7,297 research outputs found
A novel cost function to estimate parameters of oscillatory biochemical systems
Oscillatory pathways are among the most important classes of biochemical systems with examples ranging from circadian rhythms and cell cycle maintenance. Mathematical modeling of these highly interconnected biochemical networks is needed to meet numerous objectives such as investigating, predicting and controlling the dynamics of these systems. Identifying the kinetic rate parameters is essential for fully modeling these and other biological processes. These kinetic parameters, however, are not usually available from measurements and most of them have to be estimated by parameter fitting techniques. One of the issues with estimating kinetic parameters in oscillatory systems is the irregularities in the least square (LS) cost function surface used to estimate these parameters, which is caused by the periodicity of the measurements. These irregularities result in numerous local minima, which limit the performance of even some of the most robust global optimization algorithms. We proposed a parameter estimation framework to address these issues that integrates temporal information with periodic information embedded in the measurements used to estimate these parameters. This periodic information is used to build a proposed cost function with better surface properties leading to fewer local minima and better performance of global optimization algorithms. We verified for three oscillatory biochemical systems that our proposed cost function results in an increased ability to estimate accurate kinetic parameters as compared to the traditional LS cost function. We combine this cost function with an improved noise removal approach that leverages periodic characteristics embedded in the measurements to effectively reduce noise. The results provide strong evidence on the efficacy of this noise removal approach over the previous commonly used wavelet hard-thresholding noise removal methods. This proposed optimization framework results in more accurate kinetic parameters that will eventually lead to biochemical models that are more precise, predictable, and controllable
Inferring rate coefficents of biochemical reactions from noisy data with KInfer
Dynamical models of inter- and intra-cellular processes contain the rate constants of the biochemical reactions. These kinetic parameters are often not accessible directly through experiments, but they can be inferred from time-resolved data. Time resolved data, that is, measurements of reactant concentration at series of time points, are usually affected by different types of error, whose source can be both experimental and biological. The noise in the input data makes the estimation of the model parameters a very difficult task, as if the inference method is not sufficiently robust to the noise, the resulting estimates are not reliable. Therefore "noise-robust" methods that estimate rate constants with the maximum precision and accuracy are needed. In this report we present the probabilistic generative model of parameter inference implemented by the software prototype KInfer and we show the ability of this tool of estimating the rate coefficients of models of biochemical network with a good accuracy even from very noisy input data
Cellular signaling networks function as generalized Wiener-Kolmogorov filters to suppress noise
Cellular signaling involves the transmission of environmental information
through cascades of stochastic biochemical reactions, inevitably introducing
noise that compromises signal fidelity. Each stage of the cascade often takes
the form of a kinase-phosphatase push-pull network, a basic unit of signaling
pathways whose malfunction is linked with a host of cancers. We show this
ubiquitous enzymatic network motif effectively behaves as a Wiener-Kolmogorov
(WK) optimal noise filter. Using concepts from umbral calculus, we generalize
the linear WK theory, originally introduced in the context of communication and
control engineering, to take nonlinear signal transduction and discrete
molecule populations into account. This allows us to derive rigorous
constraints for efficient noise reduction in this biochemical system. Our
mathematical formalism yields bounds on filter performance in cases important
to cellular function---like ultrasensitive response to stimuli. We highlight
features of the system relevant for optimizing filter efficiency, encoded in a
single, measurable, dimensionless parameter. Our theory, which describes noise
control in a large class of signal transduction networks, is also useful both
for the design of synthetic biochemical signaling pathways, and the
manipulation of pathways through experimental probes like oscillatory input.Comment: 15 pages, 5 figures; to appear in Phys. Rev.
Global parameter identification of stochastic reaction networks from single trajectories
We consider the problem of inferring the unknown parameters of a stochastic
biochemical network model from a single measured time-course of the
concentration of some of the involved species. Such measurements are available,
e.g., from live-cell fluorescence microscopy in image-based systems biology. In
addition, fluctuation time-courses from, e.g., fluorescence correlation
spectroscopy provide additional information about the system dynamics that can
be used to more robustly infer parameters than when considering only mean
concentrations. Estimating model parameters from a single experimental
trajectory enables single-cell measurements and quantification of cell--cell
variability. We propose a novel combination of an adaptive Monte Carlo sampler,
called Gaussian Adaptation, and efficient exact stochastic simulation
algorithms that allows parameter identification from single stochastic
trajectories. We benchmark the proposed method on a linear and a non-linear
reaction network at steady state and during transient phases. In addition, we
demonstrate that the present method also provides an ellipsoidal volume
estimate of the viable part of parameter space and is able to estimate the
physical volume of the compartment in which the observed reactions take place.Comment: Article in print as a book chapter in Springer's "Advances in Systems
Biology
A temporal switch model for estimating transcriptional activity in gene expression
Motivation: The analysis and mechanistic modelling of time series gene expression data provided by techniques such as microarrays, NanoString, reverse transcription–polymerase chain reaction and advanced sequencing are invaluable for developing an understanding of the variation in key biological processes. We address this by proposing the estimation of a flexible dynamic model, which decouples temporal synthesis and degradation of mRNA and, hence, allows for transcriptional activity to switch between different states.
Results: The model is flexible enough to capture a variety of observed transcriptional dynamics, including oscillatory behaviour, in a way that is compatible with the demands imposed by the quality, time-resolution and quantity of the data. We show that the timing and number of switch events in transcriptional activity can be estimated alongside individual gene mRNA stability with the help of a Bayesian reversible jump Markov chain Monte Carlo algorithm. To demonstrate the methodology, we focus on modelling the wild-type behaviour of a selection of 200 circadian genes of the model plant Arabidopsis thaliana. The results support the idea that using a mechanistic model to identify transcriptional switch points is likely to strongly contribute to efforts in elucidating and understanding key biological processes, such as transcription and degradation
Sensitivity analysis of oscillator models in the space of phase-response curves: Oscillators as open systems
Oscillator models are central to the study of system properties such as
entrainment or synchronization. Due to their nonlinear nature, few
system-theoretic tools exist to analyze those models. The paper develops a
sensitivity analysis for phase-response curves, a fundamental one-dimensional
phase reduction of oscillator models. The proposed theoretical and numerical
analysis tools are illustrated on several system-theoretic questions and models
arising in the biology of cellular rhythms
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