Challenges for the identification of biological systems from in vivo time series data

Modern methods of high-throughput molecular biology render it possible to generate time series of metabolite concentrations and the expression of genes and proteins in vivo. These time profiles contain valuable information about the structure and dynamics of the underlying biological system. This information is implicit and its extraction is a challenging but ultimately very rewarding task for the mathematical modeler. Using a well-suited modeling framework, such as Biochemical Systems Theory (BST), it is possible to formulate the extraction of information as an inverse problem that in principle may be solved with a genetic algorithm or nonlinear regression. However, two types of issues associated with this inverse problem make the extraction task difficult. One type pertains to the algorithmic difficulties encountered in nonlinear regressions with moderate and large systems. The other type is of an entirely different nature. It is a consequence of assumptions that are often taken for granted in the design and analysis of mathematical models of biological systems and that need to be revisited in the context of inverse analyses. The article describes the extraction process and some of its challenges and proposes partial solutions.     

Automated Bayesian model development for frequency detection in biological time series

Background

The ability to perform quantitative studies using isotope tracers and metabolic flux analysis (MFA) is critical for detecting pathway bottlenecks and elucidating network regulation in biological systems, especially those that have been engineered to alter their native metabolic capacities. Mathematically, MFA models are traditionally formulated using separate state variables for reaction fluxes and isotopomer abundances. Analysis of isotope labeling experiments using this set of variables results in a non-convex optimization problem that suffers from both implementation complexity and convergence problems.

Results

This article addresses the mathematical and computational formulation of ¹³C MFA models using a new set of variables referred to as fluxomers. These composite variables combine both fluxes and isotopomer abundances, which results in a simply-posed formulation and an improved error model that is insensitive to isotopomer measurement normalization. A powerful fluxomer iterative algorithm (FIA) is developed and applied to solve the MFA optimization problem. For moderate-sized networks, the algorithm is shown to outperform the commonly used 13CFLUX cumomer-based algorithm and the more recently introduced OpenFLUX software that relies upon an elementary metabolite unit (EMU) network decomposition, both in terms of convergence time and output variability.

Conclusions

Substantial improvements in convergence time and statistical quality of results can be achieved by applying fluxomer variables and the FIA algorithm to compute best-fit solutions to MFA models. We expect that the fluxomer formulation will provide a more suitable basis for future algorithms that analyze very large scale networks and design optimal isotope labeling experiments.     

A distance-based dynamical transition analysis of time series signals and application to biological systems

This study demonstrates an application of distance-based numerical measures to the phase space of time series signals, in order to obtain a temporal analysis of complex dynamical systems. This method is capable of detecting alterations appearing in the characters of the deterministic dynamical systems and provides a simple tool for the real-time analysis of time series data obtained from a complex dynamical system even with black box functionality. The study presents a possible application of the method in the dynamical transition analysis of real EEG records from epilepsy patients.     

The organization of time in biological systems

A notion of organization of time similar to the notion of organization of space in architecture has been introduced. The level and pattern of organization of time in biological systems differs from that in physical and chemical systems, which presents an independent problem. Analysis of the problem leads to a new definition of life as a process of renormalization of possibilities described by a Bayes formula. This definition leads to the notion of self-monitoring as a property of every biological system, and of complicated structure of the biological present, including the physical past and physical future. This is naturally followed by determination by far past, and, hence, memory, and determination by future, i.e. preadaptation, surpassing reflection, aim-setting etc. A direct dependence of a number of elements of a complex system on its stability has been demonstrated. The self-monitoring and organization of time can be traced at various levels of biological hierarchy from intracellular to biosphere level.     

Modelling periodic oscillation of biological systems with multiple timescale networks

In this paper, we aim to develop a new methodology to model and design periodic oscillators of biological networks, in particular gene regulatory networks with multiple genes, proteins and time delays, by using multiple timescale networks (MTN). Fast reactions constitute a positive feedback-loop network (PFN), while slow reactions consist of a cyclic feedback-loop network (CFN), in MTN. Multiple timescales are exploited to simplify models according to singular perturbation theory. We show that a MTN has no stable equilibrium but stable periodic orbits when certain conditions are satisfied. Specifically, we first prove the basic properties of MTNs with only one PFN, and then generalise the result to MTNs with multiple PFNs. Finally, we design a biologically plausible gene regulatory network by the cI and Lac genes, to demonstrate the theoretical results. Since there is less restriction on the network structure of a MTN, it can be expected to apply to a wide variety of areas on the modelling, analysing and designing of biological systems.     

Detecting periodic patterns in unevenly spaced gene expression time series using Lomb-Scargle periodograms

MOTIVATION: Periodic patterns in time series resulting from biological experiments are of great interest. The commonly used Fast Fourier Transform (FFT) algorithm is applicable only when data are evenly spaced and when no values are missing, which is not always the case in high-throughput measurements. The choice of statistic to evaluate the significance of the periodic patterns for unevenly spaced gene expression time series has not been well substantiated. METHODS: The Lomb-Scargle periodogram approach is used to search time series of gene expression to quantify the periodic behavior of every gene represented on the DNA array. The Lomb-Scargle periodogram analysis provides a direct method to treat missing values and unevenly spaced time points. We propose the combination of a Lomb-Scargle test statistic for periodicity and a multiple hypothesis testing procedure with controlled false discovery rate to detect significant periodic gene expression patterns. RESULTS: We analyzed the Plasmodium falciparum gene expression dataset. In the Quality Control Dataset of 5080 expression patterns, we found 4112 periodic probes. In addition, we identified 243 probes with periodic expression in the Complete Dataset, which could not be examined in the original study by the FFT analysis due to an excessive number of missing values. While most periodic genes had a period of 48 h, some had a period close to 24 h. Our approach should be applicable for detection and quantification of periodic patterns in any unevenly spaced gene expression time-series data.     

Bayesian detection of periodic mRNA time profiles without use of training examples

Background  

Detection of periodically expressed genes from microarray data without use of known periodic and non-periodic training examples is an important problem, e.g. for identifying genes regulated by the cell-cycle in poorly characterised organisms. Commonly the investigator is only interested in genes expressed at a particular frequency that characterizes the process under study but this frequency is seldom exactly known. Previously proposed detector designs require access to labelled training examples and do not allow systematic incorporation of diffuse prior knowledge available about the period time.     

Controlled biological and biomimetic systems for landmine detection

Humanitarian demining requires to accurately detect, locate and deactivate every single landmine and other buried mine-like objects as safely and as quickly as possible, and in the most non-invasive manner. The quality of landmine detection affects directly the efficiency and safety of this process. Most of the available methods to detect explosives and landmines are limited by their sensitivity and/or operational complexities. All landmines leak with time small amounts of their explosives that can be found on surrounding ground and plant life. Hence, explosive signatures represent the robust primary indicator of landmines. Accordingly, developing innovative technologies and efficient techniques to identify in real-time explosives residue in mined areas represents an attractive and promising approach. Biological and biologically inspired detection technology has the potential to compete with or be used in conjunction with other artificial technology to complement performance strengths. Biological systems are sensitive to many different scents concurrently, a property that has proven difficult to replicate artificially. Understanding biological systems presents unique opportunities for developing new capabilities through direct use of trained bio-systems, integration of living and non-living components, or inspiring new design by mimicking biological capabilities. It is expected that controlled bio-systems, biotechnology and microbial techniques will contribute to the advancement of mine detection and other application domains. This paper provides directions, evaluation and analysis on the progress of controlled biological and biomimetic systems for landmine detection. It introduces and discusses different approaches developed, underlining their relative advantages and limitations, and highlighting trends, safety and ecology concern, and possible future directions.     

A benchmark test of accuracy and precision in estimating dynamical systems characteristics from a time series

Characteristics of dynamical systems are often estimated to describe physiological processes. For instance, Lyapunov exponents have been determined to assess the stability of the cardio-vascular system, respiration, and, more recently, human gait and posture. However, the systematic evaluation of the accuracy and precision of these estimates is problematic because the proper values of the characteristics are typically unknown. We fill this void with a set of standardized time series with well-defined dynamical characteristics that serve as a benchmark. Estimates ought to match these characteristics, at least to good approximation. We outline a procedure to employ this generic benchmark test and illustrate its capacity by examining methods for estimating the maximum Lyapunov exponent. In particular, we discuss algorithms by Wolf and co-workers and by Rosenstein and co-workers and evaluate their performances as a function of signal length and signal-to-noise ratio. In all scenarios, the precision of Rosenstein's algorithm was found to be equal to or greater than Wolf's algorithm. The latter, however, appeared more accurate if reasonably large signal lengths are available and noise levels are sufficiently low. Due to its modularity, the presented benchmark test can be used to evaluate and tune any estimation method to perform optimally for arbitrary experimental data.