The formation of protein condensates (droplets) via liquid-liquid phase separation (LLPS) is a commonly observed phenomenon in vitro. Changing the environmental properties with cosolutes, molecular crowders, protein partners, temperature, pressure, etc. has been shown to favor or disfavor the formation of protein droplets by fine-tuning the water-water, water-protein, and protein-protein interactions. Therefore, these environmental properties and their spatiotemporal fine-tuning are likely to be important also in a cellular context at the existing protein expression levels. One of the key physicochemical properties of biomolecules impacted by molecular crowding is diffusion, which determines the viscoelastic behavior of the condensates. Here, we investigate the change in the rotational diffusion of γD-crystallin, undergoing LLPS in vitro in aqueous solutions in the absence and presence of cosolutes. We studied its rotational dynamics using molecular dynamics simulations (MD), electron paramagnetic resonance (EPR) spectroscopy, and fluorescence spectroscopy. MD simulations performed under dilute and crowded conditions show that the rotational diffusion of crystallin in water is retarded by 1 to 2 orders of magnitude in the condensed phase. To obtain the rotational dynamics in the dilute phase, we used fluorescence anisotropy and to extract the retardation factor in the condensed phase, we used spin-labeled γD-crystallin proteins as EPR viscosity nanoprobes. Aided by a viscosity nanoruler calibrated with solutions at increasing sucrose concentrations, we validated the rotational diffusion retardation predicted by MD simulations. This study underlines the predictive power of MD simulations and showcases the use of a sensitive EPR nanoprobe to extract the viscosity of biomolecular condensates.

With the remarkable stride in computing power and advances in Molecular Dynamics (MD) simulation programs, the crucial challenge of storing and sharing large biomolecular simulation data sets has emerged. By leveraging AutoEncoders, a type of artificial neural network, we developed a method to compress MD trajectories into significantly smaller latent spaces. Our method can save up to 98% in disk space compared to xtc, a highly compressed trajectory format from the widely used MD program package GROMACS, thus facilitating storage and sharing of simulation trajectories. Atom coordinates are very accurately reconstructed from compressed data. The method was tested across a diverse sets of biomolecular systems, including folded proteins, intrinsically disordered proteins, phospholipid bilayers, protein-ligand complexes, large protein complexes and membrane-bound protein systems. The reconstructed trajectories demonstrated consistent accuracy in recovering key biophysically relevant properties for proteins, lipids and composite systems. The compression efficiency was particularly beneficial for larger systems. This approach enables the scientific community to efficiently store and share large-scale biomolecular simulation data, potentially enhancing collaborative research efforts. The workflow, termed "compresstraj", is implemented in PyTorch and is publicly available at https://github.com/SerpentByte/compresstraj, offering a practical solution for handling the increasing volumes of data generated in biomolecular simulation studies.

The formation and modulation of biomolecular condensates as well as their structural and dynamic properties are determined by an intricate interplay of different driving forces, which down at the microscopic scale involve molecular interactions of the biological macromolecules and the surrounding solvent and ions. Molecular simulations are increasingly used to provide detailed insights into the various processes and thermodynamic driving forces at play, thereby yielding mechanistic understanding and aiding the interpretation of experiments at the level of individual amino acid residues or even atoms. Here we summarize recent advances in the field of biocondensate simulations with a focus on coarse-grained and all-atom molecular dynamics (MD) simulations. We highlight possible future challenges concerning computationally efficient and physically accurate simulations of increasingly large and complex biocondensate systems.

The high doses of drugs required for biotherapeutics, such as monoclonal antibodies (mAbs), and the small volumes that can be administered to patients by subcutaneous injections pose challenges due to high-concentration formulations. The addition of excipients, such as arginine and glutamate, to high-concentration protein formulations can increase solubility and reduce the tendency of protein particle formation. Molecular dynamics (MD) simulations can provide microscopic insights into the mode of action of excipients in mAb formulations but require large system sizes and long time scales that are currently beyond reach at the fully atomistic level. Computationally efficient coarse-grained models such as the Martini 3 force field can tackle this challenge but require careful parametrization, testing, and validation. This study extends the popular Martini 3 force field toward realistic protein-excipient interactions of arginine and glutamate excipients, using the Fab domains of the therapeutic mAbs trastuzumab and omalizumab as model systems. A novel all-atom to coarse-grained mapping of the amino acid excipients is introduced, which explicitly captures the zwitterionic character of the backbone. The Fab-excipient interactions of arginine and glutamate are characterized concerning molecular contacts with the Fabs at the single-residue level. The Martini 3 simulations are compared with results from all-atom simulations as a reference. Our findings reveal an overestimation of Fab-excipient contacts with the default interaction parameters of Martini 3, suggesting a too strong attraction between protein residues and excipients. Therefore, we reparametrized the protein-excipient interaction parameters in Martini 3 against all-atom simulations. The excipient interactions obtained with the new Martini 3 mapping and Lennard-Jones (LJ) interaction parameters, coined Martini 3-exc, agree closely with the all-atom reference data. This work presents an improved parameter set for mAb-arginine and mAb-glutamate interactions in the Martini 3 coarse-grained force field, a key step toward large-scale coarse-grained MD simulations of high-concentration mAb formulations and the stabilizing effects of excipients.

Bactofilins are a widespread family of cytoskeletal proteins that are essential for bacterial morphogenesis, chromosome organization, and motility. They assemble into non-polar filaments independently of nucleotides and typically associate with the cytoplasmic membrane. Their membrane interaction is thought to involve a short N-terminal peptide, but the underlying mechanism is unclear. Here, we clarify the complete membrane-targeting sequence (MTS) of the Caulobacter crescentus bactofilin BacA and identify residues critical for its function. Using molecular dynamics simulations, we show that its affinity for membranes arises from hydrophobic residue-driven water exclusion and electrostatic interactions with negatively charged phospholipid headgroups. Bioinformatic analysis suggests that this mode of membrane binding is conserved across diverse bacterial phyla. Importantly, we observe that BacA polymerization and membrane binding stimulate each other, and both of these processes are necessary for recruiting the membrane-bound client protein PbpC, a cell wall synthase that interacts with BacA via its N-terminal cytoplasmic region. PbpC can functionally replace the MTS of BacA when overproduced, demonstrating that client proteins contribute to the bactofilin-membrane association. Thus, bactofilin assembly and localization are determined by a complex interplay of different factors, thereby enabling the adaptation of these processes to the needs of the systems they control.

A family of Pd2L4 cages prepared from ligands based on an axially chiral diamino-[1,1'-biazulene] motif (serving as a unique azulene-based surrogate of the ubiquitous BINOL moiety) is reported. We show that preparing a cage starting from the racemate of a shorter bis-monodentate ligand derivative, equipped with pyridine donor groups, leads to integrative ("social") chiral self-sorting, exclusively yielding the meso-trans product, but only in a selection of solvents. This phenomenon is driven by individual solvent molecules acting as hydrogen bonding tethers between the amino groups of neighboring ligands, thereby locking the final coordination cage in a single isomeric form. The experimental (solvent-dependent NMR, single-crystal X-ray diffraction) observations of this cooperative interaction could be explained by computational analyses only when explicit solvation was considered. Furthermore, we prepared a larger chiral ligand with isoquinoline donors, which, unlike the first one, does not undergo social self-sorting from its racemic mixture, further highlighting the importance of solvents bridging short distances between the amino groups. Homochiral cages formed from this larger ligand, however, furnish a cavity that can bind anionic and neutral metal complexes such as [Pt(CN)6]2- and Cr(CO)6 and discriminate between the two enantiomers of chiral guest camphor sulfonate.

The surface area of atoms and molecules plays a crucial role in shaping many physiochemical properties of materials. Despite its fundamental importance, precisely defining atomic and molecular surfaces has long been a puzzle. Among the available definitions, a straightforward and elegant approach by Bader describes a molecular surface as an iso-density surface beyond which electron density drops below a certain cut-off. However, so far neither this theory nor a decisive value for the density cut-off have been amenable to experimental verification due to the limitations of conventional experimental methods. In the present study, we employ a state-of-the-art experimental method based on the recently developed concept of thermodynamically effective (TE) surfaces to tackle this longstanding problem. By studying a set of 104 molecules, a close to perfect agreement between quantum chemical evaluations of iso-density surfaces for a cut-off density of 0.0016 a.u. and experimental results obtained via thermodynamic phase change data is demonstrated, with a mean unsigned percentage deviation of 1.6% and a correlation coefficient of 0.995. Accordingly, we suggest the iso-density surface contoured at an electron density value of 0.0016 a.u. as a representation of the surface of atoms and molecules.

Quantification of radii of atoms in molecules is of fundamental importance in understanding a wide range of physical and chemical phenomena. In the present study, we develop methods for evaluation of radii of atoms in molecules and assess their robustness by studying the agreement of van der Waals and solvent excluded surfaces constructed by them with reference iso-density surfaces. By studying a large dataset of 1235 molecules, we show that estimation of atomic radii via effective and free atomic volumes can accurately take the dependence of atomic radii on the chemical environment into account. A linear dependence of atomic radii on partial charge is found for radii estimated via effective volumes and partial charges computed based on iterative Hirshfeld and MBIS partitioning methods.

Atomic radius is a fundamentally important quantity shaping multiple properties of atoms, molecules, and materials. Due to its fundamental importance, precise quantification and interpretation of atomic radii has been the subject of numerous studies for more than a century. It has resulted in a broad variety of estimations of atomic radii which so far have not been amenable to extensive verification by experiment. The present study follows our recent work demonstrating that electron iso-density surfaces, contoured at a certain cut-off density, accurately represent molecular surfaces determined via thermodynamic phase change data. Here we provide thermodynamically consistent estimates of atomic radii for the main group elements.

Protein formulation development relies on the selection of excipients that inhibit protein-protein interactions preventing aggregation. Empirical strategies involve screening many excipient and buffer combinations by physicochemical characterization using forced degradation or temperature-induced stress, mostly under accelerated conditions. Such methods do not readily provide information on the inter- and intramolecular interactions responsible for the effects of excipients. Here, we describe a combined experimental and computational approach for investigating the effect of protein-excipient interactions on formulation stability, which allows the identification of preferential interaction sites and thus can aid in the selection of excipients to be experimentally screened. Model systems composed of two marketed therapeutic IgG1 monoclonal antibodies with identical Fc domain sequences, trastuzumab and omalizumab, were investigated with commonly used excipients arginine, glutamate, and equimolar arginine/glutamate mixtures. Protein-excipient interactions were studied using all-atom molecular dynamics (MD) simulations, which show accumulation of the excipients at specific antibody regions. Preferential excipient-interaction sites were particularly found for charged and aromatic residues and in the complementary-determining regions, with more pronounced arginine contacts for omalizumab than trastuzumab. These computational findings are in line with the more pronounced stabilizing effects of arginine observed in the long-term storage stability study. Furthermore, the aggregation and solubility propensity predicted by commonly used in silico tools do not align with the preferential excipient-interaction sites identified by the MD simulations, suggesting that different physicochemical mechanisms are at play.

Liquid–liquid phase separation (LLPS) plays a key role in the compartmentalization of cells via the formation of biomolecular condensates. Here, we combined atomistic molecular dynamics (MD) simulations and terahertz (THz) spectroscopy to determine the solvent entropy contribution to the formation of condensates of the human eye lens protein γD-crystallin. The MD simulations reveal an entropy tug-of-war between water molecules that are released from the protein droplets and the ones that are retained within the condensates, two categories of water molecules that were also assigned spectroscopically. A recently developed THz calorimetry method enables a quantitative comparison of the experimental and computational entropy changes of the released water molecules. The strong correlation mutually validates the two approaches and opens the way to a detailed atomic-level understanding of the different driving forces underlying LLPS.

Despite the fundamental importance of radii of atoms in molecules for numerous applications in physics and chemistry, comprehensive methods for their theoretical evaluation are still scarce. Here, we present quantum chemistry-based approaches for evaluation of radii of atoms in molecules and assess their robustness by studying the agreement of van der Waals and solvent-excluded surfaces constructed by them with reference molecular surfaces. By studying a large data set of 1235 molecules, it is shown that estimation of radii via effective and free atomic volumes can accurately take the dependence of atomic radii on the chemical environment into account.

The high concentration of proteins and other biological macromolecules inside biomolecular condensates leads to dense and confined environments, which can affect the dynamic ensembles and the time scales of the conformational transitions. Here, we use atomistic molecular dynamics (MD) simulations of the intrinsically disordered low complexity domain (LCD) of the human fused in sarcoma (FUS) RNA-binding protein to study how self-crowding inside a condensate affects the dynamic motions of the protein. We found a heterogeneous retardation of the protein dynamics in the condensate with respect to the dilute phase, with large-amplitude motions being strongly slowed by up to 2 orders of magnitude, whereas small-scale motions, such as local backbone fluctuations and side-chain rotations, are less affected. The results support the notion of a liquid-like character of the condensates and show that different protein motions respond differently to the environment.

The surface area of atoms and molecules plays a crucial role in shaping many physiochemical properties of materials. Despite its fundamental importance, precisely defining atomic and molecular surfaces has long been a puzzle. Among the available definitions, a straightforward and elegant approach by Bader describes a molecular surface as an iso-density surface beyond which the electron density drops below a certain cut-off. However, so far neither this theory nor a decisive value for the density cut-off have been amenable to experimental verification due to the limitations of conventional experimental methods. In the present study, we employ a state-of-the-art experimental method based on the recently developed concept of thermodynamically effective (TE) surfaces to tackle this longstanding problem. By studying a set of 104 molecules, a close to perfect agreement between quantum chemical evaluations of iso-density surfaces contoured at a cut-off density of 0.0016 a.u. and experimental results obtained via thermodynamic phase change data is demonstrated, with a mean unsigned percentage deviation of 1.6% and a correlation coefficient of 0.995. Accordingly, we suggest the iso-density surface contoured at an electron density value of 0.0016 a.u. as a representation of the surface of atoms and molecules. The precise definition of the surface of atoms and molecules has long been an open issue. Here, the authors combine theory and experimental thermodynamic measurements to define atomic and molecular surfaces from electron iso-density surfaces contoured at a value of 0.0016 a.u.

Metal ions are irreplaceable in many areas of chemistry, including (bio)catalysis, self-assembly and charge transfer processes. Yet, modelling their structural and dynamic properties in diverse chemical environments remains challenging for both force fields and ab initio methods. Here, we introduce a strategy to train machine learning potentials (MLPs) using MACE, an equivariant message-passing neural network, for metal-ligand complexes in explicit solvents. We explore the structure and ligand exchange dynamics of Mg2+ in water and Pd2+ in acetonitrile as two illustrative model systems. The trained potentials accurately reproduce equilibrium structures of the complexes in solution, including different coordination numbers and geometries. Furthermore, the MLPs can model structural changes between metal ions and ligands in the first coordination shell, and reproduce the free energy barriers for the corresponding ligand exchange. The strategy presented here provides a computationally efficient approach to model metal ions in solution, paving the way for modelling larger and more diverse metal complexes relevant to biomolecules and supramolecular assemblies.

Understanding macromolecular function, interactions, and stability hinges on detailed assessment of conformational ensembles. For solid proteins, accurate elucidation of the spatial aspects of dynamics at physiological temperatures is limited by the qualitative character or low abundance of solid-state nuclear magnetic resonance internuclear distance information. Here, we demonstrate access to abundant proton-proton internuclear distances for integrated structural biology and chemistry with unprecedented accuracy. Apart from highest-resolution single-state structures, the exact distances enable molecular dynamics (MD) ensemble simulations orchestrated by a dense network of experimental interproton distance boundaries gathered in the context of their physical lattices. This direct embedding of experimental ensemble distances into MD will provide access to representative, atomic-level spatial details of conformational dynamics in supramolecular assemblies, crystalline and lipidembedded proteins, and beyond.

The activity of membrane proteins depends strongly on the surrounding lipid environment. Here, we characterize the lipid stimulation of the plant plasma membrane H+-ATPase Arabidopsis thaliana H+-ATPase isoform 2 (AHA2) upon purification and reconstitution into liposomes of defined lipid compositions. We show that the proton pumping activity of AHA2 is stimulated by anionic phospholipids, especially by phosphatidylserine. This activation was independent of the cytoplasmic C-terminal regulatory domain of the pump. Molecular dynamics simulations revealed several preferential contact sites for anionic phospholipids in the transmembrane domain of AHA2. These contact sites are partially conserved in functionally different P-type ATPases from different organisms, suggesting a general regulation mechanism by the membrane lipid environment. Our findings highlight the fact that anionic lipids play an important role in the control of H+-ATPase activity.

AbstractMycobacterium tuberculosis is protected from antibiotic therapy by a multi-layered hydrophobic cell envelope. Major facilitator superfamily (MFS) transporter Rv1410 and the periplasmic lipoprotein LprG are involved in transport of triacylglycerides (TAGs) that seal the mycomembrane. Here, we report a 2.7 Å structure of a mycobacterial Rv1410 homologue, which adopts an outward-facing conformation and exhibits unusual transmembrane helix 11 and 12 extensions that protrude ~20 Å into the periplasm. A small, very hydrophobic cavity suitable for lipid transport is constricted by a functionally important ion-lock likely involved in proton coupling. Combining mutational analyses and MD simulations, we propose that TAGs are extracted from the core of the inner membrane into the central cavity via lateral clefts present in the inward-facing conformation. The functional role of the periplasmic helix extensions is to channel the extracted TAG into the lipid binding pocket of LprG.