Using machine learning to detect coronaviruses potentially infectious to humans.

Establishing the host range for novel viruses remains a challenge. Here, we address the challenge of identifying non-human animal coronaviruses that may infect humans by creating an artificial neural network model that learns from spike protein sequences of alpha and beta coronaviruses and their binding annotation to their host receptor. The proposed method produces a human-Binding Potential (h-BiP) score that distinguishes, with high accuracy, the binding potential among coronaviruses. Three viruses, previously unknown to bind human receptors, were identified: Bat coronavirus BtCoV/133/2005 and Pipistrellus abramus bat coronavirus HKU5-related (both MERS related viruses), and Rhinolophus affinis coronavirus isolate LYRa3 (a SARS related virus). We further analyze the binding properties of BtCoV/133/2005 and LYRa3 using molecular dynamics. To test whether this model can be used for surveillance of novel coronaviruses, we re-trained the model on a set that excludes SARS-CoV-2 and all viral sequences released after the SARS-CoV-2 was published. The results predict the binding of SARS-CoV-2 with a human receptor, indicating that machine learning methods are an excellent tool for the prediction of host expansion events.

Scratch-AID, a deep learning-based system for automatic detection of mouse scratching behavior with high accuracy.

Mice are the most commonly used model animals for itch research and for development of anti-itch drugs. Most laboratories manually quantify mouse scratching behavior to assess itch intensity. This process is labor-intensive and limits large-scale genetic or drug screenings. In this study, we developed a new system, Scratch-AID (Automatic Itch Detection), which could automatically identify and quantify mouse scratching behavior with high accuracy. Our system included a custom-designed videotaping box to ensure high-quality and replicable mouse behavior recording and a convolutional recurrent neural network trained with frame-labeled mouse scratching behavior videos, induced by nape injection of chloroquine. The best trained network achieved 97.6% recall and 96.9% precision on previously unseen test videos. Remarkably, Scratch-AID could reliably identify scratching behavior in other major mouse itch models, including the acute cheek model, the histaminergic model, and a chronic itch model. Moreover, our system detected significant differences in scratching behavior between control and mice treated with an anti-itch drug. Taken together, we have established a novel deep learning-based system that could replace manual quantification for mouse scratching behavior in different itch models and for drug screening.

TAaCGH Suite for Detecting Cancer-Specific Copy Number Changes Using Topological Signatures.

Copy number changes play an important role in the development of cancer and are commonly associated with changes in gene expression. Persistence curves, such as Betti curves, have been used to detect copy number changes; however, it is known these curves are unstable with respect to small perturbations in the data. We address the stability of lifespan and Betti curves by providing bounds on the distance between persistence curves of Vietoris-Rips filtrations built on data and slightly perturbed data in terms of the bottleneck distance. Next, we perform simulations to compare the predictive ability of Betti curves, lifespan curves (conditionally stable) and stable persistent landscapes to detect copy number aberrations. We use these methods to identify significant chromosome regions associated with the four major molecular subtypes of breast cancer: Luminal A, Luminal B, Basal and HER2 positive. Identified segments are then used as predictor variables to build machine learning models which classify patients as one of the four subtypes. We find that no single persistence curve outperforms the others and instead suggest a complementary approach using a suite of persistence curves. In this study, we identified new cytobands associated with three of the subtypes: 1q21.1-q25.2, 2p23.2-p16.3, 23q26.2-q28 with the Basal subtype, 8p22-p11.1 with Luminal B and 2q12.1-q21.1 and 5p14.3-p12 with Luminal A. These segments are validated by the TCGA BRCA cohort dataset except for those found for Luminal A.

Ion-dependent DNA configuration in bacteriophage capsids.

Bacteriophages densely pack their long double-stranded DNA genome inside a protein capsid. The conformation of the viral genome inside the capsid is consistent with a hexagonal liquid crystalline structure. Experiments have confirmed that the details of the hexagonal packing depend on the electrochemistry of the capsid and its environment. In this work, we propose a biophysical model that quantifies the relationship between DNA configurations inside bacteriophage capsids and the types and concentrations of ions present in a biological system. We introduce an expression for the free energy that combines the electrostatic energy with contributions from bending of individual segments of DNA and Lennard-Jones-type interactions between these segments. The equilibrium points of this energy solve a partial differential equation that defines the distributions of DNA and the ions inside the capsid. We develop a computational approach that allows us to simulate much larger systems than what is possible using the existing molecular-level methods. In particular, we are able to estimate bending and repulsion between the DNA segments as well as the full electrochemistry of the solution, both inside and outside of the capsid. The numerical results show good agreement with existing experiments and with molecular dynamics simulations for small capsids.

Chromonic liquid crystals and packing configurations of bacteriophage viruses.

We study equilibrium configurations of hexagonal columnar liquid crystals in the context of characterizing packing structures of bacteriophage viruses in a protein capsid. These are viruses that infect bacteria and are currently the focus of intense research efforts, with the goal of finding new therapies for bacteria-resistant antibiotics. The energy that we propose consists of the Oseen-Frank free energy of nematic liquid crystals that penalizes bending of the columnar directions, in addition to the cross-sectional elastic energy accounting for distortions of the transverse hexagonal structure; we also consider the isotropic contribution of the core and the energy of the unknown interface between the outer ordered region of the capsid and the inner disordered core. The problem becomes of free boundary type, with constraints. We show that the concentric, azimuthal, spool-like configuration is the absolute minimizer. Moreover, we present examples of toroidal structures formed by DNA in free solution and compare them with the analogous ones occurring in experiments with other types of lyotropic liquid crystals, such as food dyes and additives. This article is part of the theme issue 'Topics in mathematical design of complex materials'.

Quantitative Study of the Chiral Organization of the Phage Genome Induced by the Packaging Motor.

Molecular motors that translocate DNA are ubiquitous in nature. During morphogenesis of double-stranded DNA bacteriophages, a molecular motor drives the viral genome inside a protein capsid. Several models have been proposed for the three-dimensional geometry of the packaged genome, but very little is known of the signature of the molecular packaging motor. For instance, biophysical experiments show that in some systems, DNA rotates during the packaging reaction, but most current biophysical models fail to incorporate this property. Furthermore, studies including rotation mechanisms have reached contradictory conclusions. In this study, we compare the geometrical signatures imposed by different possible mechanisms for the packaging motors: rotation, revolution, and rotation with revolution. We used a previously proposed kinetic Monte Carlo model of the motor, combined with Brownian dynamics simulations of DNA to simulate deterministic and stochastic motor models. We find that rotation is necessary for the accumulation of DNA writhe and for the chiral organization of the genome. We observe that although in the initial steps of the packaging reaction, the torsional strain of the genome is released by rotation of the molecule, in the later stages, it is released by the accumulation of writhe. We suggest that the molecular motor plays a key role in determining the final structure of the encapsidated genome in bacteriophages.

Fine structure of viral dsDNA encapsidation.

Unraveling the mechanisms of packing of DNA inside viral capsids is of fundamental importance to understanding the spread of viruses. It could also help develop new applications to targeted drug delivery devices for a large range of therapies. In this article, we present a robust, predictive mathematical model and its numerical implementation to aid the study and design of bacteriophage viruses for application purposes. Exploiting the analogies between the columnar hexagonal chromonic phases of encapsidated viral DNA and chromonic aggregates formed by plank-shaped molecular compounds, we develop a first-principles effective mechanical model of DNA packing in a viral capsid. The proposed expression of the packing energy, which combines relevant aspects of the liquid crystal theory, is developed from the model of hexagonal columnar phases, together with that describing configurations of polymeric liquid crystals. The method also outlines a parameter selection strategy that uses available data for a collection of viruses, aimed at applications to viral design. The outcome of the work is a mathematical model and its numerical algorithm, based on the method of finite elements, and computer simulations to identify and label the ordered and disordered regions of the capsid and calculate the inner pressure. It also presents the tools for the local reconstruction of the DNA "scaffolding" and the center curve of the filament within the capsid.

The Rabl configuration limits topological entanglement of chromosomes in budding yeast.

The three dimensional organization of genomes remains mostly unknown due to their high degree of condensation. Biophysical studies predict that condensation promotes the topological entanglement of chromatin fibers and the inhibition of function. How organisms balance between functionally active genomes and a high degree of condensation remains to be determined. Here we hypothesize that the Rabl configuration, characterized by the attachment of centromeres and telomeres to the nuclear envelope, helps to reduce the topological entanglement of chromosomes. To test this hypothesis we developed a novel method to quantify chromosome entanglement complexity in 3D reconstructions obtained from Chromosome Conformation Capture (CCC) data. Applying this method to published data of the yeast genome, we show that computational models implementing the attachment of telomeres or centromeres alone are not sufficient to obtain the reduced entanglement complexity observed in 3D reconstructions. It is only when the centromeres and telomeres are attached to the nuclear envelope (i.e. the Rabl configuration) that the complexity of entanglement of the genome is comparable to that of the 3D reconstructions. We therefore suggest that the Rabl configuration is an essential player in the simplification of the entanglement of chromatin fibers.

Current theoretical models fail to predict the topological complexity of the human genome.

Understanding the folding of the human genome is a key challenge of modern structural biology. The emergence of chromatin conformation capture assays (e.g., Hi-C) has revolutionized chromosome biology and provided new insights into the three dimensional structure of the genome. The experimental data are highly complex and need to be analyzed with quantitative tools. It has been argued that the data obtained from Hi-C assays are consistent with a fractal organization of the genome. A key characteristic of the fractal globule is the lack of topological complexity (knotting or inter-linking). However, the absence of topological complexity contradicts results from polymer physics showing that the entanglement of long linear polymers in a confined volume increases rapidly with the length and with decreasing volume. In vivo and in vitro assays support this claim in some biological systems. We simulate knotted lattice polygons confined inside a sphere and demonstrate that their contact frequencies agree with the human Hi-C data. We conclude that the topological complexity of the human genome cannot be inferred from current Hi-C data.

Orientation of DNA Minicircles Balances Density and Topological Complexity in Kinetoplast DNA.

Kinetoplast DNA (kDNA), a unique mitochondrial structure common to trypanosomatid parasites, contains thousands of DNA minicircles that are densely packed and can be topologically linked into a chain mail-like network. Experimental data indicate that every minicircle in the network is, on average, singly linked to three other minicircles (i.e., has mean valence 3) before replication and to six minicircles in the late stages of replication. The biophysical factors that determine the topology of the network and its changes during the cell cycle remain unknown. Using a mathematical modeling approach, we previously showed that volume confinement alone can drive the formation of the network and that it induces a linear relationship between mean valence and minicircle density. Our modeling also predicted a minicircle valence two orders of magnitude greater than that observed in kDNA. To determine the factors that contribute to this discrepancy we systematically analyzed the relationship between the topological properties of the network (i.e., minicircle density and mean valence) and its biophysical properties such as DNA bending, electrostatic repulsion, and minicircle relative position and orientation. Significantly, our results showed that most of the discrepancy between the theoretical and experimental observations can be accounted for by the orientation of the minicircles with volume exclusion due to electrostatic interactions and DNA bending playing smaller roles. Our results are in agreement with the three dimensional kDNA organization model, initially proposed by Delain and Riou, in which minicircles are oriented almost perpendicular to the horizontal plane of the kDNA disk. We suggest that while minicircle confinement drives the formation of kDNA networks, it is minicircle orientation that regulates the topological complexity of the network.

Identification of Copy Number Aberrations in Breast Cancer Subtypes Using Persistence Topology.

DNA copy number aberrations (CNAs) are of biological and medical interest because they help identify regulatory mechanisms underlying tumor initiation and evolution. Identification of tumor-driving CNAs (driver CNAs) however remains a challenging task, because they are frequently hidden by CNAs that are the product of random events that take place during tumor evolution. Experimental detection of CNAs is commonly accomplished through array comparative genomic hybridization (aCGH) assays followed by supervised and/or unsupervised statistical methods that combine the segmented profiles of all patients to identify driver CNAs. Here, we extend a previously-presented supervised algorithm for the identification of CNAs that is based on a topological representation of the data. Our method associates a two-dimensional (2D) point cloud with each aCGH profile and generates a sequence of simplicial complexes, mathematical objects that generalize the concept of a graph. This representation of the data permits segmenting the data at different resolutions and identifying CNAs by interrogating the topological properties of these simplicial complexes. We tested our approach on a published dataset with the goal of identifying specific breast cancer CNAs associated with specific molecular subtypes. Identification of CNAs associated with each subtype was performed by analyzing each subtype separately from the others and by taking the rest of the subtypes as the control. Our results found a new amplification in 11q at the location of the progesterone receptor in the Luminal A subtype. Aberrations in the Luminal B subtype were found only upon removal of the basal-like subtype from the control set. Under those conditions, all regions found in the original publication, except for 17q, were confirmed; all aberrations, except those in chromosome arms 8q and 12q were confirmed in the basal-like subtype. These two chromosome arms, however, were detected only upon removal of three patients with exceedingly large copy number values. More importantly, we detected 10 and 21 additional regions in the Luminal B and basal-like subtypes, respectively. Most of the additional regions were either validated on an independent dataset and/or using GISTIC. Furthermore, we found three new CNAs in the basal-like subtype: a combination of gains and losses in 1p, a gain in 2p and a loss in 14q. Based on these results, we suggest that topological approaches that incorporate multiresolution analyses and that interrogate topological properties of the data can help in the identification of copy number changes in cancer.

Reproducibility of 3D chromatin configuration reconstructions.

It is widely recognized that the three-dimensional (3D) architecture of eukaryotic chromatin plays an important role in processes such as gene regulation and cancer-driving gene fusions. Observing or inferring this 3D structure at even modest resolutions had been problematic, since genomes are highly condensed and traditional assays are coarse. However, recently devised high-throughput molecular techniques have changed this situation. Notably, the development of a suite of chromatin conformation capture (CCC) assays has enabled elicitation of contacts-spatially close chromosomal loci-which have provided insights into chromatin architecture. Most analysis of CCC data has focused on the contact level, with less effort directed toward obtaining 3D reconstructions and evaluating the accuracy and reproducibility thereof. While questions of accuracy must be addressed experimentally, questions of reproducibility can be addressed statistically-the purpose of this paper. We use a constrained optimization technique to reconstruct chromatin configurations for a number of closely related yeast datasets and assess reproducibility using four metrics that measure the distance between 3D configurations. The first of these, Procrustes fitting, measures configuration closeness after applying reflection, rotation, translation, and scaling-based alignment of the structures. The others base comparisons on the within-configuration inter-point distance matrix. Inferential results for these metrics rely on suitable permutation approaches. Results indicate that distance matrix-based approaches are preferable to Procrustes analysis, not because of the metrics per se but rather on account of the ability to customize permutation schemes to handle within-chromosome contiguity. It has recently been emphasized that the use of constrained optimization approaches to 3D architecture reconstruction are prone to being trapped in local minima. Our methods of reproducibility assessment provide a means for comparing 3D reconstruction solutions so that we can discern between local and global optima by contrasting solutions under perturbed inputs.

Random state transitions of knots: a first step towards modeling unknotting by type II topoisomerases.

Type II topoisomerases are enzymes that change the topology of DNA by performing strand-passage. In particular, they unknot knotted DNA very efficiently. Motivated by this experimental observation, we investigate transition probabilities between knots. We use the BFACF algorithm to generate ensembles of polygons in Z(3) of fixed knot type. We introduce a novel strand-passage algorithm which generates a Markov chain in knot space. The entries of the corresponding transition probability matrix determine state-transitions in knot space and can track the evolution of different knots after repeated strand-passage events. We outline future applications of this work to DNA unknotting.

DNA knots reveal a chiral organization of DNA in phage capsids.

Icosahedral bacteriophages pack their double-stranded DNA genomes to near-crystalline density and achieve one of the highest levels of DNA condensation found in nature. Despite numerous studies, some essential properties of the packaging geometry of the DNA inside the phage capsid are still unknown. We present a different approach to the problems of randomness and chirality of the packed DNA. We recently showed that most DNA molecules extracted from bacteriophage P4 are highly knotted because of the cyclization of the linear DNA molecule confined in the phage capsid. Here, we show that these knots provide information about the global arrangement of the DNA inside the capsid. First, we analyze the distribution of the viral DNA knots by high-resolution gel electrophoresis. Next, we perform Monte Carlo computer simulations of random knotting for freely jointed polygons confined to spherical volumes. Comparison of the knot distributions obtained by both techniques produces a topological proof of nonrandom packaging of the viral DNA. Moreover, our simulations show that the scarcity of the achiral knot 4(1) and the predominance of the torus knot 5(1) over the twist knot 5(2) observed in the viral distribution of DNA knots cannot be obtained by confinement alone but must include writhe bias in the conformation sampling. These results indicate that the packaging geometry of the DNA inside the viral capsid is writhe-directed.

SCHIP: statistics for chromosome interphase positioning based on interchange data.

MOTIVATION: The position of chromosomes in the interphase nucleus is believed to be associated with a number of biological processes. Here, we present a web-based application that helps analyze the relative position of chromosomes during interphase in human cells, based on observed radiogenic chromosome aberrations. The inputs of the program are a table of yields of pairwise chromosome interchanges and a proposed chromosome geometric cluster. Each can either be uploaded or selected from provided datasets. The main outputs are P-values for the proposed chromosome clusters. SCHIP is designed to be used by a number of scientific communities interested in nuclear architecture, including cancer and cell biologists, radiation biologists and mathematical/computational biologists.

Comparing DNA damage-processing pathways by computer analysis of chromosome painting data.

Chromosome aberrations are large-scale illegitimate rearrangements of the genome. They are indicative of DNA damage and informative about damage processing pathways. Despite extensive investigations over many years, the mechanisms underlying aberration formation remain controversial. New experimental assays such as multiplex fluorescent in situ hybridyzation (mFISH) allow combinatorial "painting" of chromosomes and are promising for elucidating aberration formation mechanisms. Recently observed mFISH aberration patterns are so complex that computer and graph-theoretical methods are needed for their full analysis. An important part of the analysis is decomposing a chromosome rearrangement process into "cycles." A cycle of order n, characterized formally by the cyclic graph with 2n vertices, indicates that n chromatin breaks take part in a single irreducible reaction. We here describe algorithms for computing cycle structures from experimentally observed or computer-simulated mFISH aberration patterns. We show that analyzing cycles quantitatively can distinguish between different aberration formation mechanisms. In particular, we show that homology-based mechanisms do not generate the large number of complex aberrations, involving higher-order cycles, observed in irradiated human lymphocytes.

Genomic transcriptional response to loss of chromosomal supercoiling in Escherichia coli.

BACKGROUND: The chromosome of Escherichia coli is maintained in a negatively supercoiled state, and supercoiling levels are affected by growth phase and a variety of environmental stimuli. In turn, supercoiling influences local DNA structure and can affect gene expression. We used microarrays representing nearly the entire genome of Escherichia coli MG1655 to examine the dynamics of chromosome structure. RESULTS: We measured the transcriptional response to a loss of supercoiling caused either by genetic impairment of a topoisomerase or addition of specific topoisomerase inhibitors during log-phase growth and identified genes whose changes are statistically significant. Transcription of 7% of the genome (306 genes) was rapidly and reproducibly affected by changes in the level of supercoiling; the expression of 106 genes increased upon chromosome relaxation and the expression of 200 decreased. These changes are most likely to be direct effects, as the kinetics of their induction or repression closely follow the kinetics of DNA relaxation in the cells. Unexpectedly, the genes induced by relaxation have a significantly enriched AT content in both upstream and coding regions. CONCLUSIONS: The 306 supercoiling-sensitive genes are functionally diverse and widely dispersed throughout the chromosome. We propose that supercoiling acts as a second messenger that transmits information about the environment to many regulatory networks in the cell.

Topological domain structure of the Escherichia coli chromosome.

The circular chromosome of Escherichia coli is organized into independently supercoiled loops, or topological domains. We investigated the organization and size of these domains in vivo and in vitro. Using the expression of >300 supercoiling-sensitive genes to gauge local chromosomal supercoiling, we quantitatively measured the spread of relaxation from double-strand breaks generated in vivo and thereby calculated the distance to the nearest domain boundary. In a complementary approach, we gently isolated chromosomes and examined the lengths of individual supercoiled loops by electron microscopy. The results from these two very different methods agree remarkably well. By comparing our results to Monte Carlo simulations of domain organization models, we conclude that domain barriers are not placed stably at fixed sites on the chromosome but instead are effectively randomly distributed. We find that domains are much smaller than previously reported, approximately 10 kb on average. We discuss the implications of these findings and present models for how domain barriers may be generated and displaced during the cell cycle in a stochastic fashion.

Investigation of viral DNA packaging using molecular mechanics models.

A simple molecular mechanics model has been used to investigate optimal spool-like packing conformations of double-stranded DNA molecules in viral capsids with icosahedral symmetry. The model represents an elastic segmented chain by using one pseudoatom for each ten basepairs (roughly one turn of the DNA double helix). Force constants for the various terms in the energy function were chosen to approximate known physical properties, and a radial restraint was used to confine the DNA into a sphere with a volume corresponding to that of a typical bacteriophage capsid. When the DNA fills 90% of the spherical volume, optimal packaging is obtained for coaxially spooled models, but this result does not hold when the void volume is larger. When only 60% of the spherical volume is filled with DNA, the lowest energy structure has two layers, with a coiled core packed at an angle to an outer coaxially spooled shell. This relieves bending strain associated with tight curvature near the poles in a model with 100% coaxial spooling. Interestingly, the supercoiling density of these models is very similar to typical values observed in plasmids in bacterial cells. Potential applications of the methodology are also discussed.

Using graph theory to describe and model chromosome aberrations.

A comprehensive description of chromosome aberrations is introduced that is suitable for all cytogenetic protocols (e.g. solid staining, banding, FISH, mFISH, SKY, bar coding) and for mathematical analyses. "Aberration multigraphs" systematically characterize and interrelate three basic aberration elements: (1) the initial configuration of chromosome breaks; (2) the exchange process, whose cycle structure helps to describe aberration complexity; and (3) the final configuration of rearranged chromosomes, which determines the observed pattern but may contain cryptic misrejoinings in addition. New aberration classification methods and a far-reaching generalization of mPAINT descriptors, applicable to any protocol, emerge. The difficult problem of trying to infer actual exchange processes from cytogenetically observed final patterns is analyzed using computer algorithms, adaptations of known theorems on cubic graphs, and some new graph-theoretical constructs. Results include the following: (1) For a painting protocol, unambiguously inferring the occurrence of a high-order cycle requires a corresponding number of different colors; (2) cycle structure can be computed by a simple trick directly from mPAINT descriptors if the initial configuration has no more than one break per homologue pair; and (3) higher-order cycles are more frequent than the obligate cycle structure specifies. Aberration multigraphs are a powerful new way to describe, classify and quantitatively analyze radiation-induced chromosome aberrations. They pinpoint (but do not eliminate) the problem that, with present cytogenetic techniques, one observed pattern corresponds to many possible initial configurations and exchange processes.