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

On Signatures of Atmospheric Features in Thermal Phase Curves of Hot Jupiters

Turbulence is ubiquitous in Solar System planetary atmospheres. In hot Jupiter atmospheres, the combination of moderately slow rotation and thick pressure scale height may result in dynamical weather structures with unusually large, planetary-size scales. Using equivalent-barotropic, turbulent circulation models, we illustrate how such structures can generate a variety of features in the thermal phase curves of hot Jupiters, including phase shifts and deviations from periodicity. Such features may have been spotted in the recent infrared phase curve of HD 189733b. Despite inherent difficulties with the interpretation of disk-integrated quantities, phase curves promise to offer unique constraints on the nature of the circulation regime present on hot Jupiters.Comment: 22 pages, 6 figures, 1 table, accepted for publication in Ap

Robustness analysis of network modularity

Modules are commonly observed functional units in large-scale networks and the dynamics of networks are closely related to the organization of such modules. Modularity analysis has been widely used to investigate the organizing principle of complex networks. The information about network topology needed for such modularity analysis is, however, not complete in many real world networks. We noted that network structure is often reconstructed based on partial observation and therefore it is re-organized as more information is collected. Hence, it is critical to evaluate the robustness of network modules with respect to uncertainties. For this purpose, we have developed a robustness bounds algorithm that provides an estimation of the unknown minimal perturbation, which breaks down the original modularity. The proposed algorithm is computationally efficient and provides valuable information about the robustness of modularity for large-scale network analysis

Modelling spatially regulated B-catenin dynamics & invasion in intestinal crypts

Experimental data (e.g., genetic lineage and cell population studies) on intestinal crypts reveal that regulatory features of crypt behavior, such as control via morphogen gradients, are remarkably well conserved among numerous organisms (e.g., from mouse and rat to human) and throughout the different regions of the small and large intestines. In this article, we construct a partial differential equation model of a single colonic crypt that describes the spatial distribution of Wnt pathway proteins along the crypt axis. The novelty of our continuum model is that it is based upon assumptions that can be directly related to processes at the cellular and subcellular scales. We use the model to predict how the distributions of Wnt pathway proteins are affected by mutations. The model is then extended to investigate how mutant cell populations can invade neighboring crypts. The model simulations suggest that cell crowding caused by increased proliferation and decreased cell loss may be sufficient for a mutant cell population to colonize a neighboring healthy crypt

Color Reflection Invariance and Monopole Condensation in QCD

We review the quantum instability of the Savvidy-Nielsen-Olesen (SNO) vacuum of the one-loop effective action of SU(2) QCD, and point out a critical defect in the calculation of the functional determinant of the gluon loop in the SNO effective action. We prove that the gauge invariance, in particular the color reflection invariance, exclude the unstable tachyonic modes from the gluon loop integral. This guarantees the stability of the magnetic condensation in QCD.Comment: 28 pages, 3 figures, JHEP styl