two chains of D-trehalose, in which copper(II) adopts a type-II coordination geometry. The stereocenter of carnosine is varied both L and D, giving rise to two diastereoisomers. A thermodynamic cycle crossing the formation of the two enantiomeric copper(II) peptide cores was devised. A harmonic restraining potential that depends only on the bond distance was added to ensure reversibility in bond formation and dissociation, for an accurate estimate of the free energy. The calculation of the free energy of binding between D-trehalose and the two enantiomeric copper(II) peptide cores reproduces the free-energy quantities observed from stability constants and isothermal titration calorimetry (ITC) measurements. This is an example of chirality selection based on free-energy difference.