Semi-quantitative stability analysis constrains saturation levels in metabolic networks

Recently structural kinetic modeling has been proposed as an intermediary approach between a full kinetic descrip- tion of metabolic networks and a static constrained-based analysis of them. It extends the null-space analysis by a local stability analysis yielding a parametrization of the Jacobian in terms of saturation levels of the involved re- actions with respect to their substrate metabolite concen- tration. These levels are normalized and stay within well- defined bounds for every reaction. We utilize results from robust control theory to determine subintervals of satu- ration levels that render the steady state asymptotically stable. In particular we apply Kharitonov's theorem and parametric Lyapunov functions in conjunction with inter- val computation. A glycolytic pathway model comprising 12 reactions is used to illustrate the method

Statistics of Partial Minima

Motivated by multi-objective optimization, we study extrema of a set of N points independently distributed inside the d-dimensional hypercube. A point in this set is k-dominated by another point when at least k of its coordinates are larger, and is a k-minimum if it is not k-dominated by any other point. We obtain statistical properties of these partial minima using exact probabilistic methods and heuristic scaling techniques. The average number of partial minima, A, decays algebraically with the total number of points, A ~ N^{-(d-k)/k}, when 1<=k<d. Interestingly, there are k-1 distinct scaling laws characterizing the largest coordinates as the distribution P(y_j) of the jth largest coordinate, y_j, decays algebraically, P(y_j) ~ (y_j)^{-alpha_j-1}, with alpha_j=j(d-k)/(k-j) for 1<=j<=k-1. The average number of partial minima grows logarithmically, A ~ [1/(d-1)!](ln N)^{d-1}, when k=d. The full distribution of the number of minima is obtained in closed form in two-dimensions.Comment: 6 pages, 1 figur

Quantitative insights into the cyanobacterial cell economy

© Zavřel et al. Phototrophic microorganisms are promising resources for green biotechnology. Compared to heterotrophic microorganisms, however, the cellular economy of phototrophic growth is still insufficiently understood. We provide a quantitative analysis of light-limited, light-saturated, and light-inhibited growth of the cyanobacterium Synechocystis sp. PCC 6803 using a reproducible cultivation setup. We report key physiological parameters, including growth rate, cell size, and photosynthetic activity over a wide range of light intensities. Intracellular proteins were quantified to monitor proteome allocation as a function of growth rate. Among other physiological acclimations, we identify an upregulation of the translational machinery and downregulation of light harvesting components with increasing light intensity and growth rate. The resulting growth laws are discussed in the context of a coarse-grained model of phototrophic growth and available data obtained by a comprehensive literature search. Our insights into quantitative aspects of cyanobacterial acclimations to different growth rates have implications to understand and optimize photosynthetic productivity

Mean-risk models using two risk measures: A multi-objective approach

This paper proposes a model for portfolio optimisation, in which distributions are characterised and compared on the basis of three statistics: the expected value, the variance and the CVaR at a specified confidence level. The problem is multi-objective and transformed into a single objective problem in which variance is minimised while constraints are imposed on the expected value and CVaR. In the case of discrete random variables, the problem is a quadratic program. The mean-variance (mean-CVaR) efficient solutions that are not dominated with respect to CVaR (variance) are particular efficient solutions of the proposed model. In addition, the model has efficient solutions that are discarded by both mean-variance and mean-CVaR models, although they may improve the return distribution. The model is tested on real data drawn from the FTSE 100 index. An analysis of the return distribution of the chosen portfolios is presented

Estimating Mutual Information

We present two classes of improved estimators for mutual information $M(X,Y)$, from samples of random points distributed according to some joint probability density $\mu(x,y)$. In contrast to conventional estimators based on binnings, they are based on entropy estimates from $k$-nearest neighbour distances. This means that they are data efficient (with $k=1$ we resolve structures down to the smallest possible scales), adaptive (the resolution is higher where data are more numerous), and have minimal bias. Indeed, the bias of the underlying entropy estimates is mainly due to non-uniformity of the density at the smallest resolved scale, giving typically systematic errors which scale as functions of $k/N$ for $N$ points. Numerically, we find that both families become {\it exact} for independent distributions, i.e. the estimator $\hat M(X,Y)$ vanishes (up to statistical fluctuations) if $\mu(x,y) = \mu(x) \mu(y)$. This holds for all tested marginal distributions and for all dimensions of $x$ and $y$. In addition, we give estimators for redundancies between more than 2 random variables. We compare our algorithms in detail with existing algorithms. Finally, we demonstrate the usefulness of our estimators for assessing the actual independence of components obtained from independent component analysis (ICA), for improving ICA, and for estimating the reliability of blind source separation.Comment: 16 pages, including 18 figure

Quasiperiodic time dependent current in driven superlattices: distorted Poincare maps and strange attractors

Intriguing routes to chaos have been experimentally observed in semiconductor superlattices driven by an ac field. In this work, a theoretical model of time dependent transport in ac driven superlattices is numerically solved. In agreement with experiments, distorted Poincare maps in the quasiperiodic regime are found. They indicate the appearance of very complex attractors and routes to chaos as the amplitude of the AC signal increases. Distorted maps are caused by the discrete well-to-well jump motion of a domain wall during spiky high-frequency self-sustained oscillations of the current.Comment: 10 pages, 4 figure

The transition between stochastic and deterministic behavior in an excitable gene circuit

We explore the connection between a stochastic simulation model and an ordinary differential equations (ODEs) model of the dynamics of an excitable gene circuit that exhibits noise-induced oscillations. Near a bifurcation point in the ODE model, the stochastic simulation model yields behavior dramatically different from that predicted by the ODE model. We analyze how that behavior depends on the gene copy number and find very slow convergence to the large number limit near the bifurcation point. The implications for understanding the dynamics of gene circuits and other birth-death dynamical systems with small numbers of constituents are discussed.Comment: PLoS ONE: Research Article, published 11 Apr 201

Spin-Flip Probability in the Inelastic Scattering of 7.48-MeV Neutrons from the 4.43-MeV State of 12C

This article discusses spin-flip probability in the inelastic scattering of 7.48-MeV neutrons from the 4.43-MeV state of 12C

The functional connectome of 3,4‐methyldioxymethamphetamine‐related declarative memory impairments

The chronic intake of 3,4‐methylenedioxymethamphetamine (MDMA, “ecstasy”) bears a strong risk for sustained declarative memory impairments. Although such memory deficits have been repeatedly reported, their neurofunctional origin remains elusive. Therefore, we here investigate the neuronal basis of altered declarative memory in recurrent MDMA users at the level of brain connectivity. We examined a group of 44 chronic MDMA users and 41 demographically matched controls. Declarative memory performance was assessed by the Rey Auditory Verbal Learning Test and a visual associative learning test. To uncover alterations in the whole brain connectome between groups, we employed a data‐driven multi‐voxel pattern analysis (MVPA) approach on participants' resting‐state functional magnetic resonance imaging data. Recent MDMA use was confirmed by hair analyses. MDMA users showed lower performance in delayed recall across tasks compared to well‐matched controls with moderate‐to‐strong effect sizes. MVPA revealed a large cluster located in the left postcentral gyrus of global connectivity differences between groups. Post hoc seed‐based connectivity analyses with this cluster unraveled hypoconnectivity to temporal areas belonging to the auditory network and hyperconnectivity to dorsal parietal regions belonging to the dorsal attention network in MDMA users. Seed‐based connectivity strength was associated with verbal memory performance in the whole sample as well as with MDMA intake patterns in the user group. Our findings suggest that functional underpinnings of MDMA‐related memory impairments encompass altered patterns of multimodal sensory integration within auditory processing regions to a functional heteromodal connector hub, the left postcentral gyrus. In addition, hyperconnectivity in regions of a cognitive control network might indicate compensation for degraded sensory processing