Classification and Identification of Non-canonical Base Pairs and Structural Motifs.

The 3D structures of many ribonucleic acid (RNA) loops are characterized by highly organized networks of non-canonical interactions. Multiple computational methods have been developed to annotate structures with those interactions or automatically identify recurrent interaction networks. By contrast, the reverse problem that aims to retrieve the geometry of a look from its sequence or ensemble of interactions remains much less explored. In this chapter, we will describe how to retrieve and build families of conserved structural motifs using their underlying network of non-canonical interactions. Then, we will show how to assign sequence alignments to those families and use the software BayesPairing to build statistical models of structural motifs with their associated sequence alignments. From this model, we will apply BayesPairing to identify in new sequences regions where those loop geometries can occur.

Concurrent prediction of RNA secondary structures with pseudoknots and local 3D motifs in an integer programming framework.

MOTIVATION: The prediction of RNA structure canonical base pairs from a single sequence, especially pseudoknotted ones, remains challenging in a thermodynamic models that approximates the energy of the local 3D motifs joining canonical stems. It has become more and more apparent in recent years that the structural motifs in the loops, composed of noncanonical interactions, are essential for the final shape of the molecule enabling its multiple functions. Our capacity to predict accurate 3D structures is also limited when it comes to the organization of the large intricate network of interactions that form inside those loops. RESULTS: We previously developed the integer programming framework RNA Motifs over Integer Programming (RNAMoIP) to reconcile RNA secondary structure and local 3D motif information available in databases. We further develop our model to now simultaneously predict the canonical base pairs (with pseudoknots) from base pair probability matrices with or without alignment. We benchmarked our new method over the all nonredundant RNAs below 150 nucleotides. We show that the joined prediction of canonical base pairs structure and local conserved motifs (i) improves the ratio of well-predicted interactions in the secondary structure, (ii) predicts well canonical and Wobble pairs at the location where motifs are inserted, (iii) is greatly improved with evolutionary information, and (iv) noncanonical motifs at kink-turn locations. AVAILABILITY AND IMPLEMENTATION: The source code of the framework is available at https://gitlab.info.uqam.ca/cbe/RNAMoIP and an interactive web server at https://rnamoip.cbe.uqam.ca/.

AlphaFold2 Can Predict Single-Mutation Effects.

AlphaFold2 (AF) is a promising tool, but is it accurate enough to predict single mutation effects? Here, we report that the localized structural deformation between protein pairs differing by only 1-3 mutations-as measured by the effective strain-is correlated across 3901 experimental and AF-predicted structures. Furthermore, analysis of ∼11 000 proteins shows that the local structural change correlates with various phenotypic changes. These findings suggest that AF can predict the range and magnitude of single-mutation effects on average, and we propose a method to improve precision of AF predictions and to indicate when predictions are unreliable.

Modeling suggests that virion production cycles within individual cells is key to understanding acute hepatitis B virus infection kinetics.

Hepatitis B virus (HBV) infection kinetics in immunodeficient mice reconstituted with humanized livers from inoculation to steady state is highly dynamic despite the absence of an adaptive immune response. To recapitulate the multiphasic viral kinetic patterns, we developed an agent-based model that includes intracellular virion production cycles reflecting the cyclic nature of each individual virus lifecycle. The model fits the data well predicting an increase in production cycles initially starting with a long production cycle of 1 virion per 20 hours that gradually reaches 1 virion per hour after approximately 3-4 days before virion production increases dramatically to reach to a steady state rate of 4 virions per hour per cell. Together, modeling suggests that it is the cyclic nature of the virus lifecycle combined with an initial slow but increasing rate of HBV production from each cell that plays a role in generating the observed multiphasic HBV kinetic patterns in humanized mice.

Modeling the Interplay between HDV and HBV in Chronic HDV/HBV Patients.

Hepatitis D virus is an infectious subviral agent that can only propagate in people infected with hepatitis B virus. In this study, we modified and further developed a recent model for early hepatitis D virus and hepatitis B virus kinetics to better reproduce hepatitis D virus and hepatitis B virus kinetics measured in infected patients during anti-hepatitis D virus treatment. The analytical solutions were provided to highlight the new features of the modified model. The improved model offered significantly better prospects for modeling hepatitis D virus and hepatitis B virus interactions.

On the predictibility of A-minor motifs from their local contexts.

This study investigates the importance of the structural context in the formation of a type I/II A-minor motif. This very frequent structural motif has been shown to be important in the spatial folding of RNA molecules. We developed an automated method to classify A-minor motif occurrences according to their 3D context similarities, and we used a graph approach to represent both the structural A-minor motif occurrences and their classes at different scales. This approach leads us to uncover new subclasses of A-minor motif occurrences according to their local 3D similarities. The majority of classes are composed of homologous occurrences, but some of them are composed of non-homologous occurrences. The different classifications we obtain allow us to better understand the importance of the context in the formation of A-minor motifs. In a second step, we investigate how much knowledge of the context around an A-minor motif can help to infer its presence (and position). More specifically, we want to determine what kind of information, contained in the structural context, can be useful to characterize and predict A-minor motifs. We show that, for some A-minor motifs, the topology combined with a sequence signal is sufficient to predict the presence and the position of an A-minor motif occurrence. In most other cases, these signals are not sufficient for predicting the A-minor motif, however we show that they are good signals for this purpose. All the classification and prediction pipelines rely on automated processes, for which we describe the underlying algorithms and parameters.

Advances in Parameter Estimation and Learning from Data for Mathematical Models of Hepatitis C Viral Kinetics.

Mathematical models, some of which incorporate both intracellular and extracellular hepatitis C viral kinetics, have been advanced in recent years for studying HCV-host dynamics, antivirals mode of action, and their efficacy. The standard ordinary differential equation (ODE) hepatitis C virus (HCV) kinetic model keeps track of uninfected cells, infected cells, and free virus. In multiscale models, a fourth partial differential equation (PDE) accounts for the intracellular viral RNA (vRNA) kinetics in an infected cell. The PDE multiscale model is substantially more difficult to solve compared to the standard ODE model, with governing differential equations that are stiff. In previous contributions, we developed and implemented stable and efficient numerical methods for the multiscale model for both the solution of the model equations and parameter estimation. In this contribution, we perform sensitivity analysis on model parameters to gain insight into important properties and to ensure our numerical methods can be safely used for HCV viral dynamic simulations. Furthermore, we generate in-silico patients using the multiscale models to perform machine learning from the data, which enables us to remove HCV measurements on certain days and still be able to estimate meaningful observations with a sufficiently small error.

Finding recurrent RNA structural networks with fast maximal common subgraphs of edge-colored graphs.

RNA tertiary structure is crucial to its many non-coding molecular functions. RNA architecture is shaped by its secondary structure composed of stems, stacked canonical base pairs, enclosing loops. While stems are precisely captured by free-energy models, loops composed of non-canonical base pairs are not. Nor are distant interactions linking together those secondary structure elements (SSEs). Databases of conserved 3D geometries (a.k.a. modules) not captured by energetic models are leveraged for structure prediction and design, but the computational complexity has limited their study to local elements, loops. Representing the RNA structure as a graph has recently allowed to expend this work to pairs of SSEs, uncovering a hierarchical organization of these 3D modules, at great computational cost. Systematically capturing recurrent patterns on a large scale is a main challenge in the study of RNA structures. In this paper, we present an efficient algorithm to compute maximal isomorphisms in edge colored graphs. We extend this algorithm to a framework well suited to identify RNA modules, and fast enough to considerably generalize previous approaches. To exhibit the versatility of our framework, we first reproduce results identifying all common modules spanning more than 2 SSEs, in a few hours instead of weeks. The efficiency of our new algorithm is demonstrated by computing the maximal modules between any pair of entire RNA in the non-redundant corpus of known RNA 3D structures. We observe that the biggest modules our method uncovers compose large shared sub-structure spanning hundreds of nucleotides and base pairs between the ribosomes of Thermus thermophilus, Escherichia Coli, and Pseudomonas aeruginosa.

Modeling and Predicting RNA Three-Dimensional Structures.

Modeling the three-dimensional structure of RNAs is a milestone toward better understanding and prediction of nucleic acids molecular functions. Physics-based approaches and molecular dynamics simulations are not tractable on large molecules with all-atom models. To address this issue, coarse-grained models of RNA three-dimensional structures have been developed. In this chapter, we describe a graphical modeling based on the Leontis-Westhof extended base pair classification. This representation of RNA structures enables us to identify highly conserved structural motifs with complex nucleotide interactions in structure databases. We show how to take advantage of this knowledge to quickly predict three-dimensional structures of large RNA molecules and present the RNA-MoIP web server (http://rnamoip.cs.mcgill.ca) that streamlines the computational and visualization processes. Finally, we show recent advances in the prediction of local 3D motifs from sequence data with the BayesPairing software and discuss its impact toward complete 3D structure prediction.

Understanding Hepatitis B Virus Dynamics and the Antiviral Effect of Interferon Alpha Treatment in Humanized Chimeric Mice.

Whereas the mode of action of lamivudine (LAM) against hepatitis B virus (HBV) is well established, the inhibition mechanism(s) of interferon alpha (IFN-α) is less completely defined. To advance our understanding, we mathematically modeled HBV kinetics during 14-day pegylated IFN-α-2a (pegIFN), LAM, or pegIFN-plus-LAM (pegIFN+LAM) treatment of 39 chronically HBV-infected humanized uPA/SCID chimeric mice. Serum HBV DNA and intracellular HBV DNA were measured frequently. We developed a multicompartmental mathematical model and simultaneously fit it to the serum and intracellular HBV DNA data. Unexpectedly, even in the absence of an adaptive immune response, a biphasic decline in serum HBV DNA and intracellular HBV DNA was observed in response to all treatments. Kinetic analysis and modeling indicate that the first phase represents inhibition of intracellular HBV DNA synthesis and secretion, which was similar under all treatments with an overall mean efficacy of 98%. In contrast, there were distinct differences in HBV decline during the second phase, which was accounted for in the model by a time-dependent inhibition of intracellular HBV DNA synthesis, with the steepest decline observed during pegIFN+LAM treatment (1.28/day) and the slowest (0.1/day) during pegIFN monotherapy. Reminiscent of observations in patients treated with pegIFN and/or LAM, a biphasic HBV decline was observed in treated humanized mice in the absence of an adaptive immune response. Interestingly, combination treatment did not increase the initial inhibition of HBV production but rather enhanced second-phase decline, providing insight into the dynamics of HBV treatment response and the mode of action of IFN-α against HBV. IMPORTANCE Chronic hepatitis B virus (HBV) infection remains a global health care problem, as we lack sufficient curative treatment options. Elucidating the dynamics of HBV infection and treatment response at the molecular level could facilitate the development of novel, more effective HBV antivirals. Currently, the only well-established small animal HBV infection model available is the chimeric uPA/SCID mice with humanized livers; however, the HBV inhibition kinetics under pegylated IFN-α-2a (pegIFN) in this model system have not been determined in sufficient detail. In this study, viral kinetics in 39 humanized mice treated with pegIFN and/or lamivudine were monitored and analyzed using a mathematical modeling approach. We found that the main mode of action of IFN-α is blocking HBV DNA synthesis and that the majority of synthesized HBV DNA is secreted. Our study provides novel insights into HBV DNA dynamics within infected human hepatocytes.

HCVMultiscaleFit: A Simulator For Parameter Estimation in Multiscale Models Of Hepatitis C Virus Dynamics.

Callibration in mathematical models that are based on differential equations is known to be of fundamental importance. For sophisticated models such as age-structured models that simulate biological agents, parameter estimation or fitting (callibration) that solves all cases of data points available presents a formidable challenge, as efficiency considerations need to be employed in order for the method to become practical. In the case of multiscale models of hepatitis C virus dynamics that deal with partial differential equations (PDEs), a fully numerical parameter estimation method was developed that does not require an analytical approximation of the solution to the multiscale model equations, avoiding the necessity to derive the long-term approximation for each model. However, the method is considerably slow because of precision problems in estimating derivatives with respect to the parameters near their boundary values, making it almost impractical for general use. In order to overcome this limitation, two steps have been taken that significantly reduce the running time by orders of magnitude and thereby lead to a practical method. First, constrained optimization is used, letting the user add constraints relating to the boundary values of each parameter before the method is executed. Second, optimization is performed by derivative-free methods, eliminating the need to evaluate expensive numerical derviative approximations. These steps that were successful in significantly speeding up a highly non-efficient approach, rendering it practical, can also be adapted to multiscale models of other viruses and other sophisticated differential equation models. The newly efficient methods that were developed as a result of the above approach are described. Illustrations are provided using a user-friendly simulator that incorporates the efficient methods for multiscale models. We provide a simulator called HCVMultiscaleFit with a Graphical User Interface that applies these methods and is useful to perform parameter estimation for simulating viral dynamics during antiviral treatment.

Efficient Methods for Parameter Estimation of Ordinary and Partial Differential Equation Models of Viral Hepatitis Kinetics.

Parameter estimation in mathematical models that are based on differential equations is known to be of fundamental importance. For sophisticated models such as age-structured models that simulate biological agents, parameter estimation that addresses all cases of data points available presents a formidable challenge and efficiency considerations need to be employed in order for the method to become practical. In the case of age-structured models of viral hepatitis dynamics under antiviral treatment that deal with partial differential equations, a fully numerical parameter estimation method was developed that does not require an analytical approximation of the solution to the multiscale model equations, avoiding the necessity to derive the long-term approximation for each model. However, the method is considerably slow because of precision problems in estimating derivatives with respect to the parameters near their boundary values, making it almost impractical for general use. In order to overcome this limitation, two steps have been taken that significantly reduce the running time by orders of magnitude and thereby lead to a practical method. First, constrained optimization is used, letting the user add constraints relating to the boundary values of each parameter before the method is executed. Second, optimization is performed by derivative-free methods, eliminating the need to evaluate expensive numerical derivative approximations. The newly efficient methods that were developed as a result of the above approach are described for hepatitis C virus kinetic models during antiviral therapy. Illustrations are provided using a user-friendly simulator that incorporates the efficient methods for both the ordinary and partial differential equation models.

αßDCA method identifies unspecific binding but specific disruption of the group I intron by the StpA chaperone.

Chaperone proteins-the most disordered among all protein groups-help RNAs fold into their functional structure by destabilizing misfolded configurations or stabilizing the functional ones. But disentangling the mechanism underlying RNA chaperoning is challenging, mostly because of inherent disorder of the chaperones and the transient nature of their interactions with RNA. In particular, it is unclear how specific the interactions are and what role is played by amino acid charge and polarity patterns. Here, we address these questions in the RNA chaperone StpA. We adapted direct coupling analysis (DCA) into the αßDCA method that can treat in tandem sequences written in two alphabets, nucleotides and amino acids. With αßDCA, we could analyze StpA-RNA interactions and show consistency with a previously proposed two-pronged mechanism: StpA disrupts specific positions in the group I intron while globally and loosely binding to the entire structure. Moreover, the interactions are strongly associated with the charge pattern: Negatively charged regions in the destabilizing StpA amino-terminal affect a few specific positions in the RNA, located in stems and in the pseudoknot. In contrast, positive regions in the carboxy-terminal contain strongly coupled amino acids that promote nonspecific or weakly specific binding to the RNA. The present study opens new avenues to examine the functions of disordered proteins and to design disruptive proteins based on their charge patterns.

Augmented base pairing networks encode RNA-small molecule binding preferences.

RNA-small molecule binding is a key regulatory mechanism which can stabilize 3D structures and activate molecular functions. The discovery of RNA-targeting compounds is thus a current topic of interest for novel therapies. Our work is a first attempt at bringing the scalability and generalization abilities of machine learning methods to the problem of RNA drug discovery, as well as a step towards understanding the interactions which drive binding specificity. Our tool, RNAmigos, builds and encodes a network representation of RNA structures to predict likely ligands for novel binding sites. We subject ligand predictions to virtual screening and show that we are able to place the true ligand in the 71st-73rd percentile in two decoy libraries, showing a significant improvement over several baselines, and a state of the art method. Furthermore, we observe that augmenting structural networks with non-canonical base pairing data is the only representation able to uncover a significant signal, suggesting that such interactions are a necessary source of binding specificity. We also find that pre-training with an auxiliary graph representation learning task significantly boosts performance of ligand prediction. This finding can serve as a general principle for RNA structure-function prediction when data is scarce. RNAmigos shows that RNA binding data contains structural patterns with potential for drug discovery, and provides methodological insights for possible applications to other structure-function learning tasks. The source code, data and a Web server are freely available at http://rnamigos.cs.mcgill.ca.

incaRNAfbinv 2.0: a webserver and software with motif control for fragment-based design of RNAs.

SUMMARY: RNA design has conceptually evolved from the inverse RNA folding problem. In the classical inverse RNA problem, the user inputs an RNA secondary structure and receives an output RNA sequence that folds into it. Although modern RNA design methods are based on the same principle, a finer control over the resulting sequences is sought. As an important example, a substantial number of non-coding RNA families show high preservation in specific regions, while being more flexible in others and this information should be utilized in the design. By using the additional information, RNA design tools can help solve problems of practical interest in the growing fields of synthetic biology and nanotechnology. incaRNAfbinv 2.0 utilizes a fragment-based approach, enabling a control of specific RNA secondary structure motifs. The new version allows significantly more control over the general RNA shape, and also allows to express specific restrictions over each motif separately, in addition to other advanced features. AVAILABILITY AND IMPLEMENTATION: incaRNAfbinv 2.0 is available through a standalone package and a web-server at https://www.cs.bgu.ac.il/incaRNAfbinv. Source code, command-line and GUI wrappers can be found at https://github.com/matandro/RNAsfbinv. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

On the emergence of structural complexity in RNA replicators.

The RNA world hypothesis relies on the ability of ribonucleic acids to spontaneously acquire complex structures capable of supporting essential biological functions. Multiple sophisticated evolutionary models have been proposed for their emergence, but they often assume specific conditions. In this work, we explore a simple and parsimonious scenario describing the emergence of complex molecular structures at the early stages of life. We show that at specific GC content regimes, an undirected replication model is sufficient to explain the apparition of multibranched RNA secondary structures-a structural signature of many essential ribozymes. We ran a large-scale computational study to map energetically stable structures on complete mutational networks of 50-nt-long RNA sequences. Our results reveal that the sequence landscape with stable structures is enriched with multibranched structures at a length scale coinciding with the appearance of complex structures in RNA databases. A random replication mechanism preserving a 50% GC content may suffice to explain a natural enrichment of stable complex structures in populations of functional RNAs. In contrast, an evolutionary mechanism eliciting the most stable folds at each generation appears to help reaching multibranched structures at highest GC content.

A Parameter Estimation Method for Multiscale Models of Hepatitis C Virus Dynamics.

Mathematical models that are based on differential equations require detailed knowledge about the parameters that are included in the equations. Some of the parameters can be measured experimentally while others need to be estimated. When the models become more sophisticated, such as in the case of multiscale models of hepatitis C virus dynamics that deal with partial differential equations (PDEs), several strategies can be tried. It is possible to use parameter estimation on an analytical approximation of the solution to the multiscale model equations, namely the long-term approximation, but this limits the scope of the parameter estimation method used and a long-term approximation needs to be derived for each model. It is possible to transform the PDE multiscale model to a system of ODEs, but this has an effect on the model parameters themselves and the transformation can become problematic for some models. Finally, it is possible to use numerical solutions for the multiscale model and then use canned methods for the parameter estimation, but the latter is making the user dependent on a black box without having full control over the method. The strategy developed here is to start by working directly on the multiscale model equations for preparing them toward the parameter estimation method that is fully coded and controlled by the user. It can also be adapted to multiscale models of other viruses. The new method is described, and illustrations are provided using a user-friendly simulator that incorporates the method.

Automated, customizable and efficient identification of 3D base pair modules with BayesPairing.

RNA structures possess multiple levels of structural organization. A secondary structure, made of Watson-Crick helices connected by loops, forms a scaffold for the tertiary structure. The 3D structures adopted by these loops are therefore critical determinants shaping the global 3D architecture. Earlier studies showed that these local 3D structures can be described as conserved sets of ordered non-Watson-Crick base pairs called RNA structural modules. Unfortunately, the computational efficiency and scope of the current 3D module identification methods are too limited yet to benefit from all the knowledge accumulated in the module databases. We present BayesPairing, an automated, efficient and customizable tool for (i) building Bayesian networks representing RNA 3D modules and (ii) rapid identification of 3D modules in sequences. BayesPairing uses a flexible definition of RNA 3D modules that allows us to consider complex architectures such as multi-branched loops and features multiple algorithmic improvements. We benchmarked our methods using cross-validation techniques on 3409 RNA chains and show that BayesPairing achieves up to ∼70% identification accuracy on module positions and base pair interactions. BayesPairing can handle a broader range of motifs (versatility) and offers considerable running time improvements (efficiency), opening the door to a broad range of large-scale applications.

Mining for recurrent long-range interactions in RNA structures reveals embedded hierarchies in network families.

The wealth of the combinatorics of nucleotide base pairs enables RNA molecules to assemble into sophisticated interaction networks, which are used to create complex 3D substructures. These interaction networks are essential to shape the 3D architecture of the molecule, and also to provide the key elements to carry molecular functions such as protein or ligand binding. They are made of organised sets of long-range tertiary interactions which connect distinct secondary structure elements in 3D structures. Here, we present a de novo data-driven approach to extract automatically from large data sets of full RNA 3D structures the recurrent interaction networks (RINs). Our methodology enables us for the first time to detect the interaction networks connecting distinct components of the RNA structure, highlighting their diversity and conservation through non-related functional RNAs. We use a graphical model to perform pairwise comparisons of all RNA structures available and to extract RINs and modules. Our analysis yields a complete catalog of RNA 3D structures available in the Protein Data Bank and reveals the intricate hierarchical organization of the RNA interaction networks and modules. We assembled our results in an online database (http://carnaval.lri.fr) which will be regularly updated. Within the site, a tool allows users with a novel RNA structure to detect automatically whether the novel structure contains previously observed RINs.

Numerical schemes for solving and optimizing multiscale models with age of hepatitis C virus dynamics.

Age-structured PDE models have been developed to study viral infection and treatment. However, they are notoriously difficult to solve. Here, we investigate the numerical solutions of an age-based multiscale model of hepatitis C virus (HCV) dynamics during antiviral therapy and compare them with an analytical approximation, namely its long-term approximation. First, starting from a simple yet flexible numerical solution that also considers an integral approximated over previous iterations, we show that the long-term approximation is an underestimate of the PDE model solution as expected since some infection events are being ignored. We then argue for the importance of having a numerical solution that takes into account previous iterations for the associated integral, making problematic the use of canned solvers. Second, we demonstrate that the governing differential equations are stiff and the stability of the numerical scheme should be considered. Third, we show that considerable gain in efficiency can be achieved by using adaptive stepsize methods over fixed stepsize methods for simulating realistic scenarios when solving multiscale models numerically. Finally, we compare between several numerical schemes for the solution of the equations and demonstrate the use of a numerical optimization scheme for the parameter estimation performed directly from the equations.