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Ann. Rev. Biophys.Biophys. Chem.1988. 17:431-49
Copyright©1988by AnnualReviewsInc. All rights reserved
THE FORCES THAT MOVE
CHROMOSOMES IN MITOSIS
R. Bruce Nicklas
Department of Zoology, Duke University, Durham, North Carolina 27706
CONTENTS
PERSPECTIVES
AND
OVERVIEW
........................................................................................
FORCE
ES’nUAa~S
...........................................................................................................
FORCE
MEASUREMENTS
...................................................................................................
Approach
..................................................................................................................
Results
......................................................................................................................
Implications
..............................................................................................................
COMPARISONS
WITH
OTHER
MOTILE
SYSTEMS
...................................................................
FORCE
MEASUREMENTS
FROM
ELASTIC
CONSTANTS
...........................................................
PgOMETAFrfASE
CagOUOSOME
MOVEMENT
.......................................................................
Conyression
..............................................................................................................
Induced
Movement
...................................................................................................
FORCE
AND
STRUCTURE
.................................................................................................
TensionandStabilizationof Microtubule
Arrays......................................................
ForceandMicrotubule
Assembly
..............................................................................
PERSPECTIVES
431
432
434
434
436
436
439
441
442
442
443
444
445
446
AND OVERVIEW
By comparisonwith us and our machines, most cells and parts of cells move
slowly. The standard for sluggishness is set by chromosomemovementin
mitosis. Imagine a chromosome on a macroscopic journey, from North
Carolina to Italy, for instance. Movingat its usual stately pace, the
chromosomewould take over 14 million years. This review concerns the
mechanics of such chromosome movement--the forces and structures
that produce slow but precisely directed movement.Recent more general
reviews of mitosis include those by Inou6 (14) and Mclntosh(18).
The maximum
force the spindle can exert in anaphase has recently been
measured.It is very muchlarger than earlier estimates of the force normally
required for chromosome movementin anaphase. This new information
raises questions about the adequacy of molecular models for the motor
431
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4 3 2
NICKLA$
and about the control of chromosomevelocity. The force measurements
also make possible revealing comparisons of mitosis with other motile
systems. The spindle is in a class by itself. It is a uniquely weakengine
characterized by finesse rather than raw power; it moves chromosomes
slowly, but without error.
A new approach to measuring forces in mitosis is described, and the
first results are reviewed. In metaphaseand earlier, the spindle subjects
chromosomesto larger forces than in anaphase. Still larger forces have
been applied experimentally. These forces affect spindle structure. Thus,
tension forces stabilize microtubule arrays and probably cause microtubules.to lengthen, while compression causes microtubules to shorten.
Amongother possible explanations is a direct effect of force on the thermodynamicsof microtubule assembly, leading to changes in microtubule
length and stability. Important mitotic events maybe explained by such a
novel regulation of structure by the force the structure produces.
FORCE ESTIMATES
Chromosomemovementsand the forces involved are diagramed in Figure
1. This and the next several sections are concerned with the poleward
movementof the daughter chromosomes in anaphase; the spindle elon-
i I/ ~’
I
\
\
\
ii
/
/
’.0/
Fit~ure1 Chromosome
movements
and mitotic forces. Eachdiagramshowsa spindle in
outlinewithtwopoles(solid circles) andtwopairs of chromosomes
(meioticbivalentsin
these examples).Fromeach chromosome,
microtubules
(thin lines) extendpolewardfrom
the kinetochore
(or centromere),
depictedas an opencircle. Thearrowsindicatethe direction
andveryroughlythe magnitude
of the mitotic forces. In prometaphase
(a), chromosomes
are subjectedto forcestowardoppositepoles, whichincreasewithincreasingdistancefrom
the pole; hencethe chromosomes
move(congress)to a metaphase
position midway
between
the poles(b), wherethe poleward
forcesare equal.Partnerchromosomes
separatein anaphase
(c) andmove
poleward,againin responseto poleward
forces.
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FORCESIN MITOSIS 433
gation that occurs in anaphase is not considered, since the force has not
been measured or estimated.
The force required for normal anaphase movement has not been
measured, but it is estimated to be very low on the basis of hydrodynamic
calculations. Massand inertia do not matter; owing to the slow speed and
small size of chromosomes,viscous resistance (drag) is about a million
times more important then inertia (from the Reynold’s number) (see
22, 39). Movementat this scale has been vividly characterized by Purcell
(35), whocalculated that the distance a bacterium coasts owing to inertia
after it ceases to swimis only 0.1/~, less than the diameter of a hydrogen
atom. A chromosome would coast no farther. Thus, for normal chromosomemovementduring anaphase only friction due to viscous resistance
must be overcome. The following simple equation applies:
F = Rv,
1.
whereFis force, R is the coefficient of viscous resistance, and v is velocity.
The coefficient of resistance can be broken downinto viscosity, ~/, and a
factor that characterizes the size and shape of the movingobject, s; thus
F = qsv,
2.
whichis simply a generalized version of Stoke’s law. For s, Perrin’s formula
for prolate ellipsoids fits chromosomegeometry fairly well (22); other
formulas give about the same result (39). The justification for using these
equations is their empirically proven success in describing the sedimentation of macromoleculesin the ultracentrifuge (37).
Two independent estimates agree on a value of about 10-8 dyn for
the force required to movea relatively large chromosome(22, 39). This
small force, whenmultiplied by the small distance traveled (about 10/~m),
yields a trivial amount of work done or energy expended: The energy expended to overcomeviscous resistance could be supplied by the terminal
dephosphorylation of only 20 ATPmolecules per chromosome(22, 39).
One ingredient in the calculations, spindle viscosity, has never been
measured. The force estimates are based either on a viscosity of 0.3 poise
measured in the cytoplasm near the moving chromosomesbut not within
the spindle itself (39), or on a viscosity of 1 poise (100 times the viscosity
of water) taken as a plausible upper limit (22). Also, only viscous resistance
to movementis included in the force and energy calculations. The possibility of another, muchmore significant hindrance to chromosomemovement, a "governor," is considered below. Thus, these force and energy
estimates cover only the inescapable minimal requirements for chromosomemovement,but that information is essential in sorting out any
morecomplicated situation in living cells.
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434
NICKLAS
Anotherimportant feature of mitotic forces was established in the 1960s
by hydrodynamicanalysis: The spindle can produce substantially greater
force than the minimumrequired to overcomeviscous resistance. This was
clear from observations that (a) large chromosomesare movedas rapidly
as small ones (22),. (b) velocity is constant despite variation in viscosity
nearby (39), and (c) the spindle can stretch unseparated ~hromosomes,
thus overcomingnot only the frictional resistance to movement,but also
the resistance of the chromosometo elastic deformation (21). Thus the
spindle was shown to produce more force than the minimumrequirement
of 10- ~ dyn. However,at the time of these studies the maximum
force the
spindle can generate could not even be guessed, and for many purposes
this is the most interesting value to know.
FORCE MEASUREMENTS
Approach
Measuring the small force required to overcome only viscous resistance
would be difficult, but the maximum
force the anaphase spindle can produce is unexpectedly easy to measure (26). The method is outlined
Figure 2. A flexible glass needle is calibrated in dynes per micrometer of
tip deflection (47) (Figure 2a) and is then introduced into a living cell
anaphase (Figure 2b). The needle stretches the chromosome,opposing the
force produced by the spindle. The force from the needle is increased until
chromosomemovement ceases. At that point the force applied by the
needle just balances, and therefore equals, the maximum
force the spindle
can exert on one chromosome.Then the needle tip is released from the
chromosome,and both the tip and the chromosomerebound to their rest
positions (Figure 2b, right). The force exerted by the spindle is calculated
from the deflection of the needle times its calibration factor.
To reach the chromosome,the needle deforms both the cell surface and
the cytoplasm. Therefore, for the spindle force measurementsto be valid,
the force required to deform these other materials must be negligible
compared to that required to stretch the chromosome. This may seem
unlikely but turns out to be true, at least for grasshopper spermatocytes
(26). The test is simple and conclusive. During anaphase, the two chromatids composing each chromosomeseparate, so that the force required
to stretch two chromatids (before separation) can be compared with the
force required to stretch only one (after separation). If the force required
to stretch the cell surface were muchgreater than that required to stretch
a chromosome,the measured force would reflect mainly the propertie s of
the cell surface. In that case, about the same force would be measured
regardless of the number of chromatids stretched. On the other hand, if
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FORCES IN MITOSIS
435
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(1
".O/
b
START
",2 ’"
\oi
LOAD
"YY’’
\x~x~/
RELEASE
Fiyure 2 Diagrams of mitotic force measurement. (a) Calibration. A thin glass needle
shownat rest (left) and after a weight is hungfrom its tip (riyht); a calibration factor in
dynes per micrometerof tip deflection is calculated from the deflection, d, and the mass of
the weight. (b) Application. The graphics conventions are the same as in Figure 1.
chromosomeis snagged with the calibrated needle (left) and then the needle is moved
downward(center, arrow), opposing the poleward spindle force. After a minute or two, the
needle is pulled out of the chromosome(riyht), and both the needle and the chromosome
snap back to their rest positions. The force exerted on the chromosomeby the needle is
calculated from its deflection, d, times the calibration factor. In this example, the applied
force was great enough to temporarily halt the movementof the manipulated chromosome.
the cell surface and other materials were trivially weakrelative to chromosomes,then they would scarcely affect the measurements,and the ratio
of the force required to stretch two chromatids and to stretch one would
be 2:1. In experiments with grasshopper spermatocytes, a 2.3:1 force
ratio was obtained (26). Ratios similarly close to 2 : 1 have been found
three additional series of measurements (R. B. Nicklas, unpublished).
Clearly, the measuredforce reflects the force applied to tb, e chromosome
and opposing its movement.
Thus force measurementsin intact cells were validated under the actual
conditions in which spindle force is measured. It is unlikely that the
conclusion will hold for most cells. Grasshopper spermatocytes mayhave
exceptionally fluid surfaces; electron microscopyreveals no visible coating
on their surface membranes, and micromanipulation needles encounter
none of the resistance so obvious when cultured mammaliancells or
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436
NICKLAS
even some other insect spermatocytes are manipulated (R. B. Nicklas,
unpublished observations).
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Results
Whena chromosomeis stretched with a calibrated needle, no effect on
anaphase chromosome movement is observed until the force opposing
¯ movement reaches about 2 x 10-6dgn; above that force, chromosome
velocity rapidly falls toward zero. Chromosomemovementceases altogether at an opposing force of approximately 7x 10-Sdyn; this is the
maximumforce the spindle of a grasshopper spermatocyte can exert on
one chromosome.
The accuracy of the measurementsis estimated as _+ 50%, which is not
wonderful but is adequate for present purposes, especially because the
current molecular models for force producers are only semiquantitative at
best. Greater accuracy maybe possible if obtaining it becomesof interest
in the future (26). In addition, the measured value might be an underestimate of the maximum
force that the motors can actually produce. The
load imposed by the needle must be borne by the spindle skeleton, and a
chromosometugged by a needle might cease to move simply because the
load has disrupted spindle structure rather than because the needle has
matched the maximumforce the spindle motors can exert. During the
brief tugs that are necessary to measurethe force, no evidence of spindle
disruption has been seen, but unmistakable signs of incipient spindle collapse were seen whena similar force was applied for a longer time (26).
conclude that while an underestimate is possible, the measured force is
probably near the true maximumthe spindle motors can produce.
The force values for anaphase spindles are summarizedin Table 1. The
maximumforce developed per kinetochore microtubule is also given in
the table as another index of performance.
Implications
The maximum
force that the spindle can exert against a micromanipulation
needle is nearly 10,000 times greater than the estimated value for normal
chromosome movement, in which only viscous resistance to movement
must be overcome (Table 1). The spindle’s unexpected competence as
force producer bears on (a) molecular modelsfor the motor, (b) the control
of chromosomevelocity, and (e) the impact of force upon structure. The
first two topics are considered here; the discussion of force and structure
is deferred to a later section.
MOLECULAR
MODELS
Can the motors postulated in molecular models of
mitosis generate the measured maximumforce? Only a few of the many
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FORCESIN MITOSIS
Table 1
Forces in mitosis
Time and type of force
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437
Anaphase, chromosome-to-pole
bNormalforce, calculated
cMaximumforce, measured
Force per
chromosome
(dyn)
Force per
kinetochore
microtubule
~
(dyn)
10- 8
-5
7 × 10
10- 9
-6
5 × 10
movement
dPrometaphase
Congression
-5
0.5 x 10
-6
0.7 x 10
Induced movement
eKinetochore near pole
eKinetoehore far from pole
3 x 10- 5
8 x 10- 5
4 x 10- 6
10× 10- 6
Stabilization of microtubule arrays
2 x 10- ~
3 x 10- 6
a Kinetochore microtubule numbers from average counts by electron microscopy [45 per
anaphase and 23 per prometaphase chromosome(half-bivalent)]
(31); these numbers
divided by three to give a rough estimate of the number that actually link the chromosome
to the spindle (26).
b FromReferences 22, 39.
y Measured in grasshopper (Melanoplus san#uinipes) spermatocytes (26).
d Measured in grasshopper (Melanoplus differentialis)
spermatocytes (R. B. Nicklas,
unpublished). In all situations, the force acting on a single chromosome(half-bivalent)
given. In natural congression, for instance, two conjoined chromosomes(partner halfbivalents) are stretched by the spindle; hence the total force calculated from k(Al/lo) (see
text) was divided by two.
° "near pole" meansin the half of the spindle near the pole; "far from pole" meanson the
other side of the equator, in the farther half of the spindle.
models are sufficiently quantitative that an expected maximum
capability
can be calculated from them. No models for force production are ruled
out by the measurements, but intrinsically
weak motors such as treadmilling and assembly/disassembly would be pushed to their apparent
limits (26). A newentry on the list of weakbut apparently adequate motors
is one that invokes the free energy of interaction between a microtubule
and a sleeve in the kinetochore (10, 12). More powerful motors such
myosin and dynein can readily produce more force than is needed; kinesin
(1, 40) is probably also in this class, although definitive informationis not
yet available. The restraining of motors of this sort, those that are more
powerful than necessary, is the subject of the following section.
GOVERNORS AND MOTORS Suppose,
to be conservative, that the force required for normal chromosomemoveTHE FORCE-VELOCITY RELATIONSHIP:
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438
NICKLAS
ment is higher than the calculated estimates by an order of magnitude, i.e.
that the correct value is 10- 7 dyn. Even then, the maximum
force a spindle
can produce is 700 times the force required to sustain normal chromosome
movement.The problem this poses is clearly illustrated by a concrete
example, dynein. A single dynein arm produces a maximumforce of
10-7 dyn (16). Therefore, about 700 dynein molecules would be necessary
to produce the maximumforce the spindle can exert on one chromosome,
whereas for normal chromosomemovementa single dynein would suffice.
The problem is that any motor powerful enough to produce the observed
maximumforce would, if unconstrained, move chromosomes far faster
than is observed under normal circumstances, when the resistance to
movementis low. The speed of chromosomesmust be limited by something
other than the very small viscous resistance to movement,as Taylor (39)
appreciated more than 20 years ago. Chromosomevelocity can be limited
by a governor separate from the motor or by properties of the motor itself.
Kinetochore microtubules are the obvious choice for a governor to limit
velocity. Their length could determine kinetochore position and their rate
of depolymerization could determine the rate of poleward chromosome
movement,regardless of how hard the motors pull or push on the microtubules (7, 24, 26).
At very low opposing force, the velocity generated by a motor of the
myosin/actin or dynein/microtubule type is limited by intrinsic properties
of the motor itself: the duration of the mechanochemicalcycle and the
distance that filaments slide in each cycle (26). A good example is the
dynein motor responsible for microtubule-microtubule sliding in trypsintreated flagellar axonemes.As pairs of doublet microtubules slide against
each other and move apart, the number of dyneins that can interact
with the microtubules decreases as the zone of overlap between the pair
decreases. The opposing force remains constant, however: The viscous
resistance to movingthe microtubules does not change. Therefore, as the
numberof active dyneins decreases, the opposing force per motor increases
greatly, yet the velocity of sliding does not change (38). Evidently the
resistance to movementis so low relative to the motor’s capacity that the
motors continue to operate at their maximum
velocity. For ATPaseforce
producers such as myosin, dynein, and probably kinesin, the maximum
velocity is 2-8 #msec- ~ (1, 5, 11, 38, 40). This is the velocity at whichsuch
motors would propel chromosomesif the resistance were trivial relative
to their capacity. Such a velocity is about 100 times faster than actual
chromosome movement, but minor evolutionary changes could yield a
motor with a maximum
veloc!ty more in line with that observed in mitosis.
The important question is how large the resistance to movementcan
becomebefore the velocity is affected. According to a brief report, the
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FORCESrN Mla’OS~S 439
velocity of dynein-mediated microtubule sliding is nearly constant until
the opposing force reaches 40%of the maximum(33). This observation
fits the force-velocity relationship of the spindle very well, showingthe
feasibility of explanations of velocity constancy based on intrinsic properties of the spindle’s motor.
Nochoice is possible at present between a governor or intrinsic motor
properties as the source of velocity constancy, but one or the other is
required to fit the facts.
COMPARISONS WITH OTHER MOTILE SYSTEMS
The slow speed and low force for normal anaphase movement put the
spindle in a class by itself.
Diverse motile systems have been comparedby their force per filament
(23, 46) or power per motor performance (24), but such comparisons do
include all contributions to differences in performance.A better criterion of
performance is the specific power output, the maximumpower developed
per unit of engine volume(27). This index combinesin one figure all the
elements contributing to diversity in performance: force, velocity, and
engine volume. By including volume, it reveals howconcentrated or dilute
the force generators are. Recent measurementsof the force produced by
the spindle and other biological systems permit the specific poweroutput
to be calculated (power eqUals force times velocity; specific poweroutput
equals power divided by system volume). A related index, the power-toweight ratio, has long been used as a performance criterion by engineers.
Values for both indexes are given in Table 2. For biological engines, the
numerically identical power/volumeand power/weight values are included
in the table, to facilitate comparisons with engines of humandesign.
For most biological systems, however, what is important is the volume
occupied by the engine, not its weight.
The bacterial flagellum is the champion of high power output from a
compact engine, a powerhousethat beats all the competitors in Table 2,
including the best humandesigns (2; H. C. Berg, personal communication).
The contractile stalk ("spasmoneme")ofvorticellid protozoa also has high
power output. The output of striated muscles and eukaryotic flagella is
also high, about equal to that of a typical passenger car engine.
High power output in flagella and muscles makes good sense biologically, since the point is to movesperm or organisms efficiently. The
engine’s bulk (or weight, in the case of muscle) is part of the load, hence
the value of a compact, high-output motor.
Comparisonof the power output for muscle and for the cleavage furrow
is interesting, since variants of the same motor, myosin, are used in both.
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440
NICKLAS
Table 2 Specific power output
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Engine
bBacterial flagellum
°LycomingT-55 gas turbine engine
d
Vorticellid
spasmoneme
cTypical passenger car engine
c’e
Striated muscle
¢Eukaryotic flagellum
¢Cleavage furrow
cSpindle
Power output per
unit engine volume
(erg sec- ~ cm-3)
Power-to-weight
aratio
(erg sec- ~ g- i)
1 × 108
I × 108
8 × 107
4 × 107
3 × 106
2 x 106
~
3 × I0
3 x 102
6
4 x 107
2 × 106
3 x 105
3 x 102
6
a Only the weight of the engine is included; values for biological engines are from power
per unit engine volume divided by a density of 1.04 gcm-3 (27).
b From Reference 2 and H. C. Berg, personal communication.
c Sources of data and details of the calculations are in Reference 27.
d Recalculated from data in Reference 41.
*From References 42, 43.
Evidently, closely related proteins can powereither a high-output system
as in muscle or a system of 10,000-fold lower output as in the cleavage
furrow. Clearly, high power output motors can be tamed and therefore are
plausible candidates for the motor that drives chromosomemovement.
An important unanswered question is how the output is tamed. Are the
myosin motors in the furrow less powerful, more dilute, or subject to
greater structural constraints on output than those in muscle?
The poweroutput of the spindle is over 300,000 times less than that of
-muscle (Table 2). Twofeatures of spindle mechanics are responsible for
the enormous difference from muscle: Chromosome movement is far
slower (330-fold), and force production is far more dilute (1000-fold lower
force per unit of engine volume). Hence spindle motors are either fewer or
weaker and/or are subject to greater structural constraints than muscle
(27).
The low poweroutput of the spindle is easily related to its biological
role. The point of mitosis is an exactly equal distribution of chromosomes
to the daughter cells. Perfection is more important than speed, and there
is no necessity for a particularly compactengine.
The general conclusion is that a single number,the specific poweroutput,
represents the mechanical performanceof diverse biological motile systems
very well. It also correlates well with their diverse biological roles; what
matters most is clearly revealed.
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FORCES
IN MITOSIS
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FORCE
MEASUREMENTS
CONSTANTS
FROM
441
ELASTIC
Chromosomes
are elastic; they spring back after they are stretched by the
spindle or by a micromanipulation needle. If the chromosome’selastic
constant is known,the absolute value of the stretching force can be determined simply by measuring the length of the chromosome. The elastic
constant was determined in the first spindle force measurementswith the
calibrated, flexible needles described above (26). If the chromosomeis
Hookian elastic body, then
F-- k(Alllo),
3.
where F is the applied force, k is the elastic constant (equal to Young’s
modulustimes the cross-sectional area of the chromosome),and Al/lo, the
changein length, Al, over the original length, 10, is the strain. ,To determine
k, the force was measured as usual from thc deflection of a calibrated
needle and the strain was measured from chromosomelength changes.
The published values for k, determined for Melanoplus sanguinipes spermatocytes, are 7.5 x 10.5 dyn per unit extension of two chromatids in
anaphase and 3.2 x 10-5 dyn per unit extension for one chromatid (26;
k was given as EA). For prometaphase chromosomes of Melanoplus
differentialis, k is 10.1 x 10-5 dyn per unit extension of two chromatids
(R. B. Nicklas, unpublished; mean of 25 determinations with 95%confidence limits of ___1.7 x 10-5).
Oncek has been determined, the chromosomeis a force gauge; whenever
chromosomesare stretched, the absolute force in dynes can be computed
simply from measurements of chromosome length, using Equation 3.
This method of force measurement is valid only if reasonably accurate
measurements of k are possible in living cells and if chromosomesare
elastic. These requirements are met for grasshopper spermatocytes (26).
Chromosomes
also must lengthen linearly in response to tension force (or
a force-elongation curve must be carefully determined). Chromosome
elongation is generally linear with force, as shownby consistent values for
k for various elongations up to three fold (26); moreexact tests of linearity
are planned. In addition, force measurementsare valid only for the particular species and stage in which k was determined. There is good reason
to expect large differences in chromosomeextensibility from species to
species and in mitosis versus meiosis because chromosomesvary widely
in condensation and diameter. Hence the value of k for grasshopper
chromosomescannot be applied to other materials. The accuracy of the
force measurementmethod is estimated as _+ 30%(R. B. Nicklas, unpublished; for a similar analysis, see 26).
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442
NICKLAS
The ease and utility of the calibrated chromosomemethod for force
measurementsin living cells are illustrated in the next section.
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PROMETAPHASE
Con#ression
CHROMOSOME MOVEMENT
Whenchromosomesfirst interact with the spindle at the start of prometaphase they are scattered, but by metaphase they lie almost exactly
midwaybetween the poles, at the equator (Figure la,b). This congression
of chromosomesin prometaphase probably results from unequal poleward
forces on each chromosomepair, as illustrated in Figure la (34; reviewed
in 17, 23; see also recent observations in 8, 9, 25, 45). The oppositely
directed spindle forces produce tension and elongation of the chromosome.
I have determined the tension force during natural congression by measuring the extent of chromosomeelongation and using Equation 3. An
average value of 0.5× 10-Sdyn was obtained (Table 1) based on
measurementsin each of three cells. Congression movementsof individual
chromosomes
vary with time in velocity and in several other characteristics
(3), and the polewardtension force is equally variable. A maximum
tension
force of twice the average has been observed, but only rarely. More frequently, chromosomesare stretched very little owing to a tension force
about half the average, ~ 2.5 × 10-rdyn. The full range of variation
remains to be determined by frequent measurements of stretch in individual chromosomes.Such information will permit important correlations
between force and chromosome velocity and between force and chromosomeposition on the spindle.
Typical values for the tension force in prometaphase congression are
very much higher than the force required for normal chromosomemovement in anaphase (Table 1). The maximummeasured force in normal
prometaphaseis about 10- 5 dyn, twice the average given in the table. Thus
the spindle in prometaphase, in its normal function, can exert a force
within a factor of about seven of the absolute maximumforce it can
generate in anaphase in response to pulling by a micromanipulationneedle.
The fact that forces are higher in prometaphase than in anaphase is not
surprising. The motors in prometaphase are forced to work against each
other because the partner chromosomes are joined together; hence in
normal prometaphase movement the motors often work close to their
maximum
potential. In contrast, during normal anaphase, after the chromosomeshave separated the motors work only against viscous resistance
(unless they do workon a governor). Thus, only viscosity is an inescapable
part of the mechanical situation in anaphase, while in prometaphase both
chromosomalelasticity and viscosity impede mrvement.
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Induced
Movement
In prometaphase,chromosomes
can readily be shifted in position using a,
micromanipulation needle (25). Picture a micromanipulation needle
inserted into the chromosome
on the left in Figure la and movedupward.
The chromosome
is stretched, and it soon begins to be movedupward,
awayfromthe lower pole. I have determinedthe absolute force required
for such induced movementby measuring the extent of chromosome
elongationandmultiplyingby k. Theresults, given in Table1, are averages
for four experimentsin whichthe force wasmeasuredseveral times as a
single chromosome
was slowly pulled one step at a time from near one
spindle pole nearly to the other pole.
Theforces required to shift prometaphasechromosomes
in this fashion
are 6-16 times greater than those exerted by the spindle during normal
prometaphasemovement(Table 1). At their greatest, these forces are
somewhatgreater than the maximum
force measured in anaphase. The
original interpretation of induced movementwas as follows. Whena
chromosome
is pulled, spindle structure yields to the applied force. At
least in these experiments,and probablyin normalprometaphase
as well,
chromosomes
movebecause of forces that normally are in balance only
at the equator, midway
betweenthe poles, rather than becauseof structural
constraints such as the growthof kinetochoremicrotubulesto equal length
(25; see also 8, 9, 45). In this view,the absolutevalueof the force required
to inducemovement
reflects properties of spindle structure, not of motors.
Thatis, the valuesin Table1 represent the force at whichstructure yields
to force.
Adifferent interpretation is suggestedby recent observationsandideas.
In brief, structure and motorare identical. Particularly stimulatingis the
demonstration that both ATP-dependentmicrotubule translocation and
tubulin incorporation into kinetochoremicrotubulesoccur at the kinetochore (20). This result suggests modelsin which kinetoehore microtubules slide in sleeves in the kinetochore(10, 19, 20; reviewedin 29).
Viewedin the light of these models, induced chromosome
movementin
prometaphaseis a consequenceof experimentally induced microtubule
sliding and coordinated mierotubule assembly: Both movementand
assemblyare driven by the external force applied by the experimenter.
This impliesthat the valuesobtainedfor the force requireddo indeedreflect
properties of the motors, because the structural linkage of chromosome
to microtubulesrequires active motors. Thus, in this view, structure is
inextricably linked to function, and the force necessary to displace a
chromosome
is at once a yield strength for structure and a measureof the
maximum
output of the motors.
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444
NICKLAS
Another possibility must be considered. Induced chromosomemovement might be irrelevant to normal prometaphase movementand might
merely reflect a breakdownof spindle structure. As the needle pulls a
kinetochore awayfrom the pole, the structures that attach the kinetochore
to the pole might simply give way. Thus, the force required to induce
movementmight represent the limit that can be borne by spindle structure
rather than anything about normal movement.
The possibility that induced movementsignals a disruption of spindle
structure can be discounted because the force required is not constant. As
a chromosomeis shifted away from a spindle pole, the force required
increases with increasing distance. After the chromosomehas been shifted
across the equator into the other half of the spindle, the average force
required is over twice as great as whenthe chromosomewas in the original
half (Table 1). This dependenceof force on position supports the idea that
induced movementis related to normal prometaphase congression rather
than a simple collapse of spindle structure. Thus, there is no obvious
reason why the force required to cause spindle collapse would vary with
chromosome
position. On the contrary, an increase in force with increasing
distance would be expected if induced movementis closely related to
normal prometaphase movement. As mentioned above, it is very likely
that chromosomescongress to the equator because the poleward force on
any one kinetochore increases with increasing distance from the pole
(Figure la). Hence the oppositely directed poleward forces on partner
chromosomesare in balance only at the equator, as 0stergren (34) postulated (see also 8, 9, 25, 45). A linear increase of force with distance from
a pole is an attractive idea (17), and there is recent evidence consistent
with linearity (8, 9, 44). Linearity has important implications for the
molecular nature of the motor, but the present evidence is indirect; the
forces have not been measured. Direct measurements show that the force
resisting chromosomedisplacement increases with increasing distance
from a pole (see values for induced movementin Table 1). However, the
present data are too crude to establish whether the relationship between
force and distance is linear. More refined experiments are planned to
determine how muchapplied force is required to match exactly the normal
spindle forces and therefore cause natural congression movementsto stall.
The measurements will be made over the whole range of chromosome-topole distances.
FORCE
AND
STRUCTURE
The usual effect of force on structure is mechanical deformation. Consequently, the capacity of a spindle to bear the load is an important aspect of
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IN MITOSIS
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spindle structure; the spindle poles must remain fixed while chromosomes
movetoward them. The indications that spindle structure collapses at
abnormally great loads in anaphase and in induced chromosomemovement in prometaphase have already been mentioned. A less ordinary
impact of force on structure is the subject of this section.
Tension and Stabilization
of Microtubule
Arrays
The proper distribution of chromosomesto the daughter cells in mitosis
depends on an appropriate arrangement of kinetochore microtubules. All
the kinetochore microtubules of one daughter chromosomemust extend
toward one spindle pole, while those of its partner extend toward the other
pole, as in Figure 1 (reviewed in 28). However,almost every conceivable
misarrangement of kinetochore microtubules has been seen at the beginning of prometaphase when chromosomesfirst interact with the spindle.
These faulty arrangements would lead to unequal chromosome distribution if they persisted. Usually, however,they do not persist; a variety
of inappropriate arrays is transformed into the one array consistent with
equal chromosomedistribution (28). Dietz (4) discovered that the transformation of microtubule arrays involves stability differences rather than
a mechanismfor making specific repairs. All faulty arrangements arc
unstable and soon change, while the one appropriate arrangement of
microtubules is stable. Thus, microtubule arrangements change and
change again until the only stable arrangement is reached. Tension is the
probable source of stability. Forces toward opposite poles (Figure la)
produce tension in a properly oriented chromosomepair and in the microtubules associated with it. But if both partners are oriented to the same
pole (Figure 3a), tension is absent and changes in microtubule arrangement
soon follow. Evidence for stabilization by tension has comefrom experiments in which the tension missing in an unstable configuration was
supplied by the experimenter. A micromanipulation needle was inserted
into a chromosomelike that shownin Figure 3a and movedupward, lightly
stretching the chromosomeas in Figure 3b. This made the otherwise
unstable configuration stable for as long as the tension was maintained
(reviewed in 28).
I have determined the absolute value of the applied force required to
stabilize unstable configurations by measuring the extent of chromosome
stretching and using Equation 3 (R. B. Nicklas, unpublished). An average
value for three experiments is given in Table 1. The stabilizing force
per kinetochore or per microtubule is comparable to the lower force
values for induced movementin prometaphase and is fourfold greater
than the force in natural congression. At present, no particular significance should be attached to this comparison because no effort has yet
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446
NICKLAS
Figure 3 Diagrams of a chromosome with an unstable microtubule array and its stabilization by tension. (a) Unstable array; all the kinetochore microtubules of both partner
chromosomesextend toward one pole (not shown) and the mitotic forces (arrows) act only
toward that pole. (b) Stable array; a micromanipulationneedle (not shown) has been inserted
in the chromosomeand movedupward, creating a tension force (arrow), and the chromosome
is stretched.
been made to determine the minimumforce required to stabilize microtubule arrays.
The molecular mechanismby which force stabilizes microtubule arrays
is not known,although several possibilities have been proposed (28, 30).
It is not even certain that the force directly affects microtubules and
associated structures. For instance, tension force aligns the chromosome
and its kinetochore with the spindle axis, causing the kinetochore to point
more or less directly toward a pole; this geometryby itself could promote
stability. But whatever the mechanism,an effect of force on structural
stability has been directly demonstrate0, and the force has been measured.
Further workon stabilization by tension will contribute to the solution of
a central problemin cell biology and genetics: the molecular origins of the
exact distribution of chromosomesin cell division.
Force and Microtubule
Assembly
Mechanical force has thermodynamic effects that are particularly remarkable in the case of microtubules and actin filaments (13). Consider
a microtubule between two plates, one at each end. If the plates arb-~0~1
closer together, the microtubule is compressed;its subunits press against
one another and against the two plates. In the words of Hill & Kirschner
(13, pp. 50--51), "it seemsintuitively reasonablethat it will be moredifficult
for an incoming monomerto squeeze between the polymer and the anchor
[plate] and also that the compression will tend to push monomersout of
the polymer." Thermodynamicanalysis confirms what intuition suggests:
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FORCES
IN MITOSIS
4z~7
Significant compressionwill favor microtubulc instability and disassembly.
Conversely, consider a microtubule under tension. The subunits are pulled
further apart, providing sites for additional subunits. Hencetension force
should promote microtubule assembly and enhanced stability (13). From
Hill &Kirschncr’s results (13), I have calculated (26) that a force of ~
dyn per microtubulc should significantly affect microtubulc assembly/
disassembly: A tension force of this magnitude should approximately
double the thermodynamicforce driving assembly.
The spindle has the potential to produce a force of more than 10-6 dyn
per kinetochore microtubule in anaphase. In prometaphaseit actually does
produce a force this large (Table 1). This raises the intriguing possibility
that spindle function, i.e. force production, regulates spindle structure
by directly affecting assembly thermodynamics, altering the length and
stability of microtubules (26). Twomitotic proccsscs in particular might
be aptly explained by a thermodynamic effect of force on microtubule
assembly: the stabilization of kinctochore microtubules by tension and the
adjustments in microtubule length associated with chromosomemovement
to the equator in prometaphase.
The experiments in which tension from a microneedle stabilizes otherwise unstable microtubulearrays initially seeman ideal test in living cells
of the Hill &Kirschner (13) thermodynamicanalysis. Intrinsically unstable
microtubules were stabilized when subjected to a tension force of about
3 × 10- 6 dyn per microtubule (Table 1), in good agreement with the value
calculated from thermodynamic analysis. Unfortunately, the interpretation is not so straightforward. As already noted, the stabilizing effect of
tension in these experiments maynot affect microtubules directly (30; see
also 28). To resolve two potential problems we require more knowledge
both of cells and of thermodynamicparameters. First, microtubule arrays
are stabilized by less force than the present rough thermodynamiccalculations suggest should be required. Thus, arrays are stable in normal
prometaphasecongression although the tension is often less than half the
average given in Table 1, i.e. less than 4× 10-Tdyn per microtubule.
Second, little or no microtubule elongation, which would be expected to
accompanymicrotubule stabilization, is observed. Thus further work is
needed. The stimulus for that work is the fact that tension forces within
an order of magnitude of those calculated from thermodynamicprinciples
are associated with stable microtubules.
Induced chromosome movement in prometaphase provides evidence
consistent with the thermodynamically expected effects of both tension
and compression. Kinetochore microtubules almost certainly bear the
load whenchromosomesare pulled (6, 32). At forces of 4 × 10- 6 dyn per
microtubule and higher (Table 1) a chromosomeis slowly pulled away
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4~8 NICKLAS
from a pole; the kinetochore microtubules oriented toward that pole are
under tension and those oriented toward the opposite pole are under
compression. The tension force is probably associated with kinetochore
microtubule lengthening, because the kinetochore remains connected to
the spindle (25). Moreover, in normal conditions at least, microtubules
must lengthen as the chromosomemoves, because some kinetochore microtubules are always observed to cover the whole kinetochore-to-pole
distance (32, 36). Conversely, the microtubules under compression, lying
between the chromosomeand the pole to which it is being pulled, probably
shorten as the chromosomemoves (25).
There is other evidence that microtubule assembly in mitosis can be
affected by force, although the force has not been measured.First, as Hays
and coworkers pointed out (9), the evidence that balanced poleward forces
determine chromosomeposition in metaphase implies that force mayregulate assembly, since kinetochore microtubules oriented toward one pole
must shorten and those oriented toward the other must lengthen for the
equilibrium position to be reached. Secondly, Hays (8) has obtained direct
evidence for an effect of compression. He induced a reversible, threefold
shortening of the spindle and great microtubule depolymerization by pushing the poles together with micromanipulationneedles. It will be interesting
to measure the force required for spindle shortening in Hays’s experiment.
I conclude that force affects spindle microtubule length in a variety of
experimental situations and probably also in normal mitosis. It has not
been proven that the mechanism is a thermodynamic effect of force on
assembly, but it would certainly be satisfying if important mitotic events
have such a simple and interesting explanation.
Further force measurementswill certainly lead to rapid progress. Not
only will more delicate, revealing experiments on living cells be done, but
the effects of force on microtubules will be tested directly. In remarkable
experiments, Kamimura& Takahashi (16) determined the force produced
by flagellar microtubules attached to calibrated, flexible glass needles. It
should also be possible to impose knownforces on single microtubules or
groups of microtubules in vitro. This experiment would showconclusively
whether tension and compression have the effects expected from thermodynamic
principles and, if so, at what force per microtubule. In short,
we have an enticing problem and the technical meansfor its solution.
ACKNOWLEDG/vIENTS
I thank DonnaKubai for her critical review of the manuscript. Workfrom
mylaboratory was supported in part by grant GM13745 from the National
Institutes of Health.
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449
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