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

Evaluation and Optimization of Interface Force Fields for Water on Gold Surfaces

The structure and dynamics of water at gold surfaces are important for a variety of applications, including lab on a chip and electrowetting. Classical molecular dynamics (MD) simulations are frequently used to investigate systems with water–gold interfaces, such as biomacromolecules in gold nanoparticle dispersions, but the accuracy of the simulations depends on the suitability of the force field. Density functional theory (DFT) calculations of a water molecule on gold were used as a benchmark to assess force field accuracy. It was found that Lennard-Jones potentials did not reproduce the DFT water–gold configurational energy landscape, whereas the softer Morse and Buckingham potentials allowed for a more accurate representation. MD simulations with different force fields exhibited rather different structural and dynamic properties of water on a gold surface. This emphasizes the need for experimental data and further effort on the validation of a realistic force field for water–gold interactions

Molecular Dynamics Simulations of Peptides at the Air–Water Interface: Influencing Factors on Peptide-Templated Mineralization

Biomineralization is the intricate, biomedically highly relevant process by which living organisms deposit minerals on biological matrices to stiffen tissues and build skeletal structures and shells. Rapaport and coworkers (J. Am. Chem. Soc. 2000, 122, 12523; Adv. Funct. Mater. 2008, 18, 2889; Acta Biomater. 2012, 8, 2466) have designed a class of self-assembling amphiphilic peptides that are capable of forming hydrogels and attracting ions from the environment, generating structures akin to the extracellular matrix and promoting bone regeneration. The air–water interface serves both in experiment and in simulations as a model hydrophobic surface to mimic the cell’s organic–aqueous interface and to investigate the organization of the peptide matrix into ordered β-pleated monolayers and the subsequent onset of biomineral formation. To obtain insight into the underlying molecular mechanism, we have used molecular dynamics simulations to study the effect of peptide sequence on aggregate stability and ion–peptide interactions. We findin excellent agreement with experimental observationsthat the nature of the peptide termini (proline vs phenylalanine) affect the aggregate order, while the nature of the acidic side chains (aspartic vs glutamic acid) affect the aggregate’s stability in the presence of ions. These simulations provide valuable microscopic insight into the way ions and peptide templates mutually affect each other during the early stages of biomineralization preceding nucleation

Time evolution of the secondary structure of a dimer of LK (left) and EALA (right) at the vacuum/water interface.

<p>Typical snapshots when the peptides are associated at the interface (A and B), DSSP structural analysis (C and D), angle between the helix axis for the peptides and center-to-center distance (E and F), the h-SASA for each peptide along with the buried SASA for the whole peptide, the inter and intra molecular short-range Coulomb energies and the number of inter- and intra-molecular hydrogen bonds (G and H) are shown in figure.</p

Folding and association of a pair of LK (left) and EALA (right) peptides in bulk water.

<p>Snapshots illustrating the aggregation process (A and B), DSSP secondary structure analysis (C and D), SASA, short range Coulombic interaction energies between the charged groups and the number of intra and inter-peptide backbone hydrogen bonds (E and F) are displayed as a function of simulation time. Association of peptides take place at 180 ns for LK and 300 ns for EALA, which can be observed via the sharp drop in SASA.</p

RMSD (-carbons of core regions) distributions from simulations of isolated dimers.

<p>Open histograms: RMSDs within the monomers; shaded histograms: RMSDs of dimers. (A) atomistic simulation (400 ns); (B) CG simulation with ELNEDYN network (spring constant: 500 kJ mol⁻¹nm⁻²); (C) CG simulation with ELNEDYN network (spring constant: 200 kJ mol⁻¹nm⁻²); (D) CG simulation with IDEN elastic network.</p

Relative orientation maps from simulations of isolated dimers.

<p>(A) atomistic simulation (400 ns); (B) CG simulation with ELNEDYN network (spring constant: 500 kJ mol⁻¹nm⁻²); (C) CG simulation with ELNEDYN network (spring constant: 200 kJ mol⁻¹nm⁻²); (D) CG simulation with IDEN elastic network. Projections of the <b><i>X</i></b><i> (left panels), </i><b><i>Y</i></b><i> (middle panels), </i><b><i>Z</i></b><i> (right panels)</i>-axis of capsomer 2 on the <i>xy</i> plane when capsomer 1 is aligned to the <i>z</i> axis (see <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0060582#s4" target="_blank">Methods</a> section). Coloring according to the normalized probability of finding these relative orientations. The blue circles are drawn with a radius of the longest internal axis of the capsomer.</p

RMSD (-carbons of core regions) distributions from simulations of dimers within a larger capsid fragment.

<p>Pentamer of AB dimers with a ring of CC-dimers (POD+CC). Left side: Inner dimers of AB type (indicated in red and blue); Right side: outer dimers of CC type (indicated in green). Open histograms: RMSDs within the monomers; shaded histograms: RMSDs of dimers. (A, B) atomistic simulation; (C, D) CG simulation with ELNEDYN network (spring constant: 500 kJ mol⁻¹nm⁻²); (E, F) CG simulation with ELNEDYN network (spring constant: 200 kJ mol⁻¹nm⁻²); (G, H) CG simulation with IDEN elastic network.</p

PMF results comparing the separation of a LK dimer in bulk water for the cases where lysine residues are positively charged, lysine residues are neutral and the leucine residues are in silico mutated to alanine residues.

<p>The curves are shifted so that the maximum points are zero. The distance refers to the distance between the center of mass of backbone atoms of the peptides. For the mutated AK dimer, when the peptides are in contact they maintain their helical structures. However when they are separated or when they make a loose contact the <i>α</i>-helical structure is not conserved.</p

Different representations of the CCMV capsid and its subunits.

<p>(A) Render of the whole CCMV viral capsid, highlighting pentamer of dimers (POD) (red and blue) plus the flanking CC dimers (green). The type A chains in the POD are colored in red, while the type B chains are colored in blue. (B) Cartoon representation of the core regions for a dimer (residue 14 to 142 for each chain - without the flexible tails). This figure draws emphasis to the “hinge” (arrow points to the region) between the two capsomers, that enables them to rotate relative to each other. (C) Pentamer of dimers (red and blue) plus flanking CC dimers (green) highlighting the asymmetric unit (bottom in cartoon representation). (D) The defined internal axes (which are loosely based on the gyration tensor of the capsomer) for generating the relative orientation maps (see text). The center of mass (COM) of C atoms of residues 69–71, 92 and 122–124 defines the <b><i>X</i></b>-axis (red), the COM of the C atoms of residues 20–21 and 134–135 defines the <b><i>Y</i></b>-axis (yellow) and the COM of the C atoms of residues 56–58 and 99–100 defines the <b><i>Z</i></b>-axis (blue).</p