1,928 research outputs found
Switchable Genetic Oscillator Operating in Quasi-Stable Mode
Ring topologies of repressing genes have qualitatively different long-term
dynamics if the number of genes is odd (they oscillate) or even (they exhibit
bistability). However, these attractors may not fully explain the observed
behavior in transient and stochastic environments such as the cell. We show
here that even repressilators possess quasi-stable, travelling-wave periodic
solutions that are reachable, long-lived and robust to parameter changes. These
solutions underlie the sustained oscillations observed in even rings in the
stochastic regime, even if these circuits are expected to behave as switches.
The existence of such solutions can also be exploited for control purposes:
operation of the system around the quasi-stable orbit allows us to turn on and
off the oscillations reliably and on demand. We illustrate these ideas with a
simple protocol based on optical interference that can induce oscillations
robustly both in the stochastic and deterministic regimes.Comment: 24 pages, 5 main figure
Numerical analysis of a mechanotransduction dynamical model reveals homoclinic bifurcations of extracellular matrix mediated oscillations of the mesenchymal stem cell fate
We perform one and two-parameter numerical bifurcation analysis of a
mechanotransduction model approximating the dynamics of mesenchymal stem cell
differentiation into neurons, adipocytes, myocytes and osteoblasts. For our
analysis, we use as bifurcation parameters the stiffness of the extracellular
matrix and parameters linked with the positive feedback mechanisms that
up-regulate the production of the YAP/TAZ transcriptional regulators (TRs) and
the cell adhesion area. Our analysis reveals a rich nonlinear behaviour of the
cell differentiation including regimes of hysteresis and multistability, stable
oscillations of the effective adhesion area, the YAP/TAZ TRs and the
PPAR receptors associated with the adipogenic fate, as well as
homoclinic bifurcations that interrupt relatively high-amplitude oscillations
abruptly. The two-parameter bifurcation analysis of the Andronov-Hopf points
that give birth to the oscillating patterns predicts their existence for soft
extracellular substrates (), a regime that favours the neurogenic and
the adipogenic cell fate. Furthermore, in these regimes, the analysis reveals
the presence of homoclinic bifurcations that result in the sudden loss of the
stable oscillations of the cell-substrate adhesion towards weaker adhesion and
high expression levels of the gene encoding Tubulin beta-3 chain, thus
favouring the phase transition from the adipogenic to the neurogenic fate
Design of time delayed chaotic circuit with threshold controller
A novel time delayed chaotic oscillator exhibiting mono- and double scroll
complex chaotic attractors is designed. This circuit consists of only a few
operational amplifiers and diodes and employs a threshold controller for
flexibility. It efficiently implements a piecewise linear function. The control
of piecewise linear function facilitates controlling the shape of the
attractors. This is demonstrated by constructing the phase portraits of the
attractors through numerical simulations and hardware experiments. Based on
these studies, we find that this circuit can produce multi-scroll chaotic
attractors by just introducing more number of threshold values.Comment: 21 pages, 12 figures; Submitted to IJB
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