8 research outputs found
Autonomous Motility of Active Filaments due to Spontaneous Flow-Symmetry Breaking
We simulate the nonlocal Stokesian hydrodynamics of an elastic filament which
is active due a permanent distribution of stresslets along its contour. A
bending instability of an initially straight filament spontaneously breaks flow
symmetry and leads to autonomous filament motion which, depending on
conformational symmetry, can be translational or rotational. At high ratios of
activity to elasticity, the linear instability develops into nonlinear
fluctuating states with large amplitude deformations. The dynamics of these
states can be qualitatively understood as a superposition of translational and
rotational motion associated with filament conformational modes of opposite
symmetry. Our results can be tested in molecular-motor filament mixtures,
synthetic chains of autocatalytic particles, or other linearly connected
systems where chemical energy is converted to mechanical energy in a fluid
environment.Comment: 7 pages, 3 figures; contains supplemental text; movies at
http://proofideas.org/rjoy/gallery; published in Physical Review Letter
Endogenous Quasicycles and Stochastic Coherence in a Closed Endemic Model
We study the role of demographic fluctuations in typical endemics as
exemplified by the stochastic SIRS model. The birth-death master equation of
the model is simulated using exact numerics and analysed within the linear
noise approximation. The endemic fixed point is unstable to internal
demographic noise, and leads to sustained oscillations. This is ensured when
the eigenvalues () of the linearised drift matrix are complex, which
in turn, is possible only if detailed balance is violated. In the oscillatory
state, the phases decorrelate asymptotically, distinguishing such oscillations
from those produced by external periodic forcing. These so-called quasicycles
are of sufficient strength to be detected reliably only when the ratio
is of order unity. The coherence or regularity of
these oscillations show a maximum as a function of population size, an effect
known variously as stochastic coherence or coherence resonance. We find that
stochastic coherence can be simply understood as resulting from a non-monotonic
variation of with population size. Thus, within the
linear noise approximation, stochastic coherence can be predicted from a purely
deterministic analysis. The non-normality of the linearised drift matrix,
associated with the violation of detailed balance, leads to enhanced
fluctuations in the population amplitudes.Comment: 21 pages, 8 figure
Non-renewal statistics in the catalytic activity of enzyme molecules at mesoscopic concentrations
Recent fluorescence spectroscopy measurements of single-enzyme kinetics have
shown that enzymatic turnovers form a renewal stochastic process in which the
inverse of the mean waiting time between turnovers follows the Michaelis-Menten
equation. Under typical physiological conditions, however, tens to thousands of
enzymes react in catalyzing thousands to millions of substrates. We study
enzyme kinetics at these physiologically relevant conditions through a master
equation including stochasticity and molecular discreteness. From the exact
solution of the master equation we find that the waiting times are neither
independent nor are they identically distributed, implying that enzymatic
turnovers form a non-renewal stochastic process. The inverse of the mean
waiting time shows strong departures from the Michaelis-Menten equation. The
waiting times between consecutive turnovers are anti-correlated, where short
intervals are more likely to be followed by long intervals and vice versa.
Correlations persist beyond consecutive turnovers indicating that multi-scale
fluctuations govern enzyme kinetics.Comment: 5 pages, 4 figures, to appear in Physical Review Letter