Back-mapping based sampling: Coarse grained free energy landscapes as a guideline for atomistic exploration

Programming co-assembled peptide nanofiber morphology via anionic amino acid type: Insights from molecular dynamics simulations

Co-assembling peptides can be crafted into supramolecular biomaterials for use in biotechnological applications, such as cell culture scaffolds, drug delivery, biosensors, and tissue engineering. Peptide co-assembly refers to the spontaneous organization of two different peptides into a supramolecular architecture. Here we use molecular dynamics simulations to quantify the effect of anionic amino acid type on co-assembly dynamics and nanofiber structure in binary CATCH(+/-) peptide systems. CATCH peptide sequences follow a general pattern: CQCFCFCFCQC, where all C's are either a positively charged or a negatively charged amino acid. Specifically, we investigate the effect of substituting aspartic acid residues for the glutamic acid residues in the established CATCH(6E-) molecule, while keeping CATCH(6K+) unchanged. Our results show that structures consisting of CATCH(6K+) and CATCH(6D-) form flatter β-sheets, have stronger interactions between charged residues on opposing β-sheet faces, and have slower co-assembly kinetics than structures consisting of CATCH(6K+) and CATCH(6E-). Knowledge of the effect of sidechain type on assembly dynamics and fibrillar structure can help guide the development of advanced biomaterials and grant insight into sequence-to-structure relationships.

Visualizing the Residue Interaction Landscape of Proteins by Temporal Network Embedding

Characterizing the structural dynamics of proteins with heterogeneous conformational landscapes is crucial to understanding complex biomolecular processes. To this end, dimensionality reduction algorithms are used to produce low-dimensional embeddings of the high-dimensional conformational phase space. However, identifying a compact and informative set of input features for the embedding remains an ongoing challenge. Here, we propose to harness the power of Residue Interaction Networks (RINs) and their centrality measures, established tools to provide a graph theoretical view on molecular structure. Specifically, we combine the closeness centrality, which captures global features of the protein conformation at residue-wise resolution, with EncoderMap, a hybrid neural-network autoencoder/multidimensional-scaling like dimensionality reduction algorithm. We find that the resulting low-dimensional embedding is a meaningful visualization of the residue interaction landscape that resolves structural details of the protein behavior while retaining global interpretability. This feature-based graph embedding of temporal protein graphs makes it possible to apply the general descriptive power of RIN formalisms to the analysis of protein simulations of complex processes such as protein folding and multidomain interactions requiring no protein-specific input. We demonstrate this on simulations of the fast folding protein Trp-Cage and the multidomain signaling protein FAT10. Due to its generality and modularity, the presented approach can easily be transferred to other protein systems.

Generating a conformational landscape of ubiquitin chains at atomistic resolution by back-mapping based sampling

Ubiquitin chains are flexible multidomain proteins that have important biological functions in cellular signalling. Computational studies with all-atom molecular dynamics simulations of the conformational spaces of polyubiquitins can be challenging due to the system size and a multitude of long-lived meta-stable states. Coarse graining is an efficient approach to overcome this problem-at the cost of losing high-resolution details. Recently, we proposed the back-mapping based sampling (BMBS) approach that reintroduces atomistic information into a given coarse grained (CG) sampling based on a two-dimensional (2D) projection of the conformational landscape, produces an atomistic ensemble and allows to systematically compare the ensembles at the two levels of resolution. Here, we apply BMBS to K48-linked tri-ubiquitin, showing its applicability to larger systems than those it was originally introduced on and demonstrating that the algorithm scales very well with system size. In an extension of the original BMBS we test three different seeding strategies, i.e. different approaches from where in the CG landscape atomistic trajectories are initiated. Furthermore, we apply a recently introduced conformational clustering algorithm to the back-mapped atomistic ensemble. Thus, we obtain insight into the structural composition of the 2D landscape and illustrate that the dimensionality reduction algorithm separates different conformational characteristics very well into different regions of the map. This cluster analysis allows us to show how atomistic trajectories sample conformational states, move through the projection space and in sum converge to an atomistic conformational landscape that slightly differs from the original CG map, indicating a correction of flaws in the CG template.

Uncertainty quantification of phase transition quantities from cluster weighting calculations

In this work, we investigate how uncertainties in experimental input data influence the results of quantum cluster equilibrium calculations. In particular, we focus on the calculation of vaporization enthalpies and entropies of seven organic liquids, compare two computational approaches for their calculation and investigate how these properties are affected by changes in the experimental input data. It is observed that the vaporization enthalpies and entropies show a smooth dependence on changes in the reference density and boiling point. The reference density is found to have only a small influence on the vaporization thermodynamics, whereas the boiling point has a large influence on the vaporization enthalpy but only a small influence on the vaporization entropy. Furthermore we employed the Gauss--Hermite estimator in order to quantify the uncertainty in the thermodynamic functions that stems from inaccuracies in the experimental reference data at the example of the vaporization enthalpy of (\textit{R})-butan-2-ol. We quantify the uncertainty as 30.95~$\cdot$10$^{-3}$~kJ~mol$^{-1}$. Additionally we compare the convergence behaviour and computational effort of the Gauss--Hermite estimator with the Monte Carlo approach and show the superiority of the former. By this, we present how uncertainty quantification can be applied to examples from theoretical chemistry.

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.

Solvent-scaling as an alternative to coarse-graining in adaptive-resolution simulations: The adaptive solvent-scaling (AdSoS) scheme

A new approach termed Adaptive Solvent-Scaling (AdSoS) is introduced for performing simulations of a solute embedded in a fine-grained (FG) solvent region itself surrounded by a coarse-grained (CG) solvent region, with a continuous FG ↔ CG switching of the solvent resolution across a buffer layer. Instead of relying on a distinct CG solvent model, the AdSoS scheme is based on CG models defined by a dimensional scaling of the FG solvent by a factor s, accompanied by an s-dependent modulation of the atomic masses and interaction parameters. The latter changes are designed to achieve an isomorphism between the dynamics of the FG and CG models, and to preserve the dispersive and dielectric solvation properties of the solvent with respect to a solute at FG resolution. This scaling approach offers a number of advantages compared to traditional coarse-graining: (i) the CG parameters are immediately related to those of the FG model (no need to parameterize a distinct CG model); (ii) nearly ideal mixing is expected for CG variants with similar s-values (ideal mixing holding in the limit of identical s-values); (iii) the solvent relaxation timescales should be preserved (no dynamical acceleration typical for coarse-graining); (iv) the graining level N_G (number of FG molecules represented by one CG molecule) can be chosen arbitrarily (in particular, N_G = s³ is not necessarily an integer); and (v) in an adaptive-resolution scheme, this level can be varied continuously as a function of the position (without requiring a bundling mechanism), and this variation occurs at a constant number of particles per molecule (no occurrence of fractional degrees of freedom in the buffer layer). By construction, the AdSoS scheme minimizes the thermodynamic mismatch between the different regions of the adaptive-resolution system, leading to a nearly homogeneous scaled solvent density s³ρ. Residual density artifacts in and at the surface of the boundary layer can easily be corrected by means of a grid-based biasing potential constructed in a preliminary pure-solvent simulation. This article introduces the AdSoS scheme and provides an initial application to pure atomic liquids (no solute) with Lennard-Jones plus Coulomb interactions in a slab geometry.

Collective variable-based enhanced sampling and machine learning

ABSTRACT

Collective variable-based enhanced sampling methods have been widely used to study thermodynamic properties of complex systems. Efficiency and accuracy of these enhanced sampling methods are affected by two factors: constructing appropriate collective variables for enhanced sampling and generating accurate free energy surfaces. Recently, many machine learning techniques have been developed to improve the quality of collective variables and the accuracy of free energy surfaces. Although machine learning has achieved great successes in improving enhanced sampling methods, there are still many challenges and open questions. In this perspective, we shall review recent developments on integrating machine learning techniques and collective variable-based enhanced sampling approaches. We also discuss challenges and future research directions including generating kinetic information, exploring high-dimensional free energy surfaces, and efficiently sampling all-atom configurations.

A novel multiscale scheme to accelerate atomistic simulations of bio-macromolecules by adaptively driving coarse-grained coordinates

All-atom molecular dynamics (MD) simulations of bio-macromolecules can yield relatively accurate results while suffering from the limitation of insufficient conformational sampling. On the other hand, the coarse-grained (CG) MD simulations efficiently accelerate conformational changes in biomolecules but lose atomistic details and accuracy. Here, we propose a novel multiscale simulation method called the adaptively driving multiscale simulation (ADMS)-it efficiently accelerates biomolecular dynamics by adaptively driving virtual CG atoms on the fly while maintaining the atomistic details and focusing on important conformations of the original system with irrelevant conformations rarely sampled. Herein, the "adaptive driving" is based on the short-time-averaging response of the system (i.e., an approximate free energy surface of the original system), without requiring the construction of the CG force field. We apply the ADMS to two peptides (deca-alanine and Ace-GGPGGG-Nme) and one small protein (HP35) as illustrations. The simulations show that the ADMS not only efficiently captures important conformational states of biomolecules and drives fast interstate transitions but also yields, although it might be in part, reliable protein folding pathways. Remarkably, a ∼100-ns explicit-solvent ADMS trajectory of HP35 with three CG atoms realizes folding and unfolding repeatedly and captures the important states comparable to those from a 398-µs standard all-atom MD simulation.

Machine Learning Force Fields and Coarse-Grained Variables in Molecular Dynamics: Application to Materials and Biological Systems

Machine learning encompasses tools and algorithms that are now becoming popular in almost all scientific and technological fields. This is true for molecular dynamics as well, where machine learning offers promises of extracting valuable information from the enormous amounts of data generated by simulation of complex systems. We provide here a review of our current understanding of goals, benefits, and limitations of machine learning techniques for computational studies on atomistic systems, focusing on the construction of empirical force fields from ab initio databases and the determination of reaction coordinates for free energy computation and enhanced sampling.