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The dynamics of cellular chemical reactions are variable due to stochastic noise from intrinsic and extrinsic sources. The intrinsic noise is the intracellular fluctuations of molecular copy numbers caused by the probabilistic encounter of molecules and is modeled by the chemical master equation. The extrinsic noise, on the other hand, represents the intercellular variation of the kinetic parameters due to the variation of global factors affecting gene expression. The objective of this paper is to propose a theoretical framework to analyze the combined effect of the intrinsic and the extrinsic noise modeled by the chemical master equation with uncertain parameters. More specifically, we formulate a semidefinite program to compute the intervals of the stationary solution of uncertain moment equations whose parameters are given only partially in the form of the statistics of their distributions. The semidefinite program is derived without approximating the governing equation in contrast with many existing approaches. Thus, we can obtain guaranteed intervals of the worst possible values of the moments for all parameter distributions satisfying the given statistics, which are prohibitively hard to estimate from sample-path simulations since sampling from all possible uncertain distributions is difficult. We demonstrate the proposed optimization approach using two examples of stochastic chemical reactions and show that the solution of the optimization problem gives informative upper and lower bounds of the statistics of the stationary copy number distributions. [ABSTRACT FROM AUTHOR]

The diatom Eucampia zodiacus is a harmful species that indirectly causes bleaching to nori ( Pyropia ) cultivation through competitive utilization of nutrients during its bloom, however cellular storage and changes in physiology by asexual reproduction remains unclear. In the present study, we experimentally investigated the nitrate (N), phosphate (P) and silicic acid (Si) consumption by various cell sizes of E. zodiacus strains, the apical axis length of which ranged from 10.2 to 77.3 μm. Nutrient cell quotas of E. zodiacus ranged from 2.7 to 8.4 pM cell −1 for N, 0.34–0.76 pM cell −1 for P and 1.7–7.3 pM cell −1 for Si, and they increased with cell size, in which there is a significant correlation between these two elements. The N and P quotas were estimated to be several times higher than the minimum cell quotas. In contrast, the Si cell quotas were approximately equal to those of the minimum values. Based on the present cell quotas, total nitrate consumption by E. zodiacus population when the blooms reached maximum cell density (=1000 cells ml −1 ) were estimated to be 6.5 μM. Monthly mean concentrations of dissolved inorganic nitrogen (DIN) range from 3.5 to 8.2 μM during the period of late nori harvest season when E. zodiacus blooms occur, and nori bleaching is reported at the condition of DIN concentration of less than 3 μM in Harima-Nada, eastern Seto Inland Sea, Japan. Therefore, the present results suggest that E. zodiacus causes serious damage to nori cultivation due to high levels of nutrient consumption. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, we propose a theoretical framework to systematically analyze the existence and the profiles of chemical oscillations in gene regulatory networks with negative cyclic feedback. In particular, we analytically derive the existence conditions and the profiles of oscillations in terms of reaction kinetic parameters and reveal dimensionless quantities that essentially characterize the oscillatory dynamics. These discoveries then allow us to provide general biological insights that are useful for the design of synthetic gene circuits and wet-lab experiments. We point out that time delays due to splicing and transport play an important role for both of the existence and the profiles of oscillations. To this end, we first show that local instability leads to oscillations in cyclic gene regulatory networks, and we derive the existence conditions based on local instability analysis. Then, we analyze the period, phase and amplitude of oscillations using multivariable harmonic balance analysis. These results are demonstrated with two existing biochemical networks, the Pentilator and a self-repression network of a Hes protein. [Copyright &y& Elsevier]

Abstract: In this paper, we consider the existence conditions of periodic oscillations in large-scale cyclic gene regulatory networks. Using the Poincaré–Bendixson theorem for cyclic systems, we first show that the local instability of an equilibrium point implies the existence of periodic oscillations. We then derive the graphical and its equivalent analytic criteria for the existence of periodic oscillations based on local instability analysis. These criteria have a remarkable feature that they can be applied systematically to a large-scale cyclic gene regulatory network consisting of any number of genes. The latter part of this paper is devoted to analyze the relation between an equilibrium point and the biochemical parameters. This leads to an analytic existence criterion that explicitly takes the dependence of the equilibrium state on biochemical parameters into account, which is often overlooked in nonlinear system analyses. In particular, the novel physical quantities that are essential for determining the existence of periodic oscillations are obtained based on the rigorous analytic criterion. [Copyright &y& Elsevier]

Abstract: The diatom Eucampia zodiacus Ehrenberg is one of the harmful diatom species which indirectly cause bleachings of Nori (Porphyra thalli) in aquaculture through competitive utilizing of nutrients (especially nitrogen) and resultant nutrient depletion in water columns during the bloom events. The seasonal changes in environmental factors, cell density and cell size of E. zodiacus were investigated for 4 years (April 2002–December 2005) to understand the population ecology of this diatom in Harima-Nada, the eastern part of the Seto Inland Sea, Japan. Vegetative cells of E. zodiacus were usually detected year-round. Total cell densities of E. zodiacus annually peaked from mid-February to early April, and high cell densities were observed in the whole water columns during the bloom-period. Nutrient concentrations decreased with the increase of cell density of E. zodiacus, and low nutrients concentrations continued throughout the E. zodiacus bloom-period. The average cell size (length of apical axis) of E. zodiacus populations ranged from 10.8μm to 81.2μm, and the restoration of cell size occurred once in autumn every year just after reaching the minimum cell size. In addition, its great seasonal regularity was confirmed by the decrease and restoration of its cell size through 4-year study period. Temperature and nutrients were suitable in autumn for the growth of E. zodiacus, its blooms never occur in that season. These results strongly suggest that E. zodiacus did not have a resting stage, and it spends autumn for size restoration and starts to bloom thereafter in Harima-Nada in winter and spring, causing fishery damage to Nori aquaculture by resulting nutrient deprivation. [Copyright &y& Elsevier]

A class of networked dynamical systems with multiple homogeneous agents can be represented by a linear system with a generalized frequency variable. This paper is concerned with robust stability analysis of such class of systems under perturbations in the dynamics of agents. The perturbed agents no longer share the same dynamics and thus the analysis encompasses heterogeneous multi-agent systems consisting of slightly different agents. We first present nominal stability conditions for the system of interconnected MIMO agents. We then focus on robust stability, where we consider three types of perturbations, leading to homogeneous agents, heterogeneous agents with and without uncertain interconnections. For each case, we show that a necessary and sufficient condition for robust stability is given by an H ∞ -norm bound on a set of transfer functions parametrized by the eigenvalues of the interconnection matrix, provided the nominal interconnections have a certain structure. The robust stability condition is interpreted as the requirement that the eigenvalues of the interconnection matrix be located in a particular region on the complex plane. The usefulness of the results is demonstrated through an application to robust stability analysis for gene regulatory networks. [ABSTRACT FROM AUTHOR]

This paper is concerned with a robust instability analysis for the single-input-single-output unstable linear time-invariant (LTI) system under dynamic perturbations. The nominal system itself is possibly perturbed by the static gain of the uncertainty, which would be the case when a nonlinear uncertain system is linearized around an equilibrium point. We define the robust instability radius as the smallest H ∞ norm of the stable linear perturbation that stabilizes the nominal system. There are two main theoretical results: one is on a partial characterization of unperturbed nominal systems for which the robust instability radius can be calculated exactly, and the other is a numerically tractable procedure for calculating the exact robust instability radius for nominal systems parametrized by a perturbation parameter. The results are applied to the repressilator in synthetic biology, where hyperbolic instability of a unique equilibrium guarantees the persistence of oscillation phenomena in the global sense, and the effectiveness of our linear robust instability analysis is confirmed by numerical simulations. [ABSTRACT FROM AUTHOR]