Intracellular transport

Movement of material within a biological cell. Diffusion, movement by a molecular motor and vesicle transport operate at different scales; observing accumulation at a destination does not by itself distinguish active transport from selective retention.

A localization mechanism in which nondirected movement brings material to a selectively retaining destination. Localization does not by itself establish motor-driven transport along the entire route.

A facilitated target search combines bulk diffusion with lower-dimensional motion on a substrate, such as sliding on DNA. In the scaling model $\tau =A/\lambda +B\lambda$, positive constants $A,B$ balance relocation and local exploration. Differentiation gives ${\lambda }_{\ast }=\sqrt{A/B}$ and ${\tau }_{\min }=2\sqrt{AB}$. These expressions require an accessible optimum within the physically allowed range of sliding lengths.

For an unbiased one-dimensional walk with step size $a$, diffusion coefficient $D$ fixes step interval $a^2/(2D)$. A small dissociation probability $P$ per step gives about $1/P$ steps before release. Thus lifetime depends on $D$, while the root-mean-square net displacement before release is $a/\sqrt{P}$. Net displacement is not the cumulative distance along all backtracking steps. Dimensional consistency of the measured or assumed diffusivity is necessary before applying the estimate.

For an absorbing spherical target of radius $a$ in an infinite uniform reservoir, steady diffusion gives $c(r)=c_{\infty }(1-a/r)$. Integrating the inward flux yields $k=4\pi D_{\mathrm{rel}}a$, where $D_{\mathrm{rel}}=D_A+D_B$ if both partners diffuse. Here $k$ multiplies number densities; its units are volume per time. Molecular orientation, finite-domain transients and imperfect capture require corrections.

If $N$ independent well-mixed searchers each encounter a small absorbing target with approximate exponential hazard $k_a/V$, their minimum waiting time has hazard $N{k}_a/V$. The Smoluchowski association rate is $k_a=4\pi D_{\mathrm{rel}}{r}_0$. Cell geometry, orientational capture and nonequilibrium spatial distributions can change this idealized estimate; an arbitrary nonexponential first-passage mean does not in general divide by $N$ exactly.

Transfer of cargo in membrane-bounded vesicles. Budding selects material and produces a carrier, while targeting and vesicle fusion deliver it to another compartment, allowing transport without exposing the cargo directly to the surrounding cytoplasm.

Merger of a vesicle membrane with a target membrane. The process connects the two enclosed aqueous spaces or releases cargo outside the cell, while also transferring membrane components to the target surface.

A membrane-bounded carrier that delivers cargo toward the cell surface for release. Fusion with the cell membrane exposes the vesicle’s interior to the extracellular space, connecting intracellular packaging with secretion.