Simultaneous Coherent Structure Coloring facilitates interpretable clustering of scientific data by amplifying dissimilarity

The clustering of data into physically meaningful subsets often requires assumptions regarding the number, size, or shape of the subgroups. Here, we present a new method, simultaneous coherent structure coloring (sCSC), which accomplishes the task of unsupervised clustering without a priori guidance regarding the underlying structure of the data. sCSC performs a sequence of binary splittings on the dataset such that the most dissimilar data points are required to be in separate clusters. To achieve this, we obtain a set of orthogonal coordinates along which dissimilarity in the dataset is maximized from a generalized eigenvalue problem based on the pairwise dissimilarity between the data points to be clustered. This sequence of bifurcations produces a binary tree representation of the system, from which the number of clusters in the data and their interrelationships naturally emerge. To illustrate the effectiveness of the method in the absence of a priori assumptions, we apply it to three exemplary problems in fluid dynamics. Then, we illustrate its capacity for interpretability using a high-dimensional protein folding simulation dataset. While we restrict our examples to dynamical physical systems in this work, we anticipate straightforward translation to other fields where existing analysis tools require ad hoc assumptions on the data structure, lack the interpretability of the present method, or in which the underlying processes are less accessible, such as genomics and neuroscience

Protein folding disorders: Toward a basic biological paradigm

Mechanistic 'physics' models of protein folding fail to account for the observed spectrum of protein folding and aggregation disorders, suggesting that a more appropriately biological paradigm will be needed for understanding the etiology, prevention, and treatment of these diseases

Structural Prediction of Protein–Protein Interactions by Docking: Application to Biomedical Problems

A huge amount of genetic information is available thanks to the recent advances in sequencing technologies and the larger computational capabilities, but the interpretation of such genetic data at phenotypic level remains elusive. One of the reasons is that proteins are not acting alone, but are specifically interacting with other proteins and biomolecules, forming intricate interaction networks that are essential for the majority of cell processes and pathological conditions. Thus, characterizing such interaction networks is an important step in understanding how information flows from gene to phenotype. Indeed, structural characterization of protein–protein interactions at atomic resolution has many applications in biomedicine, from diagnosis and vaccine design, to drug discovery. However, despite the advances of experimental structural determination, the number of interactions for which there is available structural data is still very small. In this context, a complementary approach is computational modeling of protein interactions by docking, which is usually composed of two major phases: (i) sampling of the possible binding modes between the interacting molecules and (ii) scoring for the identification of the correct orientations. In addition, prediction of interface and hot-spot residues is very useful in order to guide and interpret mutagenesis experiments, as well as to understand functional and mechanistic aspects of the interaction. Computational docking is already being applied to specific biomedical problems within the context of personalized medicine, for instance, helping to interpret pathological mutations involved in protein–protein interactions, or providing modeled structural data for drug discovery targeting protein–protein interactions.Spanish Ministry of Economy grant number BIO2016-79960-R; D.B.B. is supported by a predoctoral fellowship from CONACyT; M.R. is supported by an FPI fellowship from the Severo Ochoa program. We are grateful to the Joint BSC-CRG-IRB Programme in Computational Biology.Peer ReviewedPostprint (author's final draft

A variational approach to modeling slow processes in stochastic dynamical systems

The slow processes of metastable stochastic dynamical systems are difficult to access by direct numerical simulation due the sampling problem. Here, we suggest an approach for modeling the slow parts of Markov processes by approximating the dominant eigenfunctions and eigenvalues of the propagator. To this end, a variational principle is derived that is based on the maximization of a Rayleigh coefficient. It is shown that this Rayleigh coefficient can be estimated from statistical observables that can be obtained from short distributed simulations starting from different parts of state space. The approach forms a basis for the development of adaptive and efficient computational algorithms for simulating and analyzing metastable Markov processes while avoiding the sampling problem. Since any stochastic process with finite memory can be transformed into a Markov process, the approach is applicable to a wide range of processes relevant for modeling complex real-world phenomena

Accurate and efficient description of protein vibrational dynamics: comparing molecular dynamics and Gaussian models

Current all-atom potential based molecular dynamics (MD) allow the identification of a protein's functional motions on a wide-range of time-scales, up to few tens of ns. However, functional large scale motions of proteins may occur on a time-scale currently not accessible by all-atom potential based molecular dynamics. To avoid the massive computational effort required by this approach several simplified schemes have been introduced. One of the most satisfactory is the Gaussian Network approach based on the energy expansion in terms of the deviation of the protein backbone from its native configuration. Here we consider an extension of this model which captures in a more realistic way the distribution of native interactions due to the introduction of effective sidechain centroids. Since their location is entirely determined by the protein backbone, the model is amenable to the same exact and computationally efficient treatment as previous simpler models. The ability of the model to describe the correlated motion of protein residues in thermodynamic equilibrium is established through a series of successful comparisons with an extensive (14 ns) MD simulation based on the AMBER potential of HIV-1 protease in complex with a peptide substrate. Thus, the model presented here emerges as a powerful tool to provide preliminary, fast yet accurate characterizations of proteins near-native motion.Comment: 14 pages 7 figure

Unfolding and refolding of cytochrome c driven by the interaction with lipid micelles

Binding of native cyt c to L-PG micelles leads to a partially unfolded conformation of cyt c. This micelle-bound state has no stable tertiary structure, but remains as -helical as native cyt c in solution. In contrast, binding of the acid-unfolded cyt c to L-PG micelles induces folding of the polypeptide, resulting in a similar helical state to that originated from the binding of native cyt c to L-PG micelles. Far-ultraviolet (UV) circular dichroism (CD) spectra showed that this common micelle-associated helical state (HL) has a native-like -helix content, but is highly expanded without a tightly packed hydrophobic core, as revealed by tryptophan fluorescence, near-UV, and Soret CD spectroscopy. The kinetics of the interaction of native and acid-unfolded cyt c was investigated by stopped-flow tryptophan fluorescence. Formation of HL from the native state requires the disruption of the tightly packed hydrophobic core in the native protein. This micelle-induced unfolding of cyt c occurs at a rate 0.1 s1, which is remarkably faster in the lipid environment compared with the expected rate of unfolding in solution. Refolding of acid-unfolded cyt c with L-PG micelles involves an early highly helical collapsed state formed during the burst phase (<3 ms), and the observed main kinetic event reports on the opening of this early compact intermediate prior to insertion into the lipid micelle

Hamiltonian dynamics of homopolymer chain models

The Hamiltonian dynamics of chains of nonlinearly coupled particles is numerically investigated in two and three dimensions. Simple, off-lattice homopolymer models are used to represent the interparticle potentials. Time averages of observables numerically computed along dynamical trajectories are found to reproduce results given by the statistical mechanics of homopolymer models. The dynamical treatment, however, indicates a nontrivial transition between regimes of slow and fast phase space mixing. Such a transition is inaccessible to a statistical mechanical treatment and reflects a bimodality in the relaxation of time averages to corresponding ensemble averages. It is also found that a change in the energy dependence of the largest Lyapunov exponent indicates the theta-transition between filamentary and globular polymer configurations, clearly detecting the transition even for a finite number of particles.Comment: 11 pages, 8 figures, accepted for publication in Physical Review