Structure-Based Protein Assembly Simulations Including Various Binding Sites and Conformations.

Many biological functions are mediated by large complexes formed by multiple proteins and other cellular macromolecules. Recent progress in experimental structure determination, as well as in integrative modeling and protein structure prediction using deep learning approaches, has resulted in a rapid increase in the number of solved multiprotein assemblies. However, the assembly process of large complexes from their components is much less well-studied. We introduce a rapid computational structure-based (SB) model, GoCa, that allows to follow the assembly process of large multiprotein complexes based on a known native structure. Beyond existing SB Go̅-type models, it distinguishes between intra- and intersubunit interactions, allowing us to include coupled folding and binding. It accounts automatically for the permutation of identical subunits in a complex and allows the definition of multiple minima (native) structures in the case of proteins that undergo global transitions during assembly. The model is successfully tested on several multiprotein complexes. The source code of the GoCa program including a tutorial is publicly available on Github: https://github.com/ZachariasLab/GoCa. We also provide a web source that allows users to quickly generate the necessary input files for a GoCa simulation: https://goca.t38webservices.nat.tum.de.

Liquid-Vapor Coexistence and Spontaneous Evaporation at Atmospheric Pressure of Common Rigid Three-Point Water Models in Molecular Simulations.

Molecular dynamics (MD) simulations are widely used to investigate molecular systems at atomic resolution including biomolecular structures, drug-receptor interactions, and novel materials. Frequently, MD simulations are performed in an aqueous solution with explicit models of water molecules. Commonly, such models are parameterized to reproduce the liquid phase of water under ambient conditions. However, often, simulations at significantly higher temperatures are also of interest. Hence, it is important to investigate the equilibrium of the liquid and vapor phases of molecular models of water at elevated temperatures. Here, we evaluate the behavior of 11 common rigid three-point water models over a wide range of temperatures. From liquid-vapor coexistence simulations, we estimated the critical points and studied the spontaneous evaporation of these water models. Moreover, we investigated the influence of the system size, choice of the pressure-coupling algorithm, and rate of heating on the process and compared them with the experimental data. We found that modern rigid three-point water models reproduce the critical point surprisingly well. Furthermore, we discovered that the critical temperature correlates with the quadrupole moment of the respective water model. This indicates that the spatial arrangement of the partial charges is important for reproducing the liquid-vapor phase transition. Our findings may guide the selection of water models for simulations conducted at high temperatures.

The Role of Force Fields and Water Models in Protein Folding and Unfolding Dynamics.

Protein folding is a fascinating, not fully understood phenomenon in biology. Molecular dynamics (MD) simulations are an invaluable tool to study conformational changes in atomistic detail, including folding and unfolding processes of proteins. However, the accuracy of the conformational ensembles derived from MD simulations inevitably relies on the quality of the underlying force field in combination with the respective water model. Here, we investigate protein folding, unfolding, and misfolding of fast-folding proteins by examining different force fields with their recommended water models, i.e., ff14SB with the TIP3P model and ff19SB with the OPC model. To this end, we generated long conventional MD simulations highlighting the perks and pitfalls of these setups. Using Markov state models, we defined kinetically independent conformational substates and emphasized their distinct characteristics, as well as their corresponding state probabilities. Surprisingly, we found substantial differences in thermodynamics and kinetics of protein folding, depending on the combination of the protein force field and water model, originating primarily from the different water models. These results emphasize the importance of carefully choosing the force field and the respective water model as they determine the accuracy of the observed dynamics of folding events. Thus, the findings support the hypothesis that the water model is at least equally important as the force field and hence needs to be considered in future studies investigating protein dynamics and folding in all areas of biophysics.

Structural mechanism of Fab domain dissociation as a measure of interface stability.

Therapeutic antibodies should not only recognize antigens specifically, but also need to be free from developability issues, such as poor stability. Thus, the mechanistic understanding and characterization of stability are critical determinants for rational antibody design. In this study, we use molecular dynamics simulations to investigate the melting process of 16 antigen binding fragments (Fabs). We describe the Fab dissociation mechanisms, showing a separation in the VH-VL and in the CH1-CL domains. We found that the depths of the minima in the free energy curve, corresponding to the bound states, correlate with the experimentally determined melting temperatures. Additionally, we provide a detailed structural description of the dissociation mechanism and identify key interactions in the CDR loops and in the CH1-CL interface that contribute to stabilization. The dissociation of the VH-VL or CH1-CL domains can be represented by conformational changes in the bend angles between the domains. Our findings elucidate the melting process of antigen binding fragments and highlight critical residues in both the variable and constant domains, which are also strongly germline dependent. Thus, our proposed mechanisms have broad implications in the development and design of new and more stable antigen binding fragments.

Challenges in antibody structure prediction.

Advances in structural biology and the exponential increase in the amount of high-quality experimental structural data available in the Protein Data Bank has motivated numerous studies to tackle the grand challenge of predicting protein structures. In 2020 AlphaFold2 revolutionized the field using a combination of artificial intelligence and the evolutionary information contained in multiple sequence alignments. Antibodies are one of the most important classes of biotherapeutic proteins. Accurate structure models are a prerequisite to advance biophysical property predictions and consequently antibody design. Specialized tools used to predict antibody structures based on different principles have profited from current advances in protein structure prediction based on artificial intelligence. Here, we emphasize the importance of reliable protein structure models and highlight the enormous advances in the field, but we also aim to increase awareness that protein structure models, and in particular antibody models, may suffer from structural inaccuracies, namely incorrect cis-amide bonds, wrong stereochemistry or clashes. We show that these inaccuracies affect biophysical property predictions such as surface hydrophobicity. Thus, we stress the importance of carefully reviewing protein structure models before investing further computing power and setting up experiments. To facilitate the assessment of model quality, we provide a tool "TopModel" to validate structure models.

Complexes++: Efficient and versatile coarse-grained simulations of protein complexes and their dense solutions.

The interior of living cells is densely filled with proteins and their complexes, which perform multitudes of biological functions. We use coarse-grained simulations to reach the system sizes and time scales needed to study protein complexes and their dense solutions and to interpret experiments. To take full advantage of coarse-graining, the models have to be efficiently implemented in simulation engines that are easy to use, modify, and extend. Here, we introduce the Complexes++ simulation software to simulate a residue-level coarse-grained model for proteins and their complexes, applying a Markov chain Monte Carlo engine to sample configurations. We designed a parallelization scheme for the energy evaluation capable of simulating both dilute and dense systems efficiently. Additionally, we designed the software toolbox pycomplexes to easily set up complex topologies of multi-protein complexes and their solutions in different thermodynamic ensembles and in replica-exchange simulations, to grow flexible polypeptide structures connecting ordered protein domains, and to automatically visualize structural ensembles. Complexes++ simulations can easily be modified and they can be used for efficient explorations of different simulation systems and settings. Thus, the Complexes++ software is well suited for the integration of experimental data and for method development.

Bispecific antibodies-effects of point mutations on CH3-CH3 interface stability.

A new format of therapeutic proteins is bispecific antibodies, in which two different heavy chains heterodimerize to obtain two different binding sites. Therefore, it is crucial to understand and optimize the third constant domain (CH3-CH3) interface to favor heterodimerization over homodimerization, and to preserve the physicochemical properties, as thermal stability. Here, we use molecular dynamics simulations to investigate the dissociation process of 19 CH3-CH3 crystal structures that differ from each other in few point mutations. We describe the dissociation of the dimeric interface as a two-steps mechanism. As confirmed by a Markov state model, apart from the bound and the dissociated state, we observe an additional intermediate state, which corresponds to an encounter complex. The analysis of the interdomain contacts reveals key residues that stabilize the interface. We expect that our results will improve the understanding of the CH3-CH3 interface interactions and thus advance the developability and design of new antibodies formats.

Increase of Radiative Forcing through Midinfrared Absorption by Stable CO2 Dimers?

We performed matrix-isolation infrared (MI-IR) spectroscopy of carbon dioxide monomers, CO2, and dimers, (CO2)2, trapped in neon and in air. On the basis of vibration configuration interaction (VCI) calculations accounting for mode coupling and anharmonicity, we identify additional infrared-active bands in the MI-IR spectra due to the (CO2)2 dimer. These bands are satellite bands next to the established CO2 monomer bands, which appear in the infrared window of Earth's atmosphere at around 4 and 15 µm. In a systematic carbon dioxide mixing ratio study using neon matrixes, we observe a significant fraction of the dimer at mixing ratios above 300 ppm, with a steep increase up to 1000 ppm. In neon matrix, the dimer increases the IR absorbance by about 15% at 400 ppm compared to the monomer absorbance alone. This suggests a high fraction of the (CO2)2 dimer in our matrix experiments. In atmospheric conditions, such increased absorbance would significantly amplify radiative forcings and, thus, the greenhouse warming. To enable a comparison of our laboratory experiment with various atmospheric conditions (Earth, Mars, Venus), we compute the thermodynamics of the dimerization accordingly. The dimerization is favored at low temperatures and/or high carbon dioxide partial pressures. Thus, we argue that matrix isolation does not trap the gas composition "as is". Instead, the gas is precooled to 40 K, where CO2 dimerizes before being trapped in the matrix, already at very low carbon dioxide partial pressures. In the context of planetary atmospheres, our results improve understanding of the greenhouse effect for planets of rather thick CO2 atmospheres such as Venus, where a significant fraction of the (CO2)2 dimer can be expected. There, the necessity of including the mid-IR absorption by stable (CO2)2 dimers in databases used for modeling radiative forcing, such as HITRAN, arises.

Corrigendum: Comparing Antibody Interfaces to Inform Rational Design of New Antibody Formats.

[This corrects the article DOI: 10.3389/fmolb.2022.812750.].

Comparing Antibody Interfaces to Inform Rational Design of New Antibody Formats.

As the current biotherapeutic market is dominated by antibodies, the design of different antibody formats, like bispecific antibodies and other new formats, represent a key component in advancing antibody therapy. When designing new formats, a targeted modulation of pairing preferences is key. Several existing approaches are successful, but expanding the repertoire of design possibilities would be desirable. Cognate immunoglobulin G antibodies depend on homodimerization of the fragment crystallizable regions of two identical heavy chains. By modifying the dimeric interface of the third constant domain (CH3-CH3), with different mutations on each domain, the engineered Fc fragments form rather heterodimers than homodimers. The first constant domain (CH1-CL) shares a very similar fold and interdomain orientation with the CH3-CH3 dimer. Thus, numerous well-established design efforts for CH3-CH3 interfaces, have also been applied to CH1-CL dimers to reduce the number of mispairings in the Fabs. Given the high structural similarity of the CH3-CH3 and CH1-CL domains we want to identify additional opportunities in comparing the differences and overlapping interaction profiles. Our vision is to facilitate a toolkit that allows for the interchangeable usage of different design tools from crosslinking the knowledge between these two interface types. As a starting point, here, we use classical molecular dynamics simulations to identify differences of the CH3-CH3 and CH1-CL interfaces and already find unexpected features of these interfaces shedding new light on possible design variations. Apart from identifying clear differences between the similar CH3-CH3 and CH1-CL dimers, we structurally characterize the effects of point-mutations in the CH3-CH3 interface on the respective dynamics and interface interaction patterns. Thus, this study has broad implications in the field of antibody engineering as it provides a structural and mechanistical understanding of antibody interfaces and thereby presents a crucial aspect for the design of bispecific antibodies.

Germline-Dependent Antibody Paratope States and Pairing Specific VH-VL Interface Dynamics.

Antibodies have emerged as one of the fastest growing classes of biotherapeutic proteins. To improve the rational design of antibodies, we investigate the conformational diversity of 16 different germline combinations, which are composed of 4 different kappa light chains paired with 4 different heavy chains. In this study, we systematically show that different heavy and light chain pairings strongly influence the paratope, interdomain interaction patterns and the relative VH-VL interface orientations. We observe changes in conformational diversity and substantial population shifts of the complementarity determining region (CDR) loops, resulting in distinct dominant solution structures and differently favored canonical structures. Additionally, we identify conformational changes in the structural diversity of the CDR-H3 loop upon different heavy and light chain pairings, as well as upon changes in sequence and structure of the neighboring CDR loops, despite having an identical CDR-H3 loop amino acid sequence. These results can also be transferred to all CDR loops and to the relative VH-VL orientation, as certain paratope states favor distinct interface angle distributions. Furthermore, we directly compare the timescales of sidechain rearrangements with the well-described transition kinetics of conformational changes in the backbone of the CDR loops. We show that sidechain flexibilities are strongly affected by distinct heavy and light chain pairings and decipher germline-specific structural features co-determining stability. These findings reveal that all CDR loops are strongly correlated and that distinct heavy and light chain pairings can result in different paratope states in solution, defined by a characteristic combination of CDR loop conformations and VH-VL interface orientations. Thus, these results have broad implications in the field of antibody engineering, as they clearly show the importance of considering paired heavy and light chains to understand the antibody binding site, which is one of the key aspects in the design of therapeutics.

Shark Antibody Variable Domains Rigidify Upon Affinity Maturation-Understanding the Potential of Shark Immunoglobulins as Therapeutics.

Sharks and other cartilaginous fish are the phylogenetically oldest living organisms that have antibodies as part of their adaptive immune system. As part of their humoral adaptive immune response, they produce an immunoglobulin, the so-called immunoglobulin new antigen receptor (IgNAR), a heavy-chain only antibody. The variable domain of an IgNAR, also known as V NAR , binds the antigen as an independent soluble domain. In this study, we structurally and dynamically characterized the affinity maturation mechanism of the germline and somatically matured (PBLA8) V NAR to better understand their function and their applicability as therapeutics. We observed a substantial rigidification upon affinity maturation, which is accompanied by a higher number of contacts, thereby contributing to the decrease in flexibility. Considering the static x-ray structures, the observed rigidification is not obvious, as especially the mutated residues undergo conformational changes during the simulation, resulting in an even stronger network of stabilizing interactions. Additionally, the simulations of the V NAR in complex with the hen egg-white lysozyme show that the V NAR antibodies evidently follow the concept of conformational selection, as the binding-competent state already preexisted even without the presence of the antigen. To have a more detailed description of antibody-antigen recognition, we also present here the binding/unbinding mechanism between the hen egg-white lysozyme and both the germline and matured V NAR s. Upon maturation, we observed a substantial increase in the resulting dissociation-free energy barrier. Furthermore, we were able to kinetically and thermodynamically describe the binding process and did not only identify a two-step binding mechanism, but we also found a strong population shift upon affinity maturation toward the native binding pose.

Implementation of the Freely Jointed Chain Model to Assess Kinetics and Thermodynamics of Thermosensitive Coil-Globule Transition by Markov States.

We revived and implemented a method developed by Kuhn in 1934, originally only published in German, that is, the so-called "freely jointed chain" model. This approach turned out to be surprisingly useful for analyzing state-of-the-art computer simulations of the thermosensitive coil-globule transition of N-Isopropylacrylamide 20-mer. Our atomistic computer simulations are orders of magnitude longer than those of previous studies and lead to a reliable description of thermodynamics and kinetics at many different temperatures. The freely jointed chain model provides a coordinate system, which allows us to construct a Markov state model of the conformational transitions. Furthermore, this guarantees a reliable reconstruction of the kinetics in back-and-forth directions. In addition, we obtain a description of the high diversity and variability of both conformational states. Thus, we gain a detailed understanding of the coil-globule transition. Surprisingly, conformational entropy turns out to play only a minor role in the thermodynamic balance of the process. Moreover, we show that the radius of gyration is an unexpectedly unsuitable coordinate to comprehend the transition kinetics because it does not capture the high conformational diversity within the different states. Consequently, the approach presented here allows for an exhaustive description and resolution of the conformational ensembles of arbitrary linear polymer chains.

Conformational Shifts of Stacked Heteroaromatics: Vacuum vs. Water Studied by Machine Learning.

Stacking interactions play a crucial role in drug design, as we can find aromatic cores or scaffolds in almost any available small molecule drug. To predict optimal binding geometries and enhance stacking interactions, usually high-level quantum mechanical calculations are performed. These calculations have two major drawbacks: they are very time consuming, and solvation can only be considered using implicit solvation. Therefore, most calculations are performed in vacuum. However, recent studies have revealed a direct correlation between the desolvation penalty, vacuum stacking interactions and binding affinity, making predictions even more difficult. To overcome the drawbacks of quantum mechanical calculations, in this study we use neural networks to perform fast geometry optimizations and molecular dynamics simulations of heteroaromatics stacked with toluene in vacuum and in explicit solvation. We show that the resulting energies in vacuum are in good agreement with high-level quantum mechanical calculations. Furthermore, we show that using explicit solvation substantially influences the favored orientations of heteroaromatic rings thereby emphasizing the necessity to include solvation properties starting from the earliest phases of drug design.

pyPolyBuilder: Automated Preparation of Molecular Topologies and Initial Configurations for Molecular Dynamics Simulations of Arbitrary Supramolecules.

The construction of a molecular topology file is a prerequisite for any classical molecular dynamics simulation. However, the generation of such a file may be very challenging at times, especially for large supramolecules. While many tools are available to provide topologies for large proteins and other biomolecules, the scientific community researching nonbiological systems is not equally well equipped. Here, we present a practical tool to generate topologies for arbitrary supramolecules: The pyPolyBuilder. In addition to linear polymer chains, it also provides the possibility to generate topologies of arbitrary, large, branched molecules, such as, e.g., dendrimers. Furthermore, it also generates reasonable starting structures for simulations of these molecules. pyPolyBuilder is a standalone command-line tool implemented in python. Therefore, it may be easily incorporated in persisting simulation pipelines on any operating systems and with different simulation engines. pyPolyBuilder is freely available on github: https://github.com/mssm-labmmol/pypolybuilder.

X-Entropy: A Parallelized Kernel Density Estimator with Automated Bandwidth Selection to Calculate Entropy.

X-Entropy is a Python package used to calculate the entropy of a given distribution, in this case, based on the distribution of dihedral angles. The dihedral entropy facilitates an alignment-independent measure of local protein flexibility. The key feature of our approach is a Gaussian kernel density estimation (KDE) using a plug-in bandwidth selection, which is fully implemented in a C++ backend and parallelized with OpenMP. We further provide a Python frontend, with predefined wrapper functions for classical coordinate-based dihedral entropy calculations, using a 1D approximation. This makes the package very straightforward to include in any Python-based analysis workflow. Furthermore, the frontend allows full access to the C++ backend, so that the KDE can be used on any binnable one-dimensional input data. In this application note, we discuss implementation and usage details and illustrate potential applications. In particular, we benchmark the performance of our module in calculating the entropy of samples drawn from a Gaussian distribution and the analytical solution thereof. Further, we analyze the computational performance of this module compared to well-established python libraries that perform KDE analyses. X-Entropy is available free of charge on GitHub (https://github.com/liedllab/X-Entropy).

Surprisingly Fast Interface and Elbow Angle Dynamics of Antigen-Binding Fragments.

Fab consist of a heavy and light chain and can be subdivided into a variable (V H and V L ) and a constant region (C H 1 and C L ). The variable region contains the complementarity-determining region (CDR), which is formed by six hypervariable loops, shaping the antigen binding site, the paratope. Apart from the CDR loops, both the elbow angle and the relative interdomain orientations of the V H -V L and the C H 1-C L domains influence the shape of the paratope. Thus, characterization of the interface and elbow angle dynamics is essential to antigen specificity. We studied nine antigen-binding fragments (Fab) to investigate the influence of affinity maturation, antibody humanization, and different light-chain types on the interface and elbow angle dynamics. While the CDR loops reveal conformational transitions in the micro-to-millisecond timescale, both the interface and elbow angle dynamics occur on the low nanosecond timescale. Upon affinity maturation, we observe a substantial rigidification of the V H and V L interdomain and elbow-angle flexibility, reflected in a narrower and more distinct distribution. Antibody humanization describes the process of grafting non-human CDR loops onto a representative human framework. As the antibody framework changes upon humanization, we investigated if both the interface and the elbow angle distributions are changed or shifted. The results clearly showed a substantial shift in the relative V H -V L distributions upon antibody humanization, indicating that different frameworks favor distinct interface orientations. Additionally, the interface and elbow angle dynamics of five antibody fragments with different light-chain types are included, because of their strong differences in elbow angles. For these five examples, we clearly see a high variability and flexibility in both interface and elbow angle dynamics, highlighting the fact that Fab interface orientations and elbow angles interconvert between each other in the low nanosecond timescale. Understanding how the relative interdomain orientations and the elbow angle influence antigen specificity, affinity, and stability has broad implications in the field of antibody modeling and engineering.

Thermosensitive Hydration of Four Acrylamide-Based Polymers in Coil and Globule Conformations.

To characterize the thermosensitive coil-globule transition in atomistic detail, the conformational dynamics of linear polymer chains of acrylamide-based polymers have been investigated at multiple temperatures. Therefore, molecular dynamic simulations of 30mers of polyacrylamide (AAm), poly-N-methylacrylamide (NMAAm), poly-N-ethylacrylamide (NEAAm), and poly-N-isopropylacrylamide (NIPAAm) have been performed at temperatures ranging from 250 to 360 K for 2 µs. While two of the polymers are known to exhibit thermosensitivity (NEAAm, NIPAAm), no thermosensitivity is observed for AAm and NMAAm in aqueous solution. Our computer simulations consistently reproduce these properties. To understand the thermosensitivity of the respective polymers, the conformational ensembles at different temperatures have been separated according to the coil-globule transition. The coil and globule conformational ensembles were exhaustively analyzed in terms of hydrogen bonding with the solvent, the change of the solvent accessible surface, and enthalpic contributions. Surprisingly, independent of different thermosensitive properties of the four polymers, the surface affinity to water of coil conformations is higher than for globule conformations. Therefore, polymer-solvent interactions stabilize coil conformations at all temperatures. Nevertheless, the enthalpic contributions alone cannot explain the differences in thermosensitivity. This clearly implies that entropy is the distinctive factor for thermosensitivity. With increasing side chain length, the lifetime of the hydrogen bonds between the polymer surface and water is extended. Thus, we surmise that a longer side chain induces a larger entropic penalty due to immobilization of water molecules.

Macrocycle Cell Permeability Measured by Solvation Free Energies in Polar and Apolar Environments.

The relation of surface polarity and conformational preferences is decisive for cell permeability and thus bioavailability of macrocyclic drugs. Here, we employ grid inhomogeneous solvation theory (GIST) to calculate solvation free energies for a series of six macrocycles in water and chloroform as a measure of passive membrane permeability. We perform accelerated molecular dynamics simulations to capture a diverse structural ensemble in water and chloroform, allowing for a direct profiling of solvent-dependent conformational preferences. Subsequent GIST calculations facilitate a quantitative measure of solvent preference in the form of a transfer free energy, calculated from the ensemble-averaged solvation free energies in water and chloroform. Hence, the proposed method considers how the conformational diversity of macrocycles in polar and apolar solvents translates into transfer free energies. Following this strategy, we find a striking correlation of 0.92 between experimentally determined cell permeabilities and calculated transfer free energies. For the studied model systems, we find that the transfer free energy exceeds the purely water-based solvation free energies as a reliable estimate of cell permeability and that conformational sampling is imperative for a physically meaningful model. We thus recommend this purely physics-based approach as a computational tool to assess cell permeabilities of macrocyclic drug candidates.

Quantifying Protein-Protein Interactions in Molecular Simulations.

Interactions among proteins, nucleic acids, and other macromolecules are essential for their biological functions and shape the physicochemcial properties of the crowded environments inside living cells. Binding interactions are commonly quantified by dissociation constants Kd, and both binding and nonbinding interactions are quantified by second osmotic virial coefficients B2. As a measure of nonspecific binding and stickiness, B2 is receiving renewed attention in the context of so-called liquid-liquid phase separation in protein and nucleic acid solutions. We show that Kd is fully determined by B2 and the fraction of the dimer observed in molecular simulations of two proteins in a box. We derive two methods to calculate B2. From molecular dynamics or Monte Carlo simulations using implicit solvents, we can determine B2 from insertion and removal energies by applying Bennett's acceptance ratio (BAR) method or the (binless) weighted histogram analysis method (WHAM). From simulations using implicit or explicit solvents, one can estimate B2 from the probability that the two molecules are within a volume large enough to cover their range of interactions. We validate these methods for coarse-grained Monte Carlo simulations of three weakly binding proteins. Our estimates for Kd and B2 allow us to separate out the contributions of nonbinding interactions to B2. Comparison of calculated and measured values of Kd and B2 can be used to (re-)parameterize and improve molecular force fields by calibrating specific affinities, overall stickiness, and nonbinding interactions. The accuracy and efficiency of Kd and B2 calculations make them well suited for high-throughput studies of large interactomes.