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A kinetic model for microtubule polymerization during oral regeneration in Stentor coeruleus
BioSystems, 9 (1977) 269--279 © Elsevier/North-Holland Scientific Publishers Ltd.
269
A KINETIC MODEL F O R M I C R O T U B U L E P O L Y M E R I Z A T I O N DURING ORAL REGENERATION IN S T E N T O R C O E R U L E U S
JOANNE K. KELLEHER* Department of Biolog:), Boston University, Boston, MA 02115, U.S.A.
(Received March 3rd, ]977) (Revised version receivedJune 16th, 1977) The regeneration of oral cilia in the protozoan cell, Stentor coeruleus, has been investigated in the presence of agents which do not favor the polymerization of microtubules. These agents, low temperature and the tubulin binding drugs, podophyllotoxin and ~-peltatin, slow the rate of regeneration. A kinetic model is proposed to test the hypothesis that microtubule polymerization is the rate limiting step in oral regeneration. The results suggest that the tubulin concentration of normal regenerating cells is slightly in excess of an amount which would kinetically limit the regeneration rate.
1. I n t r o d u c t i o n 1.1. Microtubule polymerization in eucaryotic microbes
The ciliated and flagellated eucaryotic microbes offer excellent systems to explore the developmental biology of microtubule formation. In many of these organisms cilia and flagella may be removed and regeneration induced, e.g., Chalmydomonas (Rosenbaum et al., 1969), Tetrahymena (Rosenbaum and Carlson, 1969) and Stentor (James, 1967). Microtubule protein, tubulin, is the major component of ciliary and flagellar axonemes. Regeneration of cilia and flagella is inhibited by agents which favour the disassembly of microtubules (anti-microtubule agents). These include physical agents, low temperature and high hydrostatic pressure in addition to tubulin binding drugs, such as colchicine and podophyllotoxin. Microtubule structures are classified as labile, easily disrupted by anti-microtubule agents, or stable, resistant to these agents * Present address: Department of Developmental Biology, Boston Biomedical Research Institute, 20 Staniford Street, Boston, MA 02114, U.S.A.
except during periods of microtubule growth (Tilney and Gibbins, 1968). In general, cilia and flagella regrow normally when removed from the anti-microtubules agents. Although the presence of high levels of anti-microtubules agents totally inhibits cilia and flagella growth in several organisms, it is well established that low levels of these agents do not totally inhibit regeneration but simply slow the rate of this process (Margulis et al., 1975; Saras and Burchill, 1975). Several hypotheses have been suggested as explanations for the recovery of regenerating microtubule structures subject to tubulinbinding drugs. Rosenbaum and Carlson (1969) proposed that regenerating Tetrahymena may selectively excrete colchicine and thereby overcome its effects. Saras and Burchill (1975) find their data compatible with the development of intracellular resistance to tubulin binding drugs in Stentor. However, specific details of this resistance are not known. This paper will examine the endogenous recovery of cilia regeneration in S t e n t o r coeruleus exposed to low temperature and the tubulin-binding drugs, podophyllotoxin and /3-peltatin. The aim of this paper is 2-fold: (1) to develop a specific hypothesis for endo-
270 its migration to the anterior portion of the cell. Scanning and transmission electron microscopy indicate that regeneration induced basal bodies to grow subpellicular microtubules as well as membranellar cilia (Paulin and Bussey, 1971). The following requirements are known for oral regeneration in St ent or coeruleus: RNA synthesis is required between stages 0 and 4 as measured by sensitivity to actinomycin D (James 1967); protein synthesis is required between stages 0 and 6 measured by sensitivity to puromycin (James 1967) and cycloheximide (Haight and Burchill, 1970). The polymerization of microtubules is apparently required over the entire regeneration period. The process is inhibited by the tubulin-binding drug, Colcemid, throughout the entire regeneration sequence (Kelleher, 1972). In order for a developmental process requiring the net polymerization of microtubu-
genous recovery in this system; (2) to analyze the possibility that the rate of microtubule polymerization limits the rate of cilia regeneration in Stentor. Towards these goals a kinetic model for cilia regeneration will be developed and tested against experimental data obtained in cilia regeneration studies. 1.2. Oral regeneration in stentor coeruleus
The heterotrichous ciliate, St ent or coeruleus may be induced to shed its ciliated oral membranellar band. The ensuing regeneration process, as described by Tartar (1961), involves the replacement of the entire oral structure including underlying basal bodies. The process requires 8 h at room temperature and has been divided into eight distinct morphological stages (see Fig. 1). The first 3 h of regeneration are occupied by the formation of the new membranellar band and the last 5 h with
SHEDDING
PAFF
I
3
5
7
REGENERATED CONTROL
TIMING OF MACROMOLECULAR PROCESSES DURING ORAL REGENERATION
M ,o ro , ,,, u ,, Po, , - -
,. o, ,o.
"//////.,A
Fig. 1. Macromolecular requirements for oral regeneration in Stentor coeruleus (modified from James, 1967). Numbers under cells indicate stages of regeneration. PAFF, protruding anterior frontal fields: OP, oral primor. dium; DOMB, developing oral membranellar band, MB, membranellar band.
271
protein synthesis l inactive tubulin
~
~
~
II~ stable stable k2 ~ labile k~ tubulin + microtubule ~ k.2 microtubules ~ microtubule (tub) (Mrs) (Mt,) (Mts) +
drug (eg,colchicine, podophyllotoxin) tubulin-drug Fig. 2. Postulated states of microtubule protein during oral regeneration in Stentor coeruleus. Inactive tubulin subunits self assembled to form dimeric active tubulin (tub), which may either assemble i n t o m i c r o t u b u l e s or bind to a drug. Stable m i c r o t u b u l e n u h i b e r is c o n s t a n t and equal t o the n u m b e r o f m i c r o t u b u l e g r o w t h points. Stable m i c r o t u b u l e length varies during p o l y m e r i z a t i o n . Labile m i c r o t u b u l e s are dissociable s u b u n i t s o n the e n d s o f microtubules. les to proceed in the presence of a tubulinbinding drug or other agent which favours the depolymerization of microtubule structures, one of the following mechanisms may be responsible: (1) The cell responds to the loss of tubulin and corapensates by making available more tubulin than the cell would have access to under normal circumstances. (2) The tubulin-binding drugs lose activity during the incubation period. (3) The process involves the conversion of labile microtubules, sensitive to anti-microtubule agents to stable forms resistant to these agents as diagrammed in Fig. 2. Results wil:[ be presented here, which indicate that mechanisms 1 and 2 are unlikely to be the reason Stentor is able to overcome the effects of these agents. A kinetic model will be constructed to test mechanism 3. 1.3. A kinetic model for microtubule polymerization in the presence o f anti-microtubule agen ts
The appendix of this paper contains the derivation of an expression relating the concentration of tubulm-binding drug to the rate of oral regeneratio~ in Stentor coeruleus. The basis of this kinetic model is the premise that differentiation may be described in terms of rate limiting events, or critical variables, (see
Wright, 1973, for discussion). In the model presented here tubulin-binding drugs are used to titrate the available cellular microtubule protein. Delays produced in regeneration time are presumed to be related to a decrease in the concentration of tubulin molecules available for polymerization. If it can be demonstrated that all the active cellular tubulin is required for regeneration to proceed at a normal rate, then the concentration of active tubulin within the cell during regeneration may be considered a critical variable for this process. Fig. 2 is a diagram of the states of association of tubulin over the course of oral regeneration. This diagram outlines the molecular species used in the kinetic model. Microtubule protein is synthesized and assembled into a 120 000 MW dimer form, tubulin, which can either participate in polymerization or bind to a drug. Labile microtubules are assumed to be in dynamic equilibrium with free tubulin subunits (Inoue and Sato, 1967). Stable microtubules are tubulin polymers resistant to the effects of anti-microtubule agents (Tilney and Gibbons, 1968). There is cytological evidence for the conversion of labile to stable microtubules in the oral membranellar band of Stentor. Haight and Burchill (1968) observed the resorption
272 of regenerating oral cilia in colchicine treated cells at stage 3 of regeneration. However, if the drug was added at later stages, the cilia were not resorbed. Makrides et al. (1970) reported the resorption of newly formed daughter cilia of dividing Stentor treated with colchicine, while the older parental cilia were not effected b y the drug. This result is particularly striking since labile and stable microtubules occur on the same cell simultaneously. In constructing this model several assumptions have been made as to the behavior of microtubule protein in living cells. These assumptions are stated here, so that the limits and constraints o f this approach will be apparent. Assumptions used in the kinetic model: (1) The essential states of microtubule protein are accurately described by Fig. 2. (2) Tubulin and labile microtubules are maintained in dynamic equilibrium (Inoue and Sato, 1967). (3) Tubulin polymerization occurs as a simple condensation polymerization between tubulin and formed microtubules. In regenerating cells the number of growing microtubules is constant, and the rmmber of growth points does not vary with microtubule length. This form of association has been discussed in vitro by Johnson and Borisy (1975) and Bryan (1976) and in vivo by Goode (1973). (4) Stentor treated with tubulin-binding drugs produce completely normal oral cilia, i.e., they polymerize the same quantity of tubulin on the same number of growth points as control cells. (5) The total amount of tubulin available for polymerization during oral regeneration is not effected by the application of tubulin-binding drugs. (6) The equilibrium between tubulin (tub) and labile microtubules (Mtl) equal to h-2/k2[Mts] or h-2/h2* is a constant since the number concentration of microtubule growth points (Mts) is constant throughtout regeneration and the equilibrium k.*2/h-2 is not affected by microtubule length (Johnson and Borisy, 1975). The value of the constant
k-z/k2* is assumed to be significantly less than 1.0, that is, a t equilibrium, there are many more tubulin molecules in solution than labile microtubule ends. (7) Intracellular drug concentration is a linear function of the external concentration. To predict K D values accurately from the data found in this study, an additional assumption that the cells are freely permeable to these drugs is required. The polymerization pattern resulting from this model is basically similar to the end-onaddition models examined in vitro with cytoplasmic brain tubulin by Bryan (1976) and Johnson and Borisy (1975). However, since their models concern the formation of labile, totally depolymerizable microtubules and this paper analyzes stable microtubule formation, differences exist in the proposed kinetics of microtubule polymerization. Models o f labile microtubule polymerization predict, and the data confirm, that the equilibrium between tubulin and labile microtubules is not a function of labile microtubule number concentration. This model predicts that the equilibrium between tubulin and labile microtubules is a function of the number concentration o f stable microtubules. (See eq. 2, appendix.) Such a model obviously represents a simplified picture of a complicated biological process. For example, factors associated with microtubules other than tubulin itself have not been considered. Thus, in this model, the function and concentration of these factors is assumed to be unaffected by the drug treatment. This kinetic model for microtubule polymerization in Stentor coeruleus has certain intrinsic limitations and requires a number of assumptions. It is offered here as a starting point in the search for critical variables in microtubule polymerization process and as a guide for future experimentation. 2. Methods and materials Detailed methods for growing Stentor coeruleus cells and inducing oral regeneration
273 have been described previously (Margulis et al., 1975). In the :~tudies r e p o r t e d here, cells were allowed to regenerate, 20 cells in 5 ml spring w a t e r of " M " solution, an artificial p o n d water. An Arrhenius activation energy for the 8--24°C :range was d e t e r m i n e d b y least square regression analysis. T e m p e r a t u r e was maintained ± 0.1°C by a Cambion water bath (Cambion Inc., Cambridge, MA} for the t e m p e r a t u r e studie~. Oral regeneration, attainm e n t o f stage 8, was d e t e r m i n e d b y observation u n d e r a dissecting microscope. In o t h e r e x p e r i m e n t s the cells were k e p t at 23°C. Unless otherwise indicated, drugs were added to the regeneration m e d i u m at state 3, 3 h after oral band removal. C o m p o u n d s n o t easily soluble in water were added in ethanol at a final c o n c e n t r a t i o n o f less t h a n 1%, a
c o n c e n t r a t i o n which had n o e f f e c t on regeneration. P o d o p h y l l o t o x i n was o b t a i n e d f r o m Aldrich Chemical Co., Milwaukee, Colchicine f r o m Sigma Chemical Co., St. Louis;/3-peltatin was a gift f r o m Dr. A. y o n Wartburg, S a n d o z Ltd., Basel. In vitro drug binding assays were p e r f o r m ed using t h e D E A E filter p a p e r assay o f Borisy ( 1 9 7 2 ) (see Kelleher, 1977, for details).
3. Results and Discussion 3.1. Temperature sensitivity o f oral regeneration An Arrhenius plot o f oral regeneration in Stentor coeruleus is shown in Fig. 3. Below 15°C, where regeneration was n o t c o m p l e t e l y
ARRHENIUS PLOT for ORAL REGENERATION n Stentor coeruleus 200
IOO % x
50 .,£:
W I.-Q~
z o
I0
I.-QZ W
z
5
W W
I 3.25
3.30
3.35
3.40 3.45 I/°K x 103
3.50
3.55
3.60
Fig. 3. Arrhenius plot of oral regeneration in Stentor coeruleus. Regeneration time, from stage 0--8, was measured by observation (a minimum of 20 cells per time point). Mean regeneration rate is plotted above 15~C, where the cells were somewhat asynchronous, the range of regeneration rates is plotted.
274 synchronous, the range of regeneration time for 20 cells is plotted. Cell death occurred at temperatures below 4°C and above 31°C. The data in Fig. 3 appear to form three straight lines indicating changes in the activation energy for the rate limiting step at 8°C and 24°C. An Arrhenius activation energy o f 19 kcal/mol (+ 0.5) was determined for the 8--24°C range. This activation energy represents an average for the rate limiting steps o f the entire regeneration process. This value is similar t o the 18--19 kcal/mol Arrhenius activation energy reported for the growth rate of the ciliate, Tetrahymena (Moner, 1972). Since oral regeneration is divided into eight distinct morphological stages, cells were observed during regeneration to determine the degree to which each stage of regeneration followed the rate pat t er n for the entire process at 24°C where each stage lasts 1 h. Results o f these observations indicated that each morphological stage lasted one-eighth of the regeneration period in the 8--24°C range. This result suggests t hat the activation energy for the rate limiting step does not change significantly during the 8 stages o f regeneration and is consistent with the hypothesis that the entire sequence is limited by the same reaction. F u r th er m or e, when moved from one t e m p e r a t u r e to another, regenerating cells quickly adjust to the regeneration timetable o f the new t e m p e r a t u r e (see Table 1). For example, cells regenerating at 10°C reach stage 6 at a b o u t 29 h or 3A of the total regeneration time at that temperature. When these cells are moved to 20°C t hey complete regeneration (stages 6 to 8) in 3 h, the same time as required for cells constantly maintained at 20°C to complete stages 6 through 8. Thus, cells regenerating at a low temperature do n o t appear to compensate for the larger energy barrier by mobilizing m o r e percursor material for the rate limiting step in regeneration. This result contrasts with studies o f sea urchin mitosis by Stephens (1972) in which he f ound t hat the time required for cell division was det er m i ned
TABLE 1. Time required for stages of oral regeneration when temperature is raised at stage 6. 20 cells were observed in each group; temperature was maintained + 0.1°C as described in Methods and Materials. Temperature
24°C 20°C 24°C IO°C
20°C
Time in h required for completion of regeneration intervals Stage 0-3 a
Stage 3--6
S t a g e Total re6--8 generation time (h)
3 4.5
3 4_5
2 3
t
> 3b
8 12 | ) 2b II 14--15 13--15 12--16 36--40
16--18
a Stage 0 -- time of oral membranellar band removal Stage 3 -- first appearance of new oral primordia Stage 6 --appearance of sausage-shaped nucleus b Cells moved to new temperature at Stage 6
primarily by t he cell t e m p e r a t u r e in early prophase. In terms o f the kinetic model t he increased regeneration time at low t em perat ure (~< 24°C may be represented by a decrease in the equilibrium k2/k-2 favoring subunits over polymerized microtubules. Microtubule polymerization is a highly e n d o t h e r m i c process. However, since t he t e m p e r a t u r e change obviously affects all cellular components, it is not possible to analyze microtubule polymerization apart from the o t h e r factors involved in oral regeneration. Temperature sensitivity, then, will not be considered in the detailed evaluation of t he kinetic model. However, these results do indicate that all stages of oral regeneration are equally t e m p e r a t u r e sensitive and t h a t the exposure to low t e m p e r a t u r e early in regeneration does not affect the subsequent rate at a higher temperature.
3.2. Sensitivity of oral regeneration to podophyllotoxin and fl-peltatin Appropriately chosen levels of p o d o p h y l l o -
275
toxin and ~-peltatin delay oral regeneration without producing cellular abnormalities or death. Both drugs effectively delay oral regeneration over at least a 3-fold concentration range. Results of these experiments are plotted in Figs. 4 and 5 as fractional increase in regeneration time vs. drug concentration. ~-Peltatin was significantly more effective than podophyllotoxin as an inhibitor of oral regeneration. This result correlates well with the greater affinity of ~-peltatin for mouse brain tubulin (Kelleher, 1977), and its increased effectiveness in inhibition of tumor growth in vitro (St~ihelin, personal communication). In vitro drug-binding studies were performed to determine if drug solutions lost tubulinbinding activity during the regeneration experiment. After cells had regenerated, samples of the medium were incubated with [3H]-colchicine and mouse brain tubulin. Separation of tubulin-bound and free colehicine indicated that podophyllotoxin and ~-peltatin displayed approximately the same inhibition of eolehieine binding, regardless of whether they had been exposed to regenerating cells. This result is consistent with the study of Sarras and Burchill (1975) and indicates that the ability of Stentor to complete regeneration in the presence of these drugs is not dependent on the loss of drug activity. Cells were preincubated with podophyl]otoxin to oral band removal to examine the possibility that cells compensate for the effect of tubulin binding drugs by producing additional quantities of rate limiting components. Stentor exposed to podophyllotoxin (15 pM) for 8 h prior to the induction of oral regeneration, regenerated in the same time as cells which were not pretreated with the drug. Thus, as in the experiments with low temperature, recovery from drug treatment does not appear to involve production of additional rate limiting components. 3.3. Evaluation o f the kinetic model
The kinetic model derived in the appendix
is designed to test the hypothesis that the cellular concentration of tubulin is a critical variable for oral regeneration in normal Stentor coeruleus. The model produced the equation: Regeneration Time in Drug Control Regeneration Time
[Drug] m + l KD
If tubulin concentration, and polymerization rates dependent on it, limit the rate of oral regeneration, then this equation (when plotted as in Figs. 4 and 5) describes a straight line with y intercept of 1.0 and slope equal to the recriprocal of the dissociation constant for the drug-tubulin interaction. The data shown in these figures produce reasonable straight lines in basic compliance with the model presented here. However, the y-intercepts are somewhat less than 1.0, approximately 0.8. A y-intercept less than 1.0 would be expected
3.0
2.6
22
EXPERIMENTAL
~18
($tentor)
E o~
14
o
(D
0.6
02 i 20
I i i J I 14 4.0 6.0 8.0 I0 12 I PODOPHYLLOTOXIN ,uM
I 16
Fig. 4. R e l a t i o n s h i p b e t w e e n p o d o p h y l l o t o x i n conc e n t r a t i o n a n d r e g e n e r a t i o n rate p l o t t e d t o test t h e kinetic m o d e l for oral r e g e n e r a t i o n .
276
3.0
./
2.6
2.2
.E
EXPERIMENTAL
(Stentor}
1.8
~, 1.4
1.0
O0 • •
0.6
0.2 0 I.
I
I
I
I 012 013 0.4 015 016 0.7 ~8 019 I.O /5' PELTATIN
pM
Fig. 5. Relationship b e t w e e n t~-peltatin c o n c e n t r a t i o n and regeneration rate plotted to test the kinetic model for oral regeneration.
in the framework of this model if the amount of tubulin available is in excess of an a m o u n t which would kinetically limit the rate of oral regeneration. In this case, the inactivation of a certain number of tubulin molecules would not affect the rate of regeneration, presumably because this rate is limited by some other factor, and tubulin concentration is not a critical variable. At higher drug concentrations, when more tubulin is drug-bound, delays appear in the rate of oral regeneration because sufficient tubulin has been inactivated to make it rate limiting for oral regeneration. The results plotted in Figs. 4 and 5 suggest that during oral regeneration S t e n t o r coeruleus does not maintain an active tubulin concentration far above an amount which would be rate-limiting. Application of the equations used in the kinetic model makes possible the
estimate that the cells contain not more than 10--15% excess tubulin. This Fig. is calculated based on the reasoning that the regeneration rate will be twice that of control cells at a drug concentration binding one-half the tubulin, which is kineticaUy required for oral regeneration. For example, if the regeneration rate is doubled at 16 pM podophyllotoxin and 2.0 t~M has no effect then it may be estimated that 2 pM binds 11% of the available tubulin necessary for oral regeneration. Similarly, ~-peltatin at 0.10 pM binds about 15% of the tubulin. From the experimental data shown in Figs. 4 and 5 the dissociation constants for the binding of drugs to S t e n t o r tubulin may be estimated. Assuming the cells are permeable to these drugs (Assumption 7), the K D for podophyllotoxin is approximately 14 pM (16 t~M, the regeneration doubling drug concentration minus 2.0 pM, the concentration having no effect on regeneration) and for ~-peltatin 0.45 pM (0.55 uM minus 0.10 #M). The K D may also be estimated as the repriprocal of the slope. It was not possible to isolate active S t e n t o r tubulin to test the correlation between the estimated K D produced with this model and in vitro measured values. In vitro dissociation constants have been measured for the interaction of mouse brain tubulin and these drugs. These values, 0.51 pM (podophyllotoxin) and 0.12 pM (/3-peltatin) are somewhat lower than the kinetic model S t e n t o r values (Kelleher, 1977). There are several reasons why these values may not correspond. If the cell is less than freely permeable to the drug, the in vitro measured dissociation constants will be lower than the values estimated by the kinetic model. In general, the tubulin of protists has been reported to be less sensitive to this class of drugs than mammalian tubulin (Haber et al., 1972). In addition, it has been suggested that colchicine may bind preferentially to a small fraction of the cellular tubulin in vivo (Olmsted and Borisy, 1973) which would produce a discrepancy between in vivo active concentrations and in vitro measured K D.
277 In conclusion, evaluation of this kinetic model for oral regeneration in Stentor coeruleus has indicated that a relationship does exist between regeneration rate and drug concentration which is consistent with this model. The data further suggest that the intraCellular active Lubulin concentration in normal regenerating Stentor coeruleus is not greatly in excess of an amount which would kinetically limit ~he rate of oral regeneration. This model makes specific predictions as to the type of microtubule polymerization which can continue in the presence of antimicrotubule agents. If the model is valid, it follows that cell..~ containing microtubules which are permanently labile should not be able to overcome the effects of antimicrotubule agents. In general, it has been found that the labile microtubules in the mitotic spindle (Inoue and Sato, 1967) and the cytoplasmic microtubules of organisms such as Ochromonas (Bouck and Brown, 1973) and Actinosphaerium (Tilney and Gibbons, 1968) do not continue to polymerize microtubules in the presence of these agents. Alternatively, stable ciliary axonemes in Tetrahymena (Rosenbaum and Carlson, 1969) and Stentor (Margulis et al., 1975) in addition to the cytopharangeal rods of Nassula (Tucker et al., 1975) do continue to polymerize in the presence of low levels of tubulin-binding drugs. Finally, the modeling approach used here is based on the premise that it is possible to analyze the degree to which a particular reaction limits the rate of differentiation, its kinetic importance, by analyzing the effect of specific inhibitors on this process. This approach should be generally applicable to many other situations, such as the evaluation of the kinetic importance of enzymatic reactions in development. If specific inhibitors are employed and models constructed which accurately reflect the kinetics of the reactions involved, this type of kinetic model may become a valuable tool in the analysis of differentiation.
Acknowledgements The author wishes to acknowledge the technical expertise of Dr S. Banerjee and M. Winston, and to thank Drs S. Mohr and L. Margulis for stimulating discussion and criticism. This work was supported by USPHS grant CA 5060 from the NCI and NASA (NGR004025) to Dr L. Margulis. Submitted in partial fulfillment of the Ph.D. degree at Boston University.
Appendix
Derivation o f a kinetic model for the oral regeneration time o f Stentor coeruleus cells exposed to tubulin-binding drugs Stentor coeruleus cells may be shed of their oral membranellar band and placed in solutions containing tubulin-binding drugs. Non drug-treated cells regenerate oral membranellar bands in 8 h. Drug-treated cells require a longer time period for regeneration. The following is a first attempt at a derivation of an expression relating the time required for oral regeneration in the presence of tubulinbinding drugs to the concentration of these drugs and their affinity for tubulin. This derivation requires several assumptions, listed in this paper, and, of course, its ultimate value in estimating the time required for this biological process is dependent on the validity of those assumptions. From assumption 1 that Fig. 2 is an accurate representation of the possible states of tubulin protein in Stentor coeruleus, the velocity or rate of stable microtubule formation, v, v = k3[Mtl]
(1)
Since tubulin and labile microtubules are in dynamic equilibrium (Assumption 2) and Mts is a constant equal to the number concentration of stable microtubule growth
278
points, the free tubulin concentration may be writtein as k_: [Mtl] [Tub] -
k: [Mts]
k_: [Mtl] -
k2*
(2)
k3k2* [Tub] k-2
- k' [Tub]
(3)
Define KD, the dissociation constant for the drug-tubulin interaction k_ 1 K D - kl
-
[Tub] • [Drug] [Tub--Drug]
(4)
Define [ T u b o ] , the total tubulin available within the cell at any m o m e n t for polymerization into permanent, stable microtubules [Tubo] = [Tub] + [Tub--Drug] + [Mtl]
(5)
substituting equations 2 and 4 [Tubo] = [Tub] +. [Tub] • [Drug] +
k' [TUbo] V ----
1 + k 2 * l k - 2 + [Drug] IK D
Since Mt s is a constant k2* is defined as k2[Mts]. The velocity of stable microtubule formation, as depicted in Fig. 2, is: v-
from Eq. 3 the rate of stable microtubule formation at any time is:
The amount of microtubule protein polymerized in the 8 h oral regeneration period of a cell not exposed to tubulin-binding drugs may be represented as one complete oral membranellar band = o~ k' [TUbo] f
(6)
idt 0
1 +k:*/k_:
However, cells treated with tubulin-binding drugs require longer periods for oral regeneration, such that one complete oral membranellar band = t
I0
k' [Tubo] 1 + k 2 * / k - : + [Drug]/K D
dt
(7)
Since drug treated cells are assumed to regenerate completely normal oral, membranellar bands identical to control cells Eq. 6 and 7 are equivalent, such that
k2* [Tub] f:
k-2
[Tub°]
dt
1 + k:*/k-2
KD k-2 At any moment, the fraction of the total tubulin available, [Tubo] , which is in the form of free tubulin, is:
= ~0
[Tub°]
dt
1 + k ~ * / k - 2 + [Drug]/K D
and oo
[Tub]
1
[TUbo]
1 +k2*/k_2
)I
r 0
1 + [Drug]/K D + k 2 * / k - 2 = rj t
therefore, [Tub] =
(
[Tubo] dt
(8)
0 [Tub o]
1 + [Drug]/g D + k2*/k-2
Assuming that [TUbo] is a function o f the stage of regeneration and not simply deter-
279 mined by the time after oral band removal ( A s s u m p t i o n 5), Eq. 8 r e d u c e s t o : [Drug]/K D 1 +
r e g e n e r a t i o n t i m e in D r u g -
1 + k2*/k_ 2
(9)
control regeneration time
T h e v a l u e o f k 2 * / h - 2 is a s s u m e d t o b e signific a n t l y less t h a n 1 ( A s s u m p t i o n 6) a n d m a y b e i g n o r e d in t h i s m o d e l . W i t h t h i s a s s u m p t i o n , Eq. 9 b e c o m e s R e g e n e r a t i o n t i m e in d r u g Control regeneration time
-
[Drug] ~ KD
+ 1 (10)
References Borisy, G.G., 1972, A rapid method for quantitative determination of microtubule protein using DEAE-cellulose fib;ers, Anal. Biochem. 50, 373-385. Bouck, G.B. and D.L. Brown, 1973, Microtubule biogenesis and cell shape in Ochromonas 1. The distrubution of cytoplasmic and mitotic microtubules, J. Cell. Biol. 56 340--359. Bryan, J., 1976, A quantitative analysis of microtubule elongation. J. Cell. Biol. 71, 749--767. Goode, D., 1973, Kinetics of Microtubule Formation after Cold Disaggregation of the Mitotic Apparatus, J. Mol. Biol. 80, 531--538. Haber, J.E., J.G. Peloquin, H.O. Halvorsen and G.G. Borisy, 1972, Colcemid inhibition of cell growth and the characterization of a Colcemidbinding activity in Saccharomyces cerevisiae, J. Cell Biol., 55, 355--367. Haight, Jr. J.M. and I].R. Burchill, 1970, The effects of colchicine and Colcemid on oral differentiation in Stentor coeruletts, J. Protozool. 17, 139--144. Inou6, S. and H. Sat(), 1967, Cell motility by labile association of molecules; The nature of mitotic spindle fibers and their role in chromosome movement, J. Gen. Physiol. 50, 259--288. James, E.A., 1967, Regeneration and division in Stentor coeruleus: The effects of microinjected and externally applied actinomycin-D and puromycin, Dev. Biol. 1,3, 577--593. Johnson, K.A. and G G. Borisy, 1975. The equilibrium assembly of microtubules in vitro. In: Molecules and cell movement, S. Inou6 and R.E. Stephens (eds.), (Raven Press, New York), 3--29.
Kelleher, J.K., 1972, Protein synthesis during oral regeneration in Stentor coeruleus. M.A. Thesis, Boston University. Kelleher, J.K., 1977, Tubulin binding affinities of podophyllotoxin and colchicine analogues, Mol. Pharmacol., in press. Margulis, L., S. Banerjee and J.K. Kelleher, 1975, Assay for anti-tubulin drugs in live cells; Oral regeneration in Stentor coeruleus. In : International Symposium of Microtubules and Microtubule Inhibitors, M. deBrander and M. Borgers (eds.), (North-Holland, Amsterdam). Makrides, E.B., S. Banerjee, L. Handler and L. Margulis, 1970, Podophyllotoxin, Colcemid and cold temperature interference with cilia regeneration in Stentor, J. Protozool., 17,548--551. Monet, J.G., 1972, The effects of temperature and heavy water on cell division in heat synchronized cells of Tetrahymena, J. Protozool., 19, 382--385. Olmsted, J.B. and G.G. Borisy, 1973, Microtubules. Ann. Rev. Biochem., 42, 507--540. Paulin, J.S. and J. Bussey, 1971, Oral regeneration in the ciliate Stentor coeruleus: A scanning and transmission electron optical study, J. Protozool. 18, 201--213. Rosenbaum, J. and K. Carlson, 1969, Cilia regeneration in Tetrahymena and its inhibition by colchicine, J. Cell. Biol., 40,415---425. Rosenbaum, J., J.E. Moulder and D.L. Ringo, 1969, Flagellar elongation and shortening in Chlamydomonas: The use of colchicine and cycloheximide to study the synthesis and assembly of flagellar proteins, J. Cell. Biol., 41,600---619. Sarras, M.P. and B.R. Burchill, 1975, Endogenous recovery of Stentor coeruleus from inhibition of oral regeneration by anti-mitotic agents. Cytobiol. 10,407--420. Stephens, R.E., 1972, Studies on the development of the sea urchin, Strongyloncentrotus droebachiensis, 11, Regulation of mitotic spindle equilibrium by environmental temperature. Biol. Bull., 142, 145--159. Tartar, V., 1961, The biology of Stentor, (Pergamon Press, New York). Tilney, L.G. and J.R. Gibbins, 1968, Differential effects of antimitotic agent s on the stability and behavior of cytoplasmic and ciliary microtubules, Protoplasma, 65,167--179. Tucker, J.B., M. Dunn and J.B. Pattisson, 1975, Control of microtubule pattern during the development of a large organelle in the ciliate Nassula, Dev. Biol., 47,439--453. Wright, B.E., 1973, Critical variables in differentiation, (Prentice Hall, Englewood Cliffs, N.J.
269
A KINETIC MODEL F O R M I C R O T U B U L E P O L Y M E R I Z A T I O N DURING ORAL REGENERATION IN S T E N T O R C O E R U L E U S
JOANNE K. KELLEHER* Department of Biolog:), Boston University, Boston, MA 02115, U.S.A.
(Received March 3rd, ]977) (Revised version receivedJune 16th, 1977) The regeneration of oral cilia in the protozoan cell, Stentor coeruleus, has been investigated in the presence of agents which do not favor the polymerization of microtubules. These agents, low temperature and the tubulin binding drugs, podophyllotoxin and ~-peltatin, slow the rate of regeneration. A kinetic model is proposed to test the hypothesis that microtubule polymerization is the rate limiting step in oral regeneration. The results suggest that the tubulin concentration of normal regenerating cells is slightly in excess of an amount which would kinetically limit the regeneration rate.
1. I n t r o d u c t i o n 1.1. Microtubule polymerization in eucaryotic microbes
The ciliated and flagellated eucaryotic microbes offer excellent systems to explore the developmental biology of microtubule formation. In many of these organisms cilia and flagella may be removed and regeneration induced, e.g., Chalmydomonas (Rosenbaum et al., 1969), Tetrahymena (Rosenbaum and Carlson, 1969) and Stentor (James, 1967). Microtubule protein, tubulin, is the major component of ciliary and flagellar axonemes. Regeneration of cilia and flagella is inhibited by agents which favour the disassembly of microtubules (anti-microtubule agents). These include physical agents, low temperature and high hydrostatic pressure in addition to tubulin binding drugs, such as colchicine and podophyllotoxin. Microtubule structures are classified as labile, easily disrupted by anti-microtubule agents, or stable, resistant to these agents * Present address: Department of Developmental Biology, Boston Biomedical Research Institute, 20 Staniford Street, Boston, MA 02114, U.S.A.
except during periods of microtubule growth (Tilney and Gibbins, 1968). In general, cilia and flagella regrow normally when removed from the anti-microtubules agents. Although the presence of high levels of anti-microtubules agents totally inhibits cilia and flagella growth in several organisms, it is well established that low levels of these agents do not totally inhibit regeneration but simply slow the rate of this process (Margulis et al., 1975; Saras and Burchill, 1975). Several hypotheses have been suggested as explanations for the recovery of regenerating microtubule structures subject to tubulinbinding drugs. Rosenbaum and Carlson (1969) proposed that regenerating Tetrahymena may selectively excrete colchicine and thereby overcome its effects. Saras and Burchill (1975) find their data compatible with the development of intracellular resistance to tubulin binding drugs in Stentor. However, specific details of this resistance are not known. This paper will examine the endogenous recovery of cilia regeneration in S t e n t o r coeruleus exposed to low temperature and the tubulin-binding drugs, podophyllotoxin and /3-peltatin. The aim of this paper is 2-fold: (1) to develop a specific hypothesis for endo-
270 its migration to the anterior portion of the cell. Scanning and transmission electron microscopy indicate that regeneration induced basal bodies to grow subpellicular microtubules as well as membranellar cilia (Paulin and Bussey, 1971). The following requirements are known for oral regeneration in St ent or coeruleus: RNA synthesis is required between stages 0 and 4 as measured by sensitivity to actinomycin D (James 1967); protein synthesis is required between stages 0 and 6 measured by sensitivity to puromycin (James 1967) and cycloheximide (Haight and Burchill, 1970). The polymerization of microtubules is apparently required over the entire regeneration period. The process is inhibited by the tubulin-binding drug, Colcemid, throughout the entire regeneration sequence (Kelleher, 1972). In order for a developmental process requiring the net polymerization of microtubu-
genous recovery in this system; (2) to analyze the possibility that the rate of microtubule polymerization limits the rate of cilia regeneration in Stentor. Towards these goals a kinetic model for cilia regeneration will be developed and tested against experimental data obtained in cilia regeneration studies. 1.2. Oral regeneration in stentor coeruleus
The heterotrichous ciliate, St ent or coeruleus may be induced to shed its ciliated oral membranellar band. The ensuing regeneration process, as described by Tartar (1961), involves the replacement of the entire oral structure including underlying basal bodies. The process requires 8 h at room temperature and has been divided into eight distinct morphological stages (see Fig. 1). The first 3 h of regeneration are occupied by the formation of the new membranellar band and the last 5 h with
SHEDDING
PAFF
I
3
5
7
REGENERATED CONTROL
TIMING OF MACROMOLECULAR PROCESSES DURING ORAL REGENERATION
M ,o ro , ,,, u ,, Po, , - -
,. o, ,o.
"//////.,A
Fig. 1. Macromolecular requirements for oral regeneration in Stentor coeruleus (modified from James, 1967). Numbers under cells indicate stages of regeneration. PAFF, protruding anterior frontal fields: OP, oral primor. dium; DOMB, developing oral membranellar band, MB, membranellar band.
271
protein synthesis l inactive tubulin
~
~
~
II~ stable stable k2 ~ labile k~ tubulin + microtubule ~ k.2 microtubules ~ microtubule (tub) (Mrs) (Mt,) (Mts) +
drug (eg,colchicine, podophyllotoxin) tubulin-drug Fig. 2. Postulated states of microtubule protein during oral regeneration in Stentor coeruleus. Inactive tubulin subunits self assembled to form dimeric active tubulin (tub), which may either assemble i n t o m i c r o t u b u l e s or bind to a drug. Stable m i c r o t u b u l e n u h i b e r is c o n s t a n t and equal t o the n u m b e r o f m i c r o t u b u l e g r o w t h points. Stable m i c r o t u b u l e length varies during p o l y m e r i z a t i o n . Labile m i c r o t u b u l e s are dissociable s u b u n i t s o n the e n d s o f microtubules. les to proceed in the presence of a tubulinbinding drug or other agent which favours the depolymerization of microtubule structures, one of the following mechanisms may be responsible: (1) The cell responds to the loss of tubulin and corapensates by making available more tubulin than the cell would have access to under normal circumstances. (2) The tubulin-binding drugs lose activity during the incubation period. (3) The process involves the conversion of labile microtubules, sensitive to anti-microtubule agents to stable forms resistant to these agents as diagrammed in Fig. 2. Results wil:[ be presented here, which indicate that mechanisms 1 and 2 are unlikely to be the reason Stentor is able to overcome the effects of these agents. A kinetic model will be constructed to test mechanism 3. 1.3. A kinetic model for microtubule polymerization in the presence o f anti-microtubule agen ts
The appendix of this paper contains the derivation of an expression relating the concentration of tubulm-binding drug to the rate of oral regeneratio~ in Stentor coeruleus. The basis of this kinetic model is the premise that differentiation may be described in terms of rate limiting events, or critical variables, (see
Wright, 1973, for discussion). In the model presented here tubulin-binding drugs are used to titrate the available cellular microtubule protein. Delays produced in regeneration time are presumed to be related to a decrease in the concentration of tubulin molecules available for polymerization. If it can be demonstrated that all the active cellular tubulin is required for regeneration to proceed at a normal rate, then the concentration of active tubulin within the cell during regeneration may be considered a critical variable for this process. Fig. 2 is a diagram of the states of association of tubulin over the course of oral regeneration. This diagram outlines the molecular species used in the kinetic model. Microtubule protein is synthesized and assembled into a 120 000 MW dimer form, tubulin, which can either participate in polymerization or bind to a drug. Labile microtubules are assumed to be in dynamic equilibrium with free tubulin subunits (Inoue and Sato, 1967). Stable microtubules are tubulin polymers resistant to the effects of anti-microtubule agents (Tilney and Gibbons, 1968). There is cytological evidence for the conversion of labile to stable microtubules in the oral membranellar band of Stentor. Haight and Burchill (1968) observed the resorption
272 of regenerating oral cilia in colchicine treated cells at stage 3 of regeneration. However, if the drug was added at later stages, the cilia were not resorbed. Makrides et al. (1970) reported the resorption of newly formed daughter cilia of dividing Stentor treated with colchicine, while the older parental cilia were not effected b y the drug. This result is particularly striking since labile and stable microtubules occur on the same cell simultaneously. In constructing this model several assumptions have been made as to the behavior of microtubule protein in living cells. These assumptions are stated here, so that the limits and constraints o f this approach will be apparent. Assumptions used in the kinetic model: (1) The essential states of microtubule protein are accurately described by Fig. 2. (2) Tubulin and labile microtubules are maintained in dynamic equilibrium (Inoue and Sato, 1967). (3) Tubulin polymerization occurs as a simple condensation polymerization between tubulin and formed microtubules. In regenerating cells the number of growing microtubules is constant, and the rmmber of growth points does not vary with microtubule length. This form of association has been discussed in vitro by Johnson and Borisy (1975) and Bryan (1976) and in vivo by Goode (1973). (4) Stentor treated with tubulin-binding drugs produce completely normal oral cilia, i.e., they polymerize the same quantity of tubulin on the same number of growth points as control cells. (5) The total amount of tubulin available for polymerization during oral regeneration is not effected by the application of tubulin-binding drugs. (6) The equilibrium between tubulin (tub) and labile microtubules (Mtl) equal to h-2/k2[Mts] or h-2/h2* is a constant since the number concentration of microtubule growth points (Mts) is constant throughtout regeneration and the equilibrium k.*2/h-2 is not affected by microtubule length (Johnson and Borisy, 1975). The value of the constant
k-z/k2* is assumed to be significantly less than 1.0, that is, a t equilibrium, there are many more tubulin molecules in solution than labile microtubule ends. (7) Intracellular drug concentration is a linear function of the external concentration. To predict K D values accurately from the data found in this study, an additional assumption that the cells are freely permeable to these drugs is required. The polymerization pattern resulting from this model is basically similar to the end-onaddition models examined in vitro with cytoplasmic brain tubulin by Bryan (1976) and Johnson and Borisy (1975). However, since their models concern the formation of labile, totally depolymerizable microtubules and this paper analyzes stable microtubule formation, differences exist in the proposed kinetics of microtubule polymerization. Models o f labile microtubule polymerization predict, and the data confirm, that the equilibrium between tubulin and labile microtubules is not a function of labile microtubule number concentration. This model predicts that the equilibrium between tubulin and labile microtubules is a function of the number concentration o f stable microtubules. (See eq. 2, appendix.) Such a model obviously represents a simplified picture of a complicated biological process. For example, factors associated with microtubules other than tubulin itself have not been considered. Thus, in this model, the function and concentration of these factors is assumed to be unaffected by the drug treatment. This kinetic model for microtubule polymerization in Stentor coeruleus has certain intrinsic limitations and requires a number of assumptions. It is offered here as a starting point in the search for critical variables in microtubule polymerization process and as a guide for future experimentation. 2. Methods and materials Detailed methods for growing Stentor coeruleus cells and inducing oral regeneration
273 have been described previously (Margulis et al., 1975). In the :~tudies r e p o r t e d here, cells were allowed to regenerate, 20 cells in 5 ml spring w a t e r of " M " solution, an artificial p o n d water. An Arrhenius activation energy for the 8--24°C :range was d e t e r m i n e d b y least square regression analysis. T e m p e r a t u r e was maintained ± 0.1°C by a Cambion water bath (Cambion Inc., Cambridge, MA} for the t e m p e r a t u r e studie~. Oral regeneration, attainm e n t o f stage 8, was d e t e r m i n e d b y observation u n d e r a dissecting microscope. In o t h e r e x p e r i m e n t s the cells were k e p t at 23°C. Unless otherwise indicated, drugs were added to the regeneration m e d i u m at state 3, 3 h after oral band removal. C o m p o u n d s n o t easily soluble in water were added in ethanol at a final c o n c e n t r a t i o n o f less t h a n 1%, a
c o n c e n t r a t i o n which had n o e f f e c t on regeneration. P o d o p h y l l o t o x i n was o b t a i n e d f r o m Aldrich Chemical Co., Milwaukee, Colchicine f r o m Sigma Chemical Co., St. Louis;/3-peltatin was a gift f r o m Dr. A. y o n Wartburg, S a n d o z Ltd., Basel. In vitro drug binding assays were p e r f o r m ed using t h e D E A E filter p a p e r assay o f Borisy ( 1 9 7 2 ) (see Kelleher, 1977, for details).
3. Results and Discussion 3.1. Temperature sensitivity o f oral regeneration An Arrhenius plot o f oral regeneration in Stentor coeruleus is shown in Fig. 3. Below 15°C, where regeneration was n o t c o m p l e t e l y
ARRHENIUS PLOT for ORAL REGENERATION n Stentor coeruleus 200
IOO % x
50 .,£:
W I.-Q~
z o
I0
I.-QZ W
z
5
W W
I 3.25
3.30
3.35
3.40 3.45 I/°K x 103
3.50
3.55
3.60
Fig. 3. Arrhenius plot of oral regeneration in Stentor coeruleus. Regeneration time, from stage 0--8, was measured by observation (a minimum of 20 cells per time point). Mean regeneration rate is plotted above 15~C, where the cells were somewhat asynchronous, the range of regeneration rates is plotted.
274 synchronous, the range of regeneration time for 20 cells is plotted. Cell death occurred at temperatures below 4°C and above 31°C. The data in Fig. 3 appear to form three straight lines indicating changes in the activation energy for the rate limiting step at 8°C and 24°C. An Arrhenius activation energy o f 19 kcal/mol (+ 0.5) was determined for the 8--24°C range. This activation energy represents an average for the rate limiting steps o f the entire regeneration process. This value is similar t o the 18--19 kcal/mol Arrhenius activation energy reported for the growth rate of the ciliate, Tetrahymena (Moner, 1972). Since oral regeneration is divided into eight distinct morphological stages, cells were observed during regeneration to determine the degree to which each stage of regeneration followed the rate pat t er n for the entire process at 24°C where each stage lasts 1 h. Results o f these observations indicated that each morphological stage lasted one-eighth of the regeneration period in the 8--24°C range. This result suggests t hat the activation energy for the rate limiting step does not change significantly during the 8 stages o f regeneration and is consistent with the hypothesis that the entire sequence is limited by the same reaction. F u r th er m or e, when moved from one t e m p e r a t u r e to another, regenerating cells quickly adjust to the regeneration timetable o f the new t e m p e r a t u r e (see Table 1). For example, cells regenerating at 10°C reach stage 6 at a b o u t 29 h or 3A of the total regeneration time at that temperature. When these cells are moved to 20°C t hey complete regeneration (stages 6 to 8) in 3 h, the same time as required for cells constantly maintained at 20°C to complete stages 6 through 8. Thus, cells regenerating at a low temperature do n o t appear to compensate for the larger energy barrier by mobilizing m o r e percursor material for the rate limiting step in regeneration. This result contrasts with studies o f sea urchin mitosis by Stephens (1972) in which he f ound t hat the time required for cell division was det er m i ned
TABLE 1. Time required for stages of oral regeneration when temperature is raised at stage 6. 20 cells were observed in each group; temperature was maintained + 0.1°C as described in Methods and Materials. Temperature
24°C 20°C 24°C IO°C
20°C
Time in h required for completion of regeneration intervals Stage 0-3 a
Stage 3--6
S t a g e Total re6--8 generation time (h)
3 4.5
3 4_5
2 3
t
> 3b
8 12 | ) 2b II 14--15 13--15 12--16 36--40
16--18
a Stage 0 -- time of oral membranellar band removal Stage 3 -- first appearance of new oral primordia Stage 6 --appearance of sausage-shaped nucleus b Cells moved to new temperature at Stage 6
primarily by t he cell t e m p e r a t u r e in early prophase. In terms o f the kinetic model t he increased regeneration time at low t em perat ure (~< 24°C may be represented by a decrease in the equilibrium k2/k-2 favoring subunits over polymerized microtubules. Microtubule polymerization is a highly e n d o t h e r m i c process. However, since t he t e m p e r a t u r e change obviously affects all cellular components, it is not possible to analyze microtubule polymerization apart from the o t h e r factors involved in oral regeneration. Temperature sensitivity, then, will not be considered in the detailed evaluation of t he kinetic model. However, these results do indicate that all stages of oral regeneration are equally t e m p e r a t u r e sensitive and t h a t the exposure to low t e m p e r a t u r e early in regeneration does not affect the subsequent rate at a higher temperature.
3.2. Sensitivity of oral regeneration to podophyllotoxin and fl-peltatin Appropriately chosen levels of p o d o p h y l l o -
275
toxin and ~-peltatin delay oral regeneration without producing cellular abnormalities or death. Both drugs effectively delay oral regeneration over at least a 3-fold concentration range. Results of these experiments are plotted in Figs. 4 and 5 as fractional increase in regeneration time vs. drug concentration. ~-Peltatin was significantly more effective than podophyllotoxin as an inhibitor of oral regeneration. This result correlates well with the greater affinity of ~-peltatin for mouse brain tubulin (Kelleher, 1977), and its increased effectiveness in inhibition of tumor growth in vitro (St~ihelin, personal communication). In vitro drug-binding studies were performed to determine if drug solutions lost tubulinbinding activity during the regeneration experiment. After cells had regenerated, samples of the medium were incubated with [3H]-colchicine and mouse brain tubulin. Separation of tubulin-bound and free colehicine indicated that podophyllotoxin and ~-peltatin displayed approximately the same inhibition of eolehieine binding, regardless of whether they had been exposed to regenerating cells. This result is consistent with the study of Sarras and Burchill (1975) and indicates that the ability of Stentor to complete regeneration in the presence of these drugs is not dependent on the loss of drug activity. Cells were preincubated with podophyl]otoxin to oral band removal to examine the possibility that cells compensate for the effect of tubulin binding drugs by producing additional quantities of rate limiting components. Stentor exposed to podophyllotoxin (15 pM) for 8 h prior to the induction of oral regeneration, regenerated in the same time as cells which were not pretreated with the drug. Thus, as in the experiments with low temperature, recovery from drug treatment does not appear to involve production of additional rate limiting components. 3.3. Evaluation o f the kinetic model
The kinetic model derived in the appendix
is designed to test the hypothesis that the cellular concentration of tubulin is a critical variable for oral regeneration in normal Stentor coeruleus. The model produced the equation: Regeneration Time in Drug Control Regeneration Time
[Drug] m + l KD
If tubulin concentration, and polymerization rates dependent on it, limit the rate of oral regeneration, then this equation (when plotted as in Figs. 4 and 5) describes a straight line with y intercept of 1.0 and slope equal to the recriprocal of the dissociation constant for the drug-tubulin interaction. The data shown in these figures produce reasonable straight lines in basic compliance with the model presented here. However, the y-intercepts are somewhat less than 1.0, approximately 0.8. A y-intercept less than 1.0 would be expected
3.0
2.6
22
EXPERIMENTAL
~18
($tentor)
E o~
14
o
(D
0.6
02 i 20
I i i J I 14 4.0 6.0 8.0 I0 12 I PODOPHYLLOTOXIN ,uM
I 16
Fig. 4. R e l a t i o n s h i p b e t w e e n p o d o p h y l l o t o x i n conc e n t r a t i o n a n d r e g e n e r a t i o n rate p l o t t e d t o test t h e kinetic m o d e l for oral r e g e n e r a t i o n .
276
3.0
./
2.6
2.2
.E
EXPERIMENTAL
(Stentor}
1.8
~, 1.4
1.0
O0 • •
0.6
0.2 0 I.
I
I
I
I 012 013 0.4 015 016 0.7 ~8 019 I.O /5' PELTATIN
pM
Fig. 5. Relationship b e t w e e n t~-peltatin c o n c e n t r a t i o n and regeneration rate plotted to test the kinetic model for oral regeneration.
in the framework of this model if the amount of tubulin available is in excess of an a m o u n t which would kinetically limit the rate of oral regeneration. In this case, the inactivation of a certain number of tubulin molecules would not affect the rate of regeneration, presumably because this rate is limited by some other factor, and tubulin concentration is not a critical variable. At higher drug concentrations, when more tubulin is drug-bound, delays appear in the rate of oral regeneration because sufficient tubulin has been inactivated to make it rate limiting for oral regeneration. The results plotted in Figs. 4 and 5 suggest that during oral regeneration S t e n t o r coeruleus does not maintain an active tubulin concentration far above an amount which would be rate-limiting. Application of the equations used in the kinetic model makes possible the
estimate that the cells contain not more than 10--15% excess tubulin. This Fig. is calculated based on the reasoning that the regeneration rate will be twice that of control cells at a drug concentration binding one-half the tubulin, which is kineticaUy required for oral regeneration. For example, if the regeneration rate is doubled at 16 pM podophyllotoxin and 2.0 t~M has no effect then it may be estimated that 2 pM binds 11% of the available tubulin necessary for oral regeneration. Similarly, ~-peltatin at 0.10 pM binds about 15% of the tubulin. From the experimental data shown in Figs. 4 and 5 the dissociation constants for the binding of drugs to S t e n t o r tubulin may be estimated. Assuming the cells are permeable to these drugs (Assumption 7), the K D for podophyllotoxin is approximately 14 pM (16 t~M, the regeneration doubling drug concentration minus 2.0 pM, the concentration having no effect on regeneration) and for ~-peltatin 0.45 pM (0.55 uM minus 0.10 #M). The K D may also be estimated as the repriprocal of the slope. It was not possible to isolate active S t e n t o r tubulin to test the correlation between the estimated K D produced with this model and in vitro measured values. In vitro dissociation constants have been measured for the interaction of mouse brain tubulin and these drugs. These values, 0.51 pM (podophyllotoxin) and 0.12 pM (/3-peltatin) are somewhat lower than the kinetic model S t e n t o r values (Kelleher, 1977). There are several reasons why these values may not correspond. If the cell is less than freely permeable to the drug, the in vitro measured dissociation constants will be lower than the values estimated by the kinetic model. In general, the tubulin of protists has been reported to be less sensitive to this class of drugs than mammalian tubulin (Haber et al., 1972). In addition, it has been suggested that colchicine may bind preferentially to a small fraction of the cellular tubulin in vivo (Olmsted and Borisy, 1973) which would produce a discrepancy between in vivo active concentrations and in vitro measured K D.
277 In conclusion, evaluation of this kinetic model for oral regeneration in Stentor coeruleus has indicated that a relationship does exist between regeneration rate and drug concentration which is consistent with this model. The data further suggest that the intraCellular active Lubulin concentration in normal regenerating Stentor coeruleus is not greatly in excess of an amount which would kinetically limit ~he rate of oral regeneration. This model makes specific predictions as to the type of microtubule polymerization which can continue in the presence of antimicrotubule agents. If the model is valid, it follows that cell..~ containing microtubules which are permanently labile should not be able to overcome the effects of antimicrotubule agents. In general, it has been found that the labile microtubules in the mitotic spindle (Inoue and Sato, 1967) and the cytoplasmic microtubules of organisms such as Ochromonas (Bouck and Brown, 1973) and Actinosphaerium (Tilney and Gibbons, 1968) do not continue to polymerize microtubules in the presence of these agents. Alternatively, stable ciliary axonemes in Tetrahymena (Rosenbaum and Carlson, 1969) and Stentor (Margulis et al., 1975) in addition to the cytopharangeal rods of Nassula (Tucker et al., 1975) do continue to polymerize in the presence of low levels of tubulin-binding drugs. Finally, the modeling approach used here is based on the premise that it is possible to analyze the degree to which a particular reaction limits the rate of differentiation, its kinetic importance, by analyzing the effect of specific inhibitors on this process. This approach should be generally applicable to many other situations, such as the evaluation of the kinetic importance of enzymatic reactions in development. If specific inhibitors are employed and models constructed which accurately reflect the kinetics of the reactions involved, this type of kinetic model may become a valuable tool in the analysis of differentiation.
Acknowledgements The author wishes to acknowledge the technical expertise of Dr S. Banerjee and M. Winston, and to thank Drs S. Mohr and L. Margulis for stimulating discussion and criticism. This work was supported by USPHS grant CA 5060 from the NCI and NASA (NGR004025) to Dr L. Margulis. Submitted in partial fulfillment of the Ph.D. degree at Boston University.
Appendix
Derivation o f a kinetic model for the oral regeneration time o f Stentor coeruleus cells exposed to tubulin-binding drugs Stentor coeruleus cells may be shed of their oral membranellar band and placed in solutions containing tubulin-binding drugs. Non drug-treated cells regenerate oral membranellar bands in 8 h. Drug-treated cells require a longer time period for regeneration. The following is a first attempt at a derivation of an expression relating the time required for oral regeneration in the presence of tubulinbinding drugs to the concentration of these drugs and their affinity for tubulin. This derivation requires several assumptions, listed in this paper, and, of course, its ultimate value in estimating the time required for this biological process is dependent on the validity of those assumptions. From assumption 1 that Fig. 2 is an accurate representation of the possible states of tubulin protein in Stentor coeruleus, the velocity or rate of stable microtubule formation, v, v = k3[Mtl]
(1)
Since tubulin and labile microtubules are in dynamic equilibrium (Assumption 2) and Mts is a constant equal to the number concentration of stable microtubule growth
278
points, the free tubulin concentration may be writtein as k_: [Mtl] [Tub] -
k: [Mts]
k_: [Mtl] -
k2*
(2)
k3k2* [Tub] k-2
- k' [Tub]
(3)
Define KD, the dissociation constant for the drug-tubulin interaction k_ 1 K D - kl
-
[Tub] • [Drug] [Tub--Drug]
(4)
Define [ T u b o ] , the total tubulin available within the cell at any m o m e n t for polymerization into permanent, stable microtubules [Tubo] = [Tub] + [Tub--Drug] + [Mtl]
(5)
substituting equations 2 and 4 [Tubo] = [Tub] +. [Tub] • [Drug] +
k' [TUbo] V ----
1 + k 2 * l k - 2 + [Drug] IK D
Since Mt s is a constant k2* is defined as k2[Mts]. The velocity of stable microtubule formation, as depicted in Fig. 2, is: v-
from Eq. 3 the rate of stable microtubule formation at any time is:
The amount of microtubule protein polymerized in the 8 h oral regeneration period of a cell not exposed to tubulin-binding drugs may be represented as one complete oral membranellar band = o~ k' [TUbo] f
(6)
idt 0
1 +k:*/k_:
However, cells treated with tubulin-binding drugs require longer periods for oral regeneration, such that one complete oral membranellar band = t
I0
k' [Tubo] 1 + k 2 * / k - : + [Drug]/K D
dt
(7)
Since drug treated cells are assumed to regenerate completely normal oral, membranellar bands identical to control cells Eq. 6 and 7 are equivalent, such that
k2* [Tub] f:
k-2
[Tub°]
dt
1 + k:*/k-2
KD k-2 At any moment, the fraction of the total tubulin available, [Tubo] , which is in the form of free tubulin, is:
= ~0
[Tub°]
dt
1 + k ~ * / k - 2 + [Drug]/K D
and oo
[Tub]
1
[TUbo]
1 +k2*/k_2
)I
r 0
1 + [Drug]/K D + k 2 * / k - 2 = rj t
therefore, [Tub] =
(
[Tubo] dt
(8)
0 [Tub o]
1 + [Drug]/g D + k2*/k-2
Assuming that [TUbo] is a function o f the stage of regeneration and not simply deter-
279 mined by the time after oral band removal ( A s s u m p t i o n 5), Eq. 8 r e d u c e s t o : [Drug]/K D 1 +
r e g e n e r a t i o n t i m e in D r u g -
1 + k2*/k_ 2
(9)
control regeneration time
T h e v a l u e o f k 2 * / h - 2 is a s s u m e d t o b e signific a n t l y less t h a n 1 ( A s s u m p t i o n 6) a n d m a y b e i g n o r e d in t h i s m o d e l . W i t h t h i s a s s u m p t i o n , Eq. 9 b e c o m e s R e g e n e r a t i o n t i m e in d r u g Control regeneration time
-
[Drug] ~ KD
+ 1 (10)
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