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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.

Membrane topology specifies the sidedness of a membrane-associated polypeptide chain: where its N-terminus, C-terminus and intervening protein domains lie relative to the lipid bilayer. Side-specific placement is essential to interpreting a cell-surface receptor.^[ref]

For an original worked example, stipulate a continuous polypeptide chain with its N-terminus outside a biological cell, exactly three complete crossings of the cell membrane, and no additional excursions into the lipid bilayer. Its segments lie, in order, outside, inside, outside, inside. A protein domain between the first and second crossings faces the cytosol; one between the second and third faces the exterior; the C-terminus faces the cytosol. Counting crossings determines these placements without specifying an atomic protein structure.

The proof is a side-switching argument. Assign exterior the sign $+1$ and interior $-1$. Each complete crossing multiplies the sign by $-1$, so after $m$ crossings,An odd number puts the termini on opposite sides, an even number on the same side. This assumes complete crossings of one boundary; a chain that enters and returns to the same side without crossing must not be counted as a complete crossing. Nor does the rule determine which side the N-terminus starts on.

As a constructed accessibility test, put an epitope on the outside segment between crossings two and three, and another on the inside segment between crossings one and two. Stipulate an intact cell membrane that excludes the test antibody and accessible epitopes that bind it. Applying the antibody outside can label only the first epitope. If both become accessible after opening the boundary, the difference tests sidedness under those assumptions. Failure to label an epitope alone is insufficient: it could also be inaccessible because of protein folding or poor antibody affinity. This is a proposed reasoning exercise, separate from the historical mixing experiment below.

In 1970 Larry Frye and Michael Edidin fused mouse C11D and human VA-2 cell lines with Sendai virus, forming heterokaryons. Suspensions were maintained in a shaking water bath at $37{}^{\circ }\mathrm{C}$. Removed aliquots were stained by indirect immunofluorescence: antibodies against parental surface antigens, then differently fluorescent secondary antibodies. A Leitz Ortholux fluorescence microscope used a mercury lamp and color-selecting filters. Green mouse and red human surface patterns became intermixed.^[ref]

Same-species fusions tested antibody specificity; stable hybrid lines supplied a two-color control. Inhibitors of biological translation did not prevent mixing; lowering temperature inhibited it. These observations supported lateral redistribution over rapid synthesis. The authors could not conclusively exclude passage through cytoplasm and return. The readout compared populations, not trajectories of a continuously observed individual biological cell, and did not establish unrestricted motion of every membrane protein.^[ref]

The decisive design idea is to begin with spatially distinguishable material. A uniformly labeled surface can look unchanged while its components move. Bringing together differently identifiable parental surfaces creates an initial pattern whose loss reveals redistribution; antibody specificity makes that loss interpretable. Membrane topology asks which side a part faces, whereas this experiment asks where it can move along that side.

A protease protection assay asks whether a barrier prevents an added protease from reaching a protein. A membrane-disruption comparison tests whether protection depends on that barrier.

The membrane-disruption test was performed by David D. Sabatini and Günter Blobel in 1970. Rat-liver microsomes purified by sucrose centrifugation incorporated radioactive leucine during cell-free translation. Samples received cold trypsin and chymotrypsin, with or without membrane-solubilizing detergents. Electron microscopy checked vesicle preservation; size-exclusion chromatography separated protected fragment sizes. Large membrane-associated fragments lost protection after disruption, whereas small ribosome-protected fragments persisted. An exposed ribosome preparation remained digestible when mixed with microsomes, checking that membranes did not simply inhibit the proteases.^[ref]

To read the qualitative diagram, first compare untreated aliquots: they establish that detectable cargo exists before digestion. Next compare external protease with intact versus disrupted membranes. Persistence only while the barrier remains intact supports enclosure, provided the exposed-cargo control confirms active protease in both chemical conditions. The detergent-only aliquot checks that disruption itself does not destroy recovery or detection. Adding membranes after synthesis tests a different alternative: capture of a completed product rather than entry during biological translation.

This is an argument from controlled accessibility. Binding predicts membrane association but generally leaves an exposed cargo digestible. Enclosure predicts protection that depends on membrane integrity. However, protein aggregation, intrinsic resistance to proteolysis, inactive protease or undetected small fragments can obscure this distinction. For a transmembrane protein, expect protection of the enclosed portion rather than necessarily the full chain. Combine fragment size, compartment controls and membrane topology; a protected signal alone does not uniquely specify the whole protein's location.

Protein targeting directs a protein to its cellular destination. Synthesis in the cytosol does not imply that the protein works there.

For entry into the endoplasmic reticulum, distinguish three questions: does the nascent chain reach the membrane, does part of it cross into the ER lumen, and does a segment remain embedded as a transmembrane protein? Cotranslational protein translocation couples these events to biological translation. A signal peptide can initiate delivery without specifying the eventual destination of the mature protein.

This distinction matters experimentally. Finding a protein in a membrane-containing centrifugation pellet could reflect surface binding or protein aggregation. The microsomal protein import experiment instead asks whether an intact membrane prevents an external protease from reaching the product. That tests accessibility across a barrier, rather than proximity to it.

A thylakoid is a membrane-enclosed sac; its thylakoid membrane contains chlorophyll and light-dependent reactions machinery. A stack is a granum.^[ref]

The membrane and its enclosed fluid answer different location questions. A soluble protein in thylakoid lumen is inside the sac; a membrane protein is embedded in its boundary and can expose different parts on the two sides. Membrane topology and organelle protein import provide the reusable language for those distinctions.