Conformational and functional characterization of artificially conjugated non-canonical ubiquitin dimers
2019-12-27, Schneider, Tobias, Berg, Andrej, Ulusoy, Zeynel, Gamerdinger, Martin, Peter, Christine, Kovermann, Michael
Ubiquitylation is an eminent posttranslational modification referring to the covalent attachment of single ubiquitin molecules or polyubiquitin chains to a target protein dictating the fate of such labeled polypeptide chains. Here, we have biochemically produced artificially Lys11-, and Lys27-, and Lys63-linked ubiquitin dimers based on click-chemistry generating milligram quantities in high purity. We show that the artificial linkage used for the conjugation of two ubiquitin moieties represents a fully reliable surrogate of the natural isopeptide bond by acquiring highly resolved nuclear magnetic resonance (NMR) spectroscopic data including ligand binding studies. Extensive coarse grained and atomistic molecular dynamics (MD) simulations allow to extract structures representing the ensemble of domain-domain conformations used to verify the experimental data. Advantageously, this methodology does not require individual isotopic labeling of both ubiquitin moieties as NMR data have been acquired on the isotopically labeled proximal moiety and complementary MD simulations have been used to fully interpret the experimental data in terms of domain-domain conformation. This combined approach intertwining NMR spectroscopy with MD simulations makes it possible to describe the conformational space non-canonically Lys11-, and Lys27-linked ubiquitin dimers occupy in a solution averaged ensemble by taking atomically resolved information representing all residues in ubiquitin dimers into account.
Anisotropic Extended-Chain Polymer Nanocrystals
2019-08-27, Rank, Christina, Häußler, Manuel, Rathenow, Patrick, King, Michael, Globisch, Christoph, Peter, Christine, Mecking, Stefan
As a concept for distinct shape polymer nanoparticles, nanoscale single crystals composed of a crystallizable chain with lyophilic end groups are explored. This differs from much studied block copolymer nanoparticles and nanostructures, in which the second (noncrystalline) blocks’ spacial demand impacts the overall structure and blurs the cores’ anisotropic shape. For precise C48 polyethylene telechelics X(CH2)46X (X = COO–M+ or CH2SO3–M+, with M+ = Na+, K+, or Cs+) as a relevant model system, a combined experimental and atomistic-level simulation study reveals them to form extended-chain, single-crystalline nanoparticles sandwiched by a layer of head groups. Their microscopic structure, order, and the resulting overall shape are decisively impacted by the mutual repulsion of the head groups, itself determined by the degree of ion pairing with the counterions and the size of the head groups. This leads to the bending of the chains at the lateral side of the crystal, preventing the particles from agglomeration, and to a chain tilt of the monolayer, thus reducing its thickness. By comparison, for a shorter analogue Cs+ –OOC(CH2)21COO– Cs+, the attractive van der Waals interactions between the hydrocarbon chains are not sufficient to overcome the head group repulsion, resulting in nanoparticle break up. These insights are instrumental for understanding and designing anisotropic organic polymer particles exploiting the principles of polymer crystallinity, which are also predestined for particle assembly.
EncoderMap : Dimensionality Reduction and Generation of Molecule Conformations
2019-02-12, Lemke, Tobias, Peter, Christine
Molecular simulation is one example where large amounts of high-dimensional (high-d) data are generated. To extract useful information e.g. about relevant states and important conformational transitions, a form of dimensionality reduction is required. Dimensionality reduction algorithms differ in their ability to efficiently project large amounts of data to an informative low-dimensional (low-d) representation and the way the low and high-d representations are linked. We propose a dimensionality reduction algorithm called encoder-map which is based on a neural network autoencoder in combination with a non-linear distance metric. A key advantage of this method is that it establishes a functional link from the high-d to the low-d representation and vice versa. This allows not only to efficiently project data points to the low-d representation but also to generate high-d representatives for any point in the low-d map. The potential of the algorithm is demonstrated for molecular simulation data of a small, highly-flexible peptide as well as for folding simulations of the 20-residue Trp-cage protein. We demonstrate that the algorithm is able to efficiently project the ensemble of high-d structures to a low-d map where major states can be identified and important conformational transitions are revealed. We also show that molecular conformations can be generated for any point or any connecting line between points on the low-d map. This ability of inverse mapping from the low-d to the high-d representation is particularly relevant for the use in algorithms that enhance the exploration of conformational space or the sampling of transitions between conformational states.
In Silico Approaches to Design and Characterize Peptide-based Nanostructures
2019, Globisch, Christoph, Isele, Marc, Peter, Christine, Jain, Alok
Molecular dynamics (MD) simulations can show structural and dynamic details on an atomistic level in a native-like environment. Conventional atomistic MD simulations have been successfully applied to many problems, however, they often do not cover the necessary timescales to sufficiently explore conformational phase and reach convergence. In this study, we discuss two examples where we have employed atomistic simulations followed by either Hamiltonian replica exchange molecular dynamics (H-REMD) or coarse-grained (CG) simulations to identify the intrinsic details of nanostructure formation processes and the influence of various factors on them. We demonstrate that combining computational approaches or resolution levels is very useful to overcome the limitations of a single method, like pure atomistic simulations, while still keeping its advantages. However, it is very important to carefully select suitable methods, parameters and approaches to get meaningful results with sufficient accuracy.
EncoderMap(II) : Visualizing important molecular motions with improved generation of protein conformations
2019-11-25, Lemke, Tobias, Berg, Andrej, Jain, Alok, Peter, Christine
Dimensionality reduction can be used to project high-dimensional molecular data into a simplified, low-dimensional map. One feature of our recently introduced dimensionality reduction technique EncoderMap, which relies on the combination of an autoencoder with multidimensional scaling, is its ability to do the reverse. It is able to generate conformations for any selected points in the low-dimensional map. This transfers the simplified, low-dimensional map back into the high-dimensional conformational space. Although the output is again high-dimensional, certain aspects of the simplification are preserved. The generated conformations only mirror the most dominant conformational differences that determine the positions of conformational states in the low-dimensional map. This allows to depict such differences and - in consequence - visualize molecular motions and gives a unique perspective on high-dimensional conformational data. In our previous work protein conformations described in backbone dihedral angle space were used as input for EncoderMap, and conformations were also generated in this space. For large proteins, however, the generation of conformations is inaccurate with this approach due to the local character of backbone dihedral angles. Here, we present an improved variant of EncoderMap which is able to generate large protein conformations that are accurate in short-range and long-range order. This is achieved by differentiable reconstruction of Cartesian coordinates from the generated dihedrals, which allows to add a contribution to the cost function that monitors the accuracy of all pairwise distances between the C α -atoms of the generated conformations. The improved capabilities to generate conformations of large, even multidomain, proteins are demonstrated for two examples: diubiquitin and a part of the Ssa1 Hsp70 yeast chaperone. We show that the improved variant of EncoderMap can nicely visualize motions of protein domains relative to each other but is also able to highlight important conformational changes within the individual domains.
Simulating and analysing configurational landscapes of protein-protein contact formation
2019-06-06, Berg, Andrej, Peter, Christine
Interacting proteins can form aggregates and protein-protein interfaces with multiple patterns and different stabilities. Using molecular simulation one would like to understand the formation of these aggregates and which of the observed states are relevant for protein function and recognition. To characterize the complex configurational ensemble of protein aggregates, one needs a quantitative measure for the similarity of structures. We present well-suited descriptors that capture the essential features of non-covalent protein contact formation and domain motion. This set of collective variables is used with a nonlinear multi-dimensional scaling-based dimensionality reduction technique to obtain a low-dimensional representation of the configurational landscape of two ubiquitin proteins from coarse-grained simulations. We show that this two-dimensional representation is a powerful basis to identify meaningful states in the ensemble of aggregated structures and to calculate distributions and free energy landscapes for different sets of simulations. By using a measure to quantitatively compare free energy landscapes we can show how the introduction of a covalent bond between two ubiquitin proteins at different positions alters the configurational states of these dimers.
Coarse-Grained Simulation of CaCO3 Aggregation and Crystallization Made Possible by Non-Bonded Three-Body Interactions
2019-02-07, King, Michael, Pasler, Simon, Peter, Christine
Calcium-containing minerals are key model systems to investigate fundamental principles of nucleation and mineral formation both experimentally and by simulation. Due to the rare event character of nucleation, the different dimensions of pre- and postnucleation stages and the possible relevance of non-classical nucleation pathways, such investigations require advanced sampling techniques and simulation models on a range of resolution levels. To this end we have developed coarse-grained (CG) models for calcium carbonate. We present a strategy to devise CG parameters - including non-bonded angular-dependent terms - such that the model correctly represents the calcite phase along with properties of the constituents in solution. We show how the CG interactions affect the crystallization pathways by stabilizing different intermediates - spanning a wide range of degrees of crystallinity and water content. This will allow us to investigate contributions to crystallization transitions and link them to experimentally observed non-classical crystallization intermediates.
Back-mapping based sampling : Coarse grained free energy landscapes as a guideline for atomistic exploration
2019-10-21, Hunkler, Simon, Lemke, Tobias, Peter, Christine, Kukharenko, Oleksandra
One ongoing topic of research in MD simulations is how to enable sampling to chemically and biologically relevant time scales. We address this question by introducing a back-mapping based sampling (BMBS) that combines multiple aspects of different sampling techniques. BMBS uses coarse grained (CG) free energy surfaces (FESs) and dimensionality reduction to initiate new atomistic simulations. These new simulations are started from atomistic conformations that were back-mapped from CG points all over the FES in order to sample the entire accessible phase space as fast as possible. In the context of BMBS, we address relevant back-mapping related questions like where to start the back-mapping from and how to judge the atomistic ensemble that results from the BMBS. The latter is done with the use of the earth mover’s distance, which allows us to quantitatively compare distributions of CG and atomistic ensembles. By using this metric, we can also show that the BMBS is able to correct inaccuracies of the CG model. In this paper, BMBS is applied to a just recently introduced neural network (NN) based approach for a radical coarse graining to predict free energy surfaces for oligopeptides. The BMBS scheme back-maps these FESs to the atomistic scale, justifying and complementing the proposed NN based CG approach. The efficiency benefit of the algorithm scales with the length of the oligomer. Already for the heptamers, the algorithm is about one order of magnitude faster in sampling compared to a standard MD simulation.
Coarse grained simulations of peptide nanoparticle formation : the role of local structure and nonbonded interactions
2019-02-12, Jain, Alok, Globisch, Christoph, Verma, Sandeep, Peter, Christine
Biocompatible nanostructures play an important role in drug delivery and tissue engineering applications. A controlled growth of peptide based nanoparticles with specific morphology needs an understanding of the role of the sequence and solvation properties. In a previous combined experimental-computational study we identified factors that govern the formation of well-defined aggregates by self-assembled pentapeptides, using single amino acid substitution (Mishra, N. K.; Jain, A.; Peter, C.; Verma, S. J. Phys. Chem. B 2017, 121, 8155-8161). The atomistic simulation study suggested a subtle interplay between various peptide properties like igidity/flexibility, hydrogen-bonding, partitioning of aromatic residues and dimerization of peptides that determine the different morphologies, while the overall aggregation propensity was mostly determined by the composition of the methanol/water solvent mixture. The size of the simulated aggregates and the timescales were rather restricted due to the atomistic character of the study. Here, we present an extension to a coarse grained representation which allows for much larger system sizes and longer time scales. To this end, we have optimized a MARTINI model so that it can deal with a system that relies on local structure formation. We combine information on local behavior from atomistic studies and apply supportive dihedral angles together with local adjustment of the bead types to find the right interplay of solvent and peptides. Finally, to mimic the dimers, an introduction of additional bonds between the monomers was necessary. By adding the modifications stepwise we were able to disentangle the influences of the various contributions, like rigidity/flexibility of the peptides, the dimer formation, or the non-bonded properties of the beads, on the overall aggregation propensity and morphology of the nanoparticles. The obtained models resemble the experimental and atomistic behavior and are able to provide mechanistic insight into peptide nanoparticle formation.
Relative Resolution : A Multipole Approximation at Appropriate Distances
2019, Chaimovich, Aviel, Kremer, Kurt, Peter, Christine
Recently, we introduced Relative Resolution as a hybrid formalism for fluid mixtures . The essence of this approach is that it switches molecular resolution in terms or relative separation: While nearest neighbors are characterized by a detailed fine-grained model, other neighbors are characterized by a simplified coarse-grained model. Once the two models are analytically connected with each other via energy conservation, Relative Resolution can capture the structural and thermal behavior of (nonpolar) multi-component and multi-phase systems across state space. The current work is a natural continuation of our original communication . Most importantly, we present the comprehensive mathematics of Relative Resolution, basically casting it as a multipole approximation at appropriate distances; the current set of equations importantly applies for all systems (e.g, polar molecules). Besides, we continue examining the capability of our multiscale approach in molecular simulations, importantly showing that we can successfully retrieve not just the statics but also the dynamics of liquid systems. We finally conclude by discussing how Relative Resolution is the inherent variant of the famous "cell-multipole" approach for molecular simulations.