Jinkyu Kim

HiTRACE: High-throughput robust analysis for capillary electrophoresis

MOTIVATION Capillary electrophoresis (CE) of nucleic acids is a workhorse technology underlying high-throughput genome analysis and large-scale chemical mapping for nucleic acid structural inference. Despite the wide availability of CE-based instruments, there remain challenges in leveraging their full power for quantitative analysis of RNA and DNA structure, thermodynamics and kinetics. In particular, the slow rate and poor automation of available analysis tools have bottlenecked a new generation of studies involving hundreds of CE profiles per experiment. RESULTS We propose a computational method called high-throughput robust analysis for capillary electrophoresis (HiTRACE) to automate the key tasks in large-scale nucleic acid CE analysis, including the profile alignment that has heretofore been a rate-limiting step in the highest throughput experiments. We illustrate the application of HiTRACE on 13 datasets representing 4 different RNAs, 3 chemical modification strategies and up to 480 single mutant variants; the largest datasets each include 87 360 bands. By applying a series of robust dynamic programming algorithms, HiTRACE outperforms prior tools in terms of alignment and fitting quality, as assessed by measures including the correlation between quantified band intensities between replicate datasets. Furthermore, while the smallest of these datasets required 7-10 h of manual intervention using prior approaches, HiTRACE quantitation of even the largest datasets herein was achieved in 3-12 min. The HiTRACE method, therefore, resolves a critical barrier to the efficient and accurate analysis of nucleic acid structure in experiments involving tens of thousands of electrophoretic bands.

A robust peak detection method for RNA structure inference by high-throughput contact mapping

MOTIVATION For high-throughput prediction of the helical arrangements of large RNA molecules, an innovative method termed multiplexed hydroxyl radical (*OH) cleavage analysis (MOHCA) has been proposed. A key step in this promising technique is to detect peaks accurately from noisy radioactivity profiles. Since manual peak finding is laborious and prone to error, an automated peak detection method to improve the accuracy and throughput of MOHCA is required. Existing methods were not applicable to MOHCA due to their high false positive rates. RESULTS We developed a two-step computational method that can detect peaks from MOHCA profiles in a robust manner. The first step exploits an ensemble of linear and non-linear signal processing techniques to find true peak candidates. In the second step, a binary classifier trained with the characteristics of true and false peaks is used to eliminate false peaks out of the peak candidates. We tested the proposed approach with 2002 MOHCA cleavage profiles and obtained the median recall, precision and F-measure values of 0.917, 0.750 and 0.830, respectively. Compared with the alternatives considered, the proposed method was able to handle false peaks substantially better, thus resulting in 51.0-71.8% higher median values of precision and F-measure. AVAILABILITY The software and supplementary data are available at http://dna.korea.ac.kr/pub/mohca.

Mixed convolved action

A stationary principle is developed for dynamical systems by formulating the concept of mixed convolved action, which is written in terms of displacement and force variables, using temporal convolutions and fractional derivatives. The classical canonical single-degree-of-freedom dynamical system is considered as an initial application. With this new formulation, a single real scalar functional provides the governing differential equations, along with all the pertinent initial conditions, as the Euler-Lagrange equations emanating from the stationarity of the mixed convolved action. Both conservative and non-conservative processes can be considered within a common framework, thus resolving a long-standing limitation of variational approaches for dynamical systems. Several results in fractional calculus also are developed.

A quadratic temporal finite element method for linear elastic structural dynamics

Recently, in order to overcome the key shortcoming in Hamilton’s principle, the extended framework of Hamilton’s principle was formulated. This new variational framework provides a sound base to develop novel temporal finite element methods with the proper use of initial conditions to the strong form. As its initial and practical application in structural dynamic analysis, this paper presents a quadratic temporal finite element method for linear elastic multi-degrees-of-freedom systems. Numerical features of the developed method are analytically and numerically investigated with comparison to the currently dominant method; the results highlight the improved performance of the proposed method.

Higher order temporal finite element methods through mixed formalisms

The extended framework of Hamilton’s principle and the mixed convolved action principle provide new rigorous weak variational formalism for a broad range of initial boundary value problems in mathematical physics and mechanics. In this paper, their potential when adopting temporally higher order approximations is investigated. The classical single-degree-of-freedom dynamical systems are primarily considered to validate and to investigate the performance of the numerical algorithms developed from both formulations. For the undamped system, all the algorithms are symplectic and unconditionally stable with respect to the time step. For the damped system, they are shown to be accurate with good convergence characteristics.

Constructing Accurate Contact Maps for Hydroxyl-Radical-Cleavage-Based High-Throughput RNA Structure Inference

For rapid ribonucleic acid (RNA) tertiary structure prediction, innovative methods have been proposed that exploit hydroxyl radical cleavage agents in a high-throughput manner. In such techniques, it is critical to determine accurately which residue a specific cleavage agent interacts with, since this information directly reveals the residue-residue interaction points needed for structure inference. Due to lack of effective automated methods, the process of locating contact points has been mostly done manually, becoming a bottleneck of the whole procedure. To address this problem, we propose a novel computational method to determine residue-residue interaction points from 2-D electrophoresis profiles. This method combines the deconvolution method for signal detection and statistical learning techniques for filtering noise, thus boosting specificity and sensitivity in harmony. According to our experiments with over 2000 actual gel profiles, the proposed technique exhibited 56.44%-90.50% higher performance than traditional methods in terms of the accuracy of reproducing manual contact maps measured by the F-measure, a widely used evaluation metric. We expect that adopting the proposed technique will significantly accelerate RNA tertiary structure inference, allowing researchers to explore more structures in given time.

Temporal finite element methods through the extended framework of Hamilton's principle

With basic ideas of mixed Lagrangian formulation and sequential assigning process for initial conditions, the extended framework of Hamilton’s principle (EHP) was recently developed for continuum dynamics. Unlike the original Hamilton’s principle, this new variational framework can fully take initial conditions into account for both linear and nonlinear dynamics, so that it provides a sound base to apply a finite element scheme over the temporal domain without any ambiguity. This paper describes temporal finite element approach stemming from the extended Hamilton’s principle, which focuses initially on classical single-degree-of-freedom oscillators such as Kelvin–Voigt damped oscillator and an elasto-viscoplastic model. In each case, an appropriate weak form is provided and a corresponding formulation is discretized in the temporal domain with the adoption of Galerkin’s method. Basic numerical properties are investigated for the developed numerical algorithms with several computational examples for the elasto-viscoplastic model. For the underlying conservative system, the present method is symplectic and unconditionally stable with respect to the time step. On the other hand, the method provides unconditionally stable and noniterative algorithm for the elasto-viscoplastic model.

Extended framework of Hamiltons principle for thermoelastic continua

Based upon the extended framework of Hamiltons principle, a variational formulation for fully coupled thermoelasticity is presented. The resulting formulation can properly account for all the governing differential equations as well as initial/boundary conditions. Thus, it provides the basis for a class of unified spacetime finite element methods. By employing bar elements in one-dimensional space along with linear shape functions temporally, the simplest spacetime finite element method is presented herein with representative examples for its validity.

Unified Space–Time Finite Element Methods for Dissipative Continua Dynamics

Based upon the extended framework of Hamilton’s principle, unified space–time finite element methods for viscoelastic and viscoplastic continuum dynamics are presented, respectively. For numerical efficiency, mixed time-step algorithm in time- and displacement-based algorithm in space are adopted. Through analytical investigation, we demonstrate that the Newmark’s constant average acceleration method and the present method are the same for viscoelasticity. With spatial eight-node brick elements, some numerical simulations are undertaken to validate and investigate the performance of the present non-iterative space–time finite element method for viscoplasticity.

Mixed Convolved Action for Thermoelasticity

In the present work, a variational formulation for fully coupled thermoelasticity is developed in the context of the mixed convolved action. This weak variational formulation recovers all the governing differential equations along with proper initial and boundary conditions as its Euler–Lagrange equations. Thus, it encapsulates the entire description of thermoelastic problems. In addition to theoretical significance, it provides sound basis for the development of novel computational methods involving unified space-time finite element approach. The simplest unified space-time finite element method is also developed here with representative examples for its viability.