Cell division in higher organisms in bacteriaakosmrlj/MAE545_F2015/lecture9_slides.pdf2 Prophase...

MAE 545: Lecture 9 (10/15)

Cell division in higher organisms

Cell division in bacteria

2

ProphaseCell division in higher organisms

PROPHASE1centrosome

formingmitoticspindle

condensing replicated chromosome, consisting oftwo sister chromatids held together along their length

intactnuclearenvelope

kinetochore

At prophase, the replicated chromosomes, each consisting of two closely associated sister chromatids, condense. Outside the nucleus, the mitotic spindle assembles between the two centrosomes, which have replicated and moved apart. For simplicity, only three chromosomes are shown. In diploid cells, there would be two copies of each chromosome present. In the fluorescence micrograph, chromosomes are stained orange and microtubules are green.

PROMETAPHASE2Prometaphase starts abruptly with the breakdown of the nuclear envelope. Chromosomes can now attach to spindle microtubules via their kinetochores and undergo active movement.

centrosomeat spindlepole

kinetochoremicrotubule

chromosome in active motion

fragments ofnuclear envelope

METAPHASE3

At metaphase, the chromosomes are aligned at the equator of the spindle, midway between the spindle poles. The kinetochore microtubules attach sister chromatids to opposite poles of the spindle.

centrosome at spindle pole


PANEL 17–1: The Principle Stages of M Phase (Mitosis and Cytokinesis) in an Animal Cell980

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kinetochore







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Prometaphase

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Anaphase

Telophase

Cytokinesis

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ANAPHASE4At anaphase, the sister chromatids synchronously separate to form two daughter chromosomes, and each is pulled slowly toward the spindle pole it faces. The kinetochore microtubules get shorter, and the spindle poles also move apart; both processes contribute to chromosome segregation.

TELOPHASE5During telophase, the two sets of daughter chromo-somes arrive at the poles of the spindle and decondense. A new nuclear envelope reassembles around each set, completing the formation of two nuclei and marking the end of mitosis. The division of the cytoplasm begins with contraction of the contractile ring.

CYTOKINESIS6During cytokinesis, thecytoplasm is divided in two by a contractile ring of actin and myosin filaments, which pinches the cell in two to create two daughters, each with one nucleus.

shorteningkinetochoremicrotubule

spindle polemoving outward

set of daughter chromosomesat spindle pole

contractile ringstarting to contract

centrosomeinterpolarmicrotubules nuclear envelope reassembling

around individual chromosomes

daughter chromosomes

completed nuclear envelopesurrounds decondensingchromosomes

contractile ringcreating cleavagefurrow

re-formation of interphasearray of microtubules nucleatedby the centrosome

(Micrographs courtesy of Julie Canman and Ted Salmon.)

PROPHASE1centrosome




kinetochore







METAPHASE3




PANEL 17–1: The Principle Stages of M Phase (Mitosis and Cytokinesis) in an Animal Cell 981981















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Alberts et al., Molecular Biology of the Cell

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Cell division

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Growing microtubules can push centrosomes to the middle of the cell

“chap16.tex” — page 673[#51] 29/9/2012 11:03

10 mm

centrosome force due to pushingon wall

growing microtubulestubulin subunits(A)

(B)

minutes 3 6

Figure 16.51: Self-centeredcentrosomes. (A) Diagrams showingtime sequence of a self-centeringexperiment. Initially, a centrosome isadded to a microfabricated squarewell along with soluble tubulinsubunits. As the centrosome nucleatesgrowth of microtubules, individualmicrotubules grow and shrink in aprocess of dynamic instability. When amicrotubule tip contacts the wall ofthe chamber, it can continue to grow,resulting in a pushing force on thecentrosome. Eventually, asmicrotubules grow longer and pushagainst the wall in all directions, thecentrosome finds a stable position ofthe geometrical center of the well. (B)Frames from a video sequence usingdifferential interference contrast (DIC)microscopy show this process over aperiod of several minutes. (Adaptedfrom T. E. Holy et al., Proc. Natl Acad.Sci. USA 94:6228, 1997.)

this phenomenon is exploited by cells to set up a universal coor-dinate system whereby they are able to position their organellesat precise geographical locations in the enormous cellular volume.Specifically, if microtubules within a cell are labeled fluorescently,it can be seen that they typically emanate in a star-like array froma single point known as the centrosome. The centrosome is a tinyobject, less than 0.5 µm across, that nonetheless can position itselfnear the middle of a cell with typical sizes of tens of microns. Howdoes the centrosome find the cell center? One possible mechanismcan be demonstrated by a clever experiment illustrated in Figure 16.51that involves isolating a centrosome and dropping it into a nanofab-ricated hole with dimensions comparable to those of a cell. Thecentrosome on its own diffuses around aimlessly. However, if tubu-lin is added so that microtubules can grow from the centrosome, thecentrosome quickly (within minutes) zooms in to the geometric cen-ter of the hole, regardless of the hole shape. If the centrosome isgrabbed with a laser trap and displaced from its central location, itwill gently but insistently return to the center. The mechanism relieson the pushing forces at the tips of all of the microtubules when theyrun into the walls. Only when the centrosome is at the geometri-cal center of the enclosure do all of the forces cancel out. In livingcells of the fission yeast Schizosaccharomyces pombe, this mechanismhas been directly observed centering the nucleus halfway down thisrod-shaped cell by virtue of microtubules pushing against the twoopposite ends.

16.3.3 The Translocation Ratchet

Another fascinating kind of motor action introduced at the begin-ning of this chapter is associated with translocation. We argued thatbecause of the division of cells into different compartments, there

POLYMERIZATION AND TRANSLOCATION 673

R. Phillips et al., Physical Biology of the Cell

5

Spindle is organized by molecular motors984 Chapter 17: The Cell Cycle

proteins, also called chromokinesins, are plus-end directed motors that associate with chromosome arms and push the attached chromosome away from the pole (or the pole away from the chromosome). Finally, dyneins are minus-end directed motors that, together with associated proteins, organize microtubules at various locations in the cell. They link the plus ends of astral microtubules to components of the actin cytoskeleton at the cell cortex, for example; by moving toward the minus end of the microtubules, the dynein motors pull the spindle poles toward the cell cortex and away from each other.

Multiple Mechanisms Collaborate in the Assembly of a Bipolar Mitotic SpindleThe mitotic spindle must have two poles if it is to pull the two sets of sister chroma-tids to opposite ends of the cell in anaphase. In most animal cells, several mecha-nisms ensure the bipolarity of the spindle. One depends on centrosomes. A typi-cal animal cell enters mitosis with a pair of centrosomes, each of which nucleates a radial array of microtubules. The two centrosomes provide prefabricated spin-dle poles that greatly facilitate bipolar spindle assembly. The other mechanisms depend on the ability of mitotic chromosomes to nucleate and stabilize microtu-bules and on the ability of motor proteins to organize microtubules into a bipolar array. These “self-organization” mechanisms can produce a bipolar spindle even in cells lacking centrosomes.

We now describe the steps of spindle assembly, beginning with centrosome-dependent assembly in early mitosis. We then consider the self-organization mechanisms that do not require centrosomes and become particularly important after nuclear-envelope breakdown.

Centrosome Duplication Occurs Early in the Cell CycleMost animal cells contain a single centrosome that nucleates most of the cell’s cytoplasmic microtubules. The centrosome duplicates when the cell enters the cell cycle, so that by the time the cell reaches mitosis there are two centrosomes. Centrosome duplication begins at about the same time as the cell enters S phase. The G1/S-Cdk (a complex of cyclin E and Cdk2 in animal cells; see Table 17–1) that triggers cell-cycle entry also helps initiate centrosome duplication. The two cen-trioles in the centrosome separate, and each nucleates the formation of a single new centriole, resulting in two centriole pairs within an enlarged pericentriolar matrix (Figure 17–26). This centrosome pair remains together on one side of the nucleus until the cell enters mitosis.

There are interesting parallels between centrosome duplication and chromo-some duplication. Both use a semiconservative mechanism of duplication, in which the two halves separate and serve as templates for construction of a new half. Centrosomes, like chromosomes, must replicate once and only once per cell cycle, to ensure that the cell enters mitosis with only two copies: an incorrect number of centrosomes could lead to defects in spindle assembly and thus errors in chromosome segregation.

spindle microtubule

dynein

kinesin-4,10

kinesin-14

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+

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+

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Figure 17–25 Major motor proteins of the spindle. Four major classes of microtubule-dependent motor proteins (yellow boxes) contribute to spindle assembly and function (see text). The colored arrows indicate the direction of motor protein movement along a microtubule—blue toward the minus end and red toward the plus end.


PROPHASE1centrosome




kinetochore







METAPHASE3





spindle(metaphase)

6

991

How does plus-end depolymerization drive the kinetochore toward the pole? As we discussed earlier (see Figure 17–31C), Ndc80 complexes in the kineto-chore make multiple low-affinity attachments along the side of the microtubule. Because the attachments are constantly breaking and re-forming at new sites, the kinetochore remains attached to a microtubule even as the microtubule depoly-merizes. In principle, this could move the kinetochore toward the spindle pole.

A second poleward force is provided in some cell types by microtubule flux, whereby the microtubules themselves are pulled toward the spindle poles and dismantled at their minus ends. The mechanism underlying this poleward move-ment is not clear, although it might depend on forces generated by motor proteins and minus-end depolymerization at the spindle pole. In metaphase, the addition of new tubulin at the plus end of a microtubule compensates for the loss of tubulin at the minus end, so that microtubule length remains constant despite the move-ment of microtubules toward the spindle pole (Figure 17–35). Any kinetochore that is attached to a microtubule undergoing such flux experiences a poleward force, which contributes to the generation of tension at the kinetochore in meta-phase. Together with the kinetochore-based forces discussed above, flux also con-tributes to the poleward forces that move sister chromatids after they separate in anaphase.

A third force acting on chromosomes is the polar ejection force, or polar wind. Plus-end directed kinesin-4 and 10 motors on chromosome arms interact with interpolar microtubules and transport the chromosomes away from the spindle poles (see Figure 17–25). This force is particularly important in prometaphase and metaphase, when it helps push chromosome arms out from the spindle. This force might also help align the sister-chromatid pairs at the metaphase plate (Figure 17–36).

One of the most striking aspects of mitosis in vertebrate cells is the continu-ous oscillatory movement of the chromosomes in prometaphase and metaphase. When studied by video microscopy in newt lung cells, the movements are seen to switch between two states—a poleward state, when the chromosomes are pulled toward the pole, and an away-from-the-pole, or neutral, state, when the poleward forces are turned off and the polar ejection force pushes the chromosomes away

MITOSIS

(B) (C)

(D)

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dist

ance

“speckles”(A)

spindle pole

TUBULINREMOVAL

TUBULINREMOVAL

TUBULINADDITION

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speckles movingpoleward

MBoC6 m17.41/17.35

Figure 17–35 Microtubule flux in the metaphase spindle. (A) To observe microtubule flux, a very small amount of fluorescent tubulin is injected into living cells so that individual microtubules form with a very small proportion of fluorescent tubulin. Such microtubules have a speckled appearance when viewed by fluorescence microscopy. (B) Fluorescence micrograph of a mitotic spindle in a living newt lung epithelial cell. The chromosomes are colored brown, and the tubulin speckles are red. (C) The movement of individual speckles can be followed by time-lapse video microscopy. Images of the thin vertical boxed region (arrow) in (B), taken at sequential times, show that individual speckles move toward the poles at a rate of about 0.75 μm/min, indicating that the microtubules are moving poleward. (D) Microtubule length in the metaphase spindle does not change significantly because new tubulin subunits are added at the microtubule plus end at the same rate as tubulin subunits are removed from the minus end. (B and C, from T.J. Mitchison and E.D. Salmon, Nat. Cell Biol. 3:E17–21, 2001. With permission from Macmillan Publishers Ltd.)

991

How does plus-end depolymerization drive the kinetochore toward the pole? As we discussed earlier (see Figure 17–31C), Ndc80 complexes in the kineto-chore make multiple low-affinity attachments along the side of the microtubule. Because the attachments are constantly breaking and re-forming at new sites, the kinetochore remains attached to a microtubule even as the microtubule depoly-merizes. In principle, this could move the kinetochore toward the spindle pole.

A second poleward force is provided in some cell types by microtubule flux, whereby the microtubules themselves are pulled toward the spindle poles and dismantled at their minus ends. The mechanism underlying this poleward move-ment is not clear, although it might depend on forces generated by motor proteins and minus-end depolymerization at the spindle pole. In metaphase, the addition of new tubulin at the plus end of a microtubule compensates for the loss of tubulin at the minus end, so that microtubule length remains constant despite the move-ment of microtubules toward the spindle pole (Figure 17–35). Any kinetochore that is attached to a microtubule undergoing such flux experiences a poleward force, which contributes to the generation of tension at the kinetochore in meta-phase. Together with the kinetochore-based forces discussed above, flux also con-tributes to the poleward forces that move sister chromatids after they separate in anaphase.

A third force acting on chromosomes is the polar ejection force, or polar wind. Plus-end directed kinesin-4 and 10 motors on chromosome arms interact with interpolar microtubules and transport the chromosomes away from the spindle poles (see Figure 17–25). This force is particularly important in prometaphase and metaphase, when it helps push chromosome arms out from the spindle. This force might also help align the sister-chromatid pairs at the metaphase plate (Figure 17–36).

One of the most striking aspects of mitosis in vertebrate cells is the continu-ous oscillatory movement of the chromosomes in prometaphase and metaphase. When studied by video microscopy in newt lung cells, the movements are seen to switch between two states—a poleward state, when the chromosomes are pulled toward the pole, and an away-from-the-pole, or neutral, state, when the poleward forces are turned off and the polar ejection force pushes the chromosomes away

MITOSIS

(B) (C)

(D)

timedi

stan

ce“speckles”

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spindle pole

TUBULINREMOVAL

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TUBULINADDITION

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speckles movingpoleward

MBoC6 m17.41/17.35

Figure 17–35 Microtubule flux in the metaphase spindle. (A) To observe microtubule flux, a very small amount of fluorescent tubulin is injected into living cells so that individual microtubules form with a very small proportion of fluorescent tubulin. Such microtubules have a speckled appearance when viewed by fluorescence microscopy. (B) Fluorescence micrograph of a mitotic spindle in a living newt lung epithelial cell. The chromosomes are colored brown, and the tubulin speckles are red. (C) The movement of individual speckles can be followed by time-lapse video microscopy. Images of the thin vertical boxed region (arrow) in (B), taken at sequential times, show that individual speckles move toward the poles at a rate of about 0.75 μm/min, indicating that the microtubules are moving poleward. (D) Microtubule length in the metaphase spindle does not change significantly because new tubulin subunits are added at the microtubule plus end at the same rate as tubulin subunits are removed from the minus end. (B and C, from T.J. Mitchison and E.D. Salmon, Nat. Cell Biol. 3:E17–21, 2001. With permission from Macmillan Publishers Ltd.)

Microtubules are depolymerized at spindle poles


extended periods (minutes),whereas the viscoelastic relaxationtime is estimated to be on theorder of milliseconds, suggestingthat the elastic forces dominate theforce balance [6]. In general,viscous drag forces are probablynegligible, as a 1 µm radius sphere(modelling a chromosome) movingat 1 µm per minute experiences adrag force of ~1 fN, about 1000-fold less than the stall force of asingle molecular motor [7].

What Goshima et al. [2] havenow done is perform a perturbationanalysis where the concentrationsof putative spindle lengthregulators are systematicallydecreased, through RNAinterference (RNAi), or increased,through overexpression, and theeffect on spindle length measuredquantitatively using an automatedmicroscope and image analysissystem. Starting with an initial dataset of about one million cells, theirmachine identified a ‘small’ subsetthat was mitotic, so that thousandsof mitotic cells were analyzed.They found that, in S2 cells, it wasthe regulators of microtubuleassembly dynamics that had thestrongest effect on spindle length.These regulators included theassembly-promoting moleculesEB1, Msps (Dis1/XMAP215/TOG),and Mast/Orbit (CLASP), and thedisassembly-promoting moleculesKlp10A (Kinesin-13) and Klp67A(Kinesin-8). Eliminating sisterchromatid cohesion also led to a

significant increase in spindlelength. Interestingly, perturbing theconcentration of Klp61F (Kinesin-5), which is thought to be the mainforce generator in the spindle, hadvery little effect on spindle lengthover a broad range ofconcentrations. Below a criticalconcentration of Klp61F, however,the spindle completely collapsedinto a monopolar array ofmicrotubules.

To explain this effect, Goshimaet al. [2] used a previouslypublished mathematical model forspindle length during anaphase,extending it to metaphase byincluding spindle elasticity,kinetochore microtubules, andsister chromatid cohesion [8,9].Even with these effects included,however, the model did not settleto a steady-state length, butrather grew to infinity. Toestablish a steady-state, theauthors then considered a‘coupling assumption,’ where theKinesin-5 sliding activity promotesmicrotubule depolymerization. Forconcreteness and illustrationpurposes only, one potentialscenario is sketched in Figure 2.This coupling, where thedepolymerization rate dependsexponentially on the sliding force,saturating to a maximum rate atlarge forces, enabled a steady-state spindle length to beachieved.

Interestingly, the model alsopredicts the collapse of the spindle

below a threshold concentration ofKinesin-5. Goshima et al. [2]acknowledge that other couplingassumptions might be consideredas well, and that further evaluationwill be needed. For example,recent analysis of budding yeastand Xenopus extract spindlessuggest that tension on thekinetochore can trigger a biastowards assembly, or attenuationof disassembly, at the plus ends[10,11]. Nevertheless, the modelmakes a surprising predictionabout spindle stability that turnsout to be true.

Spindle length regulation hasbeen studied most extensively inbudding yeast [12]. As in the S2cells, the spindle length in buddingyeast is fairly constant inmetaphase [13]. But there is noevidence for minus-enddisassembly, simplifying analysisof the system [14]. Also, only fourmotors enter the nucleus, Cin8p(Kinesin-5), Kip1p (Kinesin-5),Kar3p (Kinesin-14), and Kip3p(Kinesin-8), and from deletionmutant analysis, it was deducedthat Cin8p and Kip1p act as slidingmotors to elongate the spindle,while Kar3p acts antagonisticallyto shorten spindles [15]. Thebudding yeast system also permitsrough estimation of the magnitudeof the inward tensional force onchromatin, which fromchromosome marking experimentsis estimated in metaphase to besufficient to force nucleosomerelease [16,17]. From in vitrostudies with laser tweezers, thissuggests an average tensionalforce exceeding 15 pN perchromosome [18]. Given that thereare 16 chromosomes, then thetotal inward tensional force isestimated to be >240 pN, implyingan outward extensional force of>240 pN, neglecting net tension orcompression exerted from outsidethe spindle.

In the Xenopus extract system,the addition of monastrol, a drugthat interferes with Eg5 (Kinesin-5)function, was recently reported tocause a ‘switch-like transition’from bipolar to monopolar as afunction of increasing monastrolconcentration, with little effect onspindle length noted at sub-threshold concentrations [19].Interestingly, even though spindle

Current Biology Vol 15 No 23R958

Figure 2. A hypotheticalmodel for force-assemblycoupling at the pole.(A) Microtubule minus endsembedded in the pole (darkblue) tend to depolymerizeslowly when under lowsliding force (Fsliding). Thatdepolymerization occurs atall may be because adepolymerase (red circles),such as Klp10A (Kinesin-13), acts at the pole toincrease the depolymeriza-tion velocity (Vdepoly) locally.(B) If the sliding force isincreased, then the concen-tration of depolymeraseincreases locally so that thedepolymerization rate

increases. In their report, Goshima et al. [2] are justifiably nonspecific about the detailedmechanism of coupling, focusing instead on its mathematical form and general impor-tance in order to have a steady-state length at all. The cartoon here is meant for illus-tration purposes only, depicting just one way in which the mathematical model ofGoshima et al. [2] for force-assembly coupling could operate mechanistically.

Fsliding

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Current Biology

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extended periods (minutes),whereas the viscoelastic relaxationtime is estimated to be on theorder of milliseconds, suggestingthat the elastic forces dominate theforce balance [6]. In general,viscous drag forces are probablynegligible, as a 1 µm radius sphere(modelling a chromosome) movingat 1 µm per minute experiences adrag force of ~1 fN, about 1000-fold less than the stall force of asingle molecular motor [7].











Fsliding

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BDepolymerization is done

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D.J. Odde, Current Biol. 15, R956-R959 (2005)

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Microtubules attach to chromosomes via kinetochore

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they separate in anaphase. How is this mode of attachment, called bi-orienta-tion, achieved? What prevents the attachment of both kinetochores to the same spindle pole or the attachment of one kinetochore to both spindle poles? Part of the answer is that sister kinetochores are constructed in a back-to-back orienta-tion that reduces the likelihood that both kinetochores can face the same spindle pole. Nevertheless, incorrect attachments do occur, and elegant regulatory mech-anisms have evolved to correct them.

Incorrect attachments are corrected by a system of trial and error that is based on a simple principle: incorrect attachments are highly unstable and do not last, whereas correct attachments become locked in place. How does the kinetochore sense a correct attachment? The answer appears to be tension (Figure 17–33). When a sister-chromatid pair is properly bi-oriented on the spindle, the two kine-tochores are pulled in opposite directions by strong poleward forces. Sister-chro-matid cohesion resists these poleward forces, creating high levels of tension within the kinetochores. When chromosomes are incorrectly attached—when both sis-ter chromatids are attached to the same spindle pole, for example—tension is low

MITOSIS

(C) UNSTABLE (D) STABLE(B) UNSTABLE

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Figure 17-32 Chromosome attachment to the mitotic spindle in animal cells. (A) In late prophase of most animal cells, the mitotic spindle poles have moved to opposite sides of the nuclear envelope, with an array of overlapping microtubules between them. (B) Following nuclear envelope breakdown, the sister-chromatid pairs are exposed to the large number of dynamic plus ends of microtubules radiating from the spindle poles. In most cases, the kinetochores are first attached to the sides of these microtubules, while at the same time the arms of the chromosomes are pushed outward from the spindle interior, preventing the arms from blocking microtubule access to the kinetochores. (C) Eventually, the laterally-attached sister chromatids are arranged in a ring around the outside of the spindle. Most of the microtubules are concentrated in this ring, so that the spindle is relatively hollow inside. (D) Dynamic microtubule plus ends eventually encounter the kinetochores in an end-on orientation and are captured and stabilized. (E) Stable end-on attachment to both poles results in bi-orientation. Additional microtubules are attached to the kinetochore, resulting in a kinetochore fiber containing 10–40 microtubules.

Figure 17–33 Alternative forms of kinetochore attachment to the spindle poles. (A) Initially, a single microtubule from a spindle pole binds to one kinetochore in a sister-chromatid pair. Additional microtubules can then bind to the chromosome in various ways. (B) A microtubule from the same spindle pole can attach to the other sister kinetochore, or (C) microtubules from both spindle poles can attach to the same kinetochore. These incorrect attachments are unstable, however, so that one of the two microtubules tends to dissociate. (D) When a microtubule from the opposite pole binds to the second kinetochore, the sister kinetochores are thought to sense tension across their microtubule-binding sites. This triggers an increase in microtubule binding affinity, thereby locking the correct attachment in place.

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988 Chapter 17: The Cell Cycle

plus ends coming from two directions. However, the kinetochores do not instantly achieve the correct ‘end-on’ microtubule attachment to both spindle poles. Instead, detailed studies with light and electron microscopy show that most initial attachments are unstable lateral attachments, in which a kinetochore attaches to the side of a passing microtubule, with assistance from kinesin motor proteins in the outer kinetochore. Soon, however, the dynamic microtubule plus ends cap-ture the kinetochores in the correct end-on orientation (Figure 17–32).

Another attachment mechanism also plays a part, particularly in the absence of centrosomes. Careful microscopic analysis suggests that short microtubules in the vicinity of the chromosomes become embedded in the plus-end-binding sites of the kinetochore. Polymerization at these plus ends then results in growth of the microtubules away from the kinetochore. The minus ends of these kineto-chore microtubules are eventually cross-linked to other minus ends and focused by motor proteins at the spindle pole (see Figure 17–28).

Bi-orientation Is Achieved by Trial and ErrorThe success of mitosis demands that sister chromatids in a pair attach to opposite poles of the mitotic spindle, so that they move to opposite ends of the cell when

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Figure 17–30 The kinetochore. (A) A fluorescence micrograph of a metaphase chromosome stained with a DNA-binding fluorescent dye and with human autoantibodies that react with specific kinetochore proteins. The two kinetochores, one associated with each sister chromatid, are stained red. (B) A drawing of a metaphase chromosome showing its two sister chromatids attached to the plus ends of kinetochore microtubules. Each kinetochore forms a plaque on the surface of the centromere. (C) Electron micrograph of an anaphase chromatid with microtubules attached to its kinetochore. While most kinetochores have a trilaminar structure, the one shown here (from a green alga) has an unusually complex structure with additional layers. (A, courtesy of B.R. Brinkley; C, from J.D. Pickett-Heaps and L.C. Fowke, Aust. J. Biol. Sci. 23:71–92, 1970. With permission from CSIRO.)

Figure 17–31 Microtubule attachment sites in the kinetochore. (A) In this electron micrograph of a mammalian kinetochore, the chromosome is on the right, and the plus ends of multiple microtubules are embedded in the outer kinetochore on the left. (B) Electron tomography (discussed in Chapter 9) was used to construct a low-resolution three-dimensional image of the outer kinetochore in (A). Several microtubules (in multiple colors) are embedded in fibrous material of the kinetochore, which is thought to be composed of the Ndc80 complex and other proteins. (C) Each microtubule is attached to the kinetochore by interactions with multiple copies of the Ndc80 complex (blue). This complex binds to the sides of the microtubule near its plus end, allowing polymerization and depolymerization to occur while the microtubule remains attached to the kinetochore. (A and B, from Y. Dong et al., Nature Cell Biol. 9:516–522, 2007. With permission from Macmillan Publishers Ltd.)

plus end of microtubule

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plus ends coming from two directions. However, the kinetochores do not instantly achieve the correct ‘end-on’ microtubule attachment to both spindle poles. Instead, detailed studies with light and electron microscopy show that most initial attachments are unstable lateral attachments, in which a kinetochore attaches to the side of a passing microtubule, with assistance from kinesin motor proteins in the outer kinetochore. Soon, however, the dynamic microtubule plus ends cap-ture the kinetochores in the correct end-on orientation (Figure 17–32).

Another attachment mechanism also plays a part, particularly in the absence of centrosomes. Careful microscopic analysis suggests that short microtubules in the vicinity of the chromosomes become embedded in the plus-end-binding sites of the kinetochore. Polymerization at these plus ends then results in growth of the microtubules away from the kinetochore. The minus ends of these kineto-chore microtubules are eventually cross-linked to other minus ends and focused by motor proteins at the spindle pole (see Figure 17–28).

Bi-orientation Is Achieved by Trial and ErrorThe success of mitosis demands that sister chromatids in a pair attach to opposite poles of the mitotic spindle, so that they move to opposite ends of the cell when

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replicatedchromosome

centromere regionof chromosome kinetochore

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Figure 17–30 The kinetochore. (A) A fluorescence micrograph of a metaphase chromosome stained with a DNA-binding fluorescent dye and with human autoantibodies that react with specific kinetochore proteins. The two kinetochores, one associated with each sister chromatid, are stained red. (B) A drawing of a metaphase chromosome showing its two sister chromatids attached to the plus ends of kinetochore microtubules. Each kinetochore forms a plaque on the surface of the centromere. (C) Electron micrograph of an anaphase chromatid with microtubules attached to its kinetochore. While most kinetochores have a trilaminar structure, the one shown here (from a green alga) has an unusually complex structure with additional layers. (A, courtesy of B.R. Brinkley; C, from J.D. Pickett-Heaps and L.C. Fowke, Aust. J. Biol. Sci. 23:71–92, 1970. With permission from CSIRO.)

Figure 17–31 Microtubule attachment sites in the kinetochore. (A) In this electron micrograph of a mammalian kinetochore, the chromosome is on the right, and the plus ends of multiple microtubules are embedded in the outer kinetochore on the left. (B) Electron tomography (discussed in Chapter 9) was used to construct a low-resolution three-dimensional image of the outer kinetochore in (A). Several microtubules (in multiple colors) are embedded in fibrous material of the kinetochore, which is thought to be composed of the Ndc80 complex and other proteins. (C) Each microtubule is attached to the kinetochore by interactions with multiple copies of the Ndc80 complex (blue). This complex binds to the sides of the microtubule near its plus end, allowing polymerization and depolymerization to occur while the microtubule remains attached to the kinetochore. (A and B, from Y. Dong et al., Nature Cell Biol. 9:516–522, 2007. With permission from Macmillan Publishers Ltd.)

plus end of microtubule

kinetochore(A) (C)(B)

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100 nm

kinetochore

Tension sensed by sister kinetochores increases

binding affinity for microtubules and locks them

in the correct attachment

kinetochore


depolymerization of microtubules at spindle poles produces tension

8


the proteins that hold the sister chromatids together. APC/C also promotes cyclin destruction and thus the inactivation of M-Cdk. The resulting dephosphorylation of Cdk targets is required for the events that complete mitosis, including the disassem-bly of the spindle and the re-formation of the nuclear envelope.

CYTOKINESISThe final step in the cell cycle is cytokinesis, the division of the cytoplasm in two. In most cells, cytokinesis follows every mitosis, although some cells, such as early Drosophila embryos and some mammalian hepatocytes and heart muscle cells, undergo mitosis without cytokinesis and thereby acquire multiple nuclei. In most animal cells, cytokinesis begins in anaphase and ends shortly after the comple-tion of mitosis in telophase.

The first visible change of cytokinesis in an animal cell is the sudden appear-ance of a pucker, or cleavage furrow, on the cell surface. The furrow rapidly deep-ens and spreads around the cell until it completely divides the cell in two. The structure underlying this process is the contractile ring—a dynamic assembly composed of actin filaments, myosin II filaments, and many structural and regula-tory proteins. During anaphase, the ring assembles just beneath the plasma mem-brane (Figure 17–41; see also Panel 17–1). The ring gradually contracts, and, at the same time, fusion of intracellular vesicles with the plasma membrane inserts new membrane adjacent to the ring. This addition of membrane compensates for the increase in surface area that accompanies cytoplasmic division. When ring contraction is completed, membrane insertion and fusion seal the gap between the daughter cells.

Actin and Myosin II in the Contractile Ring Generate the Force for CytokinesisIn interphase cells, actin and myosin II filaments form a cortical network underly-ing the plasma membrane. In some cells, they also form large cytoplasmic bundles called stress fibers (discussed in Chapter 16). As cells enter mitosis, these arrays of actin and myosin disassemble; much of the actin reorganizes, and myosin II filaments are released. As the sister chromatids separate in anaphase, actin and myosin II begin to accumulate in the rapidly assembling contractile ring (Figure 17–42), which also contains numerous other proteins that provide structural sup-port or assist in ring assembly. Assembly of the contractile ring results in part from the local formation of new actin filaments, which depends on formin proteins that

Figure 17–41 Cytokinesis. (A) The actin–myosin bundles of the contractile ring are oriented as shown, so that their contraction pulls the membrane inward. (B) In this low-magnification scanning electron micrograph of a cleaving frog egg, the cleavage furrow is especially prominent, as the cell is unusually large. The furrowing of the cell membrane is caused by the activity of the contractile ring underneath it. (C) The surface of a furrow at higher magnification. (B and C, from H.W. Beams and R.G. Kessel, Am. Sci. 64:279–290, 1976. With permission from Sigma Xi.)

actin and myosin filaments of thecontractile ring

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(A)

25 µm(B)


Once all chromosomes are correctly attached to microtubules, they break into pair of chromatids, which are then pulled towards centrosomes

995

Segregated Chromosomes Are Packaged in Daughter Nuclei at TelophaseBy the end of anaphase, the daughter chromosomes have segregated into two equal groups at opposite ends of the cell. In telophase, the final stage of mitosis, the two sets of chromosomes are packaged into a pair of daughter nuclei. The first major event of telophase is the disassembly of the mitotic spindle, followed by the re-formation of the nuclear envelope. Initially, nuclear membrane fragments associate with the surface of individual chromosomes. These membrane frag-ments fuse to partly enclose clusters of chromosomes and then coalesce to re-form the complete nuclear envelope. Nuclear pore complexes are incorporated into the envelope, the nuclear lamina re-forms, and the envelope once again becomes continuous with the endoplasmic reticulum. Once the nuclear enve-lope has re-formed, the pore complexes pump in nuclear proteins, the nucleus expands, and the mitotic chromosomes are reorganized into their interphase state, allowing gene transcription to resume. A new nucleus has been created, and mitosis is complete. All that remains is for the cell to complete its division into two.

We saw earlier that phosphorylation of various proteins by M-Cdk promotes spindle assembly, chromosome condensation, and nuclear-envelope breakdown in early mitosis. It is thus not surprising that the dephosphorylation of these same proteins is required for spindle disassembly and the re-formation of daughter nuclei in telophase. In principle, these dephosphorylations and the completion of mitosis could be triggered by the inactivation of Cdks, the activation of phos-phatases, or both. Although Cdk inactivation—resulting primarily from cyclin destruction—is mainly responsible in most cells, some cells also rely on activa-tion of phosphatases. In budding yeast, for example, the completion of mitosis depends on the activation of a phosphatase called Cdc14, which dephosphory-lates a subset of Cdk substrates involved in anaphase and telophase.

SummaryM-Cdk triggers the events of early mitosis, including chromosome condensation, assembly of the mitotic spindle, and bipolar attachment of the sister-chromatid pairs to microtubules of the spindle. Spindle formation in animal cells depends largely on the ability of mitotic chromosomes to stimulate local microtubule nucle-ation and stability, as well as on the ability of motor proteins to organize micro-tubules into a bipolar array. Many cells also use centrosomes to facilitate spindle assembly. Anaphase is triggered by the APC/C, which stimulates the destruction of

MITOSIS

Figure 17–40 The two processes of anaphase in mammalian cells. Separated sister chromatids move toward the poles in anaphase A. In anaphase B, the two spindle poles move apart.

ANAPHASE A

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Contractile ring involving actin and myosin motors divides the cell in two

Cell division

9

exerted primarily at kinetochores [17, 21–24]. Klp10Aand EB1, on the other hand, are concentrated at the cen-trosome, although both are likely to modulate MT assem-bly throughout the mitotic cytoplasm as well [3, 4, 16].To interfere with sister-chromosome tension, we de-pleted the critical sister-chromatid-cohesion protein,Rad21 (cohesin) [15]. Our results show that modulatorsof MT dynamics and chromatid cohesion are the majorgovernors of spindle length. In contrast, bipolar spindlelength is robust to changes in MT sliding forces pro-duced by the Kinesin-5. We produce a mathematicalmodel that provides a framework for understandingthese observations.

Results and Discussion

Mitotic cells are relatively rare in the S2-cell population(1%–3%). Therefore, we required a method to obtainimages of sufficient numbers of mitotic spindles forquantitation and statistical comparison among differentRNAi treatments. In most cases, we employed a high-throughput procedure of image collection and analysis,as summarized below and in Figure 1 (and Figure S1 inthe Supplemental Data available with this article online)

for control GFP-tubulin-expressing cells [3]. Cells wereplated onto concanavalin-A-coated, 96-well glass-bot-tom dishes and then fixed and stained for g-tubulin (asa marker of centrosome locations) and chromosomes(Figure 1A). For the majority of our experiments, imageswere collected with a high-throughput automated mi-croscope, and a semiautomated image-analysis proce-dure was used to identify the rare mitotic cells in the im-ages. This algorithm, which took advantage of the factthat most interphase S2 cells do not exhibit punctuatesignals of g-tubulin [3], recognizes g-tubulin spots andidentifies a cell as mitotic if it contains a pair of g-tubulinspots with a DAPI-staining chromosomal mass in be-tween (Figure 1B). During this process, g-tubulin spot–spot distances were measured automatically. Potentialmetaphase cells were then displayed into visual galler-ies, and a manual selection was performed to eliminateprophase, anaphase, and aberrant interphase cells aswell as metaphase cells with multipolar spindles, whichhad been also selected by the automated selection pro-cess (see Figure S1 for an example of manual selection).The average distribution of the spindle length (herein de-finedascentrosome-to-centrosomedistance) in703con-trol cells from several experiments was 11.5 6 2.0 mm

Figure 1. High-Throughput, Semiautomated Measurement of Metaphase Spindle Length of Drosophila S2 Cells

(A) A raw image taken by the automated ImageXpress microscope with a 403 objective. Control GFP-tubulin cells were stained with g-tubulin(red) and chromosomes (blue). GFP is shown in green.(B) Enhanced signals of g-tubulin and chromosomes (see Supplemental Experimental Procedures). Two metaphase cells and one anaphase cellwere detected by the existence of two g-tubulin signals and chromosome masses in between. Most of the interphase cells were not stained byg-tubulin antibody.(C) A gallery of metaphase cells. After automated detection of g-tubulin-stained cells, all the nonmetaphase cells were eliminated by manualselection. Cell shape was estimated by the boundary of the diffuse GFP signals in the cytoplasm (white circle), and GFP expression level wasquantified as the signal intensity within the area. The bar represents 10 mm.(D) Distribution of metaphase spindle length of control GFP-tubulin cells. Data from 703 mitoticcells were combined. Average length (11.5 6 2.0 mm)was well reproduced in each experiment (see Table S1).(E) Spindle length was plotted against GFP intensity. No statistically significant correlation was found between GFP level and spindle length, in-dicating that GFP-tubulin expression itself did not perturb the spindle.

Current Biology1980

Spindle length is similar across the cells

G. Goshima et al., Current Biol. 15, 1979-1988 (2005)

10µm

exerted primarily at kinetochores [17, 21–24]. Klp10Aand EB1, on the other hand, are concentrated at the cen-trosome, although both are likely to modulate MT assem-bly throughout the mitotic cytoplasm as well [3, 4, 16].To interfere with sister-chromosome tension, we de-pleted the critical sister-chromatid-cohesion protein,Rad21 (cohesin) [15]. Our results show that modulatorsof MT dynamics and chromatid cohesion are the majorgovernors of spindle length. In contrast, bipolar spindlelength is robust to changes in MT sliding forces pro-duced by the Kinesin-5. We produce a mathematicalmodel that provides a framework for understandingthese observations.

Results and Discussion

Mitotic cells are relatively rare in the S2-cell population(1%–3%). Therefore, we required a method to obtainimages of sufficient numbers of mitotic spindles forquantitation and statistical comparison among differentRNAi treatments. In most cases, we employed a high-throughput procedure of image collection and analysis,as summarized below and in Figure 1 (and Figure S1 inthe Supplemental Data available with this article online)

for control GFP-tubulin-expressing cells [3]. Cells wereplated onto concanavalin-A-coated, 96-well glass-bot-tom dishes and then fixed and stained for g-tubulin (asa marker of centrosome locations) and chromosomes(Figure 1A). For the majority of our experiments, imageswere collected with a high-throughput automated mi-croscope, and a semiautomated image-analysis proce-dure was used to identify the rare mitotic cells in the im-ages. This algorithm, which took advantage of the factthat most interphase S2 cells do not exhibit punctuatesignals of g-tubulin [3], recognizes g-tubulin spots andidentifies a cell as mitotic if it contains a pair of g-tubulinspots with a DAPI-staining chromosomal mass in be-tween (Figure 1B). During this process, g-tubulin spot–spot distances were measured automatically. Potentialmetaphase cells were then displayed into visual galler-ies, and a manual selection was performed to eliminateprophase, anaphase, and aberrant interphase cells aswell as metaphase cells with multipolar spindles, whichhad been also selected by the automated selection pro-cess (see Figure S1 for an example of manual selection).The average distribution of the spindle length (herein de-finedascentrosome-to-centrosomedistance) in703con-trol cells from several experiments was 11.5 6 2.0 mm

Figure 1. High-Throughput, Semiautomated Measurement of Metaphase Spindle Length of Drosophila S2 Cells

(A) A raw image taken by the automated ImageXpress microscope with a 403 objective. Control GFP-tubulin cells were stained with g-tubulin(red) and chromosomes (blue). GFP is shown in green.(B) Enhanced signals of g-tubulin and chromosomes (see Supplemental Experimental Procedures). Two metaphase cells and one anaphase cellwere detected by the existence of two g-tubulin signals and chromosome masses in between. Most of the interphase cells were not stained byg-tubulin antibody.(C) A gallery of metaphase cells. After automated detection of g-tubulin-stained cells, all the nonmetaphase cells were eliminated by manualselection. Cell shape was estimated by the boundary of the diffuse GFP signals in the cytoplasm (white circle), and GFP expression level wasquantified as the signal intensity within the area. The bar represents 10 mm.(D) Distribution of metaphase spindle length of control GFP-tubulin cells. Data from 703mitoticcells were combined. Average length (11.5 6 2.0 mm)was well reproduced in each experiment (see Table S1).(E) Spindle length was plotted against GFP intensity. No statistically significant correlation was found between GFP level and spindle length, in-dicating that GFP-tubulin expression itself did not perturb the spindle.

Current Biology1980

Spindles in Drosophila cells

cell nuclei microtubulesspindle poles

10

How various factors affect the spindle length?


Certain factors are removed with RNA interference

(Figure 1D). This length distribution was broader thanthose observed in yeast or fly embryos [6, 10]. However,using a sufficient sample, we obtained consistent aver-age metaphase spindle length among experiments(10.95–11.84 mm; Table S1). By plotting spindle lengthversus GFP intensity for individual cells, we also estab-lished that the spindle length was independent of GFP-tubulin expression levels (Figure 1E).

Next, we applied the same procedure to examinemetaphase spindle length in cells depleted of variousproteins by RNAi (Figure 2; see also Table S1 for statis-tical summary). One general caveat of RNAi approach isthat the targeted proteins are not completely depletedand that the observed phenotypes (especially ‘‘no phe-notype’’) could be still ‘‘hypomorphic’’ as a result ofthe residual proteins. Although this is also the case ofour study, we confirmed significant protein-level reduc-tion for most of the genes (Figure S2A) and could ob-serve specific spindle/chromosome phenotypes (Figure2B). First, we found that reduction of Rad21, a proteinessential for sister-chromatid cohesion, led to longerspindles, as documented in yeast [10]. After Rad21RNAi, anti-Cid staining (an inner-kinetochore marker) re-vealed no paired sister-kinetochore dots, and thin chro-mosomal masses were scattered, strongly suggestingthe precocious separation of sister chromatids (FigureS4A) [15]. Statistically significant effects also were ob-served for regulators of MT dynamics. In agreement withprevious qualitative descriptions [3, 4, 16, 17, 25], RNAiof the MT stabilizers EB1, Msps, and Mast caused short-ening of metaphase spindle (61%–83%; all p values <0.0007), whereas knockdowns of MT depolymerases(Klp10A and Klp67A) caused expansion (125%–147%,all p values < 0.004). Notably, the outer-kinetochore-enriched regulators of MT plus ends (Klp67A, Mast)affected the length more severely than the global orcentrosome-localized MT regulators EB1, Msps, andKlp10A. Klp67A [3] and EB1 [16] RNAi sometimes causescentrosome detachment from the kinetochore microtu-bules (kMTs), and this detachment could skew our mea-sured centrosome-to-centrosome distance from the ac-tual spindle length. However, the degree of centrosome

separation from the kMT for EB1 RNAi is small, only ac-counting for a 0.2 mm increase to the measurement ofspindle length [26]. In the case of Klp67A, the centro-some is detached, but is not always localized alongthe axis. Indeed, by comparing measurements of cen-trosome-to-centrosome distance to the distances ofthe minus ends of the kMT in 32 bipolar spindles, we findthat the centrosome-to-centrosome distance in Klp67ARNAi cells underestimates spindle length by 0.3 mmcompared with control cells. Nevertheless, these effectsare small and do not affect our conclusions that EB1 andKlp67A RNAi treatments shorten and lengthen spindlelength, respectively.

If spindle length is controlled by a balance of MT poly-merization and depolymerization, we reasoned that aphenotype generated by depletion of the MT-depolymer-izing protein Klp67A might be rescued by depletion ofMT-polymerizing proteins (e.g., Msps or Mast). In accor-dance with this idea, the simultaneous knockdown ofKlp67A and Msps or Mast produced an average lengththat was intermediate between single Klp67A and singleMsps or Mast knockdowns (Figure 2A).

The important role played by MT-polymerization dy-namics in determining spindle length was also discov-ered recently in Xenopus egg extracts by Mitchison andcolleagues, who also argued that an unidentified non-MT tensile element, possibly a ‘‘spindle matrix’’ [27],may constrain spindle length [28]. Although we cannotexclude the existence of such an element, our resultshave not uncovered evidence for its existence. For ex-ample, shortening of MT length by EB1 or Msps RNAiproduced short metaphase spindles without signifi-cantly perturbing its shape (Figure 2B).

Previous studies have shown that the inhibition of aminus-end-directed kinesin (Kinesin-14) causes spindleelongation in yeast [5, 8]. Dynein inhibition causes dras-tic spindle elongation or shortening depending upon thecell type [6, 9]. However, RNAi of Ncd (Kinesin 14) orDhc64C (cytoplasmic DHC) only slightly changed thespindle size in S2 cells (3%–17% increase; Figure 2Aand Table S1). The slight increase after dynein knock-down can be explained by the effect of detachment of

Figure 2. Metaphase Spindle Length afterRNAi

(A) Average length of metaphase spindle aftersingle or double RNAi-knockdown of eightproteins. RNAi treatment of each gene wasrepeated at least once, and in each experi-ment, relative average length to the accom-panying control was obtained. Combined da-taset of all the treatments is described in thisgraph. Error bars represent the 95% con-fident interval. See Table S1 for individualdatasets.(B) Representative spindle images after RNAiof indicated genes. These images were takenmanually with a 633 oil immersion objective.The bar represents 10 mm.

Length Control of the Metaphase Spindle1981

11


Model for spindle length control

centrosomes from spindle poles [29, 30] because werecently found in another study that detachment of thecentrosomes from the minus end of kMT alone accountsfor an average 14% increase in the centrosome-to-centrosomedistance[26].Thespindle-length increaseaf-ter dynein RNAi is less than that observed by Morales-Mulia and Scholey [31], for reasons that are not clear.However, these authors also noted a partial misrecruit-ment of the Klp10A depolymerase to the poles, a misre-cruitment that may have contributed to this effect. Thelack of dramatic effect upon Ncd RNAi is unlikely to bedue to residual proteins because we noted splaying ofkinetochore fibers (a characteristic of Ncd RNAi knock-down [3, 26]) in the majority of the mitotic spindles exam-ined (80%), found significant depletion (>90%) of Ncd atthe population level by immunoblot analysis, and foundthat 33 of 36 mitotic spindles scored had no detectableimmunofluorescence signal for Ncd after Ncd RNAi.However, the slight increase of the spindle length mightbe explained by the reduced spindle elasticity upon un-focusing of kinetochore fibers (discussed in Box 1). De-pletion of Klp61F (Kinesin-5) by RNAi produced monop-olar spindles [3], so the length of bipolar spindles was not

a measurable parameter. Collectively, these quantitativecomparisons of spindle length following RNAi-mediatedprotein depletion indicate that MT polymer dynamicsand sister-chromatid cohesion more dramatically affectmetaphase spindle length than depletion of minus-end-directed motor proteins.

We next examined whether increasing the levels of MTsliding motors (Klp61F, Ncd) or of MT depolymerases(Klp10A, Klp67A) influences spindle length (Figure 3).To correlate expression level and spindle length on acell-to-cell basis, we expressed GFP-tagged kinesinsfrom an inducible promoter (Figure 3B) and measuredGFP levels and spindle lengths for individual cells. Insupport of our assumption that the exogenous fusionproteins are physiologically functional, we observedthat moderate expression of these kinesin-GFP fusionsrescued the loss-of-function spindle phenotypes pro-duced by depletion of the corresponding endogenouskinesin by RNAi, and this rescue suggests that GFP tag-ging did not destroy the kinesin’s function [22]. More-over, overexpressed Klp67A-GFP localized primarily tokinetochores and kinetochore MTs (kMTs), and over-expressed Ncd-GFP and Klp61F-GFP localized primarily

Box 1. Mathematical Force-Balance Model of Metaphase Spindle-Length Control

Here, we outline a simple dynamical force-balancemodel of the determinants of S2-cell metaphasespindle length, a model that is a modification of anearlier quantitative model that explains spindle-poledynamics during anaphase B [B1]. As described be-low, an important aspect of this model is that Kinesin-5-driven MT sliding activity is coupled to MT depoly-merization, and this coupling guarantees stability ofthe steady-state solution and allows robustness ofspindle stability to changes in MT dynamics.

We first define three state variables that are impor-tant for tracking spindle dynamics: spindle lengths(S), length of overlapping region of antiparallel MTs(L), and MT sliding velocity (Vsliding) (Figure A, left).In Figure A (right), we describe the total force actingdirectly on the centrosome. Outward force, Fsliding, isopposed by Ftension and Fkt.

In addition, we define the following forces (1–3 be-low) and parameters of microtubule polymerization(4–5) relevant to the metaphase spindle (Figure A):

1. Fsliding (green): The Kinesin-5-dependent forcethat slides apart antiparallel MTs (e.g., be-tween antiparallel interpolar (ip) MTs or be-tween ipMT and kMT [B2]) and acts to separatecentrosomes and also on chromosomesthrough kMTs.

2. Ftension (purple): Spindle elasticity, an assumedrestoring force that behaves as a Hookeanspring and opposes spindle extension (possi-bly MT elasticity, MT crosslinking, or a ‘‘spindlematrix’’).

3. Fkt (yellow): A force (in addition to Fsliding) thatpulls the kinetochore toward the pole and pullscentrosomes inward (Figure B) and that couldbe due to Hill sleeve mechanism [B3], minus-end-directed motors at the kinetochore,or MT depolymerization at the pole.

4. Vpoly: The rate of MT polymerization at the plusends of antiparallel ipMTs as determined bydynamic instability of MTs and as a function

Figure A. Schematic Representationof the Forces Acting on the Meta-phase Spindle

Continued on following page

Current Biology1982

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Sliding force pushes centrosomes apart














Current Biology1982

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B94:9 ;F RA49>A4 >65CC F;8:9 JH 62; 5BBA6A;45C <96G;B>E 7>A4K 9A6G9854 ;=6A:5C =;>A6A;4 :C5<= ;8 5 US9B 685=3 #G9 =;>A6A;4 :C5<=0ZEJ5>9B ;4 54 ;=6A:5C 685==A4K A4698F98;<9698E A> 29CC >7A69B 6;A>;<968A: <95>789<946> ;F >65CC F;8:90XE 54B 25> 7>9B =89IA;7>CH6; >67BH F;8:9 K949856A;4 JH A4BAIAB75C %!" =;CH<985>9<;C9:7C9>0-3 L;>A6A;4 :C5<= <95>789<946> ;4 >A4KC9 RA49>A4<;6;8> K5I9 >65CC F;8:9> 6G56 8;>9 2A6G "#L :;4:946856A;4E 5>546A:A=569B O[AK3 DJP3 "4 A4G98946 =8;JC9< 94:;746989B A4 6G9>99S=98A<946> 25> 6G9 B85<56A: B9:CA49 A4 RA49>A4 =8;:9>>AIA6H 56C;5B> 5==8;5:GA4K >65CC0@3 %5=AB B965:G<946 ;F J95B> F8;< 6G9<A:8;67J7C9 <5B9 6G9 :;CC9:6A;4 ;F 5 C58K9 B565 >96 =8;GAJA6AI9E54B 5::;7469B F;8 <7:G ;F 6G9 9S=98A<9465C >:56698 O[AK3 DJP3 #;:;4U8< 6G9 =;>A6A;4 :C5<= <95>789<946>E 29 5C>; <95>789B >65CCF;8:9> 7>A4K 5 US9B ;=6A:5C 685=3 ^A49>A4N:;569B J95B> <;IA4K;76258B> A4 5 >656A;458H 685= 9S=98A94:9 A4:895>A4K C;5B> 746AC6G9H 588AI9 56 5 =;>A6A;4 2G989 F;8258B =8;K89>> :95>9>_ 6G9 U45CBA>=C5:9<946E <7C6A=CA9B JH 6G9 685= >6AFF49>>E >7==CA9> 5 <95>789 ;F6G9 >65CC F;8:90@3 ^A49>A4 >65CC F;8:9> B9698<A49B JH 6GA> <96G;B9SGAJA6 5 >A<AC58 A4:895>9 2A6G "#L :;4:946856A;4 O[AK3 DJP3Q;2 A> 6G9 RA49>A4 "#L5>9 =56G25H :;7=C9B 6; <9:G54A:5C

<;I9<946 74B98 C;5B` )49 =;>>AJACA6H A> 6G56 RA49>A4 :;7=CA4K A>6AKG6E A4I;CIA4K 4; F76AC9 GHB8;CH>A> 9I946> 6G56 F5AC 6; K9498569<;I9<946E 9I94 74B98 C;5B O6G56 A>E ! ! 0P3 M4 6GA> :5>9E 54H :G54K9>A4 6G9 8569> ;F C;5BNB9=94B946 6854>A6A;4> <7>6 5::;746 946A89CH F;86G9 ;J>98I9B B9:895>9> A4 I9C;:A6H 74B98 C;5B3 Q;29I98E <;89:;<=CA:569B >:9458A;> <5H J9 9469865A49B3 "C6G;7KG 6G9 8A>9 A4!< 2A6G C;5B 9CA<A4569> 6G9 >A<=C98 I98>A;4> ;F C;;>9 :;7=CA4KE<9:G54;:G9<A:5C :;7=CA4K A4 RA49>A4 <AKG6 BA>=C5H 54 5B<AS6789;F J;6G 6AKG6 54B C;;>9 9C9<946>E 2A6G C;5BNB9=94B946 6854>A6A;4>54B 74=8;B7:6AI9 GHB8;CH>9> :;4>=A8A4K a;A46CH 6; C;298 6G9 I9C;N:A6H3 "4;6G98 :54BAB569 <9:G54A>< F;8 C;;>9 :;7=CA4K A4I;CI9> 54A4:895>9 A4 6G9 F89b794:H ;F -N4< J5:R258B> >69=>0,?0@ 2A6G C;5B3Q;29I98E 6G9 C56698 <9:G54A>< <5H J9 BA>:;7469B J9:57>9 6G9F85:6A;4 ;F J5:R258B> >69=> F;74B A4 6GA> >67BH OB565 4;6 >G;24P54B JH ;6G98> 89<5A4> ;4CH !W?0,] 56 J;6G 49KCAKAJC9-E00 54B>7J>6546A5C00E0@ C;5B>3#; >67BH 6G9 :;7=CA4K <9:G54A>< 74B98 C;5BE 29 =98F;8<9B 5

c7:6756A;4 545CH>A>@DE@+ ;F RA49>A4 <;I9<946 >7Ja9:69B 6; 6G9 F;8:9:C5<=3 [C7:6756A;4 545CH>A>E 2GA:G 89CA9> ;4 6G9 =8;:9>>AI9 =8;=986H9SGAJA69B JH >;<9 <;C9:7C58 <;6;8>E G5> J994 7>9B =89IA;7>CH 6;>67BH "#L :;7=CA4K A4 RA49>A4 4958 d98; C;5B-E 5> 29CC 5> 6G9 B76H856A; ;F 6G9 J5:698A5C 8;658H <;6;8 74B98 6;8b79@W3 [C7:6756A;4> A4BA>=C5:9<946 589 b7546AU9B JH 5 854B;<49>> =585<9698E #E 2GA:G<95>789> 6G9 69<=;85C A889K7C58A6H ;F <9:G54A:5C 5BI54:9>3 [;8 5494>9<JC9 ;F BA>=C5:9<946 89:;8B>E $O%PE # A> B9U49B JH

# ! CA<%!#

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2G989 & A> 6G9 <;6;8 >69= >Ad9E 54B 6G9 54KC9 J85:R96> B94;69 5494>9<JC9 5I985K9@DE@+3 " =98F9:6CH :C;:RCAR9 <;6;8 BA>=C5H> 4; >69=N=A4K A889K7C58A6HE 54B G5> # ! ,E 2G9895> 5 eL;A>>;4f<;6;8 2A6G ;49JA;:G9<A:5C 6854>A6A;4 <;I9> 56 9S=;4946A5CCH BA>68AJ769B A4698I5C>E54B G5> # ! 03 M4 K94985CE #!0 =8;IAB9> 5 :;46A47;7> <95>789 ;F 6G947<J98 ;F 8569NCA<A6A4K 6854>A6A;4> A4 6G9 ;I985CC <9:G54;:G9<A:5C:H:C93 T9698<A456A;4> ;F 854B;<49>> 589 A4>94>A6AI9 6; 6G98<5C ;8;6G98 >656A;458H 4;A>9 54B :54 6G989F;89 J9 =98F;8<9B 9I94 2G94A4BAIAB75C >69=> 589 4;6 89>;CI9B3 YG94 >69=> :54 J9 BA>:9849B 5<AB

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proportional to density of sliding motors

↵

13

Kinetochore pulls centrosome inwards














Current Biology1982


Fkt = Fkt,0

constant tension force between chromosomes

and centrosomes

14

Restoring spring forces try to keep spindle at rest length S0














Current Biology1982


S0

Ftension

= �(S � S0

)

15
















Current Biology1982

dL

dt= 2 (v

poly

� vsliding

)

dS

dt= 2 (v

sliding

� vdepoly

)

dS

dt=

2 (Fsliding

� Fkt

� Ftension

)

µ

Fsliding

= ↵L

1� v

sliding

v(max)

sliding

!

Ftension

= �(S � S0

)

Fkt = Fkt,0

dL

dt+

dS

dt= 2 (v

poly

� vdepoly

)

No steady state if rates of microtubule polymerization and depolymerization are different!

assuming viscous drag

16extended periods (minutes),whereas the viscoelastic relaxationtime is estimated to be on theorder of milliseconds, suggestingthat the elastic forces dominate theforce balance [6]. In general,viscous drag forces are probablynegligible, as a 1 µm radius sphere(modelling a chromosome) movingat 1 µm per minute experiences adrag force of ~1 fN, about 1000-fold less than the stall force of asingle molecular motor [7].











Fsliding

Fsliding

Vdepoly

Vdepoly

Pole

Pole

+

+ –

–

A

Current Biology

B

Depolymerization rate depends on the sliding force

D.J. Odde, Current Biol. 15, R956-R959 (2005)

vdepoly

= v0dep

+ v(max)

dep

⇣1� e�Fsliding/�

⌘


17
















Current Biology1982

of ‘‘general’’ MT regulators (e.g., EB1 or mini-spindles).

5. Vdepol: The rate of depolymerization of all MTsat their minus ends, this may be mainly regu-lated by Kinesin-13 (Klp10A) that acts as a MTdepolymerase.

Forces exerted by astral MTs [B4–B6] or chromo-kinesins [B7] may also play a role in spindle-lengthdetermination, but they were not considered in thisstudy for simplicity. We do not take into account aneventual limitation of the size of the spindle (i.e., lim-ited amount of tubulin or other spindle componentsor size of the cell), although these factors may alsocome into play in living cells.

The microtubule polymerization/depolymerizationrates can be combined with the rate of MT sliding,Vsliding, to form two simple kinematic equations:

dS

dt= 2!Vsliding 2 Vdepol

"(1)

dL

dt= 2!Vpoly 2 Vsliding

"(2)

This set of kinematic equations should be coupled toa third force-balance equation, which is based on thelow Reynold’s number approximation that applies atsubcellular scales (force for movement, F = velocityof movement, dS/dt 3 the drag coefficient of sepa-rating the poles, m).

dS

dt= m 2 12

#Fsliding 2 Fkt 2 Ftension

$(3)

The above forces can be defined as follows:

Fsliding = aL

#1 2

Vsliding

Vsliding, max

$(4)

Ftension = bðS 2 S0Þ (5)

Fkt = Fkt,0 (6)

The sliding force parameter a represents Kinesin-5force per unit length of overlap (L) (pN/mm), andVsliding, max is the maximal unloaded MT sliding

velocity of Kinesin-5. b is the Hookean-spring con-stant of spindle elasticity, and S0 is the spring’s restlength. For simplicity, we assume a constant forceon the kinetochore (Fkt,0). The assumption of linearforce-extension forces for the spindle spring ele-ments and of linear force-velocity curves for Kine-sin-5 activity serve to simplify the system and ensurethe existence of analytical solutions.

From these equations, it is clear that in order toreach a stable steady state in which spindle lengthand overlap length remain constant with time (ds/dt =0, dL/dt = 0), net polymerization and depolymeriza-tion must be equal (Vpoly = Vdepol). The set of assump-tions presented above state that polymerization anddepolymerization are constant parameters that natu-rally produce an unstable steady state in which everyperturbation to MT polymerization or depolymeriza-tion will result in deviations from the steady state.However, our experiments showed that we can per-turbonlypolymerizationordepolymerizationbyRNAi,yet the spindle still reaches a new steady state witha different constant length (e.g., EB1 RNAi decreasesVpoly but probably not Vdepol).

To generate a stable steady state, we propose anadditional assumption that the depolymerization rate(Vdepol) is dependent on the extent of the sliding force(Fsliding). Here, we proposed one plausible mechanismto explain this dependency on the basis of the as-sumption of a higher concentration of Klp10A at thecentrosomes than elsewhere, combined with a poly-mer ratchet theory [B8]. If a force of magnitudeFsliding pushes MT toward the centrosome, then, asa result of Brownian motion, the probability densityfor the minus end to be at distance x away from the

centrosome is e 2Fslidingx

NkbT , where kbT is the thermal en-ergy [B9] and N is the number of antiparallel overlap-ping MTs. The implicit assumption here is that thesliding force per single MT is the arithmetic mean,Fsliding

N , and we are not taking into account differencesbetween different MT populations. Integrating thisprobability density from 0 to d, we get the probabilitythat this MT end is not farther than distance d from the

depolymerizing motor: Pðx<dÞ= 1 2 e2Fslidingd

NkbT . Denot-ing Vdep, max as the maximal depolymerization rate,we arrive at the equation:

Vdepol = Vd, 0 + Vdep, max

#1 2 e

2Fslidingd

NkbT

$= Vd,0

+ Vdep, max

#1 2 e

2 daL

h1 2

Vsliding

Vsliding, max

i.NkbT

$(7)

Here we define Vd, 0 as sliding-force-independentbasal depolymerization at the pole. Our FSM/kymo-graph analysis of GFP-tubulin suggests that this isFigure B. Parameter Sensitivity Analysis in Steady State


Length Control of the Metaphase Spindle1983

S = S0

� Fkt

�+

�

�ln

v(max)

dep

v(max)

dep

+ v0dep

� vpoly

!

L =�

↵

ln

✓v(max)

dep

v(max)

dep

+v0

dep

�vpoly

◆

✓1� v

poly

v(max)

sliding

◆

proportional to density of

sliding motors

global spindle spring

constant

tension between centrosomes and

kinetochores

L<S under normal conditions in experiments.

Is there a new spindle phase when L>S?

18


Spindle bistability

metaphase is 25% longer (1.0 6 0.13 mm [n = 23], p <0.0001) than in colchicine-treated cells, which lackkMT tension (0.8 6 0.13 mm [n = 47]) (Figure S4A).Time-lapse imaging of Klp67A-GFP (as an outer-kineto-chore marker) also showed that metaphase sister-kinet-ochore distance rapidly decreased upon colchicinetreatment (n = 6, Figure S4B, Movie S1). These data sup-port the idea that sister kinetochores are under tensionduring metaphase in S2 cells.

Combining these forces via a simple force-balancemodel [13], we show that these assumptions by them-selves are not sufficient to allow a stable metaphasesteady-state (Box 1). We further tested what other as-sumptions allow the steady state to be achieved. Wefound that the addition of an assumption that the rateof MT depolymerization at spindle poles (which contrib-utes to poleward flux [1, 4, 35]) is proportional to themotor-generated sliding forces is sufficient to allow sta-bility of the metaphase steady state [Box 1, equation (7)].This feature also enables the spindle length to remainconstant despite the overexpression of the Kinesin-5motor. Although this assumption remains speculative inDrosophila cells, it is supported by recent experimentsshowing that the rate of poleward flux in meiotic spin-dles assembled in Xenopus extracts correlates withKinesin-5 activity in a dose-dependent manner [18].Kinesin-5 activity also appears to be an important factorin maintaining spindle bipolarity and generating pole-

ward flux in S2 cells because RNAi of Klp61F (Kinesin-5) causes a bipolar-to-monopolar spindle collapse anda concomitant significant reduction in the rate of pole-ward flux (Figure S5, Movies S2 and S3). Given these as-sumptions, the quantitative model explains how chang-ing the rate of MT polymerization/depolymerization canproduce changes in the metaphase spindle length with-out changing its stability while the length can remain in-sensitive to a wide range of Kinesin-5 concentration.

A novel outcome of our model is that it predicts ‘‘bi-stability’’ in spindle architecture. Specifically, at lowconcentrations of Klp61F (Kinesin-5), monopolar spin-dles are created, but as the concentration of this motorincreases, an abrupt transition to bipolar spindle forma-tion takes place [Box 1, equation (11) and Figure B]. Totest this prediction of spindle bistability, we examinedthe relationship between Klp61F expression and spindlelength over a wide range of motor concentrations byRNAi-depleting endogenous Klp61F by using dsRNA di-rected against its 50 UTR and then expressing varyinglevels of Klp61F-GFP from a plasmid with an induciblepromoter (Figure 4A and [22]). We assume that the ex-pressed fusion protein is active, an assumption that issupported by its ability to rescue bipolar spindle assem-bly in RNAi-treated cells at appropriate concentrations(Figure 4B). Significantly, we found that there was anabrupt increase in the percentage of cells that exhibitedbipolar spindles at a critical level of Klp61F-GFP protein

Figure 4. Bistability of the Spindle Morphol-ogy but Robustness of Metaphase SpindleLength to Alteration of Kinesin-5 Concentra-tion

(A) RNAi knockdown of endogenous Klp61Fwith dsRNA targeting 50 UTR region wascombined with ectopic expression of Klp61F-GFP. Immunoblot was performed by anti-Klp61F antibody.(B) Spindle ‘‘bistability.’’ At top, representa-tive images of monopolar, monastral bipolar,and bipolar spindles are shown. Red showsg-tubulin, and green shows Klp61F-GFP. Thebar represents 10 mm. At bottom, frequency ofmonopolar spindles over total monopolar andnormal bipolar spindles is shown by blue line;frequency was calculated on the basis of thedistribution of 238 spindles into 15 bins.Length distributions of the normal bipolarspindle (green dots) and monastral bipolarspindle (green open circles; g-tubulin stainingat only one pole of the bipolar spindle) aftervarious levels of Klp61F-GFP expression arealso plotted. Abrupt decrease in monopolarspindle frequency is observed at a criticalexpression level of Klp61F. The length ofmonastral bipolar spindles was measured bydoubling the distance between g-tubulin andcenter of the chromosome mass.

Current Biology1986

concentration of sliding motors

normal spindle

nospindle

19

Cell division in bacteria

20

Genetic information in bacteria

One large circular DNA

A few small circular plasmids

Plasmids carry additional genes that have recently evolved and

may benefit survival (e.g. antibiotic resistance)

21

DNA replication and segregation

WikipediaNature Reviews | Microbiology

a b

Genome-sized dsDNA

Stretching and twisting

Molecular crowding and nucleoid compactioncreate a concentric shell in the nucleoid periphery

Close packing of thestring of blobs

Stabilization by nucleoid-associated proteins

Nucleoid-associated protein

Blobs of newly synthesized DNA

Topologicallyindependentstructural unit

Supercoiledplectonemes

Blob

Sim

ulta

neou

s re

plic

atio

n an

d de

mix

ing

of th

e ch

rom

osom

e

that bacterial cytoskeletal proteins such as plasmid partition protein M (ParM) and ParA are the machinery for active transport of low-copy-number plasmids and ori loci, respectively. The system consisting of ParA, ParB and parS (the binding site for ParB) is widely conserved in many bacteria and con-tributes to ori segregation in C. crescentus and oriII segregation in V. cholerae.

However, although ParA plays an impor-tant part in chromosome segregation, its role is likely to be limited, for the following rea-sons. In C. crescentus, ParA is not required once ori loci are separated at the beginning of the cell cycle27. The absence of ParA alone has little effect on chromosome segregation in B. subtilis4, and there is no ParA homo-logue in E. coli. Also, as we discuss below, eukaryotic sister chromatids demix and move ~0.5 μm apart before their separation by spindles, without any active pushing or pulling of the replicated DNA28. A potential problem with active transport of chromo-somal ori loci for organisms that undergo multifork replication is that simple transport of multiple copies of ori may be harmful to the cell unless it also solves the ‘hierarchy dilemma’ of positioning an ori depending on its identity. An obvious experimental test of this idea would be to insert an active plasmid segregation system, such as ParM or the ParAB–parS system, into the E. coli chromo-some. We predict that chromosome segrega-tion during multifork replication in such an organism will be defective. We propose that organisms encoding ParA have adopted this protein from plasmids for a more effi-cient segregation of the ori domain, which is comparable in size to plasmids, rather than for segregation of the bulk chromosomes.

C. crescentus is smaller than E. coli and has a smaller cytoplasmic space surround-ing its nucleoid, so the outer concentric shell of this species may not be large enough for fast diffusion of newly replicated DNA. In this case, ParA might be needed to ensure rapid segregation of the duplicated ori loci in the early stage of the replication cycle, when newly synthesized DNA would oth-erwise be kinetically trapped in the cell (see Supplementary information S4 (box)). The advantage of having an outer shell leads us to predict that, even in C. crescentus, duplicated ori loci will move in the periphery of the nucleoid. Finally, as the cell grows and rep-lication continues, reducing the volume of the dense, unreplicated-DNA core, an outer shell is not needed for entropy-driven segre-gation15. The C. crescentus cell cycle is longer than those of E. coli and B. subtilis, which will further help segregation by entropy.

Several proteins are involved in active transport of DNA inside a bacterium. Examples include SpoIIIE, which moves DNA into the forespore during sporulation of B. subtilis, and FtsK, which resolves dim-ers and carries out other ‘rescue’ tasks in E. coli29. However, it is important to realize that these proteins translocate DNA at the last step of segregation by taking advantage of the directionality that is provided by the septum, which is an entirely different process from segregation of replicating chromosomes.

Segregation models based on replication, transcription, translation and tethering. In addition to the active DNA transport models, both the force of DNA ejection by DNA polymerase and the tethering of DNA polymerase have been proposed to

move DNA in the cell. The finding of a fixed replication factory in B. subtilis led to the proposal of an ‘extrusion–capture’ model30, which assumed that the energy released during replication could contrib-ute to chromosome partitioning. Recent work, however, has shown that replication forks and their associated replisomes are both independent and highly dynamic in the cell, making their role in segrega-tion unlikely31–33. It was suggested that the negative effects of streptolydigin on chromosome segregation implicate RNA polymerases in chromosome segregation34. In addition, it has been proposed that tran-sertion (the insertion of polypeptides into membranes during translation), instead of polymerases themselves, could segregate the replicating chromosomes35. Definitive experimental support for these proposals is

Figure 2 | Physical model of a bacterial chromosome and its segregation. a | A reductionist model of the Escherichia coli chromosome. First, we stretch a bacterial-genome-sized naked double-stranded DNA (dsDNA). This breaks the DNA into a series of blobs, the total volume of which gradually decreases as pulling continues. In parallel, we also twist the DNA to match the supercoil density of a bacterial chromosome. As a result, the DNA blobs will consist of supercoiled plectonemes (a shape of the DNA in which the two strands are intertwined). We stop the simultaneous pulling and twisting processes when the total volume of the blobs equals the target volume of the nucleoid inside the cell. Next, we ‘sprinkle’ the chromosome with nucleoid-associated proteins. These stabilize the supercoiled DNA blobs as topologically independent structural units of the chromosome. Finally, we connect the two ends of the chromosome to make it circular, and then pack it tightly in the cell. For the simpler case of chains without supercoiling, the phase diagram in FIG. 1 provides a model for the close-packed organi-zation and segregatability of the chains inside the cell. In general, supercoiling will only increase the tendency for chromosome demixing because of the branched structure that it induces. b | The con-centric shell model predicts extrusion of the newly synthesized DNA (blue and red) to the periphery of the nucleoid15. The newly replicated DNA is extruded to the periphery of the unreplicated nucleoid (grey) and forms a string of DNA blobs in the order of replication, promoted by SMC (structural main-tenance of chromosomes) proteins and other nucleoid-associated proteins. In our model, the two strings of blobs repel each other and drift apart owing to the excluded-volume interaction and conformational entropy.

PERSPECT IVES

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Spontaneous demixing due to steric excluded volume interactions

22

Topoisomerase 1 and 2 release tension along the DNA and speed up the separation process

Nature Reviews | Microbiology

Directionality from global polymer repulsion can compensate for mistakes by type II topoisomerase

c

Stretched chain = string of entropic springsconfined in a flexible tube of fixed width

a

b

Separation by reptation is slow

Separation by type II topoisomerase can be fast despite occasional reverse strand-passing

Force

D

Force

physical model of the E. coli nucleoid: the size of the structural unit (also called the correlation length; ξ); the Flory radius of gyration (RF) of the isolated nucleoid (namely, the diameter of the fully expanded nucleoid released from the lysed cell); and the length and width (L and D) of the nucleoid inside the cell. The most impor-tant parameter is ξ, which can be measured as described in Supplementary information S3 (box).

Experimentally, E. coli str. B/r H266 is the only organism for which these param-eters have been measured10,11 (see BOX 2 and Supplementary information S3 (box)). They are: D = 0.24 μm, L = 1.39 μm, RF = 3.3 μm; and ξ = 87 nm. Thus, E. coli str. B/r H266 belongs to regime III, in which the strongly compressed individual chromosomes gain maximum conformational entropy when they remain segregated and linearly ordered (FIG. 1c; see Supplementary information S4 (box)). Similarly, our phase diagram can be used to make a prediction for other bacteria such as Vibrio cholerae (which has two chro-mosomes), Bacillus subtilis and Caulobacter crescentus. At present, neither the size of

the isolated nucleoid nor the size of the structural unit have been measured for these organisms, although we expect B. subtilis and C. crescentus to belong to regime III, considering that both organisms have similar cell dimensions and genome sizes to E. coli. Future studies are needed to measure ξ for the nucleoids in these organ-isms, perhaps using fluorescence correlation spectroscopy techniques similar to those used in REF. 11 (explained in Supplementary information S3 (box)) in order to fully test our predictions.

The next question concerns plas-mid segregation in bacteria. Note that plasmids make little contribution to the amount of DNA in the cell because of their small sizes. Indeed, RF for plasmids is typically one-tenth of the RF value for the chromosome. This separates the plasmids from the chromosomes by one order of magnitude along the diagonal line between the two axes in the phase diagram (FIG. 1c; see Supplementary infor-mation S4 (box)). As a result, plasmids belong to the lower part of regime V in the phase diagram, in which polymers are

not confined and the entropic repulsion between them is weak. In the absence of any specific interactions with the chromo-some (such as ‘hitchhiking’), or without dedicated segregation machinery, plas-mids will distribute randomly inside the cell because of their small sizes. Indeed, recent experimental results from studies of the high mobility and random distribu-tion of the RK2 plasmid, which lacks a partitioning system, are fully consistent with our prediction12.

Segregation in round cells. Perfect symme-try of cell shape means that the confined chains do not have any preferred confor-mations between mixing and segregation, although their global reorganization is readily achieved13. Few data are available about chromosome organization in spheri-cal bacteria, so we can only speculate about possible contributing factors to segrega-tion. We think that supercoiling is the most important factor, as it gives rise to the branched structure of the bacterial chro-mosome14. We did not take into account the topological complexity of the polymer

Box 2 | Chain molecules in strong confinement or at high concentrations

The effect of a cylindrical confinement on a chain is equivalent to applying a tension, which pulls and stretches the long molecule (see the figure, part a). In polymer physics, the stretched chain is described as a series of entropic springs (or ‘blobs’), the size of which is determined by the width of the tube. There is a linear relationship between the total contour length of the chain and the total number of blobs, and the free energy stored in the chain is directly proportional to the number of blobs. In other words, a blob is also a basic unit of free energy stored in a polymer and has a thermal energy of k

BT (where T is the room

temperature (~300 Kelvin) and kB is the Boltzmann constant (2 cal per mol K)

regardless of its physical size52,53 (for comparison, ATP hydrolysis releases ~12 kBT

of energy, and a hydrogen bond is several kBT). In other words, blobs can have

different sizes but the same free energy, as long as the self-avoidance condition is met.

When the concentration of the chain is very high, transverse motions of a chain segment embedded in the meshwork of polymers is hindered. In this case, the polymer motion is best understood as sliding in a conceptual tube embedded in a polymer meshwork, also known as ‘reptation’ (see the figure, part b). Reptation is slow; it takes much longer to travel the same absolute distance by reptation in a meshwork than by diffusion in the absence of the meshwork, and the difference between the rates increases in proportion to the length of the chain itself.

Chain connectivity and excluded-volume interactions provide directionality for the segregation of intermingled chains54 (see the figure, part c). Type II topoisomerases do not need to provide or know the directionality. By occasional random strand-passing, these enzymes can accelerate the kinetics of chromosome segregation because reptation is a much slower process (see the figure, part c). However, too high a concentration of topoisomerase means that the two chains will not know their directionality, because the excluded-volume interaction between the chains and the enzyme effectively vanishes (by virtue of the high concentration of the enzyme) and the forward and reverse topoisomerase reactions will cancel each other out. We thus predict that there will be an optimal range of type II topoisomerase concentrations at which chromosome segregation is fastest, because the entropy-driven directionality and topoisomerase-dependent ‘free pass’ are in balance.

PERSPECT IVES

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23

Bacteria divide faster than DNA replicatesUnder normal conditions E. coli divides every 15-20 min

In E. coli it takes ~40 min to replicate DNA

How can bacteria divide faster than DNA replicates?

Multiple replication forks!

Bacteria starts replicating DNA for their daughters,

grand daughters, etc.

24

Plasmid segregation

897

plant cells (see Figure 19–65). As with FtsZ, MreB and Mbl filaments are highly dynamic, with half-lives of a few minutes, and nucleotide hydrolysis accompanies the polymerization process. Mutations disrupting MreB or Mbl expression cause extreme abnormalities in cell shape and defects in chromosome segregation (Fig-ure 16–8B).

Relatives of MreB and Mbl have more specialized roles. A particularly intriguing bacterial actin homolog is ParM, which is encoded by a gene on certain bacterial plasmids that also carry genes responsible for antibiotic resistance and cause the spread of multidrug resistance in epidemics. Bacterial plasmids typically encode all the gene products that are necessary for their own segregation, presumably as a strategy to ensure their inheritance and propagation in bacterial hosts fol-lowing plasmid replication. ParM assembles into filaments that associate at each end with a copy of the plasmid, and growth of the ParM filament pushes the rep-licated plasmid copies apart (Figure 16–9). This spindle-like structure apparently arises from the selective stabilization of filaments that bind to specialized proteins recruited to the origins of replication on the plasmids. A distant relative of both tubulin and FtsZ, called TubZ, has a similar function in other bacterial species.

Thus, self-association of nucleotide-binding proteins into dynamic filaments is used in all cells, and the actin and tubulin families are very ancient, predating the split between the eukaryotic and bacterial kingdoms.

At least one bacterial species, Caulobacter crescentus, appears to harbor a pro-tein with significant structural similarity to the third major class of cytoskeletal filaments found in animal cells, the intermediate filaments. A protein called cres-centin forms a filamentous structure that influences the unusual crescent shape of this species; when the gene encoding crescentin is deleted, the Caulobacter cells grow as straight rods (Figure 16–10).

Figure 16–8 Actin homologs in bacteria determine cell shape. (A) The MreB protein forms abundant patches made up of many short, interwoven linear or helical filaments that are seen to move circumferentially along the length of the bacterium and are associated with sites of cell wall synthesis. (B) The common soil bacterium Bacillus subtilis normally forms cells with a regular rodlike shape when viewed by scanning electron microscopy (left). In contrast, B. subtilis cells lacking the actin homolog MreB or Mbl grow in distorted or twisted shapes and eventually die (center and right). (A, from P. Vats and L. Rothfield, Proc. Natl Acad. Sci. USA 104:17795–17800, 2007. With permission from National Academy of Sciences; B, from A. Chastanet and R. Carballido-Lopez, Front. Biosci. 4S:1582–1606, 2012. With permission Frontiers in Bioscience.)

FUNCTION AND ORIGIN OF THE CYTOSKELETON

Figure 16–9 Role of the actin homolog ParM in plasmid segregation in bacteria. (A) Some bacterial drug-resistance plasmids (orange) encode an actin homolog, ParM, that will spontaneously nucleate to form small, dynamic filaments (green) throughout the bacterial cytoplasm. A second plasmid-encoded protein called ParR (blue) binds to specific DNA sequences in the plasmid and also stabilizes the dynamic ends of the ParM filaments. When the plasmid duplicates, both ends of the ParM filaments become stabilized, and the growing ParM filaments push the duplicated plasmids to opposite ends of the cell. (B) In these bacterial cells harboring a drug-resistance plasmid, the plasmids are labeled in red and the ParM protein in green. Left, a short ParM filament bundle connects the two daughter plasmids shortly after their duplication. Right, the fully assembled ParM filament has pushed the duplicated plasmids to the cell poles. (A, adapted from E.C. Garner, C.S. Campbell and R.D. Mullins, Science 306:1021–1025, 2004; B, from J. Møller-Jensen et al., Mol. Cell 12:1477–1487, 2003. With permission from Elsevier.)2 µm

(B)(A)

ParMmonomers

origin ofreplication

ParMfilaments

ParRproteins

plasmid

MBoC6 m16.27/16.09

ParM

plasmid

MBoC6 m16.26/16.08

1 µm1 µm 1 µm1 µm(A) (B)

Plasmids are too small to spontaneously segregate on different sides of bacteria


ParM is analogous to actin (assembly by ATP hydrolysis)

25

Contraction of FtsZ-ring divides bacterial cell in two

FtsZ is analogous to tubulin (assembly by GTP hydrolysis)

Bacterial division is extremely precise. FtsZ forms at

(0.50± 0.01)L

How does bacteria know where to place the contractile ring?

896 Chapter 16: The Cytoskeleton

Among the most fascinating proteins that associate with the cytoskeleton are the motor proteins. These proteins bind to a polarized cytoskeletal filament and use the energy derived from repeated cycles of ATP hydrolysis to move along it. Dozens of different motor proteins coexist in every eukaryotic cell. They differ in the type of filament they bind to (either actin or microtubules), the direction in which they move along the filament, and the “cargo” they carry. Many motor pro-teins carry membrane-enclosed organelles—such as mitochondria, Golgi stacks, or secretory vesicles—to their appropriate locations in the cell. Other motor pro-teins cause cytoskeletal filaments to exert tension or to slide against each other, generating the force that drives such phenomena as muscle contraction, ciliary beating, and cell division.

Cytoskeletal motor proteins that move unidirectionally along an oriented polymer track are reminiscent of some other proteins and protein complexes dis-cussed elsewhere in this book, such as DNA and RNA polymerases, helicases, and ribosomes. All of these proteins have the ability to use chemical energy to propel themselves along a linear track, with the direction of sliding dependent on the structural polarity of the track. All of them generate motion by coupling nucleo-side triphosphate hydrolysis to a large-scale conformational change (see Figure 3–75).

Bacterial Cell Organization and Division Depend on Homologs of Eukaryotic Cytoskeletal ProteinsWhile eukaryotic cells are typically large and morphologically complex, bacterial cells are usually only a few micrometers long and assume simple shapes such as spheres or rods. Bacteria also lack elaborate networks of intracellular mem-brane-enclosed organelles. Historically, biologists assumed that a cytoskeleton was not necessary in such simple cells. We now know, however, that bacteria con-tain homologs of all three of the eukaryotic cytoskeletal filaments. Furthermore, bacterial actins and tubulins are more diverse than their eukaryotic versions, both in the types of assemblies they form and in the functions they carry out.

Nearly all bacteria and many archaea contain a homolog of tubulin called FtsZ, which can polymerize into filaments and assemble into a ring (called the Z-ring) at the site where the septum forms during cell division (Figure 16–7). Although the Z-ring persists for many minutes, the individual filaments within it are highly dynamic, with an average filament half-life of about thirty seconds. As the bacte-rium divides, the Z-ring becomes smaller until it has completely disassembled. FtsZ filaments in the Z-ring are thought to generate a bending force that drives the membrane invagination necessary to complete cell division. The Z-ring may also serve as a site for localization of enzymes required for building the septum between the two daughter cells.

Many bacteria also contain homologs of actin. Two of these, MreB and Mbl, are found primarily in rod-shaped or spiral-shaped cells where they assemble to form dynamic patches that move circumferentially along the length of the cell (Figure 16–8A). These proteins contribute to cell shape by serving as a scaf-fold to direct the synthesis of the peptidoglycan cell wall, in much the same way that microtubules help organize the synthesis of the cellulose cell wall in higher

1 µm

1 µm

100 nm(B)

(C)

(A)

MBoC6 m16.24/16.07

Figure 16–7 The bacterial FtsZ protein, a tubulin homolog in prokaryotes. (A) A band of FtsZ protein forms a ring in a dividing bacterial cell. This ring has been labeled by fusing the FtsZ protein to green fluorescent protein (GFP), which allows it to be observed in living E. coli cells with a fluorescence microscope. (B) FtsZ filaments and circles, formed in vitro, as visualized using electron microscopy. (C) Dividing chloroplasts (red) from a red alga also cleave using a protein ring made from FtsZ (yellow). (A, from X. Ma, D.W. Ehrhardt and W. Margolin, Proc. Natl Acad. Sci. USA 93:12998–13003, 1996; B, from H.P. Erickson et al., Proc. Natl Acad. Sci. USA 93:519–523, 1996. Both with permission from National Academy of Sciences; C, from S. Miyagishima et al., Plant Cell 13:2257–2268, 2001, with permission from American Society of Plant Biologists.)

26

Min system oscillations provide cues for the formation of FtsZ ring

time

⇠ 50s

0sFtsZ

MinC

MinD

MinE

Predator-prey like dynamics between MinD and MinE

proteins produce oscillations on a minute time scale, which is much shorter than typical

division time (~20 min).

On average MinC/MinD proteins are depleted near the cell center,

where FtsZ ring forms!

VOLUME 87, NUMBER 27 P H Y S I C A L R E V I E W L E T T E R S 31 DECEMBER 2001

FIG. 1. Space-time plots of the total MinD (left) and MinE(right) densities. The grey scale runs from 0.0 to 2.0 timesthe average density of MinD or MinE, respectively. The MinDdepletion from midcell and the MinE enhancement at midcellare immediately evident. Time increases from top to bottom,and the pattern repeats indefinitely as time increases. The grey-scale reference bar spans 100 s. The horizontal scale spans thebacterial length (2 mm).

model (not shown). The physical origin of this instabilitylies in the disparity between the membrane and cytoplas-mic diffusion rates, and also in the slower rate at whichMinE disassociates from the membrane. This ensures thatthe MinE dynamics lags that of the MinD, setting up theoscillating patterns. The existence of the linear instabilityin Eqs. (1)–(4) is crucial, since it means that the oscillat-ing pattern will spontaneously generate itself from a vari-ety of initial conditions— including nearly homogeneousones. In our simulations, we used random initial condi-tions, although identical patterns were also observed withasymmetric initial distributions of MinD and MinE. Theeventual oscillating state is stabilized by the nonlinearitiesin Eqs. (1)–(4). At the midcell, this oscillating pattern hasa minimum of the time-averaged MinD concentration — anessential feature of division regulation — and a maximumof the time-averaged MinE concentratio.

Space-time plots of the MinD and MinE concentrationsfor a cell length of 2 mm are shown in Fig. 1. In excellentagreement with the experimental results, the MinE sponta-neously forms a single band at midcell which then sweepstowards a cell pole, displacing the MinD, which then re-forms at the opposite pole. Once the MinE band reachesthe cell pole it disappears into the cytoplasm, only to re-form at midcell where the process repeats, but in the otherhalf of the cell. These patterns are stable over at least109 iterations (104 s)— long enough for the min system to

0 1 2x (µm)

0.50

0.75

1.00

<ρ(x

)>/ρ

max

MinD

0 1 2x (µm)

MinE

0.50

0.75

1.00

FIG. 2. The time-average MinD (left) and MinE (right) densi-ties, !r"x#$%rmax, relative to their respective time-average max-ima, as a function of position x (in mm) along the bacterium.

regulate cell division throughout the division cycle of thecell. In Fig. 2, we plot the time-averaged MinD and MinEdensities as a function of position. MinD shows a pro-nounced dip in concentration close to midcell, which al-lows for the removal of division inhibition at midcell. Thisis in qualitative agreement with the experimental data ofRef. [8]. MinE peaks at midcell, with a minimum at thecell extremities.

We also investigated longer filamentous bacteria andfound a multiple MinE band structure (not shown). Multi-ple MinE bands always combined into a single MinE bandin cell lengths shorter than the natural wavelength indi-cated by linear stability analysis.

The oscillation period as a function of the average MinDconcentration is shown in Fig. 3 (left). We find a linearrelationship indicated by the best-fit line, where the pe-riod approximately doubles as the MinD concentration isquadrupled. A linear relationship has also been suggestedexperimentally [3]. The period of oscillation as a functionof cell length is shown in Fig. 3 (right). Below lengthsof 1.2 mm the bacterium does not sustain oscillating pat-terns. For lengths above this minimum, the oscillation pat-terns are stable and the period increases with length— asobserved experimentally [7]. The periods measured fromour numerics for cell lengths of 2 mm are around 100 s,in good agreement with experiments, where periods from30 120 s have been found [3]. A single MinE band stateis stable over a wide range of lengths for a given densityof min proteins. This provides strong evidence that themin system is capable of regulating accurate cell divisionover normally occurring cell lengths as the cell grows be-tween division events. At longer lengths of around 6 mm,we observe long-lived metastable states with two MinEbands. These multiple bands can survive for a thousandseconds or more before decaying into a single band. Atstill longer lengths the two band state appears stable; thisoccurs around 8.4 mm— twice the dominant wavelengthgiven by the linear stability analysis. This explains whythe characteristic wavelength of linear stability analysisis rather longer than a normal E. Coli bacterium— if thelength scale were smaller, then multiple MinE bands might

500 1000 1500 2000ρD (#/µm)

6080

100

120

6080

100

120

perio

d (s

ec)

1 2 3 4 5 6 7 length (µm)

0500

1000

1500

FIG. 3. Left: Plot of the period of oscillation (in seconds)against MinD density (in mm21), at fixed average MinE con-centration of 85 mm21. The solid line is a linear best fit. Right:Plot of oscillation period against cell length, for fixed MinD andMinE concentrations. Below bacterial lengths of 1.2 mm, oscil-lation is not observed.

278102-3 278102-3

H. Meinhardt and P.A.J. de Boer, PNAS 98, 14202 (2001)

27

Min system oscillations in large cells

“chap20.tex” — page 924[#32] 5/10/2012 16:45

is lowest right at the middle of the cell. In considering wave equationsin the context of fluid mechanics or electromagnetism, it is well appre-ciated that the same governing dynamical equations that generatepropagating waves in an extended medium will lead to standing waveswhen certain kinds of boundary conditions are imposed. Inspectionof the dynamics of MinD localization inside of living bacterial cells(see Figure 20.16) suggests that its behavior is consistent with whatmight be expected when a traveling-wave system is confined to thesmall oblong box of the bacterial cell. As shown in Figure 20.16(A),MinD oscillates from one pole to another of a pre-divisional bacterialcell, with a period T of about 40 s, which is much shorter than thecell’s division time (of the order of about 30 minutes). As the oscil-lating MinD carries MinC with it, the time-averaged concentration ofthe MinC protein will necessarily be lowest right at the cell’s center,exactly where the FtsZ ring is supposed to assemble, and preventingFtsZ ring assembly near the cell poles, which would result in forma-tion of minicells devoid of DNA. The nature of the MinD standing waveis illustrated more dramatically in long cells where division has beeninhibited, as shown in Figure 20.16(B). For these filamentous cells, thestanding-wave pattern shows a spatial periodicity that is about twicethe normal length of an individual cell.

We can use the physical dimensions of the standing wave to estimatewhether the Min traveling waves observed for the purified systemin vitro really are a plausible physical underpinning for the center-finding mechanism in living cells. Mathematically, a standing wave canbe described as two traveling waves, with the same amplitude, wave-length, and propagation speed, but moving in opposite directions. Thewavelength λ of the in vivo standing wave is about 4–6 µm, which istwice the length of the pre-divisional cell shown in Figure 20.16(A), orthe spacing between peaks shown in Figure 20.16(B). The period T isabout 40 s. Setting v = λ/T , we can estimate v to be around 0.1 µm/s.This is the same order of magnitude as the wave propagation speedfor the in vitro system, v = 0.3–0.8 µm/s, and the estimate becomeseven closer if we recall that rates of diffusion for small moleculesin cytoplasm are typically about fourfold slower than rates in water(see Figure 14.4, p. 549), which, according to our toy model, woulddecrease the propagation speed in vivo by a factor of four.

Overall the Min system in E. coli is a remarkable fulfillment of thebiological promise of reaction–diffusion mechanisms as envisionedby Turing for establishing biological patterns. Certainly, there are anumber of details in the system that he had not imagined (and we

Figure 20.16: Min oscillations andhow the bacterium finds its middle.(A) Fluorescently tagged MinD can beseen to oscillate rapidly from one poleof the cell to another with a period ofonly about 40 s, which is much lessthan the cell’s division time. (B) In cellsthat are prevented from physicallydividing, the Min oscillations continue,forming an oscillating stripe patternthroughout the entire length of thefilamentous cell. The total size of thecell is shown in the transmitted-lightmicrograph in the bottom panel.(Adapted from D. M. Raskin andP. A. J. de Boer, Proc. Natl Acad. Sci. USA96:4971, 1999.)

0 s 20 s 40 s

0 s

20 s

40 s

60 s

1 mm

5 mm

(A) (B)

924 Chapter 20 BIOLOGICAL PATTERNS: ORDER IN SPACE AND TIME

MinD oscillations in normal E. Coli

MinD oscillations in E. Coli, where division is prevented

R. Phillips et al., Physical Biology of the Cell

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