= Solution
An animal <biological cell> must generate a protrusion, couple that protrusion to its surroundings, move its body and <cell nucleus>, and release or rearrange contacts behind it. <Cell polarity> makes these events persistent in one direction. At cellular scales, <inertia> is usually negligible: active forces balance resistance continuously, rather than giving the cell momentum that carries it forward after propulsion stops. <ATP> consumption maintains the system away from <thermodynamic equilibrium>.
At the front, <actin> polymerization can push the <cell membrane> into a <lamellipodium>. Whether this produces advance depends on coupling to the environment: without a mechanical grip, the <actin> network can move backward instead. On a flat adhesive substrate, <integrins> bind the <extracellular matrix> and connect through <focal adhesions> to the <cytoskeleton>. Regulated engagement transmits traction, while rearward <myosin> contraction and adhesion turnover move the rest of the cell. Adhesions must resist slipping long enough to transmit force but release to avoid anchoring the rear indefinitely. Another protrusive mechanism is a <membrane bleb>: local separation of the <cell membrane> from the <cell cortex>, driven by intracellular pressure, expands the membrane before a new cortex assembles underneath it.
A two-dimensional culture surface offers a broad basal contact area and little geometrical obstruction above the cell. A three-dimensional environment adds pore size, fibre orientation, <matrix stiffness>, and resistance from surrounding cells. The same cells may switch between elongated, strongly adhesive migration and more rounded, weakly adhesive movement. <Proteolysis> can enlarge a path through the <extracellular matrix>, but a sufficiently permissive existing pore need not require digestion. The relatively stiff <cell nucleus> can become the main bottleneck; its passage depends on deformation, confinement and force transmission. Extensive squeezing can damage the <nuclear envelope>, so migration speed alone is not a sufficient measure of successful transit.
A decisive experiment removed all functional <integrins> from mouse <leukocytes>. Their interstitial migration in three-dimensional environments persisted, and <myosin> became particularly important for passage through narrow gaps. This distinguishes force generation from a particular adhesion mechanism: confinement and friction can provide useful coupling even without integrin anchoring.<Rapid leukocyte migration by integrin-independent flowing and squeezing by Tim Lämmermann and others>[Figures 1–3, integrin-deficient migration in vivo and in three-dimensional networks; Figure 4, passage of the nucleus through constrictions]{ref}
Thus “three-dimensional migration requires stronger adhesion” is not a general rule. A useful comparison holds ligand density, <matrix stiffness> and pore geometry as independently controlled as possible, measures whole-cell and nuclear movement, and perturbs <actin>, <myosin>, <integrins> and matrix digestion separately. Differences then identify which mechanical requirement has changed, rather than treating dimensionality as a single unexplained variable.
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