In vivo regulation of muscle glycogen synthase and the control of glycogen synthesis.

The activity of glycogen synthase (GSase; EC 2.4.1.11) is regulated by covalent phosphorylation. Because of this regulation, GSase has generally been considered to control the rate of glycogen synthesis. This hypothesis is examined in light of recent in vivo NMR experiments on rat and human muscle and is found to be quantitatively inconsistent with the data under conditions of glycogen synthesis. Our first experiments showed that muscle glycogen synthesis was slower in non-insulin-dependent diabetics compared to normals and that their defect was in the glucose transporter/hexokinase (GT/HK) part of the pathway. From these and other in vivo NMR results a quantitative model is proposed in which the GT/HK steps control the rate of glycogen synthesis in normal humans and rat muscle. The flux through GSase is regulated to match the proximal steps by "feed forward" to glucose 6-phosphate, which is a positive allosteric effector of all forms of GSase. Recent in vivo NMR experiments specifically designed to test the model are analyzed by metabolic control theory and it is shown quantitatively that the GT/HK step controls the rate of glycogen synthesis. Preliminary evidence favors the transporter step. Several conclusions are significant: (i) glucose transport/hexokinase controls the glycogen synthesis flux; (ii) the role of covalent phosphorylation of GSase is to adapt the activity of the enzyme to the flux and to control the metabolite levels not the flux; (iii) the quantitative data needed for inferring and testing the present model of flux control depended upon advances of in vivo NMR methods that accurately measured the concentration of glucose 6-phosphate and the rate of glycogen synthesis.

A fast marching level set method for monotonically advancing fronts.

A fast marching level set method is presented for monotonically advancing fronts, which leads to an extremely fast scheme for solving the Eikonal equation. Level set methods are numerical techniques for computing the position of propagating fronts. They rely on an initial value partial differential equation for a propagating level set function and use techniques borrowed from hyperbolic conservation laws. Topological changes, corner and cusp development, and accurate determination of geometric properties such as curvature and normal direction are naturally obtained in this setting. This paper describes a particular case of such methods for interfaces whose speed depends only on local position. The technique works by coupling work on entropy conditions for interface motion, the theory of viscosity solutions for Hamilton-Jacobi equations, and fast adaptive narrow band level set methods. The technique is applicable to a variety of problems, including shape-from-shading problems, lithographic development calculations in microchip manufacturing, and arrival time problems in control theory.

A theory for controlling cell cycle dynamics using a reversibly binding inhibitor

We demonstrate, by using mathematical modeling of cell division cycle (CDC) dynamics, a potential mechanism for precisely controlling the frequency of cell division and regulating the size of a dividing cell. Control of the cell cycle is achieved by artificially expressing a protein that reversibly binds and inactivates any one of the CDC proteins. In the simplest case, such as the checkpoint-free situation encountered in early amphibian embryos, the frequency of CDC oscillations can be increased or decreased by regulating the rate of synthesis, the binding rate, or the equilibrium constant of the binding protein. In a more complex model of cell division, where size-control checkpoints are included, we show that the same reversible binding reaction can alter the mean cell mass in a continuously dividing cell. Because this control scheme is general and requires only the expression of a single protein, it provides a practical means for tuning the characteristics of the cell cycle in vivo.

Active control of waves in a cochlear model with subpartitions.

Multiscale asymptotic methods developed previously to study macromechanical wave propagation in cochlear models are generalized here to include active control of a cochlear partition having three subpartitions, the basilar membrane, the reticular lamina, and the tectorial membrane. Activation of outer hair cells by stereocilia displacement and/or by lateral wall stretching result in a frequency-dependent force acting between the reticular lamina and basilar membrane. Wavelength-dependent fluid loads are estimated by using the unsteady Stokes' equations, except in the narrow gap between the tectorial membrane and reticular lamina, where lubrication theory is appropriate. The local wavenumber and subpartition amplitude ratios are determined from the zeroth order equations of motion. A solvability relation for the first order equations of motion determines the subpartition amplitudes. The main findings are as follows: The reticular lamina and tectorial membrane move in unison with essentially no squeezing of the gap; an active force level consistent with measurements on isolated outer hair cells can provide a 35-dB amplification and sharpening of subpartition waveforms by delaying dissipation and allowing a greater structural resonance to occur before the wave is cut off; however, previously postulated activity mechanisms for single partition models cannot achieve sharp enough tuning in subpartitioned models.