Development of multiscale models for complex chemical systems: from H+H₂ to biomolecules (Nobel Lecture)

Nonadiabatic Field: A Conceptually Novel Approach for Nonadiabatic Quantum Molecular Dynamics

Reliable trajectory-based nonadiabatic quantum dynamics methods at the atomic/molecular level are critical for the practical understanding and rational design of many important processes in real large/complex systems, where the quantum dynamical behavior of electrons and that of nuclei are coupled. The paper reports latest progress of nonadiabatic field (NaF), a conceptually novel approach for nonadiabatic quantum dynamics with independent trajectories. Substantially different from the mainstreams of Ehrenfest-like dynamics and surface hopping methods, the nuclear force in NaF involves the nonadiabatic force arising from the nonadiabatic coupling between different electronic states, in addition to the adiabatic force contributed by a single adiabatic electronic state. NaF is capable of faithfully describing the interplay between electronic and nuclear motion in a broad regime, which covers where the relevant electronic states keep coupled in a wide range or all the time and where the bifurcation characteristic of nuclear motion is essential. NaF is derived from the exact generalized phase space formulation with coordinate-momentum variables, where constraint phase space (CPS) is employed for discrete electronic-state degrees of freedom (DOFs) and infinite Wigner phase space is used for continuous nuclear DOFs. We propose efficient integrators for the equations of motion of NaF in both adiabatic and diabatic representations. Since the formalism in the CPS formulation is not unique, NaF can in principle be implemented with various phase space representations of the time correlation function (TCF) for the time-dependent property. They are applied to a suite of representative gas-phase and condensed-phase benchmark models where numerically exact results are available for comparison. It is shown that NaF is relatively insensitive to the phase space representation of the electronic TCF and will be a potential tool for practical and reliable simulations of the quantum mechanical behavior of both electronic and nuclear dynamics of nonadiabatic transition processes in real systems.

Efficient Training of Neural Network Potentials for Chemical and Enzymatic Reactions by Continual Learning

Machine learning (ML) methods have emerged as an efficient surrogate for high-level electronic structure theory, offering precision and computational efficiency. However, the vast conformational and chemical space remains challenging when constructing a general force field. Training data sets typically cover only a limited region of this space, resulting in poor extrapolation performance. Traditional strategies must address this problem by training models from scratch using old and new data sets. In addition, model transferability is crucial for general force field construction. Existing ML force fields, designed for closed systems with no external environmental potential, exhibit limited transferability to complex condensed phase systems such as enzymatic reactions, resulting in inferior performance and high memory costs. Our ML/MM model, based on the Taylor expansion of the electrostatic operator, showed high transferability between reactions in several simple solvents. This work extends the strategy to enzymatic reactions to explore the transferability between more complex heterogeneous environments. In addition, we also apply continual learning strategies based on memory data sets to enable autonomous and on-the-fly training on a continuous stream of new data. By combining these two methods, we can efficiently construct a force field that can be applied to chemical reactions in various environmental media.

A combined in silico approach to design peptide ligands with increased receptor-subtype selectivity

G-protein coupled receptors are major drug targets that change their conformation upon binding of ligands to their extracellular binding pocket to transduce the signal to intracellular G-proteins or arrestins. In drug screening campaigns, computational methods are frequently used to predict binding affinities for chemical compounds in silico before experimental testing. Some of these methods take into consideration the inherent flexibility of the ligand and to some extent also of the receptor. Due to high structural flexibility, peptide ligands are exceptionally difficult to handle and approaches to effectively sample in silico receptor-peptide ligand interactions are limited. Here we describe a pipeline starting from microseconds molecular dynamics simulations of receptor and receptor ligand complexes to find reasonable starting conformations and derive constraints for subsequent flexible docking of peptide ligands, using Rosetta's FlexPepDock approach. We applied this approach to predict binding affinities for dynorphin and its variants to members of the opioid receptor family. Using an ensemble of docking poses, Rosetta's fixbb protein design method explored the sequence space at defined positions, to enhance binding affinities, aiming to increase subtype selectivity towards κ-opioid receptor while decreasing it towards μ-opioid receptor. The results of our computations were validated experimentally in a related study (Zangrandi et al., 2024[1]). Four out of six proposed variants lead to a significant increase in subtype selectivity in favor of κ-opioid receptor, highlighting the potential of our approach to design subtype selective peptide variants. The established workflow may also apply for other receptor types activated by peptide ligands.

Pouring SIRAH on NAMD

Molecular dynamics (MD) simulations provide an invaluable platform for exploring the dynamics of complex biomolecular systems at atomic resolution. However, compatibility issues between force fields and MD software engines can limit the interoperability and transferability of simulations. This work demonstrates the successful use of the coarse-grained SIRAH force field on the widely used NAMD MD engine across a range of increasingly complex biomolecular systems. By leveraging NAMD's ability to read AMBER input files, SIRAH simulations can be run seamlessly on NAMD, including its recently released GPU-accelerated version, NAMD3. The benchmark systems demonstrate consistent results across AMBER, NAMD2, and NAMD3. Thus, these data highlight the enhanced simulation throughput achievable on GPU-accelerated desktop computers using all three engines along with SIRAH. Overall, this study expands the range of the SIRAH force field by utilizing advanced GPU computing resources and high-performance supercomputing facilities, which are particularly effective with NAMD.

Development of a novel representation of drug 3D structures and enhancement of the TSR-based method for probing drug and target interactions

Understanding the mechanisms underlying interactions between drugs and target proteins is critical for drug discovery. In our earlier studies, we introduced the Triangular Spatial Relationship (TSR)-based algorithm, which enables the representation of a protein's 3D structure as a vector of integers (TSR keys). These TSR keys correspond to substructures of the 3D structure of a protein and are computed based on the triangles constructed by all possible triples of Cα atoms within the protein. In this study, we report on a new TSR-based algorithm for probing drug and target interactions. Specifically, we have extended the previous algorithm in three novel directions: TSR keys for representing the 3D structure of a drug or a ligand, cross TSR keys between drugs and their targets and intra-residual TSR keys for phosphorylated amino acids. The outcomes illustrate the key contributions as follows: (i) The TSR-based method, which uses the TSR keys as features, is unique in its capability to interpret hierarchical relationships of drugs as well as drug - target complexes using common and specific TSR keys. (ii) The method can distinguish not only the binding sites from the rest of the protein structures, but also the binding sites of primary targets from those of off-targets. (iii) The method has the potential to correlate the 3D structures of drugs with their functions. (iv) Representation of 3D structures by TSR keys has its unique advantage in terms of ease of making searching for similar substructures across structure datasets easier. In summary, this study presents a novel computational methodology, with significant advantages, for providing insights into the mechanism underlying drug and target interactions.

3D physiologically-informed deep learning for drug discovery of a novel vascular endothelial growth factor receptor-2 (VEGFR2)

Angiogenesis is an essential process in tumorigenesis, tumor invasion, and metastasis, and is an intriguing pathway for drug discovery. Targeting vascular endothelial growth factor receptor 2 (VEGFR2) to inhibit tumor angiogenic pathways has been widely explored and adopted in clinical practice. However, most drugs, such as the Food and Drug Administration -approved drug axitinib (ATC code: L01EK01), have considerable side effects and limited tolerability. Therefore, there is an urgent need for the development of novel VEGFR2 inhibitors. In this study, we propose a novel strategy to design potential candidates targeting VEGFR2 using three-dimensional (3D) deep learning and structural modeling methods. A geometric-enhanced molecular representation learning method (GEM) model employing a graph neural network (GNN) as its underlying predictive algorithm was used to predict the activity of the candidates. In the structural modeling method, flexible docking was performed to screen data with high affinity and explore the mechanism of the inhibitors. Small -molecule compounds with consistently improved properties were identified based on the intersection of the scores obtained from both methods. Candidates identified using the GEM-GNN model were selected for in silico modeling using molecular dynamics simulations to further validate their efficacy. The GEM-GNN model enabled the identification of candidate compounds with potentially more favorable properties than the existing drug, axitinib, while achieving higher efficacy.

Fast, approximation-free molecular simulation of the SPC/Fw water model using non-reversible Markov chains

In a world made of atoms, computer simulations of molecular systems such as proteins in water play an enormous role in science. Software packages for molecular simulation have been developed for decades. They all discretize Hamilton's equations of motion and treat long-range potentials through cutoffs or discretization of reciprocal space. This introduces severe approximations and artifacts that must be controlled algorithmically. Here, we bring to fruition a paradigm for molecular simulation that relies on modern concepts in statistics to explore the thermodynamic equilibrium with an exact and efficient non-reversible Markov process. It is free of all discretizations, approximations, and cutoffs. We explicitly demonstrate that this approach reaches a break-even point with traditional molecular simulation performed at high precision, but without any of its approximations. We stress the potential of our paradigm for crucial applications in biophysics and other fields, and as a practical approach to molecular simulation. We set out a strategy to reach our goal of rigorous molecular simulation.

In Silico Chemical Experiments in the Age of AI: From Quantum Chemistry to Machine Learning and Back

Computational chemistry is an indispensable tool for understanding molecules and predicting chemical properties. However, traditional computational methods face significant challenges due to the difficulty of solving the Schrödinger equations and the increasing computational cost with the size of the molecular system. In response, there has been a surge of interest in leveraging artificial intelligence (AI) and machine learning (ML) techniques to in silico experiments. Integrating AI and ML into computational chemistry increases the scalability and speed of the exploration of chemical space. However, challenges remain, particularly regarding the reproducibility and transferability of ML models. This review highlights the evolution of ML in learning from, complementing, or replacing traditional computational chemistry for energy and property predictions. Starting from models trained entirely on numerical data, a journey set forth toward the ideal model incorporating or learning the physical laws of quantum mechanics. This paper also reviews existing computational methods and ML models and their intertwining, outlines a roadmap for future research, and identifies areas for improvement and innovation. Ultimately, the goal is to develop AI architectures capable of predicting accurate and transferable solutions to the Schrödinger equation, thereby revolutionizing in silico experiments within chemistry and materials science.

Targeting the conserved active site of splicing machines with specific and selective small molecule modulators

The self-splicing group II introns are bacterial and organellar ancestors of the nuclear spliceosome and retro-transposable elements of pharmacological and biotechnological importance. Integrating enzymatic, crystallographic, and simulation studies, we demonstrate how these introns recognize small molecules through their conserved active site. These RNA-binding small molecules selectively inhibit the two steps of splicing by adopting distinctive poses at different stages of catalysis, and by preventing crucial active site conformational changes that are essential for splicing progression. Our data exemplify the enormous power of RNA binders to mechanistically probe vital cellular pathways. Most importantly, by proving that the evolutionarily-conserved RNA core of splicing machines can recognize small molecules specifically, our work provides a solid basis for the rational design of splicing modulators not only against bacterial and organellar introns, but also against the human spliceosome, which is a validated drug target for the treatment of congenital diseases and cancers.

Learning QM/MM potential using equivariant multiscale model

The machine learning (ML) method emerges as an efficient and precise surrogate model for high-level electronic structure theory. Its application has been limited to closed chemical systems without considering external potentials from the surrounding environment. To address this limitation and incorporate the influence of external potentials, polarization effects, and long-range interactions between a chemical system and its environment, the first two terms of the Taylor expansion of an electrostatic operator have been used as extra input to the existing ML model to represent the electrostatic environments. However, high-order electrostatic interaction is often essential to account for external potentials from the environment. The existing models based only on invariant features cannot capture significant distribution patterns of the external potentials. Here, we propose a novel ML model that includes high-order terms of the Taylor expansion of an electrostatic operator and uses an equivariant model, which can generate a high-order tensor covariant with rotations as a base model. Therefore, we can use the multipole-expansion equation to derive a useful representation by accounting for polarization and intermolecular interaction. Moreover, to deal with long-range interactions, we follow the same strategy adopted to derive long-range interactions between a target system and its environment media. Our model achieves higher prediction accuracy and transferability among various environment media with these modifications.

Quantum-centric high performance computing for quantum chemistry

High performance computing (HPC) is renowned for its capacity to tackle complex problems. Meanwhile, quantum computing (QC) provides a potential way to accurately and efficiently solve quantum chemistry problems. The emerging field of quantum-centric high performance computing (QCHPC), which merges these two powerful technologies, is anticipated to enhance computational capabilities for solving challenging problems in quantum chemistry. The implementation of QCHPC for quantum chemistry requires interdisciplinary research and collaboration across multiple fields, including quantum chemistry, quantum physics, computer science and so on. This perspective provides an introduction to the quantum algorithms that are suitable for deployment in QCHPC, focusing on conceptual insights rather than technical details. Parallel strategies to implement these algorithms on quantum-centric supercomputers are discussed. We also summarize high performance quantum emulating simulators, which are considered a viable tool to explore QCHPC. We conclude with challenges and outlooks in this field.

Simulating chemical reaction dynamics on quantum computer

The electronic energies of molecules have been successfully evaluated on quantum computers. However, more attention is paid to the dynamics simulation of molecules in practical applications. Based on the variational quantum eigensolver (VQE) algorithm, Fedorov et al. proposed a correlated sampling (CS) method and demonstrated the vibrational dynamics of H2 molecules [J. Chem. Phys. 154, 164103 (2021)]. In this study, we have developed a quantum approach by extending the CS method based on the VQE algorithm (labeled eCS-VQE) for simulating chemical reaction dynamics. First, the CS method is extended to the three-dimensional cases for calculation of first-order energy gradients, and then, it is further generalized to calculate the second-order gradients of energies. By calculating atomic forces and vibrational frequencies for H2, LiH, H+ + H2, and Cl- + CH3Cl systems, we have seen that the approach has achieved the CCSD level of accuracy. Thus, we have simulated dynamics processes for two typical chemical reactions, hydrogen exchange and chlorine substitution, and obtained high-precision reaction dynamics trajectories consistent with the classical methods. Our eCS-VQE approach, as measurement expectations and ground-state wave functions can be reused, is less demanding in quantum computing resources and is, therefore, a feasible means for the dynamics simulation of chemical reactions on the current noisy intermediate-scale quantum-era quantum devices.

Biomolecular dynamics in the 21st century

The relevance of motions in biological macromolecules has been clear since the early structural analyses of proteins by X-ray crystallography. Computer simulations have been applied to provide a deeper understanding of the dynamics of biological macromolecules since 1976, and are now a standard tool in many labs working on the structure and function of biomolecules. In this mini-review we highlight some areas of current interest and active development for simulations, in particular all-atom molecular dynamics simulations.

Phase behaviour of coarse-grained fluids

Soft condensed matter structures often challenge us with complex many-body phenomena governed by collective modes spanning wide spatial and temporal domains. In order to successfully tackle such problems, mesoscopic coarse-grained (CG) statistical models are being developed, providing a dramatic reduction in computational complexity. CG models provide an intermediate step in the complex statistical framework of linking the thermodynamics of condensed phases with the properties of their constituent atoms and molecules. These allow us to offload part of the problem to the CG model itself and reformulate the remainder in terms of reduced CG phase space. However, such exchange of pawns to chess pieces, or 'Hamiltonian renormalization', is a radical step and the thermodynamics of the primary atomic and CG models could be quite distinct. Here, we present a comprehensive study of the phase diagram including binodal and interfacial properties of a dissipative particle dynamics (DPD) model, extended to include finite-range attraction to support the liquid-gas equilibrium. Despite the similarities with the atomic model potentials, its phase envelope is markedly different featuring several anomalies such as an unusually broad liquid range, change in concavity of the liquid coexistence branch with variation of the model parameters, volume contraction on fusion, temperature of maximum density in the liquid phase and negative thermal expansion in the solid phase. These results provide new insight into the connection between simple potential models and complex emergent condensed matter phenomena.

Accelerating therapeutic protein design with computational approaches toward the clinical stage

Therapeutic protein, represented by antibodies, is of increasing interest in human medicine. However, clinical translation of therapeutic protein is still largely hindered by different aspects of developability, including affinity and selectivity, stability and aggregation prevention, solubility and viscosity reduction, and deimmunization. Conventional optimization of the developability with widely used methods, like display technologies and library screening approaches, is a time and cost-intensive endeavor, and the efficiency in finding suitable solutions is still not enough to meet clinical needs. In recent years, the accelerated advancement of computational methodologies has ushered in a transformative era in the field of therapeutic protein design. Owing to their remarkable capabilities in feature extraction and modeling, the integration of cutting-edge computational strategies with conventional techniques presents a promising avenue to accelerate the progression of therapeutic protein design and optimization toward clinical implementation. Here, we compared the differences between therapeutic protein and small molecules in developability and provided an overview of the computational approaches applicable to the design or optimization of therapeutic protein in several developability issues.

Best Practices on QM/MM Simulations of Biological Systems

During the second half of the 20th century, following structural biology hallmark works on DNA and proteins, biochemists shifted their questions from "what does this molecule look like?" to "how does this process work?". Prompted by the theoretical and practical developments in computational chemistry, this led to the emergence of biomolecular simulations and, along with the 2013 Nobel Prize in Chemistry, to the development of hybrid QM/MM methods. QM/MM methods are necessary whenever the problem we want to address involves chemical reactivity and/or a change in the system's electronic structure, with archetypal examples being the studies of an enzyme's reaction mechanism and a metalloprotein's active site. In the last decades QM/MM methods have seen an increasing adoption driven by their incorporation in widely used biomolecular simulation software. However, properly setting up a QM/MM simulation is not an easy task, and several issues need to be properly addressed to obtain meaningful results. In the present work, we describe both the theoretical concepts and practical issues that need to be considered when performing QM/MM simulations. We start with a brief historical perspective on the development of these methods and describe when and why QM/MM methods are mandatory. Then we show how to properly select and analyze the performance of the QM level of theory, the QM system size, and the position and type of the boundaries. We show the relevance of performing prior QM model system (or QM cluster) calculations in a vacuum and how to use the corresponding results to adequately calibrate those derived from QM/MM. We also discuss how to prepare the starting structure and how to select an adequate simulation strategy, including those based on geometry optimizations as well as free energy methods. In particular, we focus on the determination of free energy profiles using multiple steered molecular dynamics (MSMD) combined with Jarzynski's equation. Finally, we describe the results for two illustrative and complementary examples: the reaction performed by chorismate mutase and the study of ligand binding to hemoglobins. Overall, we provide many practical recommendations (or shortcuts) together with important conceptualizations that we hope will encourage more and more researchers to incorporate QM/MM studies into their research projects.

Multiscale quantum algorithms for quantum chemistry

Exploring the potential applications of quantum computers in material design and drug discovery is attracting more and more attention after quantum advantage has been demonstrated using Gaussian boson sampling. However, quantum resource requirements in material and (bio)molecular simulations are far beyond the capacity of near-term quantum devices. In this work, multiscale quantum computing is proposed for quantum simulations of complex systems by integrating multiple computational methods at different scales of resolution. In this framework, most computational methods can be implemented in an efficient way on classical computers, leaving the critical portion of the computation to quantum computers. The simulation scale of quantum computing strongly depends on available quantum resources. As a near-term scheme, we integrate adaptive variational quantum eigensolver algorithms, second-order Møller-Plesset perturbation theory and Hartree-Fock theory within the framework of the many-body expansion fragmentation approach. This new algorithm is applied to model systems consisting of hundreds of orbitals with decent accuracy on the classical simulator. This work should encourage further studies on quantum computing for solving practical material and biochemistry problems.

Induction effects on the absorption maxima of photoreceptor proteins

Multiscale simulations have been established as a powerful tool to calculate and predict excitation energies in complex systems such as photoreceptor proteins. In these simulations the chromophore is typically treated using quantum mechanical (QM) methods while the protein and surrounding environment are described by a classical molecular mechanics (MM) force field. The electrostatic interactions between these regions are often treated using electrostatic embedding where the point charges in the MM region polarize the QM region. A more sophisticated treatment accounts also for the polarization of the MM region. In this work, the effect of such a polarizable embedding on excitation energies was benchmarked and compared to electrostatic embedding. This was done for two different proteins, the lipid membrane-embedded jumping spider rhodopsin and the soluble cyanobacteriochrome Slr1393g3. It was found that the polarizable embedding scheme produces absorption maxima closer to experimental values. The polarizable embedding scheme was also benchmarked against expanded QM regions and found to be in qualitative agreement. Treating individual residues as polarizable recovered between 50% and 71% of the QM improvement in the excitation energies, depending on the system. A detailed analysis of each amino acid residue in the chromophore binding pocket revealed that aromatic residues result in the largest change in excitation energy compared to the electrostatic embedding. Furthermore, the computational efficiency of polarizable embedding allowed it to go beyond the binding pocket and describe a larger portion of the environment, further improving the results.

A Guide to In Silico Drug Design

The drug discovery process is a rocky path that is full of challenges, with the result that very few candidates progress from hit compound to a commercially available product, often due to factors, such as poor binding affinity, off-target effects, or physicochemical properties, such as solubility or stability. This process is further complicated by high research and development costs and time requirements. It is thus important to optimise every step of the process in order to maximise the chances of success. As a result of the recent advancements in computer power and technology, computer-aided drug design (CADD) has become an integral part of modern drug discovery to guide and accelerate the process. In this review, we present an overview of the important CADD methods and applications, such as in silico structure prediction, refinement, modelling and target validation, that are commonly used in this area.

Computational Insights into the Catalytic Mechanism of Is-PETase: An Enzyme Capable of Degrading Poly(ethylene) Terephthalate

Is-PETase has become an enzyme of significant interest due to its ability to catalyse the degradation of polyethylene terephthalate (PET) at mesophilic temperatures. We performed hybrid quantum mechanics and molecular mechanics (QM/MM) at the DSD-PBEP86-D3/ma-def2-TZVP/CHARMM27//rev-PBE-D3/dev2-SVP/CHARMM level to calculate the energy profile for the degradation of a suitable PET model by this enzyme. Very low overall barriers are computed for serine protease-type hydrolysis steps (as low as 34.1 kJ mol-1 ). Spontaneous deprotonation of the final product, terephthalic acid, with a high computed driving force indicates that product release could be rate limiting.

Predicting Experimental Heats of Formation via Deep Learning with Limited Experimental Data

When it comes to predicting experimental values of molecular properties with deep learning, the key problem is the lack of sufficient experimental data for training. We propose a method that consists of pretraining a graph neural network that aims to reproduce first-principles quantum mechanical results, followed by fine-tuning of a fully connected neural network against experimental results. The combined pretraining and fine-tuning model is expected to yield molecular properties close to experimental accuracy. This is made possible because first-principles quantum mechanical methods are often qualitatively correct or semiquantitatively accurate; thus, a calibration of the calculation results against high-precision but limited experiment data can improve accuracy greatly. Moreover, the method is highly efficient, as first-principles quantum mechanical calculation is bypassed. To demonstrate this, we apply the combined model to determine the experimental heats of formation of organic molecules made of H, C, O, N, or F atoms (up to 30 atoms), where mere 405 experimental data are used. The overall mean absolute error is 1.8 kcal/mol for these molecules.

Multilevel simulation of hard-sphere mixtures

We present a multilevel Monte Carlo simulation method for analysing multi-scale physical systems via a hierarchy of coarse-grained representations, to obtain numerically-exact results, at the most detailed level. We apply the method to a mixture of size-asymmetric hard spheres, in the grand canonical ensemble. A three-level version of the method is compared with a previously-studied two-level version. The extra level interpolates between the full mixture and a coarse-grained description where only the large particles are present -- this is achieved by restricting the small particles to regions close to the large ones. The three-level method improves the performance of the estimator, at fixed computational cost. We analyse the asymptotic variance of the estimator, and discuss the mechanisms for the improved performance.

Quantitative molecular simulations

All-atom simulations can provide molecular-level insights into the dynamics of gas-phase, condensed-phase and surface processes. One important requirement is a sufficiently realistic and detailed description of the underlying intermolecular interactions. The present perspective provides an overview of the present status of quantitative atomistic simulations from colleagues' and our own efforts for gas- and solution-phase processes and for the dynamics on surfaces. Particular attention is paid to direct comparison with experiment. An outlook discusses present challenges and future extensions to bring such dynamics simulations even closer to reality.

Perspectives on parity violation in chiral molecules: theory, spectroscopic experiment and biomolecular homochirality

The reflection (or ‘mirror’) symmetry of space is among the fundamental symmetries of physics. It is connected to the conservation law for the quantum number parity and a fundamental ‘non-observable’ property of space (as defined by an absolute ‘left-handed’ or ‘right-handed’ coordinate system). The discovery of the violation of this symmetry – the non-conservation of parity or ‘parity violation’ – in 1956/1957 had an important influence on the further development of physics. In chemistry the mirror symmetry of space is connected to the existence of enantiomers as isomers of chiral (‘handed’) molecules. These isomers would relate to each other as idealized left or right hand or as image and mirror image and would be energetically exactly equivalent with perfect space inversion symmetry. Parity violation results in an extremely small ‘parity violating’ energy difference between the ground states of the enantiomers which can be theoretically calculated to be about 100 aeV to 1 feV (equivalent to 10⁻¹¹ to 10⁻¹⁰ J mol⁻¹), depending on the molecule, but which has not yet been detected experimentally. Its detection remains one of the great challenges of current physical–chemical stereochemistry, with implications also for fundamental problems in physics. In biochemistry and molecular biology one finds a related fundamental question unanswered for more than 100 years: the evolution of ‘homochirality’, which is the practically exclusive preference of one chiral, enantiomeric form as building blocks in the biopolymers of all known forms of life (the l-amino acids in proteins and d-sugars in DNA, not the reverse d-amino acids or l-sugars). In astrobiology the spectroscopic detection of homochirality could be used as strong evidence for the existence of extraterrestrial life, if any. After a brief conceptual and historical introduction we review the development, current status, and progress along these three lines of research: theory, spectroscopic experiment and the outlook towards an understanding of the evolution of biomolecular homochirality.

The reflection (or ‘mirror’) symmetry of space is among the fundamental symmetries of physics. It is connected to the conservation law for the quantum number purity and its violation and has a fundamental relation to stereochemistry and molecular chirality.

Adaptive partitioning molecular dynamics using an extended Hamiltonian approach

A recently proposed extended Hamiltonian approach to switching interaction potentials is generalized to enable adaptive partitioning molecular dynamics simulations. Switching is performed along a fictitious classical degree of freedom whose value determines the mixing ratio of the two potentials on a time scale determined by its associated mass. We propose to choose this associated fictitious mass adaptively so as to ensure a constant time scale for all switching processes. For different model systems, including a harmonic oscillator and a Lennard-Jones fluid, we investigate the window of switching time scales that guarantees the conservation of the extended Hamiltonian for a large number of switching events. The methodology is first applied in the microcanonical ensemble and then generalized to the canonical ensemble using a Nosé-Hoover chain thermostat. It is shown that the method is stable for thousands of consecutive switching events during a single simulation, with constant temperature and a conserved extended Hamiltonian. A slight modification of the original Hamiltonian is introduced to avoid accumulation of small numerical errors incurred after each switching process.

Machine-Learning-Assisted Free Energy Simulation of Solution-Phase and Enzyme Reactions

Despite recent advances in the development of machine learning potentials (MLPs) for biomolecular simulations, there has been limited effort on developing stable and accurate MLPs for enzymatic reactions. Here we report a protocol for performing machine-learning-assisted free energy simulation of solution-phase and enzyme reactions at the ab initio quantum-mechanical/molecular-mechanical (ai-QM/MM) level of accuracy. Within our protocol, the MLP is built to reproduce the ai-QM/MM energy and forces on both QM (reactive) and MM (solvent/enzyme) atoms. As an alternative strategy, a delta machine learning potential (ΔMLP) is trained to reproduce the differences between the ai-QM/MM and semiempirical (se) QM/MM energies and forces. To account for the effect of the condensed-phase environment in both MLP and ΔMLP, the DeePMD representation of a molecular system is extended to incorporate the external electrostatic potential and field on each QM atom. Using the Menshutkin and chorismate mutase reactions as examples, we show that the developed MLP and ΔMLP reproduce the ai-QM/MM energy and forces with errors that on average are less than 1.0 kcal/mol and 1.0 kcal mol-1 Å-1, respectively, for representative configurations along the reaction pathway. For both reactions, MLP/ΔMLP-based simulations yielded free energy profiles that differed by less than 1.0 kcal/mol from the reference ai-QM/MM results at only a fraction of the computational cost.

Integration of theory, simulation, artificial intelligence and virtual reality: a four-pillar approach for reconciling accuracy and interpretability in computational spectroscopy

The established pillars of computational spectroscopy are theory and computer based simulations. Recently, artificial intelligence and virtual reality are becoming the third and fourth pillars of an integrated strategy for the investigation of complex phenomena. The main goal of the present contribution is the description of some new perspectives for computational spectroscopy, in the framework of a strategy in which computational methodologies at the state of the art, high-performance computing, artificial intelligence and virtual reality tools are integrated with the aim of improving research throughput and achieving goals otherwise not possible. Some of the key tools (e.g., continuous molecular perception model and virtual multifrequency spectrometer) and theoretical developments (e.g., non-periodic boundaries, joint variational-perturbative models) are shortly sketched and their application illustrated by means of representative case studies taken from recent work by the authors. Some of the results presented are already well beyond the state of the art in the field of computational spectroscopy, thereby also providing a proof of concept for other research fields.

Three-Layer Multiscale Approach Based on Extremely Localized Molecular Orbitals to Investigate Enzyme Reactions

Quantum mechanics/molecular mechanics (QM/MM) calculations are widely used embedding techniques to computationally investigate enzyme reactions. In most QM/MM computations, the quantum mechanical region is treated through density functional theory (DFT), which offers the best compromise between chemical accuracy and computational cost. Nevertheless, to obtain more accurate results, one should resort to wave function-based methods, which however lead to a much larger computational cost already for relatively small QM subsystems. To overcome this drawback, we propose the coupling of our QM/ELMO (quantum mechanics/extremely localized molecular orbital) approach with molecular mechanics, thus introducing the three-layer QM/ELMO/MM technique. The QM/ELMO strategy is an embedding method in which the chemically relevant part of the system is treated at the quantum mechanical level, while the rest is described through frozen ELMOs. Since the QM/ELMO method reproduces results of fully QM computations within chemical accuracy and with a much lower computational effort, it can be considered a suitable strategy to extend the range of applicability and accuracy of the QM/MM scheme. In this paper, other than briefly presenting the theoretical bases of the QM/ELMO/MM technique, we will also discuss its validation on the well-tested deprotonation of acetyl coenzyme A by aspartate in citrate synthase.

Systematic Partitioning of Proteins for Quantum-Chemical Fragmentation Methods Using Graph Algorithms

Quantum-chemical fragmentation methods offer an efficient approach for the treatment of large proteins, in particular if local target quantities such as protein-ligand interaction energies, enzymatic reaction energies, or spectroscopic properties of embedded chromophores are sought. However, the accuracy that is achievable for such local target quantities intricately depends on how the protein is partitioned into smaller fragments. While the commonly employed naı̈ve approach of using fragments with a fixed size is widely used, it can result in large and unpredictable errors when varying the fragment size. Here, we present a systematic partitioning scheme that aims at minimizing the fragmentation error of a local target quantity for a given maximum fragment size. To this end, we construct a weighted graph representation of the protein, in which the amino acids constitute the nodes. These nodes are connected by edges weighted with an estimate for the fragmentation error that is expected when cutting this edge. This allows us to employ graph partitioning algorithms provided by computer science to determine near-optimal partitions of the protein. We apply this scheme to a test set of six proteins representing various prototypical applications of quantum-chemical fragmentation methods using a simplified molecular fractionation with conjugate caps (MFCC) approach with hydrogen caps. We show that our graph-based scheme consistently improves upon the naı̈ve approach.

Computational avenues in oral protein and peptide therapeutics

Proteins and peptides are amongst the most sought-after biomolecules because of their exceptional potential to cater to a vast range of diseases. Although widely studied and researched, the oral delivery of these biomolecules remains a challenge. Alongside formulation strategies, approaches to overcome the inherent barriers for peptide absorption are being designed at the molecular level to establish a sound rationale and to achieve higher bioavailability. Computer-aided drug design (CADD) is a modern in silico approach for developing successful bio-formulations. CADD enables intricate study of the biomolecules in conjunction with their target sites or receptors at the molecular level. Knowledge of the molecular interactions of proteins and peptides makes way for the pre-screening of suitable formulation components and facilitates their delivery.

Frontiers in Multiscale Modeling of Photoreceptor Proteins

This perspective article highlights the challenges in the theoretical description of photoreceptor proteins using multiscale modeling, as discussed at the CECAM workshop in Tel Aviv, Israel. The participants have identified grand challenges and discussed the development of new tools to address them. Recent progress in understanding representative proteins such as green fluorescent protein, photoactive yellow protein, phytochrome, and rhodopsin is presented, along with methodological developments.

A simplified charge projection scheme for long-range electrostatics in ab initio QM/MM calculations

In a previous work [Pan et al., Molecules 23, 2500 (2018)], a charge projection scheme was reported, where outer molecular mechanical (MM) charges [>10 Å from the quantum mechanical (QM) region] were projected onto the electrostatic potential (ESP) grid of the QM region to accurately and efficiently capture long-range electrostatics in ab initio QM/MM calculations. Here, a further simplification to the model is proposed, where the outer MM charges are projected onto inner MM atom positions (instead of ESP grid positions). This enables a representation of the long-range MM electrostatic potential via augmentary charges (AC) on inner MM atoms. Combined with the long-range electrostatic correction function from Cisneros et al. [J. Chem. Phys. 143, 044103 (2015)] to smoothly switch between inner and outer MM regions, this new QM/MM-AC electrostatic model yields accurate and continuous ab initio QM/MM electrostatic energies with a 10 Å cutoff between inner and outer MM regions. This model enables efficient QM/MM cluster calculations with a large number of MM atoms as well as QM/MM calculations with periodic boundary conditions.

How natural materials remove heavy metals from water: mechanistic insights from molecular dynamics simulations

Water pollution by heavy metals is of increasing concern due to its devastating effects on the environment and on human health. For the removal of heavy metals from water sources, natural materials, such as spent-coffee-grains or orange/banana/chestnut peels, appear to offer a potential cheap alternative to more sophisticated and costly technologies currently in use. However, in order to employ them effectively, it is necessary to gain a deeper understanding – at the molecular level – of the heavy metals-bioorganic-water system and exploit the power of computer simulations. As a step in this direction, we investigate via atomistic simulations the capture of lead ions from water by hemicellulose – the latter being representative of the polysaccharides that are common components of vegetables and fruit peels − as well as the reverse process. A series of independent molecular dynamics simulations, both classical and ab initio, reveals a coherent scenario which is consistent with what one would expect of an efficient capture, i.e. that it be fast and irreversible: (i) binding of the metal ions via adsorption is found to happen spontaneously on both carboxylate and hydroxide functional groups; (ii) in contrast, metal ion desorption, leading to solvation in water, involves sizable free-energy barriers.

We investigate via atomistic simulations the capture of lead ions from water by hemicellulose – as representative of the polysaccharides that are common components of vegetables and fruit peels – and the reverse process.

Emerging computational approaches for the study of regio- and stereoselectivity in organic synthesis

Computational chemistry has become important in organic synthesis as it provides a detailed understanding of molecular structures and properties and detailed reaction mechanisms.

Computational Spectroscopy in Solution by Integration of Variational and Perturbative Approaches on Top of Clusterized Molecular Dynamics

Multiscale QM/MM approaches have become the most suitable and effective methods for the investigation of spectroscopic properties of medium- or large-size chromophores in condensed phases. On these grounds, we are developing a novel workflow aimed at improving the generality, reliability, and ease of use of the available tools. In the present paper, we report the latest developments of such an approach with specific reference to a general workplan starting with the addition of acetonitrile to the panel of solvents already available in the General Liquid Optimized Boundary (GLOB) model enforcing nonperiodic boundary conditions (NPBC). Next, the solvatochromic shifts induced by acetonitrile on both rigid (uracil and thymine) and flexible (thyrosine) chromophores have been studied introducing in our software a number of new features ranging from rigid-geometry NPBC molecular dynamics based on the quaternion formalism to a full integration of variational (ONIOM) and perturbative (perturbed matrix method (PMM)) approaches for describing different solute–solvent topologies and local fluctuations, respectively. Finally, thymine and uracil have been studied also in methanol to point out the generality of the computational strategy. While further developments are surely needed, the strengths of our integrated approach even in its present version are demonstrated by the accuracy of the results obtained by an unsupervised approach and coupled to a computational cost strongly reduced with respect to that of conventional QM/MM models without any appreciable accuracy deterioration.

The challenge of non-covalent interactions: theory meets experiment for reconciling accuracy and interpretation

In the past decade, many gas-phase spectroscopic investigations have focused on the understanding of the nature of weak interactions in model systems. Despite the fact that non-covalent interactions play a key role in several biological and technological processes, their characterization and interpretation are still far from being satisfactory. In this connection, integrated experimental and computational investigations can play an invaluable role. Indeed, a number of different issues relevant to unraveling the properties of bulk or solvated systems can be addressed from experimental investigations on molecular complexes. Focusing on the interaction of biological model systems with solvent molecules (e.g., water), since the hydration of the biomolecules controls their structure and mechanism of action, the study of the molecular properties of hydrated systems containing a limited number of water molecules (microsolvation) is the basis for understanding the solvation process and how structure and reactivity vary from gas phase to solution. Although hydrogen bonding is probably the most widespread interaction in nature, other emerging classes, such as halogen, chalcogen and pnicogen interactions, have attracted much attention because of the role they play in different fields. Their understanding requires, first of all, the characterization of the directionality, strength, and nature of such interactions as well as a comprehensive analysis of their competition with other non-covalent bonds. In this review, it is shown how state-of-the-art quantum-chemical computations combined with rotational spectroscopy allow for fully characterizing intermolecular interactions taking place in molecular complexes from both structural and energetic points of view. The transition from bi-molecular complex to microsolvation and then to condensed phase is shortly addressed.

The ONIOM/PMM Model for Effective Yet Accurate Simulation of Optical and Chiroptical Spectra in Solution: Camphorquinone in Methanol as a Case Study

This paper deals with the development and first validation of a composite approach for the simulation of chiroptical spectra in solution aimed to strongly reduce the number of full QM computations without any significant accuracy loss. The approach starts from the quantum mechanical computation of reference spectra including vibrational averaging effects and taking average solvent effects into account by means of the polarizable continuum model. Next, the snapshots of classical molecular dynamics computations are clusterized and one reference configuration from each cluster is used to compute a reference spectrum. Local fluctuation effects within each cluster are then taken into account by means of the perturbed matrix model. The performance of the proposed approach is tested on the challenging case of the optical and chiroptical spectra of camphorquinone in methanol solution. Although further validations are surely needed, the results of this first study are quite promising also taking into account that agreement with experimental data is reached by just a couple of full quantum mechanical geometry optimizations and frequency computations.

Topological Dynamics of a Radical Ion Pair: Experimental and Computational Assessment at the Relevant Nanosecond Timescale

Chemical processes mostly happen in fluid environments where reaction partners encounter via diffusion. The bimolecular encounters take place at a nanosecond time scale. The chemical environment (e.g., solvent molecules, (counter)ions) has a decisive influence on the reactivity as it determines the contact time between two molecules and affects the energetics. For understanding reactivity at an atomic level and at the appropriate dynamic time scale, it is crucial to combine matching experimental and theoretical data. Here, we have utilized all-atom molecular-dynamics simulations for accessing the key time scale (nanoseconds) using a QM/MM-Hamiltonian. Ion pairs consisting of a radical ion and its counterion are ideal systems to assess the theoretical predictions because they reflect dynamics at an appropriate time scale when studied by temperature-dependent EPR spectroscopy. We have investigated a diketone radical anion with its tetra-ethylammonium counterion. We have established a funnel-like transition path connecting two (equivalent) complexation sites. The agreement between the molecular-dynamics simulation and the experimental data presents a new paradigm for ion–ion interactions. This study exemplarily demonstrates the impact of the molecular environment on the topological states of reaction intermediates and how these states can be consistently elucidated through the combination of theory and experiment. We anticipate that our findings will contribute to the prediction of bimolecular transformations in the condensed phase with relevance to chemical synthesis, polymers, and biological activity.

A Review on Applications of Computational Methods in Drug Screening and Design

Drug development is one of the most significant processes in the pharmaceutical industry. Various computational methods have dramatically reduced the time and cost of drug discovery. In this review, we firstly discussed roles of multiscale biomolecular simulations in identifying drug binding sites on the target macromolecule and elucidating drug action mechanisms. Then, virtual screening methods (e.g., molecular docking, pharmacophore modeling, and QSAR) as well as structure- and ligand-based classical/de novo drug design were introduced and discussed. Last, we explored the development of machine learning methods and their applications in aforementioned computational methods to speed up the drug discovery process. Also, several application examples of combining various methods was discussed. A combination of different methods to jointly solve the tough problem at different scales and dimensions will be an inevitable trend in drug screening and design.

Mesoscale All-Atom Influenza Virus Simulations Suggest New Substrate Binding Mechanism

Influenza virus circulates in human, avian, and swine hosts, causing seasonal epidemic and occasional pandemic outbreaks. Influenza neuraminidase, a viral surface glycoprotein, has two sialic acid binding sites. The catalytic (primary) site, which also binds inhibitors such as oseltamivir carboxylate, is responsible for cleaving the sialic acid linkages that bind viral progeny to the host cell. In contrast, the functional annotation of the secondary site remains unclear. Here, we better characterize these two sites through the development of an all-atom, explicitly solvated, and experimentally based integrative model of the pandemic influenza A H1N1 2009 viral envelope, containing ∼160 million atoms and spanning ∼115 nm in diameter. Molecular dynamics simulations of this crowded subcellular environment, coupled with Markov state model theory, provide a novel framework for studying realistic molecular systems at the mesoscale and allow us to quantify the kinetics of the neuraminidase 150-loop transition between the open and closed states. An analysis of chloride ion occupancy along the neuraminidase surface implies a potential new role for the neuraminidase secondary site, wherein the terminal sialic acid residues of the linkages may bind before transfer to the primary site where enzymatic cleavage occurs. Altogether, our work breaks new ground for molecular simulation in terms of size, complexity, and methodological analyses of the components. It also provides fundamental insights into the understanding of substrate recognition processes for this vital influenza drug target, suggesting a new strategy for the development of anti-influenza therapeutics.

Atoms to Phenotypes: Molecular Design Principles of Cellular Energy Metabolism

We report a 100-million atom-scale model of an entire cell organelle, a photosynthetic chromatophore vesicle from a purple bacterium, that reveals the cascade of energy conversion steps culminating in the generation of ATP from sunlight. Molecular dynamics simulations of this vesicle elucidate how the integral membrane complexes influence local curvature to tune photoexcitation of pigments. Brownian dynamics of small molecules within the chromatophore probe the mechanisms of directional charge transport under various pH and salinity conditions. Reproducing phenotypic properties from atomistic details, a kinetic model evinces that low-light adaptations of the bacterium emerge as a spontaneous outcome of optimizing the balance between the chromatophore's structural integrity and robust energy conversion. Parallels are drawn with the more universal mitochondrial bioenergetic machinery, from whence molecular-scale insights into the mechanism of cellular aging are inferred. Together, our integrative method and spectroscopic experiments pave the way to first-principles modeling of whole living cells.