Single file diffusion into a semi-infinite tube

Abstract

We investigate single file diffusion (SFD) of large particles entering a semi-infinite tube, such as luminal diffusion of proteins into microtubules or flagella. While single-file effects have no impact on the evolution of particle density, we report significant single-file effects for individually tracked tracer particle motion. Both exact and approximate ordering statistics of particles entering semi-infinite tubes agree well with our stochastic simulations. Considering initially empty semi-infinite tubes, with particles entering at one end starting from an initial time t = 0, tracked particles are initially super-diffusive after entering the system, but asymptotically diffusive at later times. For finite time intervals, the ratio of the net displacement of individual single-file particles to the average displacement of untracked particles is reduced at early times and enhanced at later times. When each particle is numbered, from the first to enter (n = 1) to the most recent (n = N), we find good scaling collapse of this distance ratio for all n. Experimental techniques that track individual particles, or local groups of particles, such as photo-activation or photobleaching of fluorescently tagged proteins, should be able to observe these single-file effects. However, biological phenomena that depend on local concentration, such as flagellar extension or luminal enzymatic activity, should not exhibit single-file effects.

Anomalously slow transport in single-file diffusion with slow binding kinetics

“…Our results indicate that transient binding can have further anomalous effects as the CNT diameter approaches molecular diameters [6]. Earlier studies in biomedical or biophysical systems with SFD effects on transport without binding [7,8,31] should also be revisited in light of transient binding.…”

“…Steady-state is demonstrated by superimposing the later half of the ignored data (coloured dashed lines). Parameters used here, with K A = 100, D 0 = 2.7 × 10 5 nm 2 /s and a = 7nm, correspond with what we would expect for the α-Tat1 acetylation enzyme within the microtubule lumen [8,25]. Fick's law says the flux is proportional to the gradient of the density, for sufficiently small gradients: D F ick = −Φa/∇p, where the local density is p/a.…”

“…SFD has been beautifully visualized with colloidal particles inside engineered micro-channels [4], and has been demonstrated for molecular diffusion inside various nanoporous zeolites [5]. SFD is also expected for molecular diffusion inside carbon nanotubes [6], for flagellin within bacterial flagella [7], for the acetylation enzyme α-Tat1 within microtubules [8], and for DNA-binding proteins on DNA [9]. SFD behavior can be obtained from a system of noninteracting particles undergoing simple diffusion (SD) by exchanging particle labels as their trajectories cross [1,10].…”

Coupling volume-excluding compartment-based models of diffusion at different scales: Voronoi and pseudo-compartment approaches

“…Nonlinear terms will also occur when there is more than one species of particle present, or when there is directional bias in particle movement [22]. The absence of nonlinear terms in this macroscopic description does not imply that the individual particles are unconstrained by volume exclusion: a single-tagged particle can display density-dependent behaviour [6,22]. It is also possible to derive equations describing the evolution of the variance of n ðmÞ j (variance master equations):…”

“…We describe such a model as 'partially-excluding' or 'coarse-grained' when m > 1, and as 'fully-excluding' or 'finegrained' when m = 1. In one spatial dimension, the fully-excluding model is an example of single-file diffusion, a class of model of particular relevance to biological processes such as the diffusion of αTAT1 within microtubules [6], the movement of flagellin in the formation of bacterial flagella [7], and the dispensing of proteins through in the nanochannels of drug delivery devices [8].…”