Gene Time E{chi}pression Warper: a tool for alignment, template matching and visualization of gene expression time series

An application tool for alignment, template matching and visualization of gene expression time series is presented. The core algorithm is based on dynamic time warping techniques used in the speech recognition field. These techniques allow for non-linear (elastic) alignment of temporal sequences of feature vectors and consequently enable detection of similar shapes with different phases. AVAILABILITY: The Java program, examples and a tutorial are available at http://www.psb.ugent.be/cbd/papers/gentxwarper/     

Geometry of gene expression dynamics

MOTIVATION: A gene expression trajectory moves through a high dimensional space where each axis represents the mRNA abundance of a different gene. Genome wide gene expression has a dynamic structure, especially in studies of development and temporal response. Both visualization and analyses of such data require an explicit attention to the temporal structure. RESULTS: Using three cell cycle trajectories from Saccharomyces cerevisiae to illustrate, we present several techniques which reveal the geometry of the data. We import phase-delay time plots from chaotic systems theory as a dynamic data visualization device and show how these plots capture important aspects of the trajectories. We construct an objective function to find an optimal two-dimensional projection of the cell cycle, demonstrate that the system returns to this plane after three different initial perturbations, and explore the conditions under which this geometric approach outperforms standard approaches such as singular value decomposition and Fourier analysis. Finally, we show how a geometric analysis can isolate distinct parts of the trajectories, in this case the initial perturbation versus the cell cycle. CONTACT: junhyong.kim@yale.edu     

Chromatographic peak alignment using derivative dynamic time warping

Chromatogram overlays are frequently used to monitor inter‐batch performance of bioprocess purification steps. However, the objective analysis of chromatograms is difficult due to peak shifts caused by variable phase durations or unexpected process holds. Furthermore, synchronization of batch process data may also be required prior to performing multivariate analysis techniques. Dynamic time warping was originally developed as a method for spoken word recognition, but shows potential in the objective analysis of time variant signals, such as manufacturing data. In this work we will discuss the application of dynamic time warping with a derivative weighting function to align chromatograms to facilitate process monitoring and fault detection. In addition, we will demonstrate the utility of this method as a preprocessing step for multivariate model development. © 2013 American Institute of Chemical Engineers Biotechnol. Prog., 29: 394–402, 2013     

Characterization of dynamic three-dimensional strain fields in the canine radius

This note describes a method to approximate the 3-D mechanical environment of a long bone during a normal daily activity. Our specific goal was to characterize the temporal and spatial strain distributions in the mid-shaft region of the canine radius during gait. Direct measurement of strains along the entire surface of in vivo bone is not feasible, so we employed a combination of experimental measurements and numerical interpolation techniques to approximate the time-varying longitudinal strain distribution. Using standard in vivo strain gauging techniques, we measured dynamic strains at nine locations (three locations on each of three cross sections, data pooled from two experimental animals) on the canine radius during trotting gait. These in vivo strain measurements were then used to approximate the time course of the strain field for the entire radius mid-shaft region using a 3-D numerical interpolation scheme using finite element basis functions. Despite limitations in the present implementation of the method, the results show that there are considerable time-dependent variations in the strain distribution occurring at different transverse sections along the length of the diaphysis with substantial anteroposterior bending and rotation of neutral axis locations during the gait cycle.     

Normalization strategies for microRNA profiling experiments: a ‘normal’ way to a hidden layer of complexity?

MicroRNA (miRNA) profiling is a first important step in elucidating miRNA functions. Real time quantitative PCR (RT-qPCR) and microarray hybridization approaches as well as ultra high throughput sequencing of miRNAs (small RNA-seq) are popular and widely used profiling methods. All of these profiling approaches face significant introduction of bias. Normalization, often an underestimated aspect of data processing, can minimize systematic technical or experimental variation and thus has significant impact on the detection of differentially expressed miRNAs. At present, there is no consensus normalization method for any of the three miRNA profiling approach. Several normalization techniques are currently in use, of which some are similar to mRNA profiling normalization methods, while others are specifically modified or developed for miRNA data. The characteristic nature of miRNA molecules, their composition and the resulting data distribution of profiling experiments challenges the selection of adequate normalization techniques. Based on miRNA profiling studies and comparative studies on normalization methods and their performances, this review provides a critical overview of commonly used and newly developed normalization methods for miRNA RT-qPCR, miRNA hybridization microarray, and small RNA-seq datasets. Emphasis is laid on the complexity, the importance and the potential for further optimization of normalization techniques for miRNA profiling datasets.     

Estimation of temporal gait parameters using Bayesian models on acceleration signals

The purpose of this study is to develop a system capable of performing calculation of temporal gait parameters using two low-cost wireless accelerometers and artificial intelligence-based techniques as part of a larger research project for conducting human gait analysis. Ten healthy subjects of different ages participated in this study and performed controlled walking tests. Two wireless accelerometers were placed on their ankles. Raw acceleration signals were processed in order to obtain gait patterns from characteristic peaks related to steps. A Bayesian model was implemented to classify the characteristic peaks into steps or nonsteps. The acceleration signals were segmented based on gait events, such as heel strike and toe-off, of actual steps. Temporal gait parameters, such as cadence, ambulation time, step time, gait cycle time, stance and swing phase time, simple and double support time, were estimated from segmented acceleration signals. Gait data-sets were divided into two groups of ages to test Bayesian models in order to classify the characteristic peaks. The mean error obtained from calculating the temporal gait parameters was 4.6%. Bayesian models are useful techniques that can be applied to classification of gait data of subjects at different ages with promising results     

Aligning gene expression time series with time warping algorithms

motivation: Increasingly, biological processes are being studied through time series of RNA expression data collected for large numbers of genes. Because common processes may unfold at varying rates in different experiments or individuals, methods are needed that will allow corresponding expression states in different time series to be mapped to one another. Results: We present implementations of time warping algorithms applicable to RNA and protein expression data and demonstrate their application to published yeast RNA expression time series. Programs executing two warping algorithms are described, a simple warping algorithm and an interpolative algorithm, along with programs that generate graphics that visually present alignment information. We show time warping to be superior to simple clustering at mapping corresponding time states. We document the impact of statistical measurement noise and sample size on the quality of time alignments, and present issues related to statistical assessment of alignment quality through alignment scores. We also discuss directions for algorithm improvement including development of multiple time series alignments and possible applications to causality searches and non-temporal processes ('concentration warping').     

Transform-based backprojection for volume reconstruction of large format electron microscope tilt series

Alignment of the individual images of a tilt series is a critical step in obtaining high-quality electron microscope reconstructions. We report on general methods for producing good alignments, and utilizing the alignment data in subsequent reconstruction steps. Our alignment techniques utilize bundle adjustment. Bundle adjustment is the simultaneous calculation of the position of distinguished markers in the object space and the transforms of these markers to their positions in the observed images, along the bundle of particle trajectories along which the object is projected to each EM image. Bundle adjustment techniques are general enough to encompass the computation of linear, projective or nonlinear transforms for backprojection, and can compensate for curvilinear trajectories through the object, sample warping, and optical aberration. We will also report on new reconstruction codes and describe our results using these codes.     

Symmetric time warping, Boltzmann pair probabilities and functional genomics

Given two time series, possibly of different lengths, time warping is a method to construct an optimal alignment obtained by stretching or contracting time intervals. Unlike pairwise alignment of amino acid sequences, classical time warping, originally introduced for speech recognition, is not symmetric in the sense that the time warping distance between two time series is not necessarily equal to the time warping distance of the reversal of the time series. Here we design a new symmetric version of time warping, and present a formal proof of symmetry for our algorithm as well as for one of the variants of Aach and Church [1]. We additionally design quadratic time dynamic programming algorithms to compute both the forward and backward Boltzmann partition functions for symmetric time warping, and hence compute the Boltzmann probability that any two time series points are aligned. In the future, with the availability of increasingly long and accurate time series gene expression data, our algorithm can provide a sense of biological significance for aligned time points – e.g. our algorithm could be used to provide evidence that expression values of two genes have higher Boltzmann probability (say) in the G1 and S phase than in G2 and M phases. Algorithms, source code and web interface, developed by the first author, are made publicly available via the Boltzmann Time Warping web server at bioinformatics.bc.edu/clotelab/. Research partially supported by National Science Foundation grant DBI-0543506.     

A comparison of four pair-wise sequence alignment methods

Protein sequence alignment has become an essential task in modern molecular biology research. A number of alignment techniques have been documented in literature and their corresponding tools are made available as freeware and commercial software. The choice and use of these tools for sequence alignment through the complete interpretation of alignment results is often considered non-trivial by end-users with limited skill in Bioinformatics algorithm development. Here, we discuss the comparison of sequence alignment techniques based on dynamic programming (N-W, S-W) and heuristics (LFASTA, BL2SEQ) for four sets of sequence data towards an educational purpose. The analysis suggests that heuristics based methods are faster than dynamic programming methods in alignment speed.     

TedSim: temporal dynamics simulation of single-cell RNA sequencing data and cell division history

Recently, lineage tracing technology using CRISPR/Cas9 genome editing has enabled simultaneous readouts of gene expressions and lineage barcodes, which allows for the reconstruction of the cell division tree and makes it possible to reconstruct ancestral cell types and trace the origin of each cell type. Meanwhile, trajectory inference methods are widely used to infer cell trajectories and pseudotime in a dynamic process using gene expression data of present-day cells. Here, we present TedSim (single-cell temporal dynamics simulator), which simulates the cell division events from the root cell to present-day cells, simultaneously generating two data modalities for each single cell: the lineage barcode and gene expression data. TedSim is a framework that connects the two problems: lineage tracing and trajectory inference. Using TedSim, we conducted analysis to show that (i) TedSim generates realistic gene expression and barcode data, as well as realistic relationships between these two data modalities; (ii) trajectory inference methods can recover the underlying cell state transition mechanism with balanced cell type compositions; and (iii) integrating gene expression and barcode data can provide more insights into the temporal dynamics in cell differentiation compared to using only one type of data, but better integration methods need to be developed.     

Pairwise curve synchronization for functional data

Data collected by scientists are increasingly in the form oftrajectories or curves. Often these can be viewed as realizationsof a composite process driven by both amplitude and time variation.We consider the situation in which functional variation is dominatedby time variation, and develop a curve-synchronization methodthat uses every trajectory in the sample as a reference to obtainpairwise warping functions in the first step. These initialpairwise warping functions are then used to create improvedestimators of the underlying individual warping functions inthe second step. A truncated averaging process is used to obtainrobust estimation of individual warping functions. The methodcompares well with other available time-synchronization approachesand is illustrated with Berkeley growth data and gene expressiondata for multiple sclerosis.     

Fusing time series expression data through hybrid aggregation and hierarchical merge

SUMMARY: A novel integration approach targeting the combination of multi-experiment time series expression data is proposed. A recursive hybrid aggregation algorithm is initially employed to extract a set of genes, which are eventually of interest for the biological phenomenon under study. Next, a hierarchical merge procedure is specifically developed for the purpose of fusing together the multiple-experiment expression pro.les of the selected genes. This employs dynamic time warping alignment techniques in order to account adequately for the potential phase shift between the different experiments. We subsequently demonstrate that the resulting gene expression pro.les consistently re.ect the behavior of the original expression pro.les in the different experiments. SUPPLEMENTARY INFORMATION: Supplementary data are available athttp://www.tu-plovdiv.bg/Container/bi/DataIntegration/     

Estimation of muscle forces in gait using a simulation of the electromyographic activity and numerical optimization

Clinical gait analysis provides great contributions to the understanding of gait patterns. However, a complete distribution of muscle forces throughout the gait cycle is a current challenge for many researchers. Two techniques are often used to estimate muscle forces: inverse dynamics with static optimization and computer muscle control that uses forward dynamics to minimize tracking. The first method often involves limitations due to changing muscle dynamics and possible signal artefacts that depend on day-to-day variation in the position of electromyographic (EMG) electrodes. Nevertheless, in clinical gait analysis, the method of inverse dynamics is a fundamental and commonly used computational procedure to calculate the force and torque reactions at various body joints. Our aim was to develop a generic musculoskeletal model that could be able to be applied in the clinical setting. The musculoskeletal model of the lower limb presents a simulation for the EMG data to address the common limitations of these techniques. This model presents a new point of view from the inverse dynamics used on clinical gait analysis, including the EMG information, and shows a similar performance to another model available in the OpenSim software. The main problem of these methods to achieve a correct muscle coordination is the lack of complete EMG data for all muscles modelled. We present a technique that simulates the EMG activity and presents a good correlation with the muscle forces throughout the gait cycle. Also, this method showed great similarities whit the real EMG data recorded from the subjects doing the same movement.     

Time-synchronized clustering of gene expression trajectories

Current clustering methods are routinely applied to gene expressiontime course data to find genes with similar activation patternsand ultimately to understand the dynamics of biological processes.As the dynamic unfolding of a biological process often involvesthe activation of genes at different rates, successful clusteringin this context requires dealing with varying time and shapepatterns simultaneously. This motivates the combination of anovel pairwise warping with a suitable clustering method todiscover expression shape clusters. We develop a novel clusteringmethod that combines an initial pairwise curve alignment toadjust for time variation within likely clusters. The cluster-specifictime synchronization method shows excellent performance overstandard clustering methods in terms of cluster quality measuresin simulations and for yeast and human fibroblast data sets.In the yeast example, the discovered clusters have high concordancewith the known biological processes.     

Normalization of joint moments during gait: a comparison of two techniques

Joint moments are commonly used to characterize gait. Factors like height and weight influence these moments. This study determined which of two commonly used normalization methods, body mass or body weight times height, most reduced the effects of height and weight on peak hip, knee, and ankle external moments during walking. The effectiveness of each normalization method in reducing gender differences was then tested. Gait data from 158 normal subjects were analyzed using unnormalized values, body mass normalized values, and body weight times height normalized values. Without normalization, height or weight accounted for 7-82% of the variance in all 10 peak components of the moments. With normalization, height and weight accounted for at most 6% of the variance with the exception of the hip adduction moment normalized by body weight times height and the ankle dorsiflexion moment normalized by body mass. For the hip adduction moment normalized by body weight times height, height still accounted for 13% of the variance (p<0.001) and for the ankle dorsiflexion moment normalized by body mass, 22% of the variance (p<0.001). After normalization, significant differences between males and females remained for only two out of 10 moments with the body weight times height method compared to six out of 10 moments with the body mass method. When compared to the unnormalized data, both normalization methods were highly effective in reducing height and weight differences. Even for the two cases where one normalization method was less effective than the other (hip adduction-body weight times height; ankle dorsiflexion-body mass) the normalization process reduced the variance ascribed to height or weight by 48% and 63%, respectively, as compared to the unnormalized data.     

Modeling experimental time series with ordinary differential equations

Recently some methods have been presented to extract ordinary differential equations (ODE) directly from an experimental time series. Here, we introduce a new method to find an ODE which models both the short time and the long time dynamics. The experimental data are represented in a state space and the corresponding flow vectors are approximated by polynomials of the state vector components. We apply these methods both to simulated data and experimental data from human limb movements, which like many other biological systems can exhibit limit cycle dynamics. In systems with only one oscillator there is excellent agreement between the limit cycling displayed by the experimental system and the reconstructed model, even if the data are very noisy. Furthermore, we study systems of two coupled limit cycle oscillators. There, a reconstruction was only successful for data with a sufficiently long transient trajectory and relatively low noise level.