8 research outputs found
Dynamical robustness of biological networks with hierarchical distribution of time scales
We propose the concepts of distributed robustness and r-robustness, well
adapted to functional genetics. Then we discuss the robustness of the
relaxation time using a chemical reaction description of genetic and signalling
networks. First, we obtain the following result for linear networks: for large
multiscale systems with hierarchical distribution of time scales the variance
of the inverse relaxation time (as well as the variance of the stationary rate)
is much lower than the variance of the separate constants. Moreover, it can
tend to 0 faster than 1/n, where n is the number of reactions. We argue that
similar phenomena are valid in the nonlinear case as well. As a numerical
illustration we use a model of signalling network that can be applied to
important transcription factors such as NFkB
Fluctuating Filaments I: Statistical Mechanics of Helices
We examine the effects of thermal fluctuations on thin elastic filaments with
non-circular cross-section and arbitrary spontaneous curvature and torsion.
Analytical expressions for orientational correlation functions and for the
persistence length of helices are derived, and it is found that this length
varies non-monotonically with the strength of thermal fluctuations. In the weak
fluctuation regime, the local helical structure is preserved and the
statistical properties are dominated by long wavelength bending and torsion
modes. As the amplitude of fluctuations is increased, the helix ``melts'' and
all memory of intrinsic helical structure is lost. Spontaneous twist of the
cross--section leads to resonant dependence of the persistence length on the
twist rate.Comment: 5 figure