A Parameter-Free Model Comparison Test Using Differential Algebra

We present a method for rejecting competing models from noisy time-course data that does not rely on parameter inference. First we characterize ordinary differential equation models in only measurable variables using differential-algebra elimination. This procedure gives input-output equations, which serve as invariants for time series data. We develop a model comparison test using linear algebra and statistics to reject incorrect models from their invariants. This algorithm exploits the dynamic properties that are encoded in the structure of the model equations without recourse to parameter values, and, in this sense, the approach is parameter-free. We demonstrate this method by discriminating between different models from mathematical biology.

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Parameter-free methods distinguish Wnt pathway models and guide design of experiments

Proceedings of the National Academy of Sciences ◽

10.1073/pnas.1416655112 ◽

2015 ◽

Vol 112 (9) ◽

pp. 2652-2657 ◽

Cited By ~ 18

Author(s):

Adam L. MacLean ◽

Zvi Rosen ◽

Helen M. Byrne ◽

Heather A. Harrington

Keyword(s):

Wnt Signaling ◽

Time Course ◽

Model Comparison ◽

Wnt Signaling Pathway ◽

Reaction Network ◽

Adult Stem Cell ◽

Matroid Theory ◽

Biological Insight ◽

Competing Models ◽

Parameter Values

The canonical Wnt signaling pathway, mediated by β-catenin, is crucially involved in development, adult stem cell tissue maintenance, and a host of diseases including cancer. We analyze existing mathematical models of Wnt and compare them to a new Wnt signaling model that targets spatial localization; our aim is to distinguish between the models and distill biological insight from them. Using Bayesian methods we infer parameters for each model from mammalian Wnt signaling data and find that all models can fit this time course. We appeal to algebraic methods (concepts from chemical reaction network theory and matroid theory) to analyze the models without recourse to specific parameter values. These approaches provide insight into aspects of Wnt regulation: the new model, via control of shuttling and degradation parameters, permits multiple stable steady states corresponding to stem-like vs. committed cell states in the differentiation hierarchy. Our analysis also identifies groups of variables that should be measured to fully characterize and discriminate between competing models, and thus serves as a guide for performing minimal experiments for model comparison.

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SARS-COV-2: SIR Model Limitations and Predictive Constraints

Symmetry ◽

10.3390/sym13040676 ◽

2021 ◽

Vol 13 (4) ◽

pp. 676

Author(s):

Charles Roberto Telles ◽

Henrique Lopes ◽

Diogo Franco

Keyword(s):

Time Series Data ◽

Data Extraction ◽

Sir Model ◽

Series Data ◽

Atmospheric Conditions ◽

Main Research ◽

Outdoor Spaces ◽

Model Equations ◽

Physical Features ◽

Indoor And Outdoor

Background: The main purpose of this research is to describe the mathematical asymmetric patterns of susceptible, infectious, or recovered (SIR) model equation application in the light of coronavirus disease 2019 (COVID-19) skewness patterns worldwide. Methods: The research modeled severe acute respiratory syndrome coronavirus 2 (SARS-COV-2) spreading and dissemination patterns sensitivity by redesigning time series data extraction of daily new cases in terms of deviation consistency concerning variables that sustain COVID-19 transmission. The approach opened a new scenario where seasonality forcing behavior was introduced to understand SARS-COV-2 non-linear dynamics due to heterogeneity and confounding epidemics scenarios. Results: The main research results are the elucidation of three birth- and death-forced seasonality persistence phases that can explain COVID-19 skew patterns worldwide. They are presented in the following order: (1) the environmental variables (Earth seasons and atmospheric conditions); (2) health policies and adult learning education (HPALE) interventions; (3) urban spaces (local indoor and outdoor spaces for transit and social-cultural interactions, public or private, with natural physical features (river, lake, terrain). Conclusions: Three forced seasonality phases (positive to negative skew) phases were pointed out as a theoretical framework to explain uncertainty found in the predictive SIR model equations that might diverge in outcomes expected to express the disease’s behaviour.

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Jonckheere–Terpstra–Kendall-based non-parametric analysis of temporal differential gene expression

NAR Genomics and Bioinformatics ◽

10.1093/nargab/lqab021 ◽

2021 ◽

Vol 3 (1) ◽

Author(s):

Hitoshi Iuchi ◽

Michiaki Hamada

Keyword(s):

Gene Expression ◽

Time Series ◽

Time Course ◽

Time Series Data ◽

Expression Patterns ◽

Detection Methods ◽

Series Data ◽

Expression Levels ◽

Over Time ◽

Non Parametric

Abstract Time-course experiments using parallel sequencers have the potential to uncover gradual changes in cells over time that cannot be observed in a two-point comparison. An essential step in time-series data analysis is the identification of temporal differentially expressed genes (TEGs) under two conditions (e.g. control versus case). Model-based approaches, which are typical TEG detection methods, often set one parameter (e.g. degree or degree of freedom) for one dataset. This approach risks modeling of linearly increasing genes with higher-order functions, or fitting of cyclic gene expression with linear functions, thereby leading to false positives/negatives. Here, we present a Jonckheere–Terpstra–Kendall (JTK)-based non-parametric algorithm for TEG detection. Benchmarks, using simulation data, show that the JTK-based approach outperforms existing methods, especially in long time-series experiments. Additionally, application of JTK in the analysis of time-series RNA-seq data from seven tissue types, across developmental stages in mouse and rat, suggested that the wave pattern contributes to the TEG identification of JTK, not the difference in expression levels. This result suggests that JTK is a suitable algorithm when focusing on expression patterns over time rather than expression levels, such as comparisons between different species. These results show that JTK is an excellent candidate for TEG detection.

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How to predict relapse in leukaemia using time series data: A comparative in silico study

10.1101/2020.12.04.20243907 ◽

2020 ◽

Author(s):

Helene Hoffmann ◽

Christoph Baldow ◽

Thomas Zerjatke ◽

Andrea Gottschalk ◽

Sebastian Wagner ◽

...

Keyword(s):

Data Quality ◽

Computational Methods ◽

In Silico ◽

Prediction Accuracy ◽

Time Course ◽

Time Series Data ◽

Specific Treatment ◽

Series Data ◽

Patient Specific ◽

Clinical Markers

SummaryRisk stratification and treatment decisions for leukaemia patients are regularly based on clinical markers determined at diagnosis, while measurements on system dynamics are often neglected. However, there is increasing evidence that linking quantitative time-course information to disease outcomes can improving the predictions for patient-specific treatment response.We analyzed the potential of different computational methods to accurately predict relapse for chronic and acute myeloid leukaemia, particularly focusing on the influence of data quality and quantity. Technically, we used clinical reference data to generate in-silico patients with varying levels of data quality. Based hereon, we compared the performance of mechanistic models, generalized linear models, and neural networks with respect to their accuracy for relapse prediction. We found that data quality has a higher impact on prediction accuracy than the specific choice of the method. We further show that adapted treatment and measurement schemes can considerably improve prediction accuracy. Our proof-of-principle study highlights how computational methods and optimized data acquisition strategies can improve risk assessment and treatment of leukaemia patients.

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P–368 Dynamic metabolomic profiling during early implantation period

Human Reproduction ◽

10.1093/humrep/deab130.367 ◽

2021 ◽

Vol 36 (Supplement_1) ◽

Author(s):

Y Zhang ◽

Y W Zhao ◽

C C Wang ◽

T C Li

Keyword(s):

Mass Spectrometry ◽

Time Series ◽

Embryo Transfer ◽

Study Design ◽

Empirical Bayes ◽

Time Course ◽

Time Series Data ◽

Series Data ◽

Metabolomic Profiling ◽

Implantation Period

Abstract Study question To investigate the different metabolomic profiling in serum between pregnant and non-pregnant women during early implantation period. Summary answer Metabolomics of progesterone-related hormones enhances from ET day3 for pregnancy women compared with non-pregnancy women. What is known already Metabolomics is based on high-throughput analytical methods to identify and quantify metabolites. Compared to other omics study, metabolomics is the closest one to the phenotype, allowing the observation of dynamic changes in phenotype at specific timepoints. So far there is no published work about the metabolomics profile in human early implantation period. Study design, size, duration: Study design: comparative study. Size: 14 pregnancy women and 14 non-pregnancy women. duration: time-course. Participants/materials, setting, methods Participants: pregnancy women and unpregnancy women after embryo transfer (ET). Setting: university-based study. Methods: Peripheral blood were collected at ET day0, 3, 6 and 9. metabolomic profiling in serum by platforms of capillary electrophoresis-mass spectrometry (CE-MS) and liquid chromatography–mass spectrometry (LC-MS). Main results and the role of chance There were no statistical difference of the age, BMI, basal FSH level, endometrium thickness on the day of embryo transfer, distribution of primary and secondary fertility, embryo transfer cycle as well as the infertile types between the two groups. After deleting those with over 50% missing data, we finally have 310 metabolites into statistical analysis. Among the 310 metabolite, lipid metabolites account the largest percentage, nearly half of all metabolites. The second biggest class of metabolites in our data was organic acids. Combined results in repeated measurement ANOVA (RM-ANOVA) and ANOVA-simultaneous component analysis (ASCA) as well as multivariate empirical Bayes time-series analysis (MEBA), we finally found that progesterone-related hormones were the most important metabolites for the whole time-series data. Those significant metabolites showed a significant down regulation from ET day0 to ET day3 and up regulation from ET day3 to ET day9. Limitations, reasons for caution we have limited sample size for this study and further validation is necessary for confirmation. Wider implications of the findings: The phenomenon of upregulation of progesterone-related hormones from day3 in pregnancy group might be related to the embryo-originated hcg. Because the embryo has entered into endometrium at day3 and produced cytokines, hcg and other interaction with endometrium. Trial registration number NA

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Mathematical Model for Small Size Time Series Data of Bacterial Secondary Metabolic Pathways

Bioinformatics and Biology Insights ◽

10.1177/1177932218775076 ◽

2018 ◽

Vol 12 ◽

pp. 117793221877507 ◽

Cited By ~ 1

Author(s):

Daisuke Tominaga ◽

Hideo Kawaguchi ◽

Yoshimi Hori ◽

Tomohisa Hasunuma ◽

Chiaki Ogino ◽

...

Keyword(s):

Metabolic Pathways ◽

Time Series Data ◽

Reaction Pathway ◽

Lactate Production ◽

Reaction Rates ◽

Small Sample ◽

Dynamical Analysis ◽

Series Data ◽

Sufficient Information ◽

Parameter Values

Measuring the concentrations of metabolites and estimating the reaction rates of each reaction step consisting of metabolic pathways are significant for an improvement in microorganisms used in maximizing the production of materials. Although the reaction pathway must be identified for such an improvement, doing so is not easy. Numerous reaction steps have been reported; however, the actual reaction steps activated vary or change according to the conditions. Furthermore, to build mathematical models for a dynamical analysis, the reaction mechanisms and parameter values must be known; however, to date, sufficient information has yet to be published for many cases. In addition, experimental observations are expensive. A new mathematical approach that is applicable to small sample data, and that requires no detailed reaction information, is strongly needed. S-system is one such model that can use smaller samples than other ordinary differential equation models. We propose a simplified S-system to apply minimal quantities of samples for a dynamic analysis of the metabolic pathways. We applied the model to the phenyl lactate production pathway of Escherichia coli. The model obtained suggests that actually activated reaction steps and feedback are inhibitions within the pathway.

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Sample Entropy of Human Gait Center of Pressure Displacement: A Systematic Methodological Analysis

Entropy ◽

10.3390/e20080579 ◽

2018 ◽

Vol 20 (8) ◽

pp. 579 ◽

Cited By ~ 9

Author(s):

Samira Ahmadi ◽

Nariman Sepehri ◽

Christine Wu ◽

Tony Szturm

Keyword(s):

Time Series Data ◽

Inertial Sensors ◽

Center Of Pressure ◽

Sampling Rate ◽

Sample Entropy ◽

Human Gait ◽

Series Data ◽

Low Pass ◽

Data Points ◽

Parameter Values

Sample entropy (SampEn) has been used to quantify the regularity or predictability of human gait signals. There are studies on the appropriate use of this measure for inter-stride spatio-temporal gait variables. However, the sensitivity of this measure to preprocessing of the signal and to variant values of template size (m), tolerance size (r), and sampling rate has not been studied when applied to “whole” gait signals. Whole gait signals are the entire time series data obtained from force or inertial sensors. This study systematically investigates the sensitivity of SampEn of the center of pressure displacement in the mediolateral direction (ML COP-D) to variant parameter values and two pre-processing methods. These two methods are filtering the high-frequency components and resampling the signals to have the same average number of data points per stride. The discriminatory ability of SampEn is studied by comparing treadmill walk only (WO) to dual-task (DT) condition. The results suggest that SampEn maintains the directional difference between two walking conditions across variant parameter values, showing a significant increase from WO to DT condition, especially when signals are low-pass filtered. Moreover, when gait speed is different between test conditions, signals should be low-pass filtered and resampled to have the same average number of data points per stride.

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Inferring phage-bacteria infection networks from time series data

10.1101/051581 ◽

2016 ◽

Author(s):

Luis F. Jover ◽

Justin Romberg ◽

Joshua S. Weitz

Keyword(s):

Time Series ◽

Time Course ◽

Community Dynamics ◽

Time Series Data ◽

Plaque Assay ◽

Interaction Network ◽

Series Data ◽

Factors Affecting ◽

Evolutionary Changes

In communities with bacterial viruses (phage) and bacteria, the phage-bacteria infection network establishes which virus types infects which host types. The structure of the infection network is a key element in understanding community dynamics. Yet, this infection network is often difficult to ascertain. Introduced over 60 years ago, the plaque assay remains the gold-standard for establishing who infects whom in a community. This culture-based approach does not scale to environmental samples with increased levels of phage and bacterial diversity, much of which is currently unculturable. Here, we propose an alternative method of inferring phage-bacteria infection networks. This method uses time series data of fluctuating population densities to estimate the complete interaction network without having to test each phage-bacteria pair individually. We use in silico experiments to analyze the factors affecting the quality of network reconstruction and find robust regimes where accurate reconstructions are possible. In addition, we present a multi-experiment approach where time series from different experiments are combined to improve estimates of the infection network and mitigate against the possibility of evolutionary changes to infection during the time-course of measurement.

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Evaluating the within-host dynamics of Ranavirus infection with mechanistic disease models and experimental data

10.1101/564120 ◽

2019 ◽

Author(s):

Joseph R. Mihaljevic ◽

Amy L. Greer ◽

Jesse L. Brunner

Keyword(s):

Time Series ◽

Immune System ◽

Model Comparison ◽

Time Series Data ◽

Formal Model ◽

Immune Defense ◽

Series Data ◽

System Response ◽

Mechanistic Models ◽

Viral Titer

AbstractMechanistic models are critical for our understanding of both within-host dynamics (i.e., pathogen population growth and immune system processes) and among-host dynamics (i.e., transmission). Rarely, however, have within-host models been synthesized with data to infer processes, validate hypotheses, or generate new theories. In this study we use mechanistic models and empirical, time-series data of viral titer to better understand the growth of ranaviruses within their amphibian hosts and the immune dynamics that limit viral replication. Specifically, we fit a suite of potential models to our data, where each model represents a hypothesis about the interactions between viral growth and immune defense. Through formal model comparison, we find a parsimonious model that captures key features of our time-series data: the viral titer rises and falls through time, likely due to an immune system response, and that the initial viral dosage affects both the peak viral titer and the timing of the peak. Importantly, our model makes several predictions, including the existence of long-term viral infections, that can be validated in future studies.

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Evidence for neural rhythms embedded within binocular rivalry

Proceedings of the National Academy of Sciences ◽

10.1073/pnas.1905174116 ◽

2019 ◽

Vol 116 (30) ◽

pp. 14811-14812 ◽

Cited By ~ 2

Author(s):

Oakyoon Cha ◽

Randolph Blake

Keyword(s):

Binocular Rivalry ◽

Time Course ◽

Time Series Data ◽

Brain Activity ◽

Series Data ◽

Neural Oscillations ◽

Large Dataset ◽

Perceptual Judgments ◽

Multistable Perception ◽

Periodic Fluctuations

Evidence for perceptual periodicity emerges from studies showing periodic fluctuations in visual perception and decision making that are accompanied by neural oscillations in brain activity. We have uncovered signs of periodicity in the time course of binocular rivalry, a widely studied form of multistable perception. This was done by analyzing time series data contained in an unusually large dataset of rivalry state durations associated with states of exclusive monocular dominance and states of mixed perception during transitions between exclusive dominance. Identifiable within the varying durations of dynamic mixed perception are rhythmic clusters of durations whose incidence falls within the frequency band associated with oscillations in neural activity accompanying periodicity in perceptual judgments. Endogenous neural oscillations appear to be especially impactful when perception is unusually confounding.

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