Evaluation of stochastic effects on biomolecular networks using the generalised Nyquist stability criterion

Abstract—Stochastic differential equations are now commonly used to model biomolecular networks in systems biology, and much recent research has been devoted to the development of methods to analyse their stability properties. Stability analysis of such systems may be performed using the Laplace transform, which requires the calculation of the exponential matrix involving time symbolically. However, the calculation of the symbolic exponential matrix is not feasible for problems of even moderate size, as the required computation time increases exponentially with the matrix order. To address this issue, we present a novel method for approximating the Laplace transform which does not require the exponential matrix to be calculated explicitly. The calculation time associated with the proposed method does not increase exponentially with the size of the system, and the approximation error is shown to be of the same order as existing methods. Using this approximation method, we show how a straightforward application of the generalized Nyquist stability criterion provides necessary and sufficient conditions for the stability of stochastic biomolecular networks. The usefulness and computational efficiency of the proposed method is illustrated through its application to the problem of analysing a model for limit-cycle oscillations in cAMP during aggregation of Dictyostelium cells

Robustness analysis of magnetic torquer controlled spacecraft attitude dynamics

This paper describes a systematic approach to the robustness analysis of linear periodically time-varying (LPTV) systems. The method uses the technique known as Lifting to transform the original time-varying uncertain system into linear fractional transformation (LFT) form. The stability and performance robustness of the system to structured parametric uncertainty can then be analysed non-conservatively using the structured singular value μ. The method is applied to analyse the stability robustness of an attitude control law for a spacecraft controlled by magnetic torquer bars, whose linearised dynamics can naturally be written in linear periodically time-varying form. The proposed method allows maximum allowable levels of uncertainty, as well as worst-case uncertainty combinations to be computed. The destabilising effect of these uncertain parameter combinations is verified in time-domain simulations

Validation of a model of regulation in the tryptophan operon against multiple experiment data using global optimisation

This paper is concerned with validating a mathematical model of regulation in the tryptophan operon using global optimization. Although a number of models for this biochemical network are proposed, in many cases only qualitative agreement between the model output and experimental data was demonstrated, since very little information is currently available to guide the selection of parameter values for the models. This paper presents a model validating method using both multiple experimental data and global optimization

A geometrical formulation of the μ-lower bound problem

A new problem formulation for the structured singular value μ in the case of purely real (possibly repeated) uncertainties is presented. The approach is based on a geometrical interpretation of the singularity constraint arising in the μ lower bound problem. An interesting feature of this problem formulation is that the resulting parametric search space is independent of the number of times any parameter is repeated in the structured uncertainty matrix. A corresponding lower bound algorithm combining randomisation and optimisation methods is developed, and some probabilistic performance guarantees are derived. The potential usefulness of the proposed approach is demonstrated on two high-order real μ analysis problems from the aerospace and systems biology literature

Magnetic Field Induced Charged Exciton Studies in a GaAs/Al(0.3)Ga(0.7)As Single Heterojunction

The magnetophotoluminescence (MPL) behavior of a GaAs/Al(0.3)Ga(0.7)As single heterojunction has been investigated to 60T. We observed negatively charged singlet and triplet exciton states that are formed at high magnetic fields beyond the nu=1 quantum Hall state. The variation of the charged exciton binding energies are in good agreement with theoretical predictions. The MPL transition intensities for these states showed intensity variations (maxima and minima) at the nu=1/3 and 1/5 fractional quantum Hall (FQH) state as a consequence of a large reduction of electron-hole screening at these filling factors.Comment: submitted to Phys. Rev. Let

Least-squares methods for identifying biochemical regulatory networks from noisy measurements

<b>Background</b>: We consider the problem of identifying the dynamic interactions in biochemical networks from noisy experimental data. Typically, approaches for solving this problem make use of an estimation algorithm such as the well-known linear Least-Squares (LS) estimation technique. We demonstrate that when time-series measurements are corrupted by white noise and/or drift noise, more accurate and reliable identification of network interactions can be achieved by employing an estimation algorithm known as Constrained Total Least Squares (CTLS). The Total Least Squares (TLS) technique is a generalised least squares method to solve an overdetermined set of equations whose coefficients are noisy. The CTLS is a natural extension of TLS to the case where the noise components of the coefficients are correlated, as is usually the case with time-series measurements of concentrations and expression profiles in gene networks. <b>Results</b>: The superior performance of the CTLS method in identifying network interactions is demonstrated on three examples: a genetic network containing four genes, a network describing p53 activity and <i>mdm2</i> messenger RNA interactions, and a recently proposed kinetic model for interleukin (IL)-6 and (IL)-12b messenger RNA expression as a function of ATF3 and NF-κB promoter binding. For the first example, the CTLS significantly reduces the errors in the estimation of the Jacobian for the gene network. For the second, the CTLS reduces the errors from the measurements that are corrupted by white noise and the effect of neglected kinetics. For the third, it allows the correct identification, from noisy data, of the negative regulation of (IL)-6 and (IL)-12b by ATF3. <b>Conclusion</b>: The significant improvements in performance demonstrated by the CTLS method under the wide range of conditions tested here, including different levels and types of measurement noise and different numbers of data points, suggests that its application will enable more accurate and reliable identification and modelling of biochemical networks

Chemical signatures of the Anthropocene in the Clyde Estuary, UK: sediment hosted Pb, 207/206 Pb, Total Petroleum Hydrocarbons (TPH), Polyaromatic Hydrocarbon (PAH) and Polychlorinated Bipheny (PCB) pollution records

The sediment concentrations of total petroleum hydrocarbons (TPHs), polyaromatic hydrocarbons (PAHs), polychlorinated biphenyls (PCBs), Pb and 207/206Pb isotope ratios were measured in seven cores from the middle Clyde estuary (Scotland, UK) with an aim of tracking the late Anthropocene. Concentrations of TPHs ranged from 34 to 4386 mg kg−1, total PAHs from 19 to 16 163 μg kg−1 and total PCBs between less than 4.3 to 1217 μg kg−1. Inventories, distributions and isomeric ratios of the organic pollutants were used to reconstruct pollutant histories. Pre-Industrial Revolution and modern non-polluted sediments were characterized by low TPH and PAH values as well as high relative abundance of biogenic-sourced phenanthrene and naphthalene. The increasing industrialization of the Clyde gave rise to elevated PAH concentrations and PAH isomeric ratios characteristic of both grass/wood/coal and petroleum and combustion (specifically petroleum combustion). Overall, PAHs had the longest history of any of the organic contaminants. Increasing TPH concentrations and a concomitant decline in PAHs mirrored the lessening of coal use and increasing reliance on petroleum fuels from about the 1950s. Thereafter, declining hydrocarbon pollution was followed by the onset (1950s), peak (1965–1977) and decline (post-1980s) in total PCB concentrations. Lead concentrations ranged from 6 to 631 mg kg−1, while 207/206Pb isotope ratios spanned 0.838–0.876, indicative of various proportions of ‘background’, British ore/coal and Broken Hill type petrol/industrial lead. A chronology was established using published Pb isotope data for aerosol-derived Pb and applied to the cores

NMR quantum computation with indirectly coupled gates

An NMR realization of a two-qubit quantum gate which processes quantum information indirectly via couplings to a spectator qubit is presented in the context of the Deutsch-Jozsa algorithm. This enables a successful comprehensive NMR implementation of the Deutsch-Jozsa algorithm for functions with three argument bits and demonstrates a technique essential for multi-qubit quantum computation.Comment: 9 pages, 2 figures. 10 additional figures illustrating output spectr

Standards Education Policy Development: Observations based on APEC Research

This paper stems from a research project carried out for the Asia Pacific Economic Cooperation (APEC) to make an inventory of national standards education policies. Twenty countries - sixteen Asia-Pacific economies and four European nations – have been investigated. The paper relates similarities and differences between these policies to the standardization education activities in place. The paper concludes with policy recommendations