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

Robust shape control in a sendzimir cold-rolling steel mill

The shape control problem for a Sendzimir 20-roll cold rolling steel mill is characterised by operation over a wide range of conditions arising from roll changes, changes in rolling schedules and changes in material gauge, width and hardness. Previous approaches to the problem suggest storing a large number of precompensator matrices to cater for the full range of operating conditions. This paper, on the other hand, attempts to synthesise a controller which is optimally robust to changes in the conditions associated with the rolling cluster, resulting in a reduced storage requirement for the controlling computer. The performance of the robust controller is evaluated via nonlinear simulation

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

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

Computer simulation clarifies mechanisms of carbon dioxide clearance during apnoea

BackgroundApnoeic oxygenation can come close to matching the oxygen demands of the apnoeic patient but does not facilitate carbon dioxide (CO2) elimination, potentially resulting in dangerous hypercapnia. Numerous studies have shown that high-flow nasal oxygen administration prevents hypoxaemia, and appears to reduce the rate of increase of arterial CO2 partial pressure (PaCO2), but evidence is lacking to explain these effects.MethodsWe extended a high-fidelity computational simulation of cardiopulmonary physiology to include modules allowing variable effects of: (a) cardiogenic oscillations affecting intrathoracic gas spaces, (b) gas mixing within the anatomical dead space, (c) insufflation into the trachea or above the glottis, and (d) pharyngeal pressure oscillation. We validated this model by reproducing the methods and results of five clinical studies on apnoeic oxygenation.ResultsSimulated outputs best matched clinical data for model selection of parameters reflecting: (a) significant effects of cardiogenic oscillations on alveoli, both in terms of strength of the effect (4.5 cm H2O) and percentage of alveoli affected (60%), (b) augmented gas mixing within the anatomical dead space, and (c) pharyngeal pressure oscillations between 0 and 2 cm H2O at 70 Hz.ConclusionsCardiogenic oscillations, dead space gas mixing, and micro-ventilation induced by pharyngeal pressure variations appear to be important mechanisms that combine to facilitate the clearance of CO2 during apnoea. Evolution of high-flow oxygen insufflation devices should take advantage of these insights, potentially improving apnoeic gas exchange

Stellar structure and compact objects before 1940: Towards relativistic astrophysics

Since the mid-1920s, different strands of research used stars as "physics laboratories" for investigating the nature of matter under extreme densities and pressures, impossible to realize on Earth. To trace this process this paper is following the evolution of the concept of a dense core in stars, which was important both for an understanding of stellar evolution and as a testing ground for the fast-evolving field of nuclear physics. In spite of the divide between physicists and astrophysicists, some key actors working in the cross-fertilized soil of overlapping but different scientific cultures formulated models and tentative theories that gradually evolved into more realistic and structured astrophysical objects. These investigations culminated in the first contact with general relativity in 1939, when J. Robert Oppenheimer and his students George Volkoff and Hartland Snyder systematically applied the theory to the dense core of a collapsing neutron star. This pioneering application of Einstein's theory to an astrophysical compact object can be regarded as a milestone in the path eventually leading to the emergence of relativistic astrophysics in the early 1960s.Comment: 83 pages, 4 figures, submitted to the European Physical Journal

First observation of the decay Bˉs0→D0K∗0\bar{B}^0_s \to D^0 K^{*0} and a measurement of the ratio of branching fractions B(Bˉs0→D0K∗0)B(Bˉ0→D0ρ0)\frac{{\cal B}(\bar{B}^0_s \to D^0 K^{*0})}{{\cal B}(\bar{B}^0 \to D^0 \rho^0)}

The first observation of the decay $\bar{B}^0_s \to D^0 K^{*0}$ using $pp$ data collected by the LHCb detector at a centre-of-mass energy of 7 TeV, corresponding to an integrated luminosity of 36 pb$^{-1}$, is reported. A signal of $34.4 \pm 6.8$ events is obtained and the absence of signal is rejected with a statistical significance of more than nine standard deviations. The $\bar{B}^0_s \to D^0 K^{*0}$ branching fraction is measured relative to that of $\bar{B}^0 \to D^0 \rho^0$: $\frac{{\cal B}(\bar{B}^0_s \to D^0 K^{*0})}{{\cal B}(\bar{B}^0 \to D^0 \rho^0)} = 1.48 \pm 0.34 \pm 0.15 \pm 0.12$, where the first uncertainty is statistical, the second systematic and the third is due to the uncertainty on the ratio of the $B^0$ and $B^0_s$ hadronisation fractions.Comment: 10 pages, 3 figures, submitted to Phys. Lett. B; ISSN 0370-269