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.

Grand challenges in the science of wind energy.

Harvested by advanced technical systems honed over decades of research and development, wind energy has become a mainstream energy resource. However, continued innovation is needed to realize the potential of wind to serve the global demand for clean energy. Here, we outline three interdependent, cross-disciplinary grand challenges underpinning this research endeavor. The first is the need for a deeper understanding of the physics of atmospheric flow in the critical zone of plant operation. The second involves science and engineering of the largest dynamic, rotating machines in the world. The third encompasses optimization and control of fleets of wind plants working synergistically within the electricity grid. Addressing these challenges could enable wind power to provide as much as half of our global electricity needs and perhaps beyond.

Dynamics modeling for parallel haptic interfaces with force sensing and control.

Closed-loop force control can be used on haptic interfaces (HIs) to mitigate the effects of mechanism dynamics. A single multidimensional force-torque sensor is often employed to measure the interaction force between the haptic device and the user's hand. The parallel haptic interface at the University of Colorado (CU) instead employs smaller 1D force sensors oriented along each of the five actuating rods to build up a 5D force vector. This paper shows that a particular manipulandum/hand partition in the system dynamics is induced by the placement and type of force sensing, and discusses the implications on force and impedance control for parallel haptic interfaces. The details of a "squaring down" process are also discussed, showing how to obtain reduced degree-of-freedom models from the general six degree-of-freedom dynamics formulation.