We study genetic networks that produce many species of non-coding RNA molecules that are present at a moderate density, as typically exists in the cell. The associations of the many species of these RNA are modeled physically, taking into account the
equilibrium constants between bound and unbound states. By including the pair-wise binding of the many RNA species, the network becomes highly interconnected and shows different properties than the usual type of genetic network. It shows much more robustness to mutation, and also rapid evolutionary adaptation in an environment that oscillates in time. This provides a possible explanation for the weak evolutionary constraints seen in much of the non-coding RNA that has been studied.
We analyze experimental observations of microtubules undergoing small fluctuations about a balance point when mixed in solution of two different kinesin motor proteins, KLP61F and Ncd. It has been proposed that the microtubule movement is due to stoc
hastic variations in the densities of the two species of motor proteins. We test this hypothesis here by showing how it maps onto a one-dimensional random walk in a random environment. Our estimate of the amplitude of the fluctuations agrees with experimental observations. We point out that there is an initial transient in the position of the microtubule where it will typically move of order its own length. We compare the physics of this gliding assay to a recent theory of the role of antagonistic motors on restricting interpolar microtubule sliding of a cells mitotic spindle during prometaphase. It is concluded that randomly positioned antagonistic motors can restrict relative movement of microtubules, however they do so imperfectly. A variation in motor concentrations is also analyzed and shown to lead to greater control of spindle length.
We study self avoiding random walks in an environment where sites are excluded randomly, in two and three dimensions. For a single polymer chain, we study the statistics of the time averaged monomer density and show that these are well described by m
ultifractal statistics. This is true even far from the percolation transition of the disordered medium. We investigate solutions of chains in a disordered environment and show that the statistics cease to be multifractal beyond the screening length of the solution.
