Steady-state fluctuations of a genetic feedback loop:an exact solution

Genetic feedback loops in cells break detailed balance and involve bimolecular reactions; hence exact solutions revealing the nature of the stochastic fluctuations in these loops are lacking. We here consider the master equation for a gene regulatory feedback loop: a gene produces protein which then binds to the promoter of the same gene and regulates its expression. The protein degrades in its free and bound forms. This network breaks detailed balance and involves a single bimolecular reaction step. We provide an exact solution of the steady-state master equation for arbitrary values of the parameters, and present simplified solutions for a number of special cases. The full parametric dependence of the analytical non-equilibrium steady-state probability distribution is verified by direct numerical solution of the master equations. For the case where the degradation rate of bound and free protein is the same, our solution is at variance with a previous claim of an exact solution (Hornos et al, Phys. Rev. E {\bf 72}, 051907 (2005) and subsequent studies). We show explicitly that this is due to an unphysical formulation of the underlying master equation in those studies.Comment: 31 pages, 3 figures. Accepted for publication in the Journal of Chemical Physics (2012

Sampling bias in systems with structural heterogeneity and limited internal diffusion

Complex systems research is becomingly increasingly data-driven, particularly in the social and biological domains. Many of the systems from which sample data are collected feature structural heterogeneity at the mesoscopic scale (i.e. communities) and limited inter-community diffusion. Here we show that the interplay between these two features can yield a significant bias in the global characteristics inferred from the data. We present a general framework to quantify this bias, and derive an explicit corrective factor for a wide class of systems. Applying our analysis to a recent high-profile survey of conflict mortality in Iraq suggests a significant overestimate of deaths

Accurate discretization of advection-diffusion equations

We present an exact mathematical transformation which converts a wide class of advection-diffusion equations into a form allowing simple and direct spatial discretization in all dimensions, and thus the construction of accurate and more efficient numerical algorithms. These discretized forms can also be viewed as master equations which provides an alternative mesoscopic interpretation of advection-diffusion processes in terms of diffusion with spatially varying hopping rates

Generation of a porous scaffold with a starting composition in the CaO-SiO2-MgO-P2O5 system in a simulated physiological environment

Magnesium-based ceramics are involved in orthopedic applications such as bone scaffolds or implant coatings. They provide structural support to cells for bone ingrowth, but highly porous matrices cannot resist severe mechanical stress during implantation. In this study, the laser floating zone (LFZ) technique is used to prepare a dense crystalline material with composition in the CaO-SiO2-MgO-P2O5 system. This material, under physiological conditions, is able to generate a porous scaffold controlled by the dissolution of the MgO phase, meeting the mechanical advantages of a dense material and the biological features of a porous scaffold. FESEM (Field emission scanning electron microscopy), XRD (X-ray Diffraction), EDS (Energy Dispersive X-rays spectroscopy), and ICP ((Inductively Coupled Plasma) analysis were carried out in order to characterize the samples before and after immersion in simulated body fluid (SBF)

The applicability of the social enterprise in a small state : the case of Malta

The main objective of this study is to assess the social, financial and corporate governance (CG) implications of the proposed social enterprise (SE) legislation in Malta. In light of such implications, the study also assesses the applicability of the SE under such legislation. A mixed methodology was adopted. Fifteen interviews were held with experts. Such data was supplemented by 52 valid responses to a questionnaire sent both to co-operatives and voluntary organisations (VOs) in Malta. The study concludes that the proposed legislation has various positive social, financial and CG implications and that the SE, as being proposed, is applicable and filling a void within the Maltese environment. Although such legislation offers both a new legal form and a label, its reference to the Companies Act which ignores SEs’ unique social dimension is questionable. Alternatively, a holistic SE regulatory framework may be developed. Furthermore, statutory thresholds, such as for dividend distribution and trade income, are to be possibly rendered more flexible. This study aspires to raise awareness about the implications of a proposed regulatory framework in Malta, hence hopefully promoting the application of the concept.peer-reviewe

Effects of bursty protein production on the noisy oscillatory properties of downstream pathways

Experiments show that proteins are translated in sharp bursts; similar bursty phenomena have been observed for protein import into compartments. Here we investigate the effect of burstiness in protein expression and import on the stochastic properties of downstream pathways. We consider two identical pathways with equal mean input rates, except in one pathway proteins are input one at a time and in the other proteins are input in bursts. Deterministically the dynamics of these two pathways are indistinguishable. However the stochastic behavior falls in three categories: (i) both pathways display or do not display noise-induced oscillations; (ii) the non-bursty input pathway displays noise-induced oscillations whereas the bursty one does not; (iii) the reverse of (ii). We derive necessary conditions for these three cases to classify systems involving autocatalysis, trimerization and genetic feedback loops. Our results suggest that single cell rhythms can be controlled by regulation of burstiness in protein production

Respirometric assessment of bacterial kinetics in algae-bacteria and activated sludge processes

Algae-bacteria (AB) consortia can be exploited for effective wastewater treatment, based on photosynthetic oxygenation to reduce energy requirements for aeration. While algal kinetics have been extensively evaluated, bacterial kinetics in AB systems are still based on parameters taken from the activated sludge models, lacking an experimental validation for AB consortia. A respirometric procedure was therefore proposed, to estimate bacterial kinetics in both activated sludge and AB, under different conditions of temperature, pH, dissolved oxygen, and substrate availability. Bacterial activities were differently influenced by operational/environmental conditions, suggesting that the adoption of typical activated sludge parameters could be inadequate for AB modelling. Indeed, respirometric results show that bacteria in AB consortia were adapted to a wider range of conditions, compared to activated sludge, confirming that a dedicated calibration of bacterial kinetics is essential for effectively modelling AB systems, and respirometry was proven to be a powerful and reliable tool to this purpose

Parameter estimation for biochemical reaction networks using Wasserstein distances

We present a method for estimating parameters in stochastic models of biochemical reaction networks by fitting steady-state distributions using Wasserstein distances. We simulate a reaction network at different parameter settings and train a Gaussian process to learn the Wasserstein distance between observations and the simulator output for all parameters. We then use Bayesian optimization to find parameters minimizing this distance based on the trained Gaussian process. The effectiveness of our method is demonstrated on the three-stage model of gene expression and a genetic feedback loop for which moment-based methods are known to perform poorly. Our method is applicable to any simulator model of stochastic reaction networks, including Brownian Dynamics.Comment: 22 pages, 8 figures. Slight modifications/additions to the text; added new section (Section 4.4) and Appendi

A characteristic lengthscale causes anomalous size effects and boundary programmability in mechanical metamaterials

The architecture of mechanical metamaterialsis designed to harness geometry, non-linearity and topology to obtain advanced functionalities such as shape morphing, programmability and one-way propagation. While a purely geometric framework successfully captures the physics of small systems under idealized conditions, large systems or heterogeneous driving conditions remain essentially unexplored. Here we uncover strong anomalies in the mechanics of a broad class of metamaterials, such as auxetics, shape-changers or topological insulators: a non-monotonic variation of their stiffness with system size, and the ability of textured boundaries to completely alter their properties. These striking features stem from the competition between rotation-based deformations---relevant for small systems---and ordinary elasticity, and are controlled by a characteristic length scale which is entirely tunable by the architectural details. Our study provides new vistas for designing, controlling and programming the mechanics of metamaterials in the thermodynamic limit.Comment: Main text has 4 pages, 4 figures + Methods and Supplementary Informatio