scholarly journals Markov Chain-Based Sampling for Exploring RNA Secondary Structure under the Nearest Neighbor Thermodynamic Model and Extended Applications

2020 ◽  
Vol 25 (4) ◽  
pp. 67
Author(s):  
Anna Kirkpatrick ◽  
Kalen Patton ◽  
Prasad Tetali ◽  
Cassie Mitchell
Keyword(s):  
Markov Chain ◽  
Secondary Structure ◽  
Thermodynamic Model ◽  
Energy Function ◽  
Rna Secondary Structure ◽  
Nearest Neighbor ◽  
Spectral Gap ◽  
Mixing Time ◽  
Gibbs Distribution ◽  
Plane Trees

Ribonucleic acid (RNA) secondary structures and branching properties are important for determining functional ramifications in biology. While energy minimization of the Nearest Neighbor Thermodynamic Model (NNTM) is commonly used to identify such properties (number of hairpins, maximum ladder distance, etc.), it is difficult to know whether the resultant values fall within expected dispersion thresholds for a given energy function. The goal of this study was to construct a Markov chain capable of examining the dispersion of RNA secondary structures and branching properties obtained from NNTM energy function minimization independent of a specific nucleotide sequence. Plane trees are studied as a model for RNA secondary structure, with energy assigned to each tree based on the NNTM, and a corresponding Gibbs distribution is defined on the trees. Through a bijection between plane trees and 2-Motzkin paths, a Markov chain converging to the Gibbs distribution is constructed, and fast mixing time is established by estimating the spectral gap of the chain. The spectral gap estimate is obtained through a series of decompositions of the chain and also by building on known mixing time results for other chains on Dyck paths. The resulting algorithm can be used as a tool for exploring the branching structure of RNA, especially for long sequences, and to examine branching structure dependence on energy model parameters. Full exposition is provided for the mathematical techniques used with the expectation that these techniques will prove useful in bioinformatics, computational biology, and additional extended applications.

scholarly journals Rapid mixing of path integral Monte Carlo for 1D stoquastic Hamiltonians

Quantum ◽  
2021 ◽  
Vol 5 ◽  
pp. 395
Author(s):  
Elizabeth Crosson ◽  
Aram W. Harrow
Keyword(s):  
Monte Carlo ◽  
Markov Chain ◽  
Path Integral ◽  
Equilibrium Distribution ◽  
Mixing Time ◽  
Gibbs Distribution ◽  
Convergence Time ◽  
Spin Models ◽  
Classical Spin ◽  
Classical Spin Models

Path integral quantum Monte Carlo (PIMC) is a method for estimating thermal equilibrium properties of stoquastic quantum spin systems by sampling from a classical Gibbs distribution using Markov chain Monte Carlo. The PIMC method has been widely used to study the physics of materials and for simulated quantum annealing, but these successful applications are rarely accompanied by formal proofs that the Markov chains underlying PIMC rapidly converge to the desired equilibrium distribution. In this work we analyze the mixing time of PIMC for 1D stoquastic Hamiltonians, including disordered transverse Ising models (TIM) with long-range algebraically decaying interactions as well as disordered XY spin chains with nearest-neighbor interactions. By bounding the convergence time to the equilibrium distribution we rigorously justify the use of PIMC to approximate partition functions and expectations of observables for these models at inverse temperatures that scale at most logarithmically with the number of qubits. The mixing time analysis is based on the canonical paths method applied to the single-site Metropolis Markov chain for the Gibbs distribution of 2D classical spin models with couplings related to the interactions in the quantum Hamiltonian. Since the system has strongly nonisotropic couplings that grow with system size, it does not fall into the known cases where 2D classical spin models are known to mix rapidly.

scholarly journals Quantitative high-throughput tests of ubiquitous RNA secondary structure prediction algorithms via RNA/protein binding

2019 ◽  
Author(s):  
Winston R. Becker ◽  
Inga Jarmoskaite ◽  
Kalli Kappel ◽  
Pavanapuresan P. Vaidyanathan ◽  
Sarah K. Denny ◽  
...  
Keyword(s):  
Secondary Structure ◽  
Protein Binding ◽  
Rna Structure ◽  
Structure Prediction ◽  
Rna Secondary Structure ◽  
Nearest Neighbor ◽  
Secondary Structure Prediction ◽  
Structural Features ◽  
Vast Number ◽  
Prediction Algorithms

AbstractNearest-neighbor (NN) rules provide a simple and powerful quantitative framework for RNA structure prediction that is strongly supported for canonical Watson-Crick duplexes from a plethora of thermodynamic measurements. Predictions of RNA secondary structure based on nearest-neighbor (NN) rules are routinely used to understand biological function and to engineer and control new functions in biotechnology. However, NN applications to RNA structural features such as internal and terminal loops rely on approximations and assumptions, with sparse experimental coverage of the vast number of possible sequence and structural features. To test to what extent NN rules accurately predict thermodynamic stabilities across RNAs with non-WC features, we tested their predictions using a quantitative high-throughput assay platform, RNA-MaP. Using a thermodynamic assay with coupled protein binding, we carried out equilibrium measurements for over 1000 RNAs with a range of predicted secondary structure stabilities. Our results revealed substantial scatter and systematic deviations between NN predictions and observed stabilities. Solution salt effects and incorrect or omitted loop parameters contribute to these observed deviations. Our results demonstrate the need to independently and quantitatively test NN computational algorithms to identify their capabilities and limitations. RNA-MaP and related approaches can be used to test computational predictions and can be adapted to obtain experimental data to improve RNA secondary structure and other prediction algorithms.Significance statementRNA secondary structure prediction algorithms are routinely used to understand, predict and design functional RNA structures in biology and biotechnology. Given the vast number of RNA sequence and structural features, these predictions rely on a series of approximations, and independent tests are needed to quantitatively evaluate the accuracy of predicted RNA structural stabilities. Here we measure the stabilities of over 1000 RNA constructs by using a coupled protein binding assay. Our results reveal substantial deviations from the RNA stabilities predicted by popular algorithms, and identify factors contributing to the observed deviations. We demonstrate the importance of quantitative, experimental tests of computational RNA structure predictions and present an approach that can be used to routinely test and improve the prediction accuracy.

scholarly journals RNA secondary structure prediction using deep learning with thermodynamic integration

2021 ◽  
Vol 12 (1) ◽  
Author(s):  
Kengo Sato ◽  
Manato Akiyama ◽  
Yasubumi Sakakibara
Keyword(s):  
Free Energy ◽  
Deep Learning ◽  
Secondary Structure ◽  
Structure Prediction ◽  
Rna Secondary Structure ◽  
Nearest Neighbor ◽  
Secondary Structure Prediction ◽  
Secondary Structures ◽  
Rna Secondary Structures ◽  
Non Coding Rnas

AbstractAccurate predictions of RNA secondary structures can help uncover the roles of functional non-coding RNAs. Although machine learning-based models have achieved high performance in terms of prediction accuracy, overfitting is a common risk for such highly parameterized models. Here we show that overfitting can be minimized when RNA folding scores learnt using a deep neural network are integrated together with Turner’s nearest-neighbor free energy parameters. Training the model with thermodynamic regularization ensures that folding scores and the calculated free energy are as close as possible. In computational experiments designed for newly discovered non-coding RNAs, our algorithm (MXfold2) achieves the most robust and accurate predictions of RNA secondary structures without sacrificing computational efficiency compared to several other algorithms. The results suggest that integrating thermodynamic information could help improve the robustness of deep learning-based predictions of RNA secondary structure.

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