Studying the Early Stages of Protein Aggregation Using Replica Exchange Molecular Dynamics Simulations

Effect of Pressure on the Conformational Landscape of Human γD-Crystallin from Replica Exchange Molecular Dynamics Simulations

Human γD-crystallin belongs to a crucial family of proteins known as crystallins located in the fiber cells of the human lens. Since crystallins do not undergo any turnover after birth, they need to possess remarkable thermodynamic stability. However, their sporadic misfolding and aggregation, triggered by environmental perturbations or genetic mutations, constitute the molecular basis of cataracts, which is the primary cause of blindness in the globe according to the World Health Organization. Here, we investigate the impact of high pressure on the conformational landscape of wild-type HγD-crystallin using replica exchange molecular dynamics simulations augmented with principal component analysis. We find pressure to have a modest impact on global measures of protein stability, such as root-mean-square displacement and radius of gyration. Upon projecting our trajectories along the first two principal components from principal component analysis, however, we observe the emergence of distinct free energy basins at high pressures. By screening local order parameters previously shown or hypothesized as markers of HγD-crystallin stability, we establish correlations between a tyrosine-tyrosine aromatic contact within the N-terminal domain and the protein's end-to-end distance with projections along the first and second principal components, respectively. Furthermore, we observe the simultaneous contraction of the hydrophobic core and its intrusion by water molecules. This exploration sheds light on the intricate responses of HγD-crystallin to elevated pressures, offering insights into potential mechanisms underlying its stability and susceptibility to environmental perturbations, crucial for understanding cataract formation.

Genetic Algorithm for Automated Parameterization of Network Hamiltonian Models of Amyloid Fibril Formation

The time scales of long-time atomistic molecular dynamics simulations are typically reported in microseconds, while the time scales for experiments studying the kinetics of amyloid fibril formation are typically reported in minutes or hours. This time scale deficit of roughly 9 orders of magnitude presents a major challenge in the design of computer simulation methods for studying protein aggregation events. Coarse-grained molecular simulations offer a computationally tractable path forward for exploring the molecular mechanism driving the formation of these structures, which are implicated in diseases such as Alzheimer's, Parkinson's, and type-II diabetes. Network Hamiltonian models of aggregation are centered around a Hamiltonian function that returns the total energy of a system of aggregating proteins, given the graph structure of the system as an input. In the graph, or network, representation of the system, each protein molecule is represented as a node, and noncovalent bonds between proteins are represented as edges. The parameter, i.e., a set of coefficients that determine the degree to which each topological degree of freedom is favored or disfavored, must be determined for each network Hamiltonian model, and is a well-known technical challenge. The methodology is first demonstrated by beginning with an initial set of randomly parametrized models of low fibril fraction (<5% fibrillar), and evolving to subsequent generations of models, ultimately leading to high fibril fraction models (>70% fibrillar). The methodology is also demonstrated by applying it to optimizing previously published network Hamiltonian models for the 5 key amyloid fibril topologies that have been reported in the Protein Data Bank (PDB). The models generated by the AI produced fibril fractions that surpass previously published fibril fractions in 3 of 5 cases, including the most naturally abundant amyloid fibril topology, the 1,2 2-ribbon, which features a steric zipper. The authors also aim to encourage more widespread use of the network Hamiltonian methodology for fitting a wide variety of self-assembling systems by releasing a free open-source implementation of the genetic algorithm introduced here.

MDSCAN: RMSD-based HDBSCAN clustering of long molecular dynamics

MOTIVATION

The term clustering designates a comprehensive family of unsupervised learning methods allowing to group similar elements into sets called clusters. Geometrical clustering of molecular dynamics (MD) trajectories is a well-established analysis to gain insights into the conformational behavior of simulated systems. However, popular variants collapse when processing relatively long trajectories because of their quadratic memory or time complexity. From the arsenal of clustering algorithms, HDBSCAN stands out as a hierarchical density-based alternative that provides robust differentiation of intimately related elements from noise data. Although a very efficient implementation of this algorithm is available for programming-skilled users (HDBSCAN*), it cannot treat long trajectories under the de facto molecular similarity metric RMSD.

RESULTS

Here, we propose MDSCAN, an HDBSCAN-inspired software specifically conceived for non-programmers users to perform memory-efficient RMSD-based clustering of long MD trajectories. Methodological improvements over the original version include the encoding of trajectories as a particular class of vantage-point tree (decreasing time complexity), and a dual-heap approach to construct a quasi-minimum spanning tree (reducing memory complexity). MDSCAN was able to process a trajectory of 1 million frames using the RMSD metric in about 21 h with <8 GB of RAM, a task that would have taken a similar time but more than 32 TB of RAM with the accelerated HDBSCAN* implementation generally used.

AVAILABILITY AND IMPLEMENTATION

The source code and documentation of MDSCAN are free and publicly available on GitHub (https://github.com/LQCT/MDScan.git) and as a PyPI package (https://pypi.org/project/mdscan/).

SUPPLEMENTARY INFORMATION

Supplementary data are available at Bioinformatics online.

On Quality Thresholds for the Clustering of Molecular Structures

It has been recently suggested that diametral (so-called quality) similarity thresholds are superior to radial ones for the clustering of molecular three-dimensional structures (González-Alemán et al., 2020). The argument has been made for two clustering algorithms available in various software packages for the analysis of molecular structures from ensembles generated by computer simulations, attributed to Daura et al. (1999) (radial threshold) and Heyer et al. (1999) (diametral threshold). Here, we compare these two algorithms using the root-mean-squared difference (rmsd) between the Cartesian coordinates of selected atoms as pairwise similarity metric. We discuss formally the relation between these two methods and illustrate their behavior with two examples, a set of points in two dimensions and the coordinates of the tau polypeptide along a trajectory extracted from a replica-exchange molecular-dynamics simulation (Shea and Levine, 2016). We show that the two methods produce equally sized clusters as long as adequate choices are made for the respective thresholds. The real issue is not whether the threshold is radial or diametral but how to choose in either case a threshold value that is physically meaningful. We will argue that, when clustering molecular structures with the rmsd as a metric, the simplest best guess for a threshold is actually radial in nature.

RCDPeaks: memory-efficient density peaks clustering of long molecular dynamics

MOTIVATION

Density Peaks is a widely spread clustering algorithm that has been previously applied to Molecular Dynamics (MD) simulations. Its conception of cluster centers as elements displaying both a high density of neighbors and a large distance to other elements of high density, particularly fits the nature of a geometrical converged MD simulation. Despite its theoretical convenience, implementations of Density Peaks carry a quadratic memory complexity that only permits the analysis of relatively short trajectories.

RESULTS

Here, we describe DP+, an exact novel implementation of Density Peaks that drastically reduces the RAM consumption in comparison to the scarcely available alternatives designed for MD. Based on DP+, we developed RCDPeaks, a refined variant of the original Density Peaks algorithm. Through the use of DP+, RCDPeaks was able to cluster a one-million frames trajectory using less than 4.5 GB of RAM, a task that would have taken more than 2 TB and about 3× more time with the fastest and less memory-hunger alternative currently available. Other key features of RCDPeaks include the automatic selection of parameters, the screening of center candidates and the geometrical refining of returned clusters.

AVAILABILITY AND IMPLEMENTATION

The source code and documentation of RCDPeaks are free and publicly available on GitHub (https://github.com/LQCT/RCDPeaks.git).

SUPPLEMENTARY INFORMATION

Supplementary data are available at Bioinformatics online.

BitQT: a graph-based approach to the quality threshold clustering of molecular dynamics

MOTIVATION

Classical Molecular Dynamics (MD) is a standard computational approach to model time-dependent processes at the atomic level. The inherent sparsity of increasingly huge generated trajectories demands clustering algorithms to reduce other post-simulation analysis complexity. The Quality Threshold (QT) variant is an appealing one from the vast number of available clustering methods. It guarantees that all members of a particular cluster will maintain a collective similarity established by a user-defined threshold. Unfortunately, its high computational cost for processing big data limits its application in the molecular simulation field.

RESULTS

In this work, we propose a methodological parallel between QT clustering and another well-known algorithm in the field of Graph Theory, the Maximum Clique Problem. Molecular trajectories are represented as graphs whose nodes designate conformations, while unweighted edges indicate mutual similarity between nodes. The use of a binary-encoded RMSD matrix coupled to the exploitation of bitwise operations to extract clusters significantly contributes to reaching a very affordable algorithm compared to the few implementations of QT for MD available in the literature. Our alternative provides results in good agreement with the exact one while strictly preserving the collective similarity of clusters.

AVAILABILITY AND IMPLEMENTATION

The source code and documentation of BitQT are free and publicly available on GitHub (https://github.com/LQCT/BitQT.git) and ReadTheDocs (https://bitqt.readthedocs.io/en/latest/), respectively.

SUPPLEMENTARY INFORMATION

Supplementary data are available at Bioinformatics online.

Interactions between Curcumin Derivatives and Amyloid-β Fibrils: Insights from Molecular Dynamics Simulations

The aggregation of amyloid-β (Aβ) peptides into senile plaques is a hallmark of Alzheimer's disease (AD) and is hypothesized to be the primary cause of AD related neurodegeneration. Previous studies have shown the ability of curcumin to both inhibit the aggregation of Aβ peptides into oligomers or fibrils and reduce amyloids in vivo. Despite the promise of curcumin and its derivatives to serve as diagnostic, preventative, and potentially therapeutic AD molecules, the mechanism by which curcumin and its derivatives bind to and inhibit Aβ fibrils' formation remains elusive. Here, we investigated curcumin and a set of curcumin derivatives in complex with a hexamer peptide model of the Aβ1-42 fibril using nearly exhaustive docking, followed by multi-ns molecular dynamics simulations, to provide atomistic-detail insights into the molecules' binding and inhibitory properties. In the vast majority of the simulations, curcumin and its derivatives remain firmly bound in complex with the fibril through primarily three different principle binding modes, in which the molecules interact with residue domain 17LVFFA21, in line with previous experiments. In a small subset of these simulations, the molecules partly dissociate the outermost peptide of the Aβ1-42 fibril by disrupting β-sheets within the residue domain 12VHHQKLVFF20. A comparison between binding modes leading or not leading to partial dissociation of the outermost peptide suggests that the latter is attributed to a few subtle key structural and energetic interaction-based differences. Interestingly, partial dissociation appears to be either an outcome of high affinity interactions or a cause leading to high affinity interactions between the molecules and the fibril, which could partly serve as a compensation for the energy loss in the fibril due to partial dissociation. In conjunction with this, we suggest a potential inhibition mechanism of Αβ1-42 aggregation by the molecules, where the partially dissociated 16KLVFF20 domain of the outermost peptide could either remain unstructured or wrap around to form intramolecular interactions with the same peptide's 29GAIIG33 domain, while the molecules could additionally act as a patch against the external edge of the second outermost peptide's 16KLVFF20 domain. Thereby, individually or concurrently, these could prohibit fibril elongation.

BitClust: Fast Geometrical Clustering of Long Molecular Dynamics Simulations

The growing computational capacity allows the investigation of large biomolecular systems by increasingly extensive molecular dynamics simulations. The resulting huge trajectories demand efficient partition methods to discern relevant structural dissimilarity. Clustering algorithms are available to address this task, but their implementations still need to be improved to gain in computational speed and to reduce the consumption of random access memory. We propose the BitClust code which, based on a combination of Python and C programming languages, performs fast structural clustering of long molecular trajectories. BitClust takes advantage of bitwise operations applied to a bit-encoded pairwise similarity matrix. Our approach allowed us to process a half-million frame trajectory in 6 h using less than 35 GB, a task that is not affordable with any of the similar alternatives.

Quality Threshold Clustering of Molecular Dynamics: A Word of Caution

Clustering Molecular Dynamics trajectories is a common analysis that allows grouping together similar conformations. Several algorithms have been designed and optimized to perform this routine task, and among them, Quality Threshold stands as a very attractive option. This algorithm guarantees that in retrieved clusters no pair of frames will have a similarity value greater than a specified threshold, and hence, a set of strongly correlated frames are obtained for each cluster. In this work, it is shown that various commonly used software implementations are flawed by confusing Quality Threshold with another simplistic well-known clustering algorithm published by Daura et al. (Daura, X.; van Gunsteren, W. F.; Jaun, B.; Mark, A. E.; Gademann, K.; Seebach, D. Peptide Folding: When Simulation Meets Experiment. Angew. Chemie Int. Ed. 1999, 38 (1/2), 236-240). Daura's algorithm does not impose any quality threshold for the frames contained in retrieved clusters, bringing unrelated structural configurations altogether. The advantages of using Quality Threshold whenever possible to explore Molecular Dynamic trajectories is exemplified. An in-house implementation of the original Quality Threshold algorithm has been developed in order to illustrate our comments, and its code is freely available for further use by the scientific community.

Protein Aggregation and Molecular Crowding: Perspectives From Multiscale Simulations

Cells are extremely crowded environments, thus the use of diluted salted aqueous solutions containing a single protein is too simplistic to mimic the real situation. Macromolecular crowding might affect protein structure, folding, shape, conformational stability, binding of small molecules, enzymatic activity, interactions with cognate biomolecules, and pathological aggregation. The latter phenomenon typically leads to the formation of amyloid fibrils that are linked to several lethal neurodegenerative diseases, but that can also play a functional role in certain organisms. The majority of molecular simulations performed before the last few years were conducted in diluted solutions and were restricted both in the timescales and in the system dimensions by the available computational resources. In recent years, several computational solutions were developed to get close to physiological conditions. In this review we summarize the main computational techniques used to tackle the issue of protein aggregation both in a diluted and in a crowded environment.