Robustness and dissipation of mitogen-activated protein kinases signal transduction network: Underlying funneled landscape against stochastic fluctuations

We uncovered the underlying energy landscape of the mitogen-activated protein kinases signal transduction cellular network by exploring the statistical natures of the Brownian dynamical trajectories. We introduce a dimensionless quantity: The robustness ratio of energy gap versus local roughness to measure the global topography of the underlying landscape. A high robustness ratio implies funneled landscape. The landscape is quite robust against environmental fluctuations and variants of the intrinsic chemical reaction rates.

Single molecule dynamics and statistical fluctuations of gene regulatory networks: A repressilator

The authors developed a time dependent method to study the single molecule dynamics of a simple gene regulatory network: a repressilator with three genes mutually repressing each other. They quantitatively characterize the time evolution dynamics of the repressilator. Furthermore, they study purely dynamical issues such as statistical fluctuations and noise evolution. They illustrated some important features of the biological network such as monostability, spirals, and limit cycle oscillation. Explicit time dependent Fano factors which describe noise evolution and show statistical fluctuations out of equilibrium can be significant and far from the Poisson distribution. They explore the phase space and the interrelationships among fluctuations, order, amplitude, and period of oscillations of the repressilators. The authors found that repressilators follow ordered limit cycle orbits and are more likely to appear in the lower fluctuating regions. The amplitude of the repressilators increases as the suppressing of the genes decreases and production of proteins increases. The oscillation period of the repressilators decreases as the suppressing of the genes decreases and production of proteins increases.

Dynamics and intrinsic statistical fluctuations of a gene switch

We studied a simple gene regulatory network, the toggle switch. Specifically, we examined the means and statistical fluctuations in numbers of proteins. We found that when omega, the ratio of rates of protein-gene unbinding to protein degradation, was between similar to 10(-3) and similar to 10, the fluctuations were much larger than those we would have expected from Poisson statistics. In addition, we examined characteristic time values for system relaxation and found both that they increased with omega and that they have significant phase transition effects, with a secondary time scale appearing near the boundary between bistable and other phases. Last, we discuss the bistability of the toggle switch.

Behavioral responses of tilapia (Oreochromis niloticus) to acute fluctuations in dissolved oxygen levels as monitored by computer vision

Behavioral and ventilatory parameters have the possibility of predicting the stress state of fish in vivo and in situ. This paper presents a new image-processing algorithm for quantifying the average swimming speed of a fish school in an aquarium. This method is based on the alteration in projected area caused by the movement of individual fish during frame sequences captured at given time intervals. The image enhancement method increases the contrast between fish and background, and is thus suitable for use in turbid aquaculture water. Behavioral parameters (swimming activity and distribution parameters) and changes in ventilation frequency (VF) of tilapia (Oreochromis niloticus) responded to acute fluctuations in dissolved oxygen (DO) which were monitored continuously in the course of normoxia, falling DO level, maintenance of hypoxia (three levels of 1.5, 0.8 and 0.3 mg l(-1)) and subsequent recovery to normoxia. These parameters responded sensitively to acute variations in DO level; they displayed significant changes (P < 0.05) during severe hypoxia (0.8 and 0.3 mg l(-1) level) compared with normoxic condition, but there was no significant difference under conditions of mild hypoxia (1.5 mg l(-1) level). There was no significant difference in VF between two levels of severe hypoxia 0.8 and 0.3 mg l(-1) level during the low DO condition. The activity and distribution parameters displayed distinguishable differences between the 0.8 and 0.3 mg l(-1) levels. The behavioral parameters are thus capable of distinguishing between different degrees of severe hypoxia, though there were relatively large fluctuations. (c) 2006 Elsevier B.V. All rights reserved.

Interannual fluctuations in floral longevity, pollinator visitation and pollination limitation of an alpine plant (Gentiana straminea Maxim., Gentianaceae) at two altitudes in the Qinghai-Tibetan Plateau

Prolonged floral longevity and bumblebees as dominate pollinators in alpine ecosystem have been suggested to overcome pollination limitation of alpine plants arising from the decrease of pollinator activity with increasing altitude. However, this conclusion has never been examined in the Qinghai-Tibetan Plateau (QTP), the highest and largest plateau in the world. In this study, we intended to test year-to-year correlations between floral longevity, visiting frequency and pollen limitation of this species between two populations (at 3200 m and 4000 m) of Gentiana straminea in this plateau. Pollinator exclusion elongated both male and female phases greatly at both sites, and durations of both male and female phases in natural condition varied greatly over three years. The visiting frequency of bumblebees varied greatly at the higher altitude, but seemed to be stable at the lower altitude. Seed production was pollination limited in both populations in most studied years. The floral durations, pollinator frequency and pollination limitation showed no significant and consistent variations with the increase of altitude. The previous hypothesis that the prolonged floral longevity of alpine plants can compensate for low levels of pollinator visitation therefore could not be confirmed, and our results further suggested that in the QTP platform, the altitude shows no consistent effect on the reproductive performance of this species, despite that the fluctuation of visit frequency intensified at the higher altitude.