Stability analysis of the GAL regulatory network in Saccharomyces cerevisiae and Kluyveromyces lactis.

BACKGROUND: In the yeast Saccharomyces cerevisiae, interactions between galactose, Gal3p, Gal80p, and Gal4p determine the transcriptional status of the genes required for the galactose utilization. Increase in the cellular galactose concentration causes the galactose molecules to bind onto Gal3p which, via Gal80p, activates Gal4p, which induces the GAL3 and GAL80 gene transcription. Recently, a linear time-invariant multi-input multi-output (MIMO) model of this GAL regulatory network has been proposed; the inputs being galactose and Gal4p, and the outputs being the active Gal4p and galactose utilization. Unfortunately, this model assumes the cell culture to be homogeneous, although it is not so in practice. We overcome this drawback by including more biochemical reactions, and derive a quadratic ordinary differential equation (ODE) based model. RESULTS: We show that the model, referred to above, does not exhibit bistability. We establish sufficiency conditions for the domain of attraction of an equilibrium point of our ODE model for the special case of full-state feedback controller. We observe that the GAL regulatory system of Kluyveromyces lactis exhibits an aberration of monotone nonlinearity and apply the Rantzer multipliers to establish a class of stabilizing controllers for this system. CONCLUSION: Feedback in a GAL regulatory system can be used to enhance the cellular memory. We show that the system can be modeled as a quadratic nonlinear system for which the effect of feedback on the domain of attraction of the equilibrium point can be characterized using linear matrix inequality (LMI) conditions that are easily implementable in software. The benefit of this result is that a mathematically sound approach to the synthesis of full-state and partial-state feedback controllers to regulate the cellular memory is now possible, irrespective of the number of state-variables or parameters of interest.

Adaptive power control for wireless networks using multiple controllers and switching.

Controlling transmitted power in a wireless network is critical for maintaining quality of service, maximizing channel utilization and minimizing near-far effect for suboptimal receivers. In this paper, a general proportional-integral-derivative (PID) type algorithm for controlling transmitted powers in wireless networks is studied and a systematic way to adapt or tune the parameters of the controller in a distributed fashion is suggested. The proposed algorithm utilizes multiple candidate PID gains. Depending on the prevailing channel conditions, it selects an optimal PID gain from the candidate gain set at each instant and places it in the feedback loop. The algorithm is data driven and can distinguish between stabilizing and destabilizing controller gains as well as rank the stabilizing controllers based on their performance. Simulation results indicate that the proposed scheme performs better than several candidate controllers, including a well known distributed power control (DPC) algorithm.