英语翻译
In the present paper we study a diffusing particle that escapes from a cavity to the outside world through a narrow cylindrical tunnel.While earlier studies of the problem1–3 are focused on the mean particle lifetime,which is only the rst moment of the distribution,we develop a theory that allows us to derive expressions for the Laplace transforms of the particle lifetime probability density and its survival probability.The former is used to obtain an expression for the mean lifetime that contains the results earlier reported in the literature as special cases,which correspond to different escape scenarios.This is a consequence of the fact that our approach is quite general in the sense that it does not assume any particular scenario.The results obtained in the paper show how the escape kinetics depends on the geometric and trans-port parameters of the system,namely,the cavity volume,the length and radius of the tunnel,and the particle diffusion coef?cients in the tunnel and cavity,which may be different.
The model of a diffusing particle escaping from a cavity through a narrow tunnel has been proposed and used when discussing escape of signaling ions and proteins from den-dritic spines,1–4which are small,micrometer in size protrusions on dendrites.Although there is enormous variability in spine morphology,5the classical dendritic spine consists of a bulbous head connected to the parent dendrite by a narrow neck.It is believed that dendritic spines are important for communication between nerve cells,since the majority of excitatory synapses in the brain are on spines rather than dendrites.Cells use spines as sites where suf?ciently high concentrations of signals can be generated and kept long enough to initiate signaling cascades.1–4 Therefore,the signal lifetime in the spine is an important parameter.