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Lateral mobility of membrane proteins is movement along a membrane surface. It differs from membrane transport through the boundary and from reversing membrane topology. Attachment, crowding and barriers can restrict diffusion; the fluid mosaic model does not require every membrane protein to wander freely.^[ref]

An original local model treats a small, approximately flat patch as an unbounded plane with uniform diffusion coefficient $D$, no drift and no trapping. Represent the two displacement coordinates by independent Brownian motions, each with zero expected value and variance $2Dt$. Since $r^2=x^2+y^2$, addition of the two coordinate expectations givesThis is a root-mean-square displacement, not distance traveled along a jagged trajectory or the displacement of every protein. For a stipulated $D=0.08\mu {\mathrm{m}}^2{\mathrm{s}}^{-1}$ and $t=5\mathrm{s}$, $⟨r^2⟩=1.6\mu {\mathrm{m}}^2$ and $r_{\mathrm{rms}}\approx 1.265\mu \mathrm{m}$. Reaching a stipulated root-mean-square scale $L=2\mu \mathrm{m}$ gives $t=L^2/(4D)=12.5\mathrm{s}$. These model values are not measured diffusion coefficients or mixing times from the historical experiment.

Multiplying the target displacement scale by two multiplies the model time by four. This quadratic scaling is a useful way to see why local encounters and redistribution over an entire biological cell need not happen on the same timescale. A curved, bounded cell membrane, restricted paths and different mobile populations require more than this flat-patch model; disappearance of an initial pattern alone does not determine $D$.

A membrane protein is a protein associated with a biological membrane. Its association, orientation and mobility are separate properties: being embedded does not imply spanning, and spanning does not imply moving freely. Membrane proteins supply routes for membrane transport and recognition for signal transduction.^[ref]

An ion channel supplies a pathway for ions; a carrier protein changes which side can reach a bound solute; a cell-surface receptor connects an external ligand to intracellular signal transduction. These examples distinguish passage from communication: a signal can cross the boundary as a change of protein activity without the ligand itself crossing.^[ref]

The same boundary can therefore retain substances and communicate selectively with its surroundings. Membrane topology tells us which parts can meet a given ligand; lateral mobility of membrane proteins tells us whether two parts can approach each other along the boundary. A diagram of a cell membrane becomes more useful when it answers both questions.