Robust inference of causality in high-dimensional dynamical processes from the Information Imbalance of distance ranks.

We introduce an approach which allows detecting causal relationships between variables for which the time evolution is available. Causality is assessed by a variational scheme based on the Information Imbalance of distance ranks, a statistical test capable of inferring the relative information content of different distance measures. We test whether the predictability of a putative driven system Y can be improved by incorporating information from a potential driver system X, without explicitly modeling the underlying dynamics and without the need to compute probability densities of the dynamic variables. This framework makes causality detection possible even between high-dimensional systems where only few of the variables are known or measured. Benchmark tests on coupled chaotic dynamical systems demonstrate that our approach outperforms other model-free causality detection methods, successfully handling both unidirectional and bidirectional couplings. We also show that the method can be used to robustly detect causality in human electroencephalography data.

Improving acute stroke assessment in non-enhanced computed tomography: automated tool for early ischemic lesion volume detection.

BACKGROUND AND OBJECTIVES: ASPECTs is a widely used marker to identify early stroke signs on non-enhanced computed tomography (NECT), yet it presents interindividual variability and it may be hard to use for non-experts. We introduce an algorithm capable of automatically estimating the NECT volumetric extension of early acute ischemic changes in the 3D space. We compared the power of this marker with ASPECTs evaluated by experienced practitioner in predicting the clinical outcome. METHODS: We analyzed and processed neuroimaging data of 153 patients admitted with acute ischemic stroke. All patients underwent a NECT at admission and on follow-up. The developed algorithm identifies the early ischemic hypodense region based on an automatic comparison of the gray level in the images of the two hemispheres, assumed to be an approximate mirror image of each other in healthy patients. RESULTS: In the two standard axial slices used to estimate the ASPECTs, the regions identified by the algorithm overlap significantly with those identified by experienced practitioners. However, in many patients, the regions identified automatically extend significantly to other slices. In these cases, the volume marker provides supplementary and independent information. Indeed, the clinical outcome of patients with volume marker = 0 can be distinguished with higher statistical confidence than the outcome of patients with ASPECTs = 10. CONCLUSION: The volumetric extension and the location of acute ischemic region in the 3D-space, automatically identified by our algorithm, provide data that are mostly in agreement with the ASPECTs value estimated by expert practitioners, and in some cases complementary and independent.

Intrinsic Dimension Estimation for Discrete Metrics.

Real-world datasets characterized by discrete features are ubiquitous: from categorical surveys to clinical questionnaires, from unweighted networks to DNA sequences. Nevertheless, the most common unsupervised dimensional reduction methods are designed for continuous spaces, and their use for discrete spaces can lead to errors and biases. In this Letter we introduce an algorithm to infer the intrinsic dimension (ID) of datasets embedded in discrete spaces. We demonstrate its accuracy on benchmark datasets, and we apply it to analyze a metagenomic dataset for species fingerprinting, finding a surprisingly small ID, of order 2. This suggests that evolutive pressure acts on a low-dimensional manifold despite the high dimensionality of sequences' space.

DPCfam: Unsupervised protein family classification by Density Peak Clustering of large sequence datasets.

Proteins that are known only at a sequence level outnumber those with an experimental characterization by orders of magnitude. Classifying protein regions (domains) into homologous families can generate testable functional hypotheses for yet unannotated sequences. Existing domain family resources typically use at least some degree of manual curation: they grow slowly over time and leave a large fraction of the protein sequence space unclassified. We here describe automatic clustering by Density Peak Clustering of UniRef50 v. 2017_07, a protein sequence database including approximately 23M sequences. We performed a radical re-implementation of a pipeline we previously developed in order to allow handling millions of sequences and data volumes of the order of 3 TeraBytes. The modified pipeline, which we call DPCfam, finds ∼ 45,000 protein clusters in UniRef50. Our automatic classification is in close correspondence to the ones of the Pfam and ECOD resources: in particular, about 81% of medium-large Pfam families and 72% of ECOD families can be mapped to clusters generated by DPCfam. In addition, our protocol finds more than 14,000 clusters constituted of protein regions with no Pfam annotation, which are therefore candidates for representing novel protein families. These results are made available to the scientific community through a dedicated repository.

Unsupervised Learning Methods for Molecular Simulation Data.

Unsupervised learning is becoming an essential tool to analyze the increasingly large amounts of data produced by atomistic and molecular simulations, in material science, solid state physics, biophysics, and biochemistry. In this Review, we provide a comprehensive overview of the methods of unsupervised learning that have been most commonly used to investigate simulation data and indicate likely directions for further developments in the field. In particular, we discuss feature representation of molecular systems and present state-of-the-art algorithms of dimensionality reduction, density estimation, and clustering, and kinetic models. We divide our discussion into self-contained sections, each discussing a specific method. In each section, we briefly touch upon the mathematical and algorithmic foundations of the method, highlight its strengths and limitations, and describe the specific ways in which it has been used-or can be used-to analyze molecular simulation data.

Density Peak clustering of protein sequences associated to a Pfam clan reveals clear similarities and interesting differences with respect to manual family annotation.

BACKGROUND: The identification of protein families is of outstanding practical importance for in silico protein annotation and is at the basis of several bioinformatic resources. Pfam is possibly the most well known protein family database, built in many years of work by domain experts with extensive use of manual curation. This approach is generally very accurate, but it is quite time consuming and it may suffer from a bias generated from the hand-curation itself, which is often guided by the available experimental evidence. RESULTS: We introduce a procedure that aims to identify automatically putative protein families. The procedure is based on Density Peak Clustering and uses as input only local pairwise alignments between protein sequences. In the experiment we present here, we ran the algorithm on about 4000 full-length proteins with at least one domain classified by Pfam as belonging to the Pseudouridine synthase and Archaeosine transglycosylase (PUA) clan. We obtained 71 automatically-generated sequence clusters with at least 100 members. While our clusters were largely consistent with the Pfam classification, showing good overlap with either single or multi-domain Pfam family architectures, we also observed some inconsistencies. The latter were inspected using structural and sequence based evidence, which suggested that the automatic classification captured evolutionary signals reflecting non-trivial features of protein family architectures. Based on this analysis we identified a putative novel pre-PUA domain as well as alternative boundaries for a few PUA or PUA-associated families. As a first indication that our approach was unlikely to be clan-specific, we performed the same analysis on the P53 clan, obtaining comparable results. CONCLUSIONS: The clustering procedure described in this work takes advantage of the information contained in a large set of pairwise alignments and successfully identifies a set of putative families and family architectures in an unsupervised manner. Comparison with the Pfam classification highlights significant overlap and points to interesting differences, suggesting that our new algorithm could have potential in applications related to automatic protein classification. Testing this hypothesis, however, will require further experiments on large and diverse sequence datasets.

Automatic classification of single-molecule force spectroscopy traces from heterogeneous samples.

MOTIVATION: Single-molecule force spectroscopy (SMFS) experiments pose the challenge of analysing protein unfolding data (traces) coming from preparations with heterogeneous composition (e.g. where different proteins are present in the sample). An automatic procedure able to distinguish the unfolding patterns of the proteins is needed. Here, we introduce a data analysis pipeline able to recognize in such datasets traces with recurrent patterns (clusters). RESULTS: We illustrate the performance of our method on two prototypical datasets: ∼50 000 traces from a sample containing tandem GB1 and ∼400 000 traces from a native rod membrane. Despite a daunting signal-to-noise ratio in the data, we are able to identify several unfolding clusters. This work demonstrates how an automatic pattern classification can extract relevant information from SMFS traces from heterogeneous samples without prior knowledge of the sample composition. AVAILABILITY AND IMPLEMENTATION: https://github.com/ninailieva/SMFS_clustering. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

A Rosetta-based protein design protocol converging to natural sequences.

Computational protein design has emerged as a powerful tool capable of identifying sequences compatible with pre-defined protein structures. The sequence design protocols, implemented in the Rosetta suite, have become widely used in the protein engineering community. To understand the strengths and limitations of the Rosetta design framework, we tested several design protocols on two distinct folds (SH3-1 and Ubiquitin). The sequence optimization, when started from native structures and natural sequences or polyvaline sequences, converges to sequences that are not recognized as belonging to the fold family of the target protein by standard bioinformatic tools, such as BLAST and Hmmer. The sequences generated from both starting conditions (native and polyvaline) are instead very similar to each other and recognized by Hmmer as belonging to the same "family." This demonstrates the capability of Rosetta to converge to similar sequences, even when sampling from distinct starting conditions, but, on the other hand, shows intrinsic inaccuracy of the scoring function that drifts toward sequences that lack identifiable natural sequence signatures. To address this problem, we developed a protocol embedding Rosetta Design simulations in a genetic algorithm, in which the sequence search is biased to converge to sequences that exist in nature. This protocol allows us to obtain sequences that have recognizable natural sequence signatures and, experimentally, the designed proteins are biochemically well behaved and thermodynamically stable.

Brain network dynamics during spontaneous strategy shifts and incremental task optimization.

With practice, humans improve their performance in a task by either optimizing a known strategy or discovering a novel, potentially more fruitful strategy. We investigated the neural processes underlying these two fundamental abilities by applying fMRI in a task with two possible alternative strategies. For analysis we combined time-resolved network analysis with Coherence Density Peak Clustering (Allegra et al., 2017), univariate GLM, and multivariate pattern classification. Converging evidence showed that the posterior portion of the default network, i.e. the precuneus and the angular gyrus bilaterally, has a central role in the optimization of the current strategy. These regions encoded the relevant spatial information, increased the strength of local connectivity as well as the long-distance connectivity with other relevant regions in the brain (e.g., visual cortex, dorsal attention network). The connectivity increase was proportional to performance optimization. By contrast, the anterior portion of the default network (i.e. medial prefrontal cortex) and the rostral portion of the fronto-parietal network were associated with new strategy discovery: an early increase of local and long-range connectivity centered on these regions was only observed in the subjects who would later shift to a new strategy. Overall, our findings shed light on the dynamic interactions between regions related to attention and with cognitive control, underlying the balance between strategy exploration and exploitation. Results suggest that the default network, far from being "shut-down" during task performance, has a pivotal role in the background exploration and monitoring of potential alternative courses of action.

The intrinsic dimension of protein sequence evolution.

It is well known that, in order to preserve its structure and function, a protein cannot change its sequence at random, but only by mutations occurring preferentially at specific locations. We here investigate quantitatively the amount of variability that is allowed in protein sequence evolution, by computing the intrinsic dimension (ID) of the sequences belonging to a selection of protein families. The ID is a measure of the number of independent directions that evolution can take starting from a given sequence. We find that the ID is practically constant for sequences belonging to the same family, and moreover it is very similar in different families, with values ranging between 6 and 12. These values are significantly smaller than the raw number of amino acids, confirming the importance of correlations between mutations in different sites. However, we demonstrate that correlations are not sufficient to explain the small value of the ID we observe in protein families. Indeed, we show that the ID of a set of protein sequences generated by maximum entropy models, an approach in which correlations are accounted for, is typically significantly larger than the value observed in natural protein families. We further prove that a critical factor to reproduce the natural ID is to take into consideration the phylogeny of sequences.

The permeation mechanism of organic cations through a CNG mimic channel.

Several channels, ranging from TRP receptors to Gap junctions, allow the exchange of small organic solute across cell membrane. However, very little is known about the molecular mechanism of their permeation. Cyclic Nucleotide Gated (CNG) channels, despite their homology with K+ channels and in contrast with them, allow the passage of larger methylated and ethylated ammonium ions like dimethylammonium (DMA) and ethylammonium (EA). We combined electrophysiology and molecular dynamics simulations to examine how DMA interacts with the pore and permeates through it. Due to the presence of hydrophobic groups, DMA enters easily in the channel and, unlike the alkali cations, does not need to cross any barrier. We also show that while the crystal structure is consistent with the presence of a single DMA ion at full occupancy, the channel is able to conduct a sizable current of DMA ions only when two ions are present inside the channel. Moreover, the second DMA ion dramatically changes the free energy landscape, destabilizing the crystallographic binding site and lowering by almost 25 kJ/mol the binding affinity between DMA and the channel. Based on the results of the simulation the experimental electron density maps can be re-interpreted with the presence of a second ion at lower occupancy. In this mechanism the flexibility of the channel plays a key role, extending the classical multi-ion permeation paradigm in which conductance is enhanced by the plain interaction between the ions.

Predicting the Affinity of Peptides to Major Histocompatibility Complex Class II by Scoring Molecular Dynamics Simulations.

Predicting the binding affinity of peptides able to interact with major histocompatibility complex (MHC) molecules is a priority for researchers working in the identification of novel vaccines candidates. Most available approaches are based on the analysis of the sequence of peptides of known experimental affinity. However, for MHC class II receptors, these approaches are not very accurate, due to the intrinsic flexibility of the complex. To overcome these limitations, we propose to estimate the binding affinity of peptides bound to an MHC class II by averaging the score of the configurations from finite-temperature molecular dynamics simulations. The score is estimated for 18 different scoring functions, and we explored the optimal manner for combining them. To test the predictions, we considered eight peptides of known binding affinity. We found that six scoring functions correlate with the experimental ranking of the peptides significantly better than the others. We then assessed a set of techniques for combining the scoring functions by linear regression and logistic regression. We obtained a maximum accuracy of 82% for the predicted sign of the binding affinity using a logistic regression with optimized weights. These results are potentially useful to improve the reliability of in silico protocols to design high-affinity binding peptides for MHC class II receptors.

Vibrational entropy estimation can improve binding affinity prediction for non-obligatory protein complexes.

Predicting the binding affinity between protein monomers is of paramount importance for the understanding of thermodynamical and structural factors that guide the formation of a complex. Several numerical techniques have been developed for the calculation of binding affinities with different levels of accuracy. Approaches such as thermodynamic integration and Molecular Mechanics/Poisson-Boltzmann Surface Area (MM/PBSA) methodologies which account for well defined physical interactions offer good accuracy but are computationally demanding. Methods based on the statistical analysis of experimental structures are much cheaper but good performances have only been obtained throughout consensus energy functions based on many different molecular descriptors. In this study we investigate the importance of the contribution to the binding free energy of the entropic term due to the fluctuations around the equilibrium structures. This term, which we estimated employing an elastic network model, is usually neglected in most statistical approaches. Our method crucially relies on a novel calibration procedure of the elastic network force constant. The residue mobility profile is fitted to the one obtained through a short all-atom molecular dynamics simulation on a subset of residues only. Our results show how the proper consideration of vibrational entropic contributions can improve the quality of the prediction on a set of non-obligatory protein complexes whose binding affinity is known.

Assessing the capability of in silico mutation protocols for predicting the finite temperature conformation of amino acids.

Mutation protocols are a key tool in computational biophysics for modelling unknown side chain conformations. In particular, these protocols are used to generate the starting structures for molecular dynamics simulations. The accuracy of the initial side chain and backbone placement is crucial to obtain a stable and quickly converging simulation. In this work, we assessed the performance of several mutation protocols in predicting the most probable conformer observed in finite temperature molecular dynamics simulations for a set of protein-peptide crystals differing only by single-point mutations in the peptide sequence. Our results show that several programs which predict well the crystal conformations fail to predict the most probable finite temperature configuration. Methods relying on backbone-dependent rotamer libraries have, in general, a better performance, but even the best protocol fails in predicting approximately 30% of the mutations.

Binding affinity prediction of nanobody-protein complexes by scoring of molecular dynamics trajectories.

Nanobodies offer a viable alternative to antibodies for engineering high affinity binders. Their small size has an additional advantage: it allows exploiting computational protocols for optimizing their biophysical features, such as the binding affinity. The efficient prediction of this quantity is still considered a daunting task especially for modelled complexes. We show how molecular dynamics can successfully assist in the binding affinity prediction of modelled nanobody-protein complexes. The approximate initial configurations obtained by in silico design must undergo large rearrangements before achieving a stable conformation, in which the binding affinity can be meaningfully estimated. The scoring functions developed for the affinity evaluation of crystal structures will provide accurate estimates for modelled binding complexes if the scores are averaged over long finite temperature molecular dynamics simulations.

Toward a unified scoring function for native state discrimination and drug-binding pocket recognition.

Protein folding and receptor-ligand recognition are fundamental processes for any living organism. Although folding and ligand recognition are based on the same chemistry, the existing empirical scoring functions target just one problem: predicting the correct fold or the correct binding pose. We here introduce a statistical potential which considers moieties as fundamental units. The scoring function is able to deal with both folding and ligand pocket recognition problems with a performance comparable to the scoring functions specifically tailored for one of the two tasks. We foresee that the capability of the new scoring function to tackle both problems in a unified framework will be a key to deal with the induced fit phenomena, in which a target protein changes significantly its conformation upon binding. Moreover, the new scoring function might be useful in docking protocols towards intrinsically disordered proteins, whose flexibility cannot be handled with the available docking software.

Preface: Special Topic on Enhanced Sampling for Molecular Systems.

This special topic highlights recent developments in enhanced sampling methods for molecular-level simulations of chemical and biological systems. These methods are designed to enable more efficient exploration of phase space and extend the time scales that can be explored by simulations.

A structural, functional, and computational analysis suggests pore flexibility as the base for the poor selectivity of CNG channels.

Cyclic nucleotide-gated (CNG) ion channels, despite a significant homology with the highly selective K(+) channels, do not discriminate among monovalent alkali cations and are permeable also to several organic cations. We combined electrophysiology, molecular dynamics (MD) simulations, and X-ray crystallography to demonstrate that the pore of CNG channels is highly flexible. When a CNG mimic is crystallized in the presence of a variety of monovalent cations, including Na(+), Cs(+), and dimethylammonium (DMA(+)), the side chain of Glu66 in the selectivity filter shows multiple conformations and the diameter of the pore changes significantly. MD simulations indicate that Glu66 and the prolines in the outer vestibule undergo large fluctuations, which are modulated by the ionic species and the voltage. This flexibility underlies the coupling between gating and permeation and the poor ionic selectivity of CNG channels.

fMRI single trial discovery of spatio-temporal brain activity patterns.

There is growing interest in the description of short-lived patterns in the spatiotemporal cortical activity monitored via neuroimaging. Most traditional analysis methods, designed to estimate relatively long-term brain dynamics, are not always appropriate to capture these patterns. Here we introduce a novel data-driven approach for detecting short-lived fMRI brain activity patterns. Exploiting Density Peak Clustering (Rodriguez and Laio [2014]), our approach reveals well localized clusters by identifying and grouping together voxels whose time-series are similar, irrespective of their brain location, even when very short time windows (∼10 volumes) are used. The method, which we call Coherence Density Peak Clustering (CDPC), is first tested on simulated data and compared with a standard unsupervised approach for fMRI analysis, independent component analysis (ICA). CDPC identifies activated voxels with essentially no false-positives and proves more reliable than ICA, which is troubled by a number of false positives comparable to that of true positives. The reliability of the method is demonstrated on real fMRI data from a simple motor task, containing brief iterations of the same movement. The clusters identified are found in regions expected to be involved in the task, and repeat synchronously with the paradigm. The methodology proposed is especially suitable for the study of short-time brain dynamics and single trial experiments, where the event or task of interest cannot be repeated for the same subject, as happens, for instance, in problem-solving, learning and decision-making. A GUI implementation of our method is available for download at https://github.com/micheleallegra/CDPC. Hum Brain Mapp 38:1421-1437, 2017. © 2016 Wiley Periodicals, Inc.