Dynamical robustness of biological networks with hierarchical distribution of time scales

We propose the concepts of distributed robustness and r-robustness, well adapted to functional genetics. Then we discuss the robustness of the relaxation time using a chemical reaction description of genetic and signalling networks. First, we obtain the following result for linear networks: for large multiscale systems with hierarchical distribution of time scales the variance of the inverse relaxation time (as well as the variance of the stationary rate) is much lower than the variance of the separate constants. Moreover, it can tend to 0 faster than 1/n, where n is the number of reactions. We argue that similar phenomena are valid in the nonlinear case as well. As a numerical illustration we use a model of signalling network that can be applied to important transcription factors such as NFkB

Synthetic Mechanochemical Molecular Swimmer

A minimal design for a molecular swimmer is proposed that is a based on a mechanochemical propulsion mechanism. Conformational changes are induced by electrostatic actuation when specific parts of the molecule temporarily acquire net charges through catalyzed chemical reactions involving ionic components. The mechanochemical cycle is designed such that the resulting conformational changes would be sufficient for achieving low Reynolds number propulsion. The system is analyzed within the recently developed framework of stochastic swimmers to take account of the noisy environment at the molecular scale. The swimming velocity of the device is found to depend on the concentration of the fuel molecule according to the Michaelis-Menten rule in enzymatic reactions.Comment: 4 pages, 3 figure

Properties of Random Complex Chemical Reaction Networks and Their Relevance to Biological Toy Models

We investigate the properties of large random conservative chemical reaction networks composed of elementary reactions endowed with either mass-action or saturating kinetics, assigning kinetic parameters in a thermodynamically-consistent manner. We find that such complex networks exhibit qualitatively similar behavior when fed with external nutrient flux. The nutrient is preferentially transformed into one specific chemical that is an intrinsic property of the network. We propose a self-consistent proto-cell toy model in which the preferentially synthesized chemical is a precursor for the cell membrane, and show that such proto-cells can exhibit sustainable homeostatic growth when fed with any nutrient diffusing through the membrane, provided that nutrient is metabolized at a sufficient rate

Deconvolving the Wedge: Maximum-Likelihood Power Spectra via Spherical-Wave Visibility Modeling

Direct detection of the Epoch of Reionization (EoR) via the red-shifted 21-cm line will have unprecedented implications on the study of structure formation in the infant Universe. To fulfill this promise, current and future 21-cm experiments need to detect this weak EoR signal in the presence of foregrounds that are several orders of magnitude larger. This requires extreme noise control and improved wide-field high dynamic-range imaging techniques. We propose a new imaging method based on a maximum likelihood framework which solves for the interferometric equation directly on the sphere, or equivalently in the $uvw$-domain. The method uses the one-to-one relation between spherical waves and spherical harmonics (SpH). It consistently handles signals from the entire sky, and does not require a $w$-term correction. The spherical-harmonics coefficients represent the sky-brightness distribution and the visibilities in the $uvw$-domain, and provide a direct estimate of the spatial power spectrum. Using these spectrally-smooth SpH coefficients, bright foregrounds can be removed from the signal, including their side-lobe noise, which is one of the limiting factors in high dynamics range wide-field imaging. Chromatic effects causing the so-called "wedge" are effectively eliminated (i.e. deconvolved) in the cylindrical ($k_{\perp}, k_{\parallel}$) power spectrum, compared to a power spectrum computed directly from the images of the foreground visibilities where the wedge is clearly present. We illustrate our method using simulated LOFAR observations, finding an excellent reconstruction of the input EoR signal with minimal bias.Comment: 13 pages, 8 figures. Replaced to match accepted MNRAS version; few typos corrected & textual clarification added (no changes to results