Diffusion crosses a bacterium in a millisecond and a nerve axon in thirty years, so any cell larger than a bacterium needs a way of putting things where it wants them.
The first lesson of this course derived that limit and the previous one left a newly folded protein with an address but no transport. This lesson is the internal architecture that solves both problems at once: a set of protein filaments that give a cell its shape and provide tracks, and motors that walk along the tracks carrying cargo.
Three systems, distinguished by what they are for
Eukaryotic cells build three kinds of filament from three unrelated protein families, and the differences between them are functional rather than incidental.
Actin filaments are the thinnest, about 7 nm across, built from a 42 kilodalton monomer into a two-stranded helix. They are concentrated just under the plasma membrane, where they set the shape of the cell surface, and they are the tracks for myosin motors. They bind and hydrolyse ATP.
Microtubules are hollow tubes 25 nm across, built from a dimer of alpha and beta tubulin, about 100 kilodaltons, stacked head to tail into protofilaments of which thirteen lie side by side to make the wall. Each dimer occupies 8 nm of length, so a micrometre of microtubule contains about 1600 dimers. They radiate from an organising centre near the nucleus and are the tracks for kinesin and dynein. They bind and hydrolyse GTP.
Intermediate filaments are about 10 nm across and are the outlier in every respect. They are built from a large and diverse family, keratins in epithelia, lamins lining the nuclear envelope, neurofilaments in axons. They bind no nucleotide, they are not polar, and they support no motors. They are rope-like and their job is purely mechanical: resisting tension. A cell layer that is pulled and stretched, such as skin, depends on them, and the blistering disease epidermolysis bullosa simplex is caused by keratin mutations that let cells tear apart under ordinary handling.
The first two are polar, meaning the two ends of a filament are chemically distinct, conventionally plus and minus. Polarity is what makes directional transport possible: a motor that walks towards the plus end of a microtubule is thereby walking in a defined direction relative to the cell.
Polymers that spend energy to stay unstable
Actin and tubulin both hydrolyse a nucleotide when they polymerise, and the obvious explanation, that hydrolysis provides the energy for assembly, is wrong. Both proteins polymerise perfectly well with non-hydrolysable analogues. Hydrolysis buys something else, and what it buys is instability.
Consider a microtubule. A tubulin dimer arrives carrying GTP and adds to the plus end. Some time later the GTP is hydrolysed, and the resulting GDP-bound dimer would rather adopt a curved conformation that does not fit in a straight tube. So the body of a microtubule is built of subunits under strain, held straight only by their neighbours, and the whole structure is stable only because a cap of newly added, still GTP-bound dimers holds the end together.
Lose the cap, by adding subunits more slowly than hydrolysis proceeds, and the end springs apart. Tim Mitchison and Marc Kirschner discovered this in 1984 and called it dynamic instability: an individual microtubule grows steadily at one to two micrometres per minute, then abruptly switches to shrinking at ten to twenty micrometres per minute, roughly ten times faster, and may abruptly switch back. At any moment in a cell some microtubules are growing and others are collapsing, and the population is in steady state while no individual filament is.
The point of paying for this is search. A microtubule growing out from the centre of a cell explores in a straight line, collapses if it finds nothing, and is stabilised if its tip encounters a target that caps it. Repeated many times by many filaments, this is a search algorithm that finds targets anywhere in the cell volume without any information about where they are, and it is how a dividing cell finds its chromosomes, as the next lesson describes. Actin filaments do something related, treadmilling, in which subunits add at one end and leave at the other so the filament moves through space while keeping its length.
Example. Cells can be treated with drugs that destabilise microtubules, such as the vinca alkaloids, or that stabilise them, such as taxol. Both are used as anticancer chemotherapy, and both kill dividing cells. Why does the same clinical effect follow from opposite chemical effects?
Because what a dividing cell needs is not microtubules but microtubule dynamics. The spindle has to assemble rapidly, search for chromosomes, correct wrong attachments by releasing and retrying, and then shorten to pull chromosomes apart, and every one of those steps requires filaments that can grow and shrink. A drug that prevents growth removes the spindle; a drug that prevents shrinkage freezes it, so it cannot search, cannot correct errors and cannot pull. Either way the cell arrests in mitosis and eventually dies. That the two opposite treatments converge on the same outcome is strong evidence that the dynamics rather than the polymer is the functional entity, which is a conclusion no single drug could have supported. It also explains the characteristic side effects of both classes. The tissues that suffer are the ones that divide fastest, which is bone marrow, gut lining and hair follicle, and the other common toxicity is peripheral neuropathy, because axonal transport also depends on microtubules and a metre-long axon is the cell least able to tolerate its tracks being disrupted.
Now you. A microtubule grows at 1.5 µm/min and shrinks at 15 µm/min, and spends roughly equal time doing each. Colchicine, used for gout since antiquity, binds free tubulin dimers and prevents them adding to a filament. At low concentrations it does not measurably reduce the amount of polymer, yet it suppresses mitosis. Explain.
Answer
A drug that removes free dimers from the pool slows the rate of addition without removing anything already polymerised. Growth depends on addition and shrinkage does not, so growth slows while shrinkage does not, and the filament ends spend more time capped-marginal and less time growing robustly. What that suppresses is the dynamic behaviour, and at low occupancy the effect on total polymer mass is small because only a fraction of the free pool has been sequestered. This is the standard explanation for a general and initially puzzling observation, that these drugs suppress dynamics at concentrations far below those needed to depolymerise the cytoskeleton, and it is why the therapeutic doses of vinca alkaloids and taxol are much lower than their depolymerising or polymerising doses. The gout connection follows from the same mechanism by a different route: colchicine at low dose impairs the migration of neutrophils into an inflamed joint, and neutrophil crawling depends on cytoskeletal dynamics too. A drug used for two thousand years for a joint disease and a modern cytotoxic act on the same protein for the same reason.
Where a filament starts
Nothing so far said where a filament begins, and that turns out to be the step a cell actually controls.
Purified tubulin above a threshold concentration does not polymerise immediately. It shows a lag, then a burst of rapid growth, then a plateau. The lag is nucleation: forming the first small aggregate is unfavourable, because a two or three subunit cluster has almost all of its surface exposed and gains few contacts, while adding to an existing end is favourable. Adding pre-formed filament fragments as seeds abolishes the lag entirely, which is the direct demonstration that the slow step is starting rather than growing.
That asymmetry is a gift to a cell. Elongation is fast and spontaneous, so controlling the number of filaments only requires controlling how many are started, and a cell does that with dedicated nucleators rather than by changing subunit concentration. Microtubules are nucleated by rings of gamma-tubulin, mostly at the centrosome, which is why a microtubule array radiates from one place and why all the minus ends are anchored there. Actin is nucleated by the Arp2/3 complex, which binds the side of an existing filament and starts a new one at 70 degrees, generating the branched network that pushes a crawling cell forward, and by formins, which nucleate unbranched filaments and stay at the growing tip. Which nucleator is activated where is what decides whether a region of a cell produces a branched pushing meshwork or a long cable.
Example. Listeria was described above as recruiting the host's actin machinery. Given the nucleation argument, which host protein must the bacterial surface protein be activating, and why is that a more economical strategy than carrying its own actin?
It must be activating Arp2/3, the nucleator, and it does: the bacterial surface protein ActA mimics the host proteins that normally switch Arp2/3 on. The economy is exactly the asymmetry above. Elongation is spontaneous and needs no help, so a parasite that wants a large actin structure does not have to supply actin, or energy, or a motor. It only has to supply the signal that starts filaments, and the host's own subunit pool and ATP do the rest. One protein on a bacterial surface converts the host cytoskeleton into a propulsion system. The general principle is that in any process with a slow committed step and a fast spontaneous remainder, control and subversion both concentrate on the slow step, which is the same reasoning that put metabolic regulation at phosphofructokinase and transcriptional regulation at initiation.
Now you. A drug is wanted that blocks cell migration in metastatic tumour cells without paralysing the patient's muscles. Given this section, where would you aim it?
Answer
At a nucleator, not at actin or myosin. Actin and its motors are shared by the crawling cell and the muscle fibre, and anything that binds actin itself will hit both, which is why the classic actin drugs, phalloidin and the cytochalasins, are laboratory tools and not medicines. Nucleation is where the two differ: migration depends on Arp2/3 generating a branched network at a leading edge, and on the upstream regulators that activate it in response to signalling, whereas a sarcomere's filaments are stable, long-lived and not being continuously renucleated. Aiming at the branching machinery, or at the signalling proteins that switch it on, targets a process that migrating cells run continuously and muscle does not. The honest caveat is that Arp2/3 is also used by other motile cells including immune cells, so selectivity here buys separation from muscle and not from everything, and the same reasoning that identifies the target also predicts the side effects.
Motors
A motor protein binds a filament, binds a cargo, and converts ATP hydrolysis into directed movement. Three families do this: kinesins and dyneins walk on microtubules, myosins on actin.
Kinesin-1 is the best characterised and the numbers are worth having. It has two heads that alternate, moving hand over hand, verified in 2004 by labelling one head and watching it advance in 16 nm increments while the molecule as a whole advanced 8 nm each time. Each step is 8 nm, exactly the length of one tubulin dimer, and consumes exactly one ATP. It develops a stall force of about 5 to 7 piconewtons, travels at up to 800 nm/s, and stays attached for around a hundred steps, so it covers roughly 800 nm before falling off.
Two calculations put those numbers in context.
The work done in one step against a 5 piconewton load is J. One ATP, at 50 kJ/mol, is J. The motor is therefore about 48 per cent efficient, which is a remarkable figure for a machine of that size and comparable to the best heat engines.
And thermal energy at body temperature is J. So one ATP is about 19 and one working stroke about 9 . A motor protein operates less than an order of magnitude above the thermal noise it is immersed in, which is why individual steps are stochastic, why a motor sometimes steps backwards, and why the mechanism cannot be a rigid push. It is closer to a ratchet that biases motion that thermal agitation is providing anyway.
The payoff for a large cell is enormous. Fast axonal transport runs at about 1 µm/s, so a metre takes s, or 11.6 days. Diffusion over the same distance, from the first lesson, would take 32 years, a thousand times longer.
What the machinery is used for
Vesicle traffic. Everything the previous lesson routed, from endoplasmic reticulum to Golgi to surface, moves on microtubules with kinesin and dynein carrying the vesicles. Disrupt microtubules and the Golgi disperses within minutes, because its position is maintained rather than fixed.
Cell crawling. A migrating cell pushes its leading edge forward by polymerising actin against the membrane, and the force comes from polymerisation itself rather than from a motor. The clearest natural evidence comes from a pathogen: Listeria monocytogenes, once inside a cell, recruits the host's actin machinery to one pole and propels itself through the cytoplasm at up to 0.4 µm/s on a comet tail of polymerised actin, with no motor protein involved at all. That a bacterium carrying one surface protein can hijack the system and move was what convinced the field that polymerisation alone generates force.
Muscle. Skeletal muscle is the sliding of actin filaments past thick filaments of myosin, established by Andrew Huxley and Hugh Huxley independently in 1954 from the observation that the light and dark bands of a sarcomere change width in a pattern that filament shortening cannot explain and filament sliding can. It is the same actin and a relative of the same myosin as in a crawling amoeba, organised into a crystalline array.
Cilia and flagella. A eukaryotic cilium is a bundle of microtubules in the famous nine-plus-two arrangement, with dynein motors between adjacent doublets. Because the doublets are anchored, a motor trying to walk along its neighbour instead makes the bundle bend, and coordinated bending is a beat. Failure of the dynein arms causes primary ciliary dyskinesia, whose sufferers have chronic airway disease from unswept mucus, are usually infertile, and about half of whom have their internal organs mirror-reversed, because the left-right axis of a vertebrate embryo is set by cilia driving a directional flow across a node of cells. A defect in a motor protein determines which side your heart is on.
Why swimming is nothing like swimming
A bacterial flagellum is a different object again, a rigid helical propeller turned by a rotary motor in the membrane driven by the proton gradient rather than by ATP. Understanding why it rotates instead of beating requires one number.
The Reynolds number compares inertial to viscous forces, . For E. coli swimming at 30 µm/s with a body 2 µm long in water, . Inertia is irrelevant by five orders of magnitude. A bacterium that stops swimming coasts a distance smaller than an atom, and the water it moves through behaves, from its point of view, more like treacle than like water.
Edward Purcell drew the consequence in a 1977 lecture: at low Reynolds number, any motion that is reciprocal, the same sequence run backwards, produces no net displacement, because with no inertia the return stroke exactly undoes the power stroke. A scallop opening and closing goes nowhere. Swimming therefore requires a motion that is not its own reverse, which means either a rotating helix, as bacteria use, or a wave travelling along a flexible appendage, as a sperm tail does. The physics dictates the two available designs, and life uses both and nothing else.
Example. Vesicles are often carried by several motors at once, and a cargo pulled by two kinesins moves at much the same speed as one but detaches far less often. Why should the two quantities behave so differently?
Because speed and processivity depend on different things. An unloaded motor's speed is set by its own ATPase cycle, and adding a second motor does not make the first cycle faster, so the cargo moves at roughly one motor's speed. Detachment, by contrast, requires all attached motors to let go at the same time, and if each has an independent chance of releasing per unit time, the chance that two release simultaneously is much smaller than the chance that one does. Run length therefore grows steeply with motor number while velocity does not, which is exactly what is measured. Two consequences follow. A cell can tune how far a cargo travels simply by varying how many motors it attaches, without changing anything about the motor itself, which is a cheap control knob. And because opposite-polarity motors are frequently both present on the same vesicle, cargo often moves in a tug of war with reversals, and net direction is decided by which team is currently winning rather than by a switch. That sounds wasteful and it makes the system responsive, since changing the balance slightly redirects the cargo.
Now you. A large neuron may hold a hundred thousand mitochondria, and the ones at the far end of a metre-long axon were made in the cell body. Mitochondrial proteins have half-lives of days to weeks. What does the arithmetic imply about how such a cell is maintained?
Answer
Transport cannot be a one-off delivery, it has to be a continuous circulation. At 1 µm/s a mitochondrion takes about twelve days to reach the far end, which is comparable to the lifetime of the proteins inside it, so anything that simply travelled out and stayed would be degraded roughly as fast as it arrived. What actually happens is bidirectional traffic: mitochondria move outward on kinesin, inward on dynein, pause where energy demand is high, fuse with one another to exchange contents, and damaged ones are returned or degraded locally by autophagy. The cell maintains a distributed population rather than delivering to fixed positions. Two further implications are worth drawing. Transport is a major and permanent energy cost for a neuron, not an occasional activity, and anything that impairs it should damage the longest axons first, which is exactly the pattern of the length-dependent peripheral neuropathies caused by cytoskeletal drugs, by diabetes and by several inherited mutations in motor and mitochondrial proteins. And a cell shaped like this cannot rely on anything reaching its periphery by diffusion, which is why the first lesson's calculation, done on the back of an envelope with no biology in it at all, still constrains everything a neuron does.
The cytoskeleton has so far been described as infrastructure: shape, tracks, transport, position. Once a cell divides, the same components take on a different role. The microtubules that were searching the cytoplasm build a spindle and pull chromosomes apart; the actin that was shaping the cell surface forms a ring and cuts the cell in two. What decides when this happens, what makes sure it happens exactly once per copy of the genome, and what goes wrong when the checks fail is the last lesson of this course, and it closes the loop back to the first: every cell from a cell.