120 research outputs found
A Small-Gain Theorem with Applications to Input/Output Systems, Incremental Stability, Detectability, and Interconnections
A general ISS-type small-gain result is presented. It specializes to a
small-gain theorem for ISS operators, and it also recovers the classical
statement for ISS systems in state-space form. In addition, we highlight
applications to incrementally stable systems, detectable systems, and to
interconnections of stable systems.Comment: 16 pages, no figure
Deterministic characterization of stochastic genetic circuits
For cellular biochemical reaction systems where the numbers of molecules is
small, significant noise is associated with chemical reaction events. This
molecular noise can give rise to behavior that is very different from the
predictions of deterministic rate equation models. Unfortunately, there are few
analytic methods for examining the qualitative behavior of stochastic systems.
Here we describe such a method that extends deterministic analysis to include
leading-order corrections due to the molecular noise. The method allows the
steady-state behavior of the stochastic model to be easily computed,
facilitates the mapping of stability phase diagrams that include stochastic
effects and reveals how model parameters affect noise susceptibility, in a
manner not accessible to numerical simulation. By way of illustration we
consider two genetic circuits: a bistable positive-feedback loop and a
negative-feedback oscillator. We find in the positive feedback circuit that
translational activation leads to a far more stable system than transcriptional
control. Conversely, in a negative-feedback loop triggered by a
positive-feedback switch, the stochasticity of transcriptional control is
harnessed to generate reproducible oscillations.Comment: 6 pages (Supplementary Information is appended
Optimal metabolic pathway activation
This paper deals with temporal enzyme distribution in the activation of
biochemical pathways. Pathway activation arises when production of a certain
biomolecule is required due to changing environmental conditions. Under the
premise that biological systems have been optimized through evolutionary
processes, a biologically meaningful optimal control problem is posed. In this
setup, the enzyme concentrations are assumed to be time dependent and
constrained by a limited overall enzyme production capacity, while the
optimization criterion accounts for both time and resource usage.
Using geometric arguments we establish the bang-bang nature of the solution
and reveal that each reaction must be sequentially activated in the same order
as they appear in the pathway. The results hold for a broad range of enzyme
dynamics which includes, but is not limited to, Mass Action, Michaelis-Menten
and Hill Equation kinetics.Comment: 14 pages, 3 figures. Paper to be presented at the 17th IFAC World
Congress, Seoul, Korea, July 200
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