Analytical Study of Robustness of a Negative Feedback Oscillator by Multiparameter Sensitivity

BACKGROUND:One of the distinctive features of biological oscillators such as circadian clocks and cell cycles is robustness which is the ability to resume reliable operation in the face of different types of perturbations. In the previous study, we proposed multiparameter sensitivity (MPS) as an intelligible measure for robustness to fluctuations in kinetic parameters. Analytical solutions directly connect the mechanisms and kinetic parameters to dynamic properties such as period, amplitude and their associated MPSs. Although negative feedback loops are known as common structures to biological oscillators, the analytical solutions have not been presented for a general model of negative feedback oscillators.RESULTS:We present the analytical expressions for the period, amplitude and their associated MPSs for a general model of negative feedback oscillators. The analytical solutions are validated by comparing them with numerical solutions. The analytical solutions explicitly show how the dynamic properties depend on the kinetic parameters. The ratio of a threshold to the amplitude has a strong impact on the period MPS. As the ratio approaches to one, the MPS increases, indicating that the period becomes more sensitive to changes in kinetic parameters. We present the first mathematical proof that the distributed time-delay mechanism contributes to making the oscillation period robust to parameter fluctuations. The MPS decreases with an increase in the feedback loop length (i.e., the number of molecular species constituting the feedback loop).CONCLUSIONS:Since a general model of negative feedback oscillators was employed, the results shown in this paper are expected to be true for many of biological oscillators. This study strongly supports that the hypothesis that phosphorylations of clock proteins contribute to the robustness of circadian rhythms. The analytical solutions give synthetic biologists some clues to design gene oscillators with robust and desired period

Compact embedding from W01,2(Ω) to Lq(x)(Ω) and its application to nonlinear elliptic boundary value problem with variable critical exponent

AbstractWe study the compact embedding from W01,2(Ω) to Lq(x)(Ω) with a variable critical exponent 1⩽q(x)⩽2N/(N−2), N⩾3 if there exist a point x0∈Ω, a small η>0, 0<l<1 and C0>0 such that q(x0)=2N/(N−2) and q(x)⩽2N/(N−2)−C0/(log(1/|x−x0|))l for |x−x0|⩽η. As an application, we show an existence of a positive solution to the nonlinear elliptic boundary value problem −Δu=uq(x)−1 in Ω, u(x)=0 on ∂Ω

Development of an accurate kinetic model for the central carbon metabolism of Escherichia coli

Additional file 2. Comparison of our kinetic model with other existing models

Cyclic Behavior of Multi-Row Slit Shear Walls Made from Low Yield Point Steel

The steel slit shear wall has attracted much attention as a lateral force-resisting system. However, issues such as fractures formed at the slit ends and pinched hysteresis reduce energy dissipation. To address these issues, the authors have developed a steel slit shear wall made from low yield point steel that has a low yield stress and large ductility and strain hardening. Steel slit shear walls made from low-yield-point steel dissipated energy at small lateral drifts, shear deformation was evenly distributed among all rows, fracture was eliminated, and fat hysteresis without the requirement for out-of-plane constraints was feasible. By adjusting dimensions of the link (segment divided by slits) and the number of rows of links while maintaining the required shear strength and stiffness, a small width-to-thickness ratio for the links was achievable to ensure the in-plane behavior of links and thus good energy dissipation. The combined hardening model developed using commercially available software simulated well the large strain hardening of low-yield-point steel. A proposed design procedure that ensures good energy dissipation was given

CADLIVE Optimizer: Web-based Parameter Estimation for Dynamic Models

Computer simulation has been an important technique to capture the dynamics of biochemical networks. In most networks, however, few kinetic parameters have been measured in vivo because of experimental complexity. We develop a kinetic parameter estimation system, named the CADLIVE Optimizer, which comprises genetic algorithms-based solvers with a graphical user interface. This optimizer is integrated into the CADLIVE Dynamic Simulator to attain efficient simulation for dynamic models

CADLIVE optimizer: web-based parameter estimation for dynamic models

Computer simulation has been an important technique to capture the dynamics of biochemical networks. In most networks, however, few kinetic parameters have been measured in vivo because of experimental complexity. We develop a kinetic parameter estimation system, named the CADLIVE Optimizer, which comprises genetic algorithms-based solvers with a graphical user interface. This optimizer is integrated into the CADLIVE Dynamic Simulator to attain efficient simulation for dynamic models