We consider directed walk models of a polymer that is adsorbing at a surface due to
polymer–surface interactions, and is also pulled away from the surface by an elongational
force. We obtain force–temperature, force–extension, and density–extension curves
for the Dyck path and partially directed walk models for the situation where
the polymer is pulled from one end, and for Dyck paths when the polymer is
pulled from a central location in the polymer. We obtain force–extension and
density–extension curves for these models, and their dependence on the length of the
polymer.
We explore stochastic models for the study of ion transport in biological cells. Analysis of these models explains and explores an interesting feature of ion transport observed by biophysicists. Namely, the average time it takes ions to cross certain ion channels is the same in either direction, even if there is an electric potential difference across the channels. It is shown for simple single ion models that the distribution of a path (i.e., the history of location versus time) of an ion crossing the channel in one direction has the same distribution as the time-reversed path of an ion crossing the channel in the reverse direction. Therefore, not only is the mean duration of these paths equal, but other measures, such as the variance of passage time or the mean time a path spends within a specified section of the channel, are also the same for both directions of traversal. The feature is also explored for channels with interacting ions. If a system of interacting ions is in reversible equilibrium (net flux is zero), then the equivalence of the left-to-right trans paths with the time-reversed right-to-left trans paths still holds. However, if the system is in equilibrium, but not reversible equilibrium, then such equivalence need not hold.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.