 |
INTRODUCTION |
FtsZ, a homolog of tubulin (1-3), is a cell division
protein found in almost all bacteria, archaea, chloroplasts and some mitochondria (4-7). Light microscopy has shown that FtsZ assembles into a ring that constricts and divides the cell (8-10). The
substructure of Z-ring has not been visualized by electron
microscopy of bacteria, but much has been learned from in
vitro assembly studies. FtsZ forms straight protofilaments with
longitudinal bonds similar to those in microtubules (11, 12). Under
many conditions the protofilaments tend to associate laterally into
pairs or small bundles (13-15), but in most studies at least some
polymers appear to be single protofilaments. Romberg et
al. (16) used mass measurement by scanning transmission electron
microscopy to demonstrate that protofilaments were indeed only 1 subunit thick. The existence of single protofilaments is quite
different from tubulin, where protofilaments are stable only when
assembled into parallel sheets in which the protofilaments are
connected by lateral bonds (17). A single protofilament should have
only a single type of longitudinal bond, and all bonds should be
identical. This type of assembly is now referred to as isodesmic (16,
18).
Isodesmic assembly was demonstrated for glutamate dehydrogenase (19,
20) and
-lactoglobulin (21), and the thermodynamic principles of the
assembly were developed. Tubulin has been interpreted to assemble
isodesmically in the presence of GDP (18, 22). The assembly of
glutamate dehydrogenase and
-lactoglobin are probably not
physiologically important, and the GDP-tubulin polymer is probably only
transiently important during microtubule disassembly.
In contrast to isodesmic assembly, all physiologically relevant
filaments studied so far, in particular tubulin and actin, assemble in
a cooperative manner. The key distinction of cooperative assembly is
that subunits are connected by two types of bonds to form a helical or
two-dimensional polymer (17, 23). In addition to the longitudinal bonds
within a protofilament, adjacent protofilaments are connected by
lateral or diagonal bonds.
Cooperative assembly produces two features that are very important for
cytoskeletal filaments like microtubules and actin. First,
fragmentation in the middle is many orders of magnitude less favorable
than removing a subunit from the end, and so the filament can last for
long periods without breaking (23). Isodesmic assembly, in contrast,
produces a population of relatively short filaments, in which
fragmentation of every interface in the middle is equivalent to
dissociation of a subunit from the end. Second, cooperative assembly
exhibits a critical concentration
(Cc).1
There is a sharp transition from disassembly to assembly as the pool of
free subunits rises above Cc (24). This sharp
transition at the Cc, coupled with
unfavorable nucleation, results in a population of very long polymers,
in equilibrium with monomers at a concentration
Cc. Assembly and disassembly at the ends can be
finely controlled by the concentration of free subunits.
Several studies have suggested that FtsZ assembly is cooperative based
on the observation of an apparent critical concentration. Mukherjee and
Lutkenhaus (13) proposed a Cc for
Escherichia coli FtsZ of 1 µM using a
centrifugation assay and 2 µM using light scattering.
White et al. (14) proposed a Cc of 3 µM for Mycobacterium tuberculosis FtsZ
based on light scattering data. One of the most convincing indications
of a Cc was obtained from GTPase assays. GTPase,
which is thought to be coupled to assembly, is highly dependent on FtsZ
concentration. Relative specific activity was not measurable below 2 µM for Bacillus subtilis FtsZ and rose rapidly
to a plateau at 5 µM (25). Similar curves were obtained for E. coli FtsZ, with activity beginning at an apparent
Cc of 0.5 µM (Ref. 16 and Footnote
2) and reaching a plateau at 2 µM.
Romberg et al. (16) proposed that FtsZ may assemble
isodesmically. The primary basis for this proposal was an analysis of protofilaments by scanning transmission electron microscopy,
which determined the mass density to be that of a 1-subunit-thick
protofilament. If the protofilaments are 1 subunit thick they could
only have one type of bond, and hence assembly should be isodesmic.
Romberg et al. (16) repeated centrifugation and light
scattering assays, suggesting that might not support a critical
concentration. A problem with these assays is that they under-report
short protofilaments, which is particularly problematic at low FtsZ
concentrations. Romberg et al. (16), however, did note that
the GTPase assays provided strong evidence for a critical concentration
and thus cooperative assembly. There was therefore a significant
controversy as to whether FtsZ assembly is isodesmic or cooperative.
One of the most distinctive predictions of the isodesmic theory is that
the association constant for each interface should be quite high,
KA = 3.3 × 108
M
1, (KD = 3 nM). This high affinity bond was necessary to fit the
observed filament lengths of 30 to 50 subunits. This leads to the
prediction that short protofilaments should form above 3 nM
FtsZ, and for FtsZ above 10-30 nM almost all of the subunits should be assembled (only the subunits at the ends of the
protofilaments would not be involved in two interfaces). In contrast,
in a cooperative assembly there will be no assembly until FtsZ exceeds
the critical concentration, near 1 µM.
To test the theory further, we sought a technique that could quantitate
the extent of assembly at different protein concentrations, reporting
the total number of interfaces formed without any bias from filament
length. The formation of a protein-protein interface is typically
associated with a release of heat, and isothermal titration calorimetry
(ITC) can be used to measure the association. Because the heat
generated by the association should be the same for each interface, ITC
should meet the above criterion.
This application of ITC is different from the typical study of a
heterodimer association, where one subunit is placed in the reaction
cell and the other in the syringe. In our case the entire FtsZ sample
is initially in the syringe at high concentration and then is
diluted by being injected into the reaction cell. In general the
protein in the syringe will be assembled for the most part, and
injection will result in disassembly, which is sometimes followed by
reassembly. We found that informative data on FtsZ assembly can be
obtained with this novel approach to ITC.
 |
MATERIALS AND METHODS |
FtsZ Purification--
The following protocol was adapted from
Romberg et al. (16). BL21 cells were transformed with
Pet11b-wtFtsZ (wild type E. coli FtsZ). A 50-ml culture (LB
with 100 µg/ml ampicillin) was grown overnight in a shaker at
37 °C, centrifuged to pellet the cells, resuspended in fresh LB, and
added to two 500-ml cultures (LB with 100 µg/ml ampicillin). These
were grown in a shaker at 37 °C to A600 nm
~1.0 and then induced with 0.5 mM
isopropyl-1-thio-
-D-galactopyranoside. After
2 h the cultures were centrifuged at 2350 × g
(5000 rpm, Type 19 rotor, Beckman L8 ultracentrifuge) for 10 min, the
pellets were resuspended in lysis buffer (50 mM Tris, pH
8.0, 100 mM NaCl, 1 mM EDTA) to give a total
volume of ~20 ml, and the suspension was frozen at
80 °C.
Immediately after thawing, 2 mM phenylmethylsulfonyl fluoride and ~100 µg/ml lysozyme were added; the suspension was rotated at room temperature for 15 min. After the suspension was cooled
on ice for 10 min, it was sonicated (Virsonic 50 (115 V, 1 A, 60 Hz),
Virtis Co., Inc., Gardiner, NY) with four 30-s pulses at 50% power
with 1 min on ice between pulses to keep the sample cold. 10 mM MgCl2 and ~10 µg/ml DNase was then added
followed by rotation at room temperature for 15 min. After
centrifugation at 96,000 × g (35,000 rpm, 45 Ti rotor,
Beckman L8) for 30 min, the 20 ml of supernatant was mixed with 5 ml of
saturated ammonium sulfate (pH 8.0), incubated on ice for 20 min, and
then centrifuged at 17,600 × g (15,000 rpm,
Beckman 45 Ti rotor). This 20% ammonium sulfate pellet was discarded,
and the supernatant was mixed with 1.333 ml of saturated ammonium
sulfate (pH 8.0), incubated on ice for 20 min, and then centrifuged at
17,600 × g (15,000 rpm, 45 Ti rotor, Beckman L8). This
25% ammonium sulfate pellet was resuspended in 5 ml of buffer A (50 mM NaMES brought to pH 6.5 with KOH, 100 mM
KCl, 1 mM EGTA, 2.5 mM magnesium acetate)
followed by centrifugation at 70,000 × g (30,000 rpm,
45 Ti rotor, Beckman L8). The supernatant was brought to 10% glycerol
and 50 µM GDP, and then aliquots were frozen in liquid
nitrogen and stored at
80 °C.
The day prior to an experiment, FtsZ was cycled through one round of
assembly to further reduce the concentration of contaminants and to
increase the fraction of FtsZ capable of assembly into protofilaments.
An aliquot (0.5 ml) from the above preparation was thawed and dialyzed
(8000 molecular weight cutoff, 6.4-mm wet diameter dialysis
tubing, BioDesigns Inc., Carmel, NY) at 4 °C against two changes of
50 ml of buffer A for 1 h each. The sample was brought to room
temperature, 2.0 ml of buffer A was added, and the diluted sample was
brought to 20 mM CaCl2 and 2 mM GTP
after which the sample was allowed to polymerize for 3 min. After
centrifugation at 15,000 × g (13,000 rpm, Biofuge A, Baxter Scientific Products) at room temperature for 5 min, the supernatant was discarded, and the pellet (consistency of a soft gel)
was resuspended in ~1 ml of buffer A. EGTA was added to 5 mM, and the sample was incubated on ice for 30 min to allow
disassembly. Subsequent centrifugation at 15,000 × g
for 5 min removed any particles unable to resolubilize. The
concentration of the resultant solution was determined colorimetrically
by BCA assay (Pierce) and corrected for the 25% color
difference between FtsZ and the BSA standard (26).
Sample Preparation--
For FtsZ samples containing no
magnesium, the solution described above was brought to 10 mM EDTA (by adding 500 mM EDTA pH 8.0) and then
diluted with buffer B (50 mM NaMES brought to pH 6.5 with
KOH, 100 mM KCl, 1 mM EGTA, 1 mM
EDTA) to the desired injectant concentration. For FtsZ samples
containing magnesium, the solution from calcium cycling was diluted
with buffer A. These samples were dialyzed against their appropriate
buffers, buffer B and buffer A, respectively, at 4 °C. The buffer
was changed after 1 h and again after a second hour; the last 50 ml of buffer was allowed to reach equilibrium overnight.
Isothermal Titration Calorimetry--
ITC measurements were made
in a MicroCal Systems ITC unit (MicroCal, Northampton, MA). The
reaction cell was loaded (using a 5-ml gas-tight syringe, Hamilton Co.,
Reno, NV) with 2.5 ml of the final dialysate of the injectant brought
to either 200 µM GDP or 1 mM GTP and degassed
immediately before the experiment was run. The FtsZ solution was loaded
into the injection syringe (250 µl capacity, 101.8 µl/inch) with no
added nucleotide. Mg2+ was the same concentration in the
syringe as in the reaction cell. All FtsZ experiments were performed at
25 °C with data points taken every 2 s. For the GDP experiments
(representative data shown in Fig. 1), 50 injections at 4.995 µl/injection and 12.56 s/injection were made after a 300-s initial
delay and with 180 s between the start of each injection
(reference offset = 10%). For the GTP experiments (represented in
Figs. 2 and 3), 25 injections at 5.058 µl/injection and 12.72 s/injection were made after a 300-s initial delay, with 180 s
between the start of each injection (reference offset = 10% for
no magnesium, 20% for 2.5 mM magnesium).
The base line automatically generated by the MicroCal Systems
analysis software (MicroCal Origin, version 5.0) was used except when
it was obviously accepting an errant data point as reference, and then these base-line points were corrected by hand before further
analysis. The software then integrated each peak to yield integrated
heats; these were normalized to the moles of protein in the injectant.
Because the base line for the FtsZ experiment with magnesium and GTP
(Fig. 3) was highly variable, plots of raw data without base-line
subtraction are presented to allow direct comparison (Figs.
1a, 2a, and 3). Three repetitions of each
experiment were performed to ensure reproducibility. However, only
representative samples are shown in the figures.
Modeling--
We used numerical modeling to test whether the
isodesmic assembly model would match the experimental data. The goal of
the calculation was to estimate the total number of FtsZ-FtsZ
interfaces as a function of CT, the total
concentration of subunits in the reaction cell. The model is based on
two equations from Romberg et al. (16),
|
(Eq. 1)
|
|
(Eq. 2)
|
where Ci is the concentration of
protofilaments consisting of i subunits,
KA is the equilibrium association constant,
N is the longest protofilament modeled, and
CT is the total concentration of FtsZ in the
solution. This differs from early formulations of isodesmic assembly
(19, 20, 27) in the factor 2 in front of KA,
which accounts for the equal probability of adding a subunit at either
end (16). When we present values of KA from
previous studies, we will report the numbers as given in the original
papers but will refer to them as 2KA (or the
equivalent (1/2)KD).
To estimate the total number of interfaces, we used a numerical
iteration. Taking FtsZ injected into buffer with GDP as an example, the
sample calculation began with choosing KA
arbitrarily. For the first calculated injection (concentration = 2.2 µM after injection), C1 was
chosen arbitrarily, Ci values were
calculated using Equation 1 (to n = 50, at which the
concentration is generally very low), and finally
CT was calculated using Equation 2. The value of
C1 was changed, and the calculation was repeated
until the CT value equaled 2.2 µM.
The total moles of FtsZ-FtsZ interfaces (NINT,2.2 µM) were
calculated
|
(Eq. 3)
|
where V is the volume of the solution
(2.5 ml in the case of the initial injection). Because an ITC data
point consists of a change from the injectant state to the sample
state, we also calculated the number of interfaces in the injectant.
The KA value was the same, but a new set of
calculations for Ci and
CT was required (iterating
C1) until CT equaled the
injectant concentration (1100 µM). The total moles of
interfaces in one injection (NINT, inj) was
calculated using Equation 3 with a volume of 5 µl. Finally the
normalized heat of injection was calculated using the equation
|
(Eq. 4)
|
where
H is the enthalpy of forming one FtsZ-FtsZ
interface. We have now calculated the data point for the first injection.
Subsequent injections were calculated similarly. The desired
CT value changes with each injection, and
therefore the iteration of C1 must vary
accordingly. The only other change was in calculating the normalized
heat of injection. The number of interfaces in the sample prior to
injection and the number of interfaces in the injectant must both be
subtracted from the number of interfaces in the sample after
injection.
|
(Eq. 5)
|
After an entire set of data points (2.2-110 µM)
had been calculated, the square of the difference between the
calculated points and the experimentally determined points was determined.
We found that the curve needed to be shifted down, and therefore we
introduced a shift factor that was simply added to the calculated
normalized heats of injection. This parameter and
H were
optimized using the Solver tool in Microsoft Excel to minimize the sum
of the squared differences between the calculated points and the
experimental points. Finally, the shape of the curve depends on the
value chosen for KA. Changing this value
required repeating the iteration of all C1
values to achieve the desired CT for all injections; thus, this parameter was best-fit by trial and error, using
several values and selecting the one that gave the best overall fit.
It is worth noting at this point that the isodesmic assembly model
always predicts net disassembly from injectant to reaction cell, when
the buffers are the same in both, and a curve in which amplitude
decreases monotonically with an asymptote of zero (before shifting).
This curve fitting procedure was attempted for the data in Figs. 2 and
3, but no reasonable fit was obtained. It is therefore shown only
in Fig. 1.
 |
RESULTS |
Isodesmic Assembly in GDP--
The nature of ITC experiments
necessitates that the concentration of protein in the injection syringe
be about 20 times greater than the midpoint of the range of
concentrations of interest. To explore assembly/disassembly at ~50
µM concentrations, the protein in the syringe needs to be
at least 1000 µM. Rivas et al. (27) reported a
magnesium-dependent assembly of FtsZ-GDP with a
(1/2)KD ~8 µM at 2.5 mM
Mg (thus, 2KA = 1.25 × 105
M
1). The model of Rivas et al.
(27), termed indefinite assembly, is identical to isodesmic assembly
except that the 2KA value is allowed to vary
with protofilament length. Because their 2KA did not vary more than the error expected for our experiments, here we
treated the Rivas et al. (27) model as isodesmic with a
fixed KA derived from their Fig.
5a.
Because assembly in GDP is not complicated by hydrolysis, we decided
first to establish the behavior of FtsZ when injected into a solution
containing only buffer and GDP. FtsZ at 1100 µM, in
buffer A, was injected into the chamber containing the same buffer with 200 µM GDP. The protein in the injection
chamber is assumed to contain approximately equimolar amounts of FtsZ
and bound GDP, and no free nucleotide. Fig.
1a shows the raw data (with no
base-line subtraction to allow for direct comparison to Fig. 3) for an
experiment in which the sample concentration was raised 2.2 µM by each injection. In Fig. 1b the data are
replotted as integrated heats of mixing for each injection. The
first heat of injection is the largest with heats decreasing
monotonically as the FtsZ concentration in the sample increases. The
interpretation is that at the 1100 µM concentration in
the syringe, almost all of the FtsZ is associated into polymers. During
the first injection a large fraction of these interfaces disassembled
as the concentration dropped to 2.2 µM in the reaction
cell; the second injection yielded a slightly smaller fraction of
interface disassembly and thus a smaller heat of injection. The
heat of injection continued decreasing until the fraction of
disassembling interfaces approached zero as the concentration in
the chamber rose substantially above KD.

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Fig. 1.
FtsZ injected into buffer with GDP.
a, raw data are shown for an ITC experiment in which
1100 µM FtsZ was injected into buffer with 200 µM GDP. Each peak corresponds to one injection, and each
injection increased the FtsZ concentration in the sample by 2.2 µM. The 50 injections shown here provide data for
2.2-110 µM. b, integrated heat/injection was
calculated by subtracting the base line from the raw data and
normalizing to the moles of FtsZ in each injection for each peak in
panel a (diamonds). Calculations described under
"Modeling" were used to obtain a best fit (solid line,
2KA = 2.5 × 105
M 1, H = 13,645 cal/mol,
shift = 1169 cal/mol inj) and the closest fit with the
literature value of 2KA = 1.25 × 105 M 1 (dashed line,
H = 9,821 cal/mol, shift = 1,719 cal/mol
inj).
|
|
To derive more information from these data, we calculated the response
we would expect from an isodesmic disassembly of FtsZ protofilaments
(Fig. 1b, solid and dashed lines). The
curves were calculated as described under "Modeling" and were fit
using three parameters: KA,
H, and
a shift factor. In Fig. 1b the solid line shows
the best fit (optimized
H and shift factor) using the
value 2KA = 2.50 × 105
M
1 (KD = 8 µM). The fit was only slightly worse when it was repeated
with the 2KA determined previously by Rivas
et al. (27) (dashed line;
2KA = 1.25 × 105 was
extrapolated from their Fig. 5A for a magnesium
concentration of 2.5 mM). Although there is no
corroborating evidence for the
H value, the model does
match the trend of the data, specifically the monotonic decrease in
amplitude of the peaks. The best fit was obtained with
H +
13.6 kcal/mol and a shift factor of
1.17 kcal/mol injectant for
each calculated injection. Possible explanations for a shift factor are
a difference between the temperature of the injectant and the reaction
cell, a heat of mixing for dilution of the protein, or adding buffer
with no GDP to the 200 µM GDP in the reaction cell.
Apparent Cooperative Assembly in GTP--
Because FtsZ has GTPase
activity, we performed two experiments to determine the effects of GTP
binding and GTP hydrolysis on assembly. The first experiment used a
buffer with no magnesium and contained 1 mM EDTA to chelate
any residual magnesium. In the absence of magnesium, E. coli
FtsZ binds GTP and assembles into protofilaments, but hydrolysis of the
nucleotide is blocked completely (16, 28). Fig.
2a shows the raw data for 98.7 µM FtsZ injected into buffer B with 1 mM GTP.
The FtsZ in the syringe contained only its residual GDP. The key
features of these data are the initial positive peaks that are obtained
up to the 12th injection, at 3.2 µM. The 13th injection,
at 3.4 µM, produces a distinctly smaller positive peak
and initiates a sharp transition to negative peaks. This transition is
complete by 4.5 µM, after which the peaks are uniformly
negative. This can be seen even more clearly in Fig. 2b,
which shows the integrated heats of mixing for each peak. We
believe the positive peaks are due to disassembly of FtsZ-GDP from the
highly concentrated injectant state. We attribute the negative peaks to
reassembly of subunits supported by GTP. The abruptness of the
transition suggests a critical concentration of about 3.5 µM, with little to no assembly at concentrations below
CC and almost complete assembly of all added
FtsZ above CC. This transition could not be
modeled by an isodesmic assembly process regardless of the
KA or
H chosen. Therefore, we
conclude that, in the presence of GTP, FtsZ assembles in an apparently cooperative manner. It is important to note that the switch to cooperative assembly requires only that FtsZ bind, not hydrolyze, GTP.

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Fig. 2.
FtsZ injected into buffer with GTP and
EDTA. a, raw data are shown for an ITC experiment in
which 98.7 µM FtsZ was injected into buffer with 1 mM GTP and 1 mM EDTA. Each peak corresponds to
one injection, and each injection increased the FtsZ concentration in
the sample by 0.267 µM. The 25 injections shown here
provide data for 0.27-6.68 µM. b, integrated
heat/injection is calculated by subtracting the base line from the raw
data and normalizing to the moles of FtsZ in each injection for each
peak in panel a (diamonds). Because the data
generate an S-shaped curve (rather than a monotonic decrease in
amplitude), the isodesmic model does not fit regardless of the
KA, H, and shift parameters
chosen, and thus, no calculated curve is shown.
|
|
The addition of 2.5 mM magnesium acetate (and removing
EDTA) allows FtsZ to hydrolyze GTP during the assembly process.
Injecting FtsZ at 24.7 µM into buffer A containing 1 mM GTP yielded the results shown in Fig.
3. Qualitatively the base line begins
straight (ITC base lines are rarely exactly horizontal) with a small
positive peak at each injection. At about 0.4 µM there
are two abrupt changes; each injection now results in a substantial
negative displacement, and this is maintained rather than returning to
the base line, resulting in a continuous downward slope of the base
line. This behavior may be attributed to continuous GTP hydrolysis at
concentrations above 0.4 µM. This exothermic process
should last at least 30 min to 1 h before the GTP is exhausted,
similar to the time scale of the experiment. We had expected the base
line to become more negative as more FtsZ was injected, leading to
increased GTP hydrolysis, but instead the base-line slope remained
constant for the remainder of the experiment. Because the GTP
concentration is decreasing with time, we speculate that this behavior
may be due to a balance of these factors. We attempted to test this
hypothesis by adding a greater concentration of GTP (5 mM),
but this created too large a mismatch between the buffer and the
injectant, resulting in large heats of mixing that masked the heats
from FtsZ-FtsZ binding and GTP hydrolysis (data not shown).

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Fig. 3.
FtsZ injected into buffer with GTP and
magnesium. Raw data are shown for an ITC experiment in which 24.7 µM FtsZ was injected into buffer with 1 mM
GTP and 2.5 mM magnesium acetate. Each peak
corresponds to one injection, and each injection increased the FtsZ
concentration in the sample by 0.067 µM. The 25 injections shown here provide data for 0.067-1.65 µM
FtsZ.
|
|
These experiments were done three times each, with the transitions
(beginning-ending) being 2.4-3.5 and 2.9-4.0 µM and
3.5-4.5 µM for assembly in GTP-EDTA. For assembly in
GTP-Mg, the beginning of the transition was observed at 0.4, 0.26, and
0.26 µM. Taking the average of beginnings of the
transition as the estimate of Cc, we estimate
Cc = 2.9 µM for GTP-EDTA and
Cc = 0.31 µM for Mg-GTP.
 |
DISCUSSION |
One of the most distinctive predictions of the isodesmic assembly
model is that the association constant for each interface should be
very high (KA = 3.3 × 108
M
1 (KD = 3 nM)) for assembly in GTP (16). This implies that most FtsZ
subunits should be associated into short protofilaments at
concentrations 3-10 times above KD,
~10-30 nM. The ITC experiments reported here
should report the total formation of interfaces, without the
complication of underestimating short protofilaments. ITC experiments
in GTP showed no evidence for assembly below micromolar concentrations
and therefore do not support the isodesmic assembly model. On the
contrary, they gave a clear indication of a critical concentration,
which is characteristic of a cooperative assembly.
We first analyzed disassembly of FtsZ-GDP and found that it did fit the
isodesmic assembly model, with a 2KA close to
that derived from a previous study using sedimentation techniques (27). This 2KA = 2.50 × 105
M
1 is 1000 times weaker than that predicted
in the isodesmic model. Because the 1100 µM FtsZ in the
syringe is well above the KD (16 µM),
it will be almost completely assembled. In the ITC experiments the
first injections resulted in a dilution in the reaction cell that was
well below KD, giving a positive peak corresponding to the disassembly of the polymer. As the concentration in the reaction
cell approached KD the peaks decreased, and at
concentrations well above KD the peaks approached zero.
The experiment was more complicated when FtsZ was injected into the
reaction cell containing GTP. The concentration in the syringe was 98.7 and 24.7 µM for the assemblies in EDTA and Mg, respectively. In the experiment using Mg, the 24.7 µM concentration was less than twice the
KD; nevertheless, based upon the isodesmic assembly
model, which seems to apply for FtsZ-GDP, we expect about two-thirds of
the FtsZ to be assembled in the syringe. For the experiment using EDTA
we cannot predict the KD, but because Rivas et
al. (27) found the KA to be proportional to
the Mg concentration, we can assume that in the absence of Mg the
association will be very weak and the KD high. In
this experiment the FtsZ in the syringe should be largely unassembled, consistent with the much smaller positive peaks.
In both cases reassembly following the transition generates a
substantial negative peak instead of the asymptote to zero seen in the
dilution into GDP. This may be due to two factors. First, the
disassembly applies only to the two-thirds or less of FtsZ that was
assembled in the syringe, whereas reassembly following the transition
may be close to 100%. Second, the bond formed in GTP is of higher
affinity that that in GDP and may evolve more heat per bond. These two
factors should explain why more heat is evolved in the reassembly in
GTP than was lost upon the disassembly from GDP.
Assembly in magnesium differed from assembly in EDTA in two major
respects: the critical concentration was about 10-fold lower, and once
the transition occurred there was a continuous downward slope. In both
cases the transitions were very sharp. In EDTA, as shown in Fig. 2, the
transition began at 3.5 µM and was complete by 4.5 µM, which is only a 33% increase. In Mg the transition was perhaps even sharper, beginning at 0.4 µM and,
although we cannot be exact because of the difficulty in integrating
the heats of injection due to the changing base line, it seems the heat of injection reached a plateau after only two more injections (0.13 µM).
The abrupt transition to assembly at a critical concentration of 0.31 or 2.9 µM is characteristic of cooperative assembly. At
present we do not know the mechanism for this apparent cooperativity. Cooperative assembly typically involves two types of bonds, one longitudinal and one lateral, to make a helical or two-dimensional polymer (23). Although protofilaments do seem to associate side-by-side later in assembly and at high protein concentrations (13-15), this association does not seem to be essential because the single
subunit-wide protofilaments appear to be the basic polymer under the
conditions used here (16). We have sought to explain how a
single-stranded protofilament can show features of cooperativity, but
several avenues of structural modeling and thermodynamics failed to
provide a compelling mechanism. Understanding the mechanism for the
apparent cooperativity of FtsZ assembly thus remains a major challenge.