Lemke, Tobias
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Three Reasons Why Aspartic Acid and Glutamic Acid Sequences Have a Surprisingly Different Influence on Mineralization
Understanding the role of polymers rich in aspartic acid (Asp) and glutamic acid (Glu) is the key to gaining precise control over mineralization processes. Despite their chemical similarity, experiments revealed a surprisingly different influence of Asp and Glu sequences. We conducted molecular dynamics simulations of Asp and Glu peptides in the presence of calcium and chloride ions to elucidate the underlying phenomena. In line with experimental differences, in our simulations, we indeed find strong differences in the way the peptides interact with ions in solution. The investigated Asp pentapeptide tends to pull a lot of ions into its vicinity, and many structures with clusters of calcium and chloride ions on the surface of the peptide can be observed. Under the same conditions, comparatively fewer ions can be found in proximity of the investigated Glu pentapeptide, and the structures are characterized by single calcium ions bound to multiple carboxylate groups. Based on our simulation data, we identified three reasons contributing to these differences, leading to a new level of understanding additive-ion interactions.
Back-mapping based sampling : Coarse grained free energy landscapes as a guideline for atomistic exploration
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.
Neural Network Based Prediction of Conformational Free Energies : a New Route toward Coarse-Grained Simulation Models
Coarse-grained (CG) simulation models have become very popular tools to study complex molecular systems with great computational efficiency on length and time scales that are inaccessible to simulations at atomistic resolution. In so-called bottom-up coarse-graining strategies, the interactions in the CG model are devised such that an accurate representation of an atomistic sampling of configurational phase space is achieved. This means the coarse-graining methods use the underlying multibody potential of mean force (i.e., free-energy surface) derived from the atomistic simulation as parametrization target. Here, we present a new method where a neural network (NN) is used to extract high-dimensional free energy surfaces (FES) from molecular dynamics (MD) simulation trajectories. These FES are used for simulations on a CG level of resolution. The method is applied to simulating homo-oligo-peptides (oligo-glutamic-acid (oligo-glu) and oligo-aspartic-acid (oligo-asp)) of different lengths. We show that the NN not only is able to correctly describe the free-energy surface for oligomer lengths that it was trained on but also is able to predict the conformational sampling of longer chains.
Simultaneous Monitoring of Macroscopic and Microscopic Diffusion of Guest Molecules in Silica and Organosilica Aerogels by Spatially and Time-Resolved Electron Paramagnetic Resonance Spectroscopy
We used spatially and time-resolved electron paramagnetic resonance (EPR) spectroscopy to study diffusion of guest molecules within solvent filled aerogel monoliths. We experimentally obtained the time-dependent spin density of EPR active guest molecules ρ1d(y,t), numerically solved the diffusion equation to simulate ρ1d(y,t), and determined the macroscopic translational diffusion coefficients for different aerogels and guest molecules. Simultaneously, we determined the microscopic diffusion coefficient by spectral simulation. We show that diffusion in the aerogels under study is dominated by the tortuosity of the pore system but not by surface effects.
EncoderMap : Dimensionality Reduction and Generation of Molecule Conformations
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.
Soluble Oligomeric Nucleants : Simulations of Chain Length, Binding Strength, and Volume Fraction Effects
Recent theories and simulations suggest that molecular additives can bind to the surfaces of nuclei, lower the surface energy, and accelerate nucleation. Experiments have shown that oligomeric and polymeric additives can also modify nucleation rates of proteins, ice, and minerals; however, general design principles for oligomeric or polymeric promoters do not yet exist. Here we investigate oligomeric additives for which each segment of the oligomer can bind to surfaces of nuclei. We use semigrand canonical Monte Carlo simulations in a Potts lattice gas model to study the effects of oligomer chain length, volume fraction, and binding strength. We find that increasing each of those parameters lowers the nucleation barrier. At extremely low oligomer concentrations, the nucleation kinetics can be modeled as though each oligomer is a heterogeneous nucleation site in solution.
EncoderMap(II) : Visualizing important molecular motions with improved generation of protein conformations
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.
Efficient Sampling and Characterization of Free Energy Landscapes of Ion-Peptide Systems
Proteins that influence nucleation, growth, or polymorph selection during biomineralization processes are often rich in glutamic- or aspartic acid. Here, the interactions between carboxylate side chains and ions lead to an interplay of peptide conformations and ion structuring in solution. Molecular dynamics simulations are an ideal tool to mechanistically investigate these processes. Unfortunately, the formation of strong ion-peptide contacts and ion bridges drastically impedes structural reorganization of ionic bonds and conformational transitions of the polymers. Thus, to obtain a complete thermodynamical picture of such systems, enhanced sampling techniques become necessary as well as the methods to characterize the conformational states of these partially disordered polymer-ion systems. Here, we propose a new set of Hamiltonian replica exchange (HRE) parameters for efficient simulations of peptide-ion systems, with an aspartic acid trimer in the presence of Ca2+ and Cl- ions as a test system. We introduce dimensionality reduction and clustering strategies to characterize the states of such a multicomponent system and to analyze the outcome of the proposed HRE with different reweighting methods.
In situ monitoring of diffusion of guest molecules in porous media using electron paramagnetic resonance imaging
A method is demonstrated to monitor macroscopic translational diffusion using electron paramagnetic resonance (EPR) imaging. A host-guest system with nitroxide spin probe 3-(2-Iodoacetamido)-2,2,5,5-tetramethyl-1-pyrrolidinyloxy (IPSL) as a guest inside the periodic mesoporous organosilica (PMO) aerogel UKON1-GEL as a host and ethanol as a solvent is used as an example to describe the protocol. Data is shown from a previous publication, where the protocol has been applied to both IPSL and Tris(8-carboxy-2,2,6,6-perdeutero-tetramethyl-benzo[1,2-d:4,5-d′]bis(1,3)dithiole) methyl (Trityl) as guest molecules and UKON1-GEL and SILICA-GEL as host systems. A method is shown to prepare aerogel samples that cannot be synthesized directly in the sample tube for measurement due to a size change during synthesis. The aerogel is attached to sample tubes using heat shrink tubing and a pressure cooker to reach the necessary temperature without evaporating the solvent in the process. The method does not assume a clearly defined initial distribution of guest molecules at the start of the measurement. Instead, it requires a reservoir on top of the aerogel and experimentally determines the influx rate during data analysis. The diffusion is monitored continually over a period of 20 hr by recording the 1d spin density profile within the sample. The spectrometer settings for the imaging experiment are described quantitatively. Data analysis software is provided to take the resonator sensitivity profile into account and to numerically solve the diffusion equation. The software determines the macroscopic translational diffusion coefficient by least square minimization of the difference between the experiment and the numerical solution of the diffusion equation.