Variable-free exploration of stochastic models: a gene regulatory network example

Finding coarse-grained, low-dimensional descriptions is an important task in the analysis of complex, stochastic models of gene regulatory networks. This task involves (a) identifying observables that best describe the state of these complex systems and (b) characterizing the dynamics of the observables. In a previous paper [13], we assumed that good observables were known a priori, and presented an equation-free approach to approximate coarse-grained quantities (i.e, effective drift and diffusion coefficients) that characterize the long-time behavior of the observables. Here we use diffusion maps [9] to extract appropriate observables ("reduction coordinates") in an automated fashion; these involve the leading eigenvectors of a weighted Laplacian on a graph constructed from network simulation data. We present lifting and restriction procedures for translating between physical variables and these data-based observables. These procedures allow us to perform equation-free coarse-grained, computations characterizing the long-term dynamics through the design and processing of short bursts of stochastic simulation initialized at appropriate values of the data-based observables.Comment: 26 pages, 9 figure

Coarse graining molecular dynamics with graph neural networks

Coarse graining enables the investigation of molecular dynamics for larger systems and at longer timescales than is possible at an atomic resolution. However, a coarse graining model must be formulated such that the conclusions we draw from it are consistent with the conclusions we would draw from a model at a finer level of detail. It has been proved that a force matching scheme defines a thermodynamically consistent coarse-grained model for an atomistic system in the variational limit. Wang et al. [ACS Cent. Sci. 5, 755 (2019)] demonstrated that the existence of such a variational limit enables the use of a supervised machine learning framework to generate a coarse-grained force field, which can then be used for simulation in the coarse-grained space. Their framework, however, requires the manual input of molecular features to machine learn the force field. In the present contribution, we build upon the advance of Wang et al. and introduce a hybrid architecture for the machine learning of coarse-grained force fields that learn their own features via a subnetwork that leverages continuous filter convolutions on a graph neural network architecture. We demonstrate that this framework succeeds at reproducing the thermodynamics for small biomolecular systems. Since the learned molecular representations are inherently transferable, the architecture presented here sets the stage for the development of machine-learned, coarse-grained force fields that are transferable across molecular systems

Persistence Bag-of-Words for Topological Data Analysis

Persistent homology (PH) is a rigorous mathematical theory that provides a robust descriptor of data in the form of persistence diagrams (PDs). PDs exhibit, however, complex structure and are difficult to integrate in today's machine learning workflows. This paper introduces persistence bag-of-words: a novel and stable vectorized representation of PDs that enables the seamless integration with machine learning. Comprehensive experiments show that the new representation achieves state-of-the-art performance and beyond in much less time than alternative approaches.Comment: Accepted for the Twenty-Eight International Joint Conference on Artificial Intelligence (IJCAI-19). arXiv admin note: substantial text overlap with arXiv:1802.0485

Exploring the Free Energy Landscape: From Dynamics to Networks and Back

The knowledge of the Free Energy Landscape topology is the essential key to understand many biochemical processes. The determination of the conformers of a protein and their basins of attraction takes a central role for studying molecular isomerization reactions. In this work, we present a novel framework to unveil the features of a Free Energy Landscape answering questions such as how many meta-stable conformers are, how the hierarchical relationship among them is, or what the structure and kinetics of the transition paths are. Exploring the landscape by molecular dynamics simulations, the microscopic data of the trajectory are encoded into a Conformational Markov Network. The structure of this graph reveals the regions of the conformational space corresponding to the basins of attraction. In addition, handling the Conformational Markov Network, relevant kinetic magnitudes as dwell times or rate constants, and the hierarchical relationship among basins, complete the global picture of the landscape. We show the power of the analysis studying a toy model of a funnel-like potential and computing efficiently the conformers of a short peptide, the dialanine, paving the way to a systematic study of the Free Energy Landscape in large peptides.Comment: PLoS Computational Biology (in press

The envirome and the connectome: exploring the structural noise in the human brain associated with socioeconomic deprivation

Complex cognitive functions are widely recognized to be the result of a number of brain regions working together as large-scale networks. Recently, complex network analysis has been used to characterize various structural properties of the large scale network organization of the brain. For example, the human brain has been found to have a modular architecture i.e. regions within the network form communities (modules) with more connections between regions within the community compared to regions outside it. The aim of this study was to examine the modular and overlapping modular architecture of the brain networks using complex network analysis. We also examined the association between neighborhood level deprivation and brain network structure – modularity and grey nodes. We compared network structure derived from anatomical MRI scans of 42 middle-aged neurologically healthy men from the least (LD) and the most deprived (MD) neighborhoods of Glasgow with their corresponding random networks. Cortical morphological covariance networks were constructed from the cortical thickness derived from the MRI scans of the brain. For a given modularity threshold, networks derived from the MD group showed similar number of modules compared to their corresponding random networks, while networks derived from the LD group had more modules compared to their corresponding random networks. The MD group also had fewer grey nodes – a measure of overlapping modular structure. These results suggest that apparent structural difference in brain networks may be driven by differences in cortical thicknesses between groups. This demonstrates a structural organization that is consistent with a system that is less robust and less efficient in information processing. These findings provide some evidence of the relationship between socioeconomic deprivation and brain network topology

iMapD: intrinsic Map Dynamics exploration for uncharted effective free energy landscapes

We describe and implement iMapD, a computer-assisted approach for accelerating the exploration of uncharted effective Free Energy Surfaces (FES), and more generally for the extraction of coarse-grained, macroscopic information from atomistic or stochastic (here Molecular Dynamics, MD) simulations. The approach functionally links the MD simulator with nonlinear manifold learning techniques. The added value comes from biasing the simulator towards new, unexplored phase space regions by exploiting the smoothness of the (gradually, as the exploration progresses) revealed intrinsic low-dimensional geometry of the FES

Embedding Comparator: Visualizing Differences in Global Structure and Local Neighborhoods via Small Multiples

Embeddings mapping high-dimensional discrete input to lower-dimensional continuous vector spaces have been widely adopted in machine learning applications as a way to capture domain semantics. Interviewing 13 embedding users across disciplines, we find comparing embeddings is a key task for deployment or downstream analysis but unfolds in a tedious fashion that poorly supports systematic exploration. In response, we present the Embedding Comparator, an interactive system that presents a global comparison of embedding spaces alongside fine-grained inspection of local neighborhoods. It systematically surfaces points of comparison by computing the similarity of the $k$-nearest neighbors of every embedded object between a pair of spaces. Through case studies, we demonstrate our system rapidly reveals insights, such as semantic changes following fine-tuning, language changes over time, and differences between seemingly similar models. In evaluations with 15 participants, we find our system accelerates comparisons by shifting from laborious manual specification to browsing and manipulating visualizations.Comment: Equal contribution by first two author