The Cytoskeleton

Part two of my panicky revision series!

This is probably one of my weaker topics, so if you're going to use my answers here as your "study guide," be warned that you might be hindered more than helped unless you cross-check everything as well. (And if you do cross-check and find discrepancies, please let me know so that I don't screw up anyone else :) )

Q1: The role of ATP hydrolysis in actin polymerisation is similar to the role of GTP hydrolysis in tubulin polymerisation: both serve to weaken the bonds in the polymer and thereby promote depolymerisation. (True/False, explain why)

I think that this is true. The hydrolysed forms of ATP and GTP (ADP and GDP, respectively) do indeed promote depolymerisation as the free-energy change for a subunit with ADP/GDP bound is less than that for ATP/GTP.

Q2: Motor neurons trigger action potentials in muscle cell membranes that open voltage-sensitive Ca2+ channels in T tubules, allowing extracellular Ca2+ to enter the cytosol, bind to troponin C, and initiate rapid muscle contraction.

True. This is indeed how muscle neurons work to "fire" a muscle cell, provided that I comprehended the textbook correctly ;)

Q3: In most animal cells, minus-end directed microtubule motors deliver their cargo to the periphery of the cell, whereas plus-end directed microtubule motors deliver their cargo to the interior of the cell.

False. Microtubules grow out from a microtubule organising centre (MTOC), with minus ends at the middle and rapidly-growing plus ends radiating outwards. Hence minus-end directed motors take their cargo towards the MTOC (i.e. towards the interior of the cell), whereas plus-end directed microtubule motors travel away from the MTOC (i.e. towards the periphery of the cell).

Q4: The concentration of actin in cells is 50-100 times greater than the critical concentration observed for pure actin in a test tube. How is this possible? What prevents the actin subunits in cells from polymerising into filaments? Why is it advantageous to the cell to maintain such a large pool of actin subunits?

It is possible for the concentration of actin to be much greater than the critical concentration due to the presence of certain proteins that make polymerisation less favourable. One of these enzymes is thymosin. The large pool of actin filaments may serve as reserve "building blocks" when actin filaments are required for cell surface protrusions etc.

Q5: Detailed measurements of sarcomere length and tension during isometric contraction in striated muscle provided crucial early support for the sliding-filament model of muscle contraction. Based on your understanding of the sliding-filament model and the structure of a sarcomere, propose a molecular explanation for the relationship of tension to sarcomere length in the portions of figure Q16-1 marked I, II, III and IV. (In this muscle, the length of the myosin filament is 1.6 micrometres, and the lengths of the actin thin filaments that project from the Z discs are 1.0 micrometres.)

(Figure Q16-1 is a line graph with sarcomere length in micrometres along the x-axis and tension in % along the y-axis. At roughly 1.3 micrometres, there is 0% tension, at 1.6 micrometres, there is over 75% tension, at 2 and ~2.2 micrometres, there is 100% tension, and at 3.6 micrometres there is 0% tension.)

I'm going to go from longest to shortest, simply because that's easier for me. This is a question that I'm pretty shaky about, so please do correct me if there are errors in my logic.

At 3.6 micrometres, there is 0% tension because the filaments are simply laid out end-to-end. You see, there is a 1.0 micrometre actin filament, plus a 1.6 micrometre myosin filament, then another 1.0 micrometre actin filament, leading to a total of 3.6 micrometres at full length.

At 2 and ~2.2 micrometres, there is 100% tension because the sarcomere has contracted enough for the two actin filaments on either side to meet.

Since I've just noted that 2 micrometres is the length of the filament when actin filaments on either side have met, the question remains of how sarcomeres can shorten further. Perhaps myosin can continue to "crawl down" the actin filaments, with the actin filaments in the middle either overlapping or peeling off. This would probably contribute to the decrease in tension at 1.6 micrometres. However, if this were to continue, eventually the Z-discs would get in the way. At the moment I can't imagine how the sarcomere would be able to get down to 1.3 micrometres (less than the length of the myosin filament) without it "popping out" which may be why the tension has dropped down to 0%.

As I've said, I'm really shaky about this, so don't take my word for it.

Q6: At 1.4mg/mL pure tubulin, microtubules grow at a rate of about 2 micrometres/minute. At this growth rate, how many alpha/beta-tubulin dimers (8nm in length) are added to the ends of a microtubule each second?

Maths question... at least this one looks reasonably easy. 2 micrometres is equivalent to 2000 nanometres. 2000 nanometres divided by 60 seconds gives 33.3 nanometres per second (1 d.p.). 33.3/8 gives 4 alpha/beta tubulin dimers per second (nearest whole number).

Q7: A solution of pure alpha/beta-tubulin dimers is thought to nucleate microtubules by forming a linear protofilament about seven dimers in length. At that point, the probabilities that the next alpha-beta dimer will bind laterally or to the end of the protofilament are about equal. The critical event for microtubule formation is thought to be the first lateral association. How does lateral association promote the subsequent rapid formation of a microtubule?

I have no idea. My best guess is that it provides a larger surface area and more places where new molecules can make contact.

Q8: How does a centrosome "know" when it has found the centre of the cell?

If I remember correctly, the microtubules that radiate out from the centrosome will all exert roughly the same amount of tension when they are all roughly the same length. This helps the centrosome "know" when it has found the centre of the cell.

Q9: (warning this is long) The movements of single motor-protein molecules can be analysed directly. Using polarised laser light, it is possible to create interference patterns that exert a centrally directed force, ranging from zero at the centre to a few piconewtons at the periphery (about 200nm from the centre). Individual molecules that enter the interference pattern are rapidly pushed to the centre, allowing them to be captured and moved at the experimenter's discretion.

Using such "optical tweezers," single kinesin molecules can be positioned on a microtubule that is fixed to a coverslip. Although a single kinesin molecule cannot be seen optically, it can be tagged with a silica bead and tracked indirectly by following the bead. In the absence of ATP, the kinesin molecule remains at the centre of the interference pattern, but with ATP it moves toward the plus end of the microtubule. As kinesin moves along the microtubule, it encounters the force of the interference pattern, which stimulates the load kinesin carries during its actual function in the cell. Moreover, the pressure against the silica bead counters the effects of Brownian (thermal) motion, so that the position of the bead more accurately reflects the position of the kinesin molecule on the microtubule.

A. As shown in the figure (in the textbook), all movement of kinesin is one direction (toward the plus end of the microtubule). What supplies the free energy needed to ensure a unidirectional movement along the microtubule?

As movement only occurred in the presence of ATP, I think that it is safe to assume that ATP supplies the energy required for movement. I'm not sure if this alone actually guarantees unidirectional movement, however, or if it's related to some other part of kinesin's structure.

B. What is the average rate of movement of kinesin along the microtubule?

From the diagram in the book, it appears to be a bit less than 10nm/s- maybe around 9nm/s but hard to tell from the scale.

C. What is the length of each step that a kinesin takes as it moves along a microtubule?

Again from the size of the "steps" in the diagram in the book, it appears to be around 9-10nm/s, so it appears that kinesin takes one "step" per second.

D. From other studies it is known that kinesin has two globular domains that can each bind to beta-tubulin, and that kinesin moves along a single protofilament in a microtubule. In each protofilament, the beta-tubulin subunit repeats at 8-nm intervals. Given the step length and the interval between beta-tubulin subunits, how do you suppose a kinesin molecule moves along a microtubule?

Since kinesin has two globular domains, it wouldn't surprise me if kinesin walked in a sort of "hand-over-hand" motion, with the two domains acting as the "hands." These "hands" would grip onto beta-tubulin subunits.

E. Is there anything in the data that tells you how many ATP molecules are hydrolysed per step?

I don't think that there is, though I could be wrong.

Q10: A mitochondrion 1 micrometre long can travel the 1 metre length of the axon from the spinal cord to the big toe in a day. The Olympic men's freestyle swimming record for 200 metres is 1.75 minutes. In terms of body lengths per day, who is moving faster: the mitochondrion or the Olympic record holder? (Assume that the swimmer is 2 metres tall.)

1 metre = 1000 millimetres = 1 x 10^6 micrometres. The mitochondrion thus travels 1 x 10^6 body lengths in one day.

If the swimmer is 2 metres tall, then he travels 100 body lengths in 1.75 minutes. 100/1.75 = 57.14 body lengths a minute (2 d.p.). 57.14*60*24 = 82 286 body lengths in one day (nearest whole number).

Hence, in terms of body lengths per day, the mitochondrion is travelling faster.

Q11: Cofilin preferentially binds to older actin filaments and promotes their disassembly. How does cofilin distinguish old filaments from new ones?

New actin filaments have ATP bound to them. Over time, this ATP hydrolyses to form ADP. Cofilin can distinguish old filaments from new ones by recognising the presence of ADP or ATP.

Q12: Why is it that intermediate filaments have identical ends and lack polarity, whereas actin filaments and microtubules have two distinct ends with a defined polarity?

While the monomers that make up intermediate filaments have distinct ends (an amino and a carboxyl terminus), they line up anti-parallel with each other, so that half of the monomers are pointing in one direction and the other half are pointing in the other direction. This gives a net polarity of zero.

Actin filaments and microtubules, on the other hand, have distinct ends and do not line up anti-parallel with other monomers. This gives these filaments negative and positive ends.

Q13: How is the unidirectional motion of a lamellipodium maintained?

The unidirectional motion of a lamellipodium is maintained by the assembly of actin filaments at the leading edge, with depolymerisation, aided by cofilin, occurring away from the leading edge. This gives a net effect of the filament network appearing to "move forward."