13
Induction of Polarity in Fucus Eggs by Potassium Ion Gradients1 By Friedrieh Bentrup, Tadashi Sandan, and Lionel Jaffe Department of Biology, University of Pennsylvania, Philadelphia, Pennsylvania, U.S.A. Width 5 Fi, gur~s (Received May I0, 1966) Introduction The idea of electrophoresis as a mechanism o[ localization in develop- ment is quite old, going back at least to Josef S p e k (1930) and a relatively definite electrophoretic theory has been published by Wen t (1932). Yet the evidence has been weak and confusing (B ii n n i n g 1958), for the most essential information has been entirely lacking: That is, no measurements of the current densities through developing cells were available. However, one of us has recently succeeded in making a crude but convincing measurement of the current through a developing Fucus egg (J a f f e 1966) : A current density of the order of 5/zamperes/cm 2 develops as the egg starts elongating, the field inside the cell being more clectropositive at the growing end, i.e., at the basal or rhizoidal pole. Passing through a cytoplasm with a measured resistivity of 300 ohm cm, this current should generate a transcytoplasmic voltage gradient steep enough to concentrate large electronegative particles at the rhizoidal pole. Thus it should significantly stratify the cytoplasm and thus further differ- entiate the rhizoidal and apical regions. However, it is not at all clear from this result whether or not the current feeds back to augment the structural membrane changes that must in turn generate the current; that is whether the current serves to localize the growth point in the first place. To help answer this latter question, we wished to impose currents across the cytoplasm of each of a population of eggs comparable to those found to develop naturally, and to observe whether or not the rhizoids tend to start at the cytoplasmically electro- positive poles. 1 Th,i,s work was s.upport~ed by a re,s,eareh grant from the Nat,ion.al Science Fo~tm(~a~io,n (GD-2446). A preliminary report appeared in J. Cell Biol.ogy 2?, 10 A (1965).

Induction of polarity inFucus eggs by potassium ion gradients

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Induction of Polarity in Fucus Eggs by Potassium Ion Gradients1

By

Friedrieh Bentrup, Tadashi Sandan, and Lionel Jaffe

Department of Biology, University of Pennsylvania, Philadelphia, Pennsylvania, U.S.A.

Width 5 Fi, g ur~s

(Received May I0, 1966)

Introduction

The idea of electrophoresis as a mechanism o[ localization in develop- ment is quite old, going back at least to Josef S p e k (1930) and a relatively definite electrophoretic theory has been published by W e n t (1932). Yet the evidence has been weak and confusing (B ii n n i n g 1958), for the most essential information has been entirely lacking:

That is, no measurements of the current densities through developing cells were available. However, one of us has recently succeeded in making a crude but convincing measurement of the current through a developing Fucus egg (J a f f e 1966) : A current density of the order of 5/zamperes/cm 2 develops as the egg starts elongating, the field inside the cell being more clectropositive at the growing end, i.e., at the basal or rhizoidal pole. Passing through a cytoplasm with a measured resistivity of 300 ohm cm, this current should generate a transcytoplasmic voltage gradient steep enough to concentrate large electronegative particles at the rhizoidal pole. Thus it should significantly stratify the cytoplasm and thus further differ- entiate the rhizoidal and apical regions.

However, it is not at all clear from this result whether or not the current feeds back to augment the structural membrane changes that must in turn generate the current; that is whether the current serves to localize the growth point in the first place. To help answer this latter question, we wished to impose currents across the cytoplasm of each of a population of eggs comparable to those found to develop naturally, and to observe whether or not the rhizoids tend to start at the cytoplasmically electro- positive poles.

1 Th,i,s work was s.upport~ed by a re,s,eareh grant from the Nat,ion.al Science Fo ~tm(~a~io,n (GD-2446). A preliminary report appeared in J. Cell Biol.ogy 2?, 10 A (1965).

F. Bentrup et al.: Induction of Polarity in Fucus Eggs 255

Long ago, L u n d (1925) found that the imposition of around 10 milli- ~r across developing Fucus eggs sufficed to initiate the rhizoids at the eggs' eleetropositive poles. We have no measurement of the membrane resistance of the Fucus egg, but if we assume the order of 10 kohm cm 2, one found for a nmnber of other algal cells, then we calculate a current densi ty of the order of l ~uampere/cm 2 through the Fucus egg in L u n d's exper iment . This is close enough to the measured na tura l current densities to suppor t a localizing funct ion for these currents.

5~et this is a weak argument. For almost all, perhaps 99.9%, of the voltage drop must have occurred across the plasma membranes. Moreover, all of it occurred across the medimn outside of the cell (Fig. 1). Might it

ig.ta

Fig'. 1. S,upp.o.s.ed p,otea~tial pr,ofile,s across the Fucus ,egg'. Left: A,s imposed by an external battery, tlight: As es,taMis.hed by the cell's plasana membr'ane, or by a

potassium gradient, g.p. = growth po.int.

not be, then, that the effective voltage drop in L u n d's exper iment was the large one across the membrane or the large one across the medium rather than the re la t ively small one across the cytoplasm?

To Better test the question, we felt that one needed to somehow impose a potent ia l profile much closer to the na tura l one across the egg, i.e., one in which the t ransmembrane ~-oltage drop is near ly equal to in size and opposite in direction to the t ranscytoplasmie one ra ther than much larger and in the same direction, and one in which the t ransmedium one is re la t ively small (Fig. 1).

I f it is not too dilute, the potassium J[c~n is usual ly found to be among those that move both most r ap id ly and most near ly passively across plasma membranes. This is well known for metazoan cells snell as those in frog muscle, those on the inner side of frog skin, the squid axon etc. There is also substantial evidence of potassium's high mobil i ty in the more rele~ant ease of lower p lant cells such as those in the th i& h y p h ae of Ne~trospora (S t a y m a n 1965), the large internodal cells of Chara (O d a 1962), and Nitellopsis (D a i n t y 1964), and the large subepidermal cells of the marine red alga, Rhodymenia (M a c t l o b b i e and D a i n t y 1958).

As a working hypothesis, then, we assumed that the Fucus egg's plasma membrane would allow the usual passive and rap id movement of potassium ions provided that this potassium was sufficiently concentrated. Imposit ion of a sufficient potassium ion gradient across the Fucus egg then should

256 F. Bentrup, T. Sandan, and L. Jaffe

produce the desired potential profile, with the membrane being relatively depolarized and the cytoplasm relatively electropositive at the high potas- sium pole. If transcytoplasmic currents help localize the growth point or rhizoidal pole, then imposition of such potassium gradients across a popu- lation of Fucus eggs should to some degree determine their growth points to be toward the high potassium pole.

The critical quantitative question remains. What order of averagc potassium ion concentration and what order of potassium ion difference across an egg can be anticipated as sufficient to produce the desired current?

A survey of the literature on many other cells shows that rapid passive potassium movement usually bccomcs evident at external concentrations of the order of 10 mM or more. This, then, suggests the aoerage potassium concentration to be needed.

If potassium movement is passive, then it can be shown (see Appendix) thai the current density produced by an imposed gradient through a cell will be given approximately by:

=_ 0.2. PK" A K (9 where ~ ~-~ current density in amperes/era ~-

PK ~ Potassium permeability in cm/sec A K ~-~ Difference in potassium concentration across the cell in milli-

moles per liter

We have no measurements of the Fucus egg's potassium permeability, but values of PK measured for other algae lie between 10 -5 and 10 -6 cm/sec (D a i n t y 1962). So by inserting these PK values, one calculates that a potassium difference of 3 to 50 millimo]ar should be needed to establish the desired current density of 5 ffamperes/cm 2.

In this paper, we report the degree of orientation produced by such potassium gradients.

Methods

O b t a i n i n g Z y g o t e s

Ripe Fucus furcatus fronds were collected for us on the central Cali- fornia coast by Mr. R. C 1 a w s o n of San Francisco State College and by Mrs. A. Phillips of the Hopkins Marine Station, Pacific Grove. Zygotes were obtained from these fronds as previously described (J a f f e 1958). They average about 65 to 75 # in diameter.

G e n e r a l G r a d i e n t M e t h o d

In order to accomplish our purpose, we needed a method for establishing controlled, known, and steady concentration gradients across each of large numbers of individual, developing and observeable cells in an otherwise non-orienting environment. With the exception of the relatively impractical agar film technique of W h i t a k e r and B e r g (1944)--one which has not been used subsequently--no such technique was available, so we developed one.

Induction of Polarity in Fucus Eggs; by Potassium Ion Gradients 257

It consists essentially of a way to grow cells within a nar row slit which connects two large reservoirs of media; appropr ia te agar walls block flow while allowing diffusion between these reservoirs.

C h a m b e r D e s i g n

Fig. 2 a shows a device which defines such a slit. A glass ring (47 mm in diameter, 20 mm high) is cemented to a microslide. The resultant chamber is par t i t ioned by a stiff bridge cat from a microslide and a 0.08 mm thick glass coverslip waxed to the bridge. The slip is aligned to leave a slit 0.1 mm high and 22 mm long between its edge and the chamber's floor.

F i l l i n g t h e C h a m b e r

Figs. 2 b and 2 c show views of the eggs in the slit. They are introduced as follows:

1. A straight-edged 50,u thick Tef- lon ribbon is c lamped against the face of the coverslip so that one edge is flush against the chamber bottom. The corner between the Teflon ribbon and the bottom is filled with a 2 mm thick strip of 2% agar in sea water. (The Teflon proves to be so hydro- phobic that the agar does not creep under it.) Af ter the agar gels, the Teflon is carefu l ly pnlled up so as to slip out between the agar and the coverstip. To sea lo f f the passage thus left by the wi thd rawn Teflon, a little more fluid agar is then appl ied to the uppe r margin of the gelled agar strip.

2. Soon af ter this step, about one hal f cc. of a suspension of recent ly fert i l ized eggs is placed on the bot- tom near the open side of the slit. The

bpLd~e

Z

SLIT

1"0

Fig. 2a. Perspective view of gradient cl~Lamber, b. Magnified bottom view of slit. c. Magnified cross-section of slit. d. Steady concentration profile through

chamber.

chamber is t i l ted to slide the eggs into the; slit and against the agar barrier. If is usual ly found that no fluid leaks past the agar barr ier and that the large major i ty of eggs come to rest just under the coverslips edge (Figs. 2 b and 2 c). I f these conditions are not met, the p repara t ion is not used.

In the main series of exper iments we tr ied to approx ima te a single close packed row of eggs as closely as possible. I f this were attained, about 290 eggs would each provide a meaningful outgrowth direction in each chamber. However, even at the end of the exper iments reported, when our skill had been well developed, gaps in the first row, beginning of a second

Yrotoplasma, Bd. LXIV;3 18

258 F. Bentrup, T. Sandan, and L. Jaffe

row, and cells lying too far off the midline of the slips edge, combined to reduce the number of counted eggs per chamber to about 100.

3. The slit is quickly sealed from the other side by a second 2 mm thick strip of 2% agar in sea water.

4. Seven co. of the desired solution is placed in each chamber half.

S o l u t i o n s U s e d

For the exper iments with hydrogen ion gradients, natura] sea water was buffered wi th 0.1 M tris (hydroxymethyl ) aminomethane to the desired pH.

For the main exper iments with potassium ion gradients, we used an artificial sea water containing the following salts: 4.59 X 10-~M NaC1, 2.76 X 10 -2 M MgSO~ 2.49 X 10 -e M MgCI:, 1.0 )< 10 -2 M CaC1, and 9.7 X 10-~ M KC1. It was buffered with 12 X 10-e molar iris to pHS.10 • .05, and equi l ibrated wi th room air to establish the concentrat ions of the carbonate system. The potassium ion concentrat ion was modified as desired by adding or subtract ing isotonic KC1 solution from J~he Jnixture.

I n c u b a t i o n o f C h a m b e r s a n d E s t a b l i s h m e n t o f G r a d i e n t s

Incubat ion was begun at about 2 hours, and cont inued unti l IS hours af ter ferti l ization, when the eggs have normal ly all germinated. If was done at 15 o C in the dark. Dur ing incubation, the fluid in both halves of each chamber was gently st irred to mainta in un i form concentrations in the following manner : Two Teflon beads each 2 mm in diameter were placed in each half chamber. The beads were rolled back and for th paral le l to the par t i t ion by tilt ing the chambers _+ 6 o at two cycles per minute.

In most experiments , the agar strips were made up wi th either na tura l sea wafer or an equivalent artificial sea water. When the solutions placed in the reservoirs differed from these compositions, it took some time for s teady gradients to be established. If is calculated that the s teady state was largely a t ta ined in about one hour. In order to test for effects intro- duced before a t ta inment of the s teady state, it was approached by other routes. In some, each agar strip was made lip wi th a solution of the composition in the reservoir it faced; in others each strip consisted of two portions, an inner pa r t facing the eggs was made wi th na tura l sea wafer while the outer pa r t was made up wi th its reservoir 's composition. No differences were detected in the eggs' responses to these different paths to the s teady state.

Assuming that no leakage occurred between the reservoirs, calculation shows that the change in the size of ~he gradient during the course of incubat ion a f t e r a s teady state was a t ta ined was negligible. We assured ourselves tha t no leakage occurred in two ways: First, af ter each exper iment was over, the fluid in one reservoir was removed leaving a 10 mm head of fluid pressing against the barrier. This head is est imated to be at least 30 to 100 times greater than any which pressed upon the barr ier during incubation. In almost all cases, no leakage was observed even af ter 10 minutes. In a few cases, gross leakage occurred immediately; these data

Induction of Polarity in Fucus Eggs by Potassium Ion Gradients 259

were discarded. Secondly we ran tests in which one reservoir contained a dye, either eosin y or potassium dichromate. The rate of appearance o f dye in the other reservoir was followed spectrophotometrically; it proved to be in satisfactory agreement with rates calculated upon the basis of diffusion alone. This again indicated that leakage was negligible.

S i z e o [ t h e G r a d i e n t s

The size of the steady state gradients established across the eggs could be roughly calculated but in order to confirm and refine these theoretical results, the concentration profile was de, ermined using an electrical analog. This was based upon the identity in the equations governing steady diffusion and steady current flow; concentration is analogous to potential. In the model, the eggs were represented b-y ~ 25 mm diameter nylon balls, the barrier and bottom by 25 mm thi& lucite sheets, the conductive medimn by an appropriate dilute KCI solution, and the uniform concentration reservoirs by large current passing Ag-AgC1 electrodes. A small Ag-AgCI probe electrode was embedded in one nylon bali's surface and connected *o a voltmeter. Rotation of the ball allowed a determination of the potential profile on the "eggs" surface. The profile outside of the slit was calculated.

The concentration profile determined in this way is shown in Fig. 2 d. Suppose that one reservoir contained {he concentration, C of a substance; the other, none. Then the concentrations at the poles of the egg are 0.62 C and 0.38 C, and the difference across the egg is 0.23 C.

The situation is somewhat modified in the case of the hydrogen ion gradients by the buffer molecules. Theoretical analysis provides the follow- ing steady state solutions.

2 1 1 -~ - - - - (2)

Hc q- K HI ~ K ' H2-+- K

where H c is the hydrogen ion concentration at the center, K is the dissociation constant of the buffer whidl in this case, that of tris

in sea water at 15 ~ C, is 3.6 X 10 -9. H 1 and H~ are the hydrogen ion concentrations in the two reservoirs.

A H = 4 / (H~ + K) (H2 + K) (H~ - - H2) (H1 @ H2 -}- 2 K) 2

(3)

where A H is the difference in hydrogen ion concentration across the egg. f is the fraction of the total diffusional resistance between the reservoirs

which exists across the egg row. In this case f is 0.23.

D e t e r m i n i n g G r o w l L h O r i e n t a t i o n

We counted all embryos in the slit except those which protruded by more than one half egg diameter from it or lay in a section containing two rows of eggs. The direction in which an outgrowth originated was defined as the horizontal component of the direction running from the egg's center

18"

260 F. Bentrup, T. Sandan, and L. Jaffe

to the outgrowth 's base. The degree of orientation of each popula t ion of outgrowth angles was characterized by its average cosine:

V: = Z p cos 0 (4)

where p __~ the percentage of all outgrowths lying at an angle 0 to one of the rescrvoirs. Recording of the angles was electrically speeded as described before (M il l 1 e r and J a f f e 1965). Calculations were speeded by the Johnson Foundat ion 's Control Data 160-A computer 2.

Control populations, grown in chambers containing the same medium in both reservoirs, showed about 5% orientation toward the first made agar wall. Hence the effect of any gradient was determined both in chambers in which the gradient was directed toward the first wall and toward the second. The comparable orientation values reported for controls in Tables l and 2 were obtained by arbi t rar i ly reversing the sign of the orientation observed with reference to the first wall in half the chambers, the reversed chambers being selected by a random procedure, and then averaging the orientations thus obtained in all the chambers.

Results and Analysis

H y d r o g e n I o n G r a d i e n t s

Before executing our main study with potassium ion gradients, we carried out a preliminary one with hydrogen ion gradients. We did this

Table 1. Response to Hydrogen Ion Gradients. Positive Orientation Means Growth toward the More Acid Side

pH's in reservoirs

8.1 vs. 8.1 7.9 8.1 8.0 8.2 7.6 8.0 7.6 8.1 7.9 8.3 7.1 8.1

Number of chambers cells

14 329 6 157 3 154 3 104 5 94 3 53 3 52

Average pit near

egg

8.1 8.0 8.1 7.8 7.9 8.1 7.8

A pK across

egg

0.000 0.047 0.055 0.089 0.110 0.137 0.187

% [H+] : difference across egg

0 11 10 18 23 27 35

% orientation

5 • 12 14 24 40 43 48

1 This is the difference in [H +] divided by the higher H+.

because this was near ly the only chemical gradient in which a previous s tudy was available: W h i t a k e r (1938), using as essentially quali tative method, found that F. f u r c a t u s eggs exposed to gradients of the order of ten fold per egg diameter showed a very strong tendency to germinate toward the acid side.

This facility is supported by Public Health Grant FR-15.

Induction of Polarity in Fucus Eggs by Potassium Ion Gradients 261

O u r results are shown in Table 1 and Fig. 3. The tendency to germinate toward the acid pole is confirmed. The observed quant i ta t ive relat ionship between the st imulus and the response is given by:

H 1 1 He v : 1.5 • (~)

H1

where H~ is the s teady hydrogen ion concentrat ion at the more acid pole of the egg,

H2 is this concentrat ion at the less acid pole, V is the degree of orientation.

% 50-

,40--

3 0 -

c,,r 20 -

.N lo

o o

../ / /i

10 2.0 3O 40% [hi § D/Z=r'SReNCe "~CROSS r

Fig. 3. R,esipon,s~e to hydr,ogen io,n grad,ten,is. Po,sit;ive o rientat~io,n means a tendency for the o~utgrowths t,o start ,on the side of h~,gher hydrogen ion coneentratfi,on.

I t is interest ing to note tha t this same rule that per cent or ientat ion a p p r o x i m a t e s per cent evoking gradient has been found to hold for the other cases invest igated: nam e l y the or ientat ion by light of Botrytis and Osmunda spores (J a f f e and E t z o 1 d 1962), as well as the or ientat ion by a flow established gradient of a secreted growth s t imulator in Botrytis spores (M ti 1 l e r and J a f f e 1965), and Fucus eggs (B e n t r u p and J a f f e, 1967). In addi t ion to its inherent interest, this result assures us that the method is reasonably reliable.

P o t a s s i u m / o n G r a d i e n t s

One cannot establish a gradient of one substance in an aqueous system wi thout in t roducing a counter gradient of another ba lancing substance (or substances). In our ma in exper iments wi th K + gradients, the solutions were made up so as to dis tr ibute the necessary counter gradient among the other ma jo r cations present (i.e. Na +, Mg ++, and Ca++), in p ropor t ion to their concentrat ion, and thus minimize the per cent counter gradients present .

262 F. Bentrup, T. Sandan, and L. Jaffe

The main results of these exper iments are shown in Table 2 and Fig. &. I t is seen that there is a marked orientat ion of the outgrowths toward the higher K + side for differences of 9 to 36 mill imolar across the egg. For differences of 18 and 36 mill imolar the degree of orientat ion is more than */a maximal .

Table 2,

Response to K + Gradients wi th Distr ibuted Cation Counter Gradients. Posi t ive Orientation

Indicates Germination, i.e. 2~ormation o] the Rhizoid Pole, Toward the Higher K + Side

Rese rvo i r K +

(mil l imolar)

10 vs . 10

10 0

20 0 40 0

80 0 160 0

N u m b e r of

c h a m b e r s cells

~o counter

ion gradient

% [K+] difference

across egg a

Ave rage K +

ou ts ide egg

(m)~)

A K +

across egg

(raM)

26

16

20

25

7

8

1072

883

946

1804

723

625

0.0

0.4

0.7

1.5

2.9 5.6

0

37

37

37

37

37

l0 t 0

5 2.2 l0 t 4.5

20 9

40 ' 18

80 I 36

% or ien ta t ion b

- - 1 t 3 - - 1 7 t : 6

- - 9 1 7

9 1 4

3 6 t 6 3 7 •

1 N a t u r a l sea wa t e r concen t ra t ion .

a Th i s is t he difference in [K +] d iv ided b y t h e h igher [K+].

b E r ro r s g iven are empi r ica l s t a n d a r d dev ia t ions of t he average .

%

!

0 10 20 ~] di//erence ~cro~s e g q ~

- - I , 1 - - 3 0 4omM

Fig. &. Respo,nses t,o p,otass,ium ion gr:a,~,en;ts (with d~i's4ributed eaSt,on co,unter gra~dien~s). Pos,~tive ,or ienmfl ion m e a n s a t e n d c , n e y fo r t h e o u t g r o w t i h s to s t a r t

t , oward t h e h,ighe:r potas,s~ium e o n c e n t , r a t i o n .

T h i s o r i e n t a t i o n i s i n t h e e x p e c t e d d i r e c t i o n a n d i n r e s p o n s e t o t h e e x p e c t e d o r d e r o f K + d i f f e r e n c e i f t h e t r a n s c y t o p l a s m i c g r o w t h c u r r e n t i s i n d e e d a c a u s e a s w e l l a s a n e f f e c t o f l o c a l i z a t i o n . So we consider this finding as substantial suppor t for a localizing role of a t ranscytoplasmic current and hence of a positive feedback loop involving this current.

Induction of Polarity in Fucus Eggs by Potassium Ion Gradients 263

A l t e r n a t i v e I n t e r p r e t a t i o n s

We gave this conclusion some further support by showing the improb- ability of two alternative interpretations of the results:

1. That the observed orientation is caused by the counter ion gradients. 2. That the observed orientation is caused by the potassium ion gradients,

but acting through a chemical rather than an electrical mechanism. The strongest argument against both of these alternatives lies in the

quantitative stimulus-response relationship. Consider the apparent response to an 18 mM K + difference. If one of the counter ions were the effective stimulus, then a 2.9% difference would have caused 36% orientation. Both experiment and theory render this most improbable.

Table 3. Response to K + and Water Gradients

Reservoir 1 l~eservoir 2 N u m b e r of Counter A across Orientat ion 1 cells gradient cell to I~es. 1 I chambers i

S .W. + 80mMKC1

95% s.w. 90% S .W.

sea wate r 1 80 18 mosmolar 18 m H K +

sea wate r 2 l 30 1 2% ions 12 mosM !

' 2.3% ions 25 mosM sea wate r 1 ~ 78

1 Er ro rs are theoretical s t andard errors based upon popula t ion size.

214 . 8

18 4" 13

26 4- 8

From the results with many other cells, particularly algal cells (D a in t y 1962), we infer that the Fucus egg is raore permeable to K + than to the other cations in sea water. Hence the counter gradients would have to act, if they acted at all, through some directly chemical mechanism rather than an electrical one. The available data (reviewed in the discussion of hydrogen ion gradients above) indicates that in the various other cases of orienting gradients which seem to act through a chemical mechanism, that per cent orientation approximately equals and certainly is no more than twice the evoking gradient. Moreover, this makes good theoretical sense. Orientation by a chenfically acting gradient must involve some relative reaction rates at various points on the cell surface. These relative rates, in turn, must be some function of the ratio of the concentrations of the effective components. Now if one molecule of this component participates in the localizing reaction, then the relative rates and hence relative likeli- hood of growth initiation, i.e. orientation, will be a linear function of the concentration ratio, and orientation will equal or be less than per cent concentration difference; if two molecules participate, orientation will equal or be less than twice the relative concentration difference etc. Since few reactions involve more than two molecules of a given component, orientation through a chemical mechanism should rarely be more than twice the relative concentration difference.

This same stimulus-response relationship is a serious objection to any chemical mechanism of action by the potassium ion gradients. For all of the K + gradients used in this series resulted in the same 37~ difference across the egg, yet gave the widely different responses shown.

264 F. Bentrup, T. Sandan, and L. Jaffe

Finally, we report one further experimental confirmation that the effective gradient in the main experiment was that of the potassium ions (Table 3):

Eggs were exposed to an i8 millimolar K + gradient attained by simply adding solid KC1 to the sea water used in one reservoir. This established an iS milliosmolar counter gradient of water concentration instead of a cation counter gradient. In response, the eggs still tended to grow toward the high K +, but to a degree (21%) lower than the 31% obtained with counter cations. Finally, the effect of this counter gradient of water con- centration was tested (Table 3): The eggs were found to grow toward the h i g h e r water concentration. Evidently then the KC1 gradient had to overcome a counteracting osmotic effect thus accounting for the somewhat reduced effect of a K + gradient applied in this way.

Appendix

F o r m u l a f o r t h e C u r r e n t D e n s i t y t h r o u g h a C e l l P r o d u c e d b y a G r a d i e n t of a P a s s i v e l y T r a n s p o r t e d I o n

The concrete problem which stimulated this analysis involves a spherical cell exposed to a continuous gradient of potassium ion. In order to simplify the analysis, however, we consider the model system shown in Fig. 5. It

Potes 0 I ~ i ti.!~:~!!!!!iii:i~!{: 0 Potassium: Kz t~-J{l-- K2

Ion f loW" I~:::::::::1 >

Fig. 5. Potassium grad,ien~ mo,del.

consists of a sheet-shaped "cell" bounded by two extended parallel membranes which are relatively permeable to potassium. A relatively high potassium concentration, K i is maintained inside the cell; two lower but different concentrations K, and K 2 a r e maintained in the two outside com- partments. The two outside compartments are maintained at zero potential; the inside compartment at - - V , the membrane potential. K1 exceeds Kz so potassium ion, hence positive charge or current flows steadily from com- partment 1 to compartment 2 through the cell. Since almost all of the resistance to this ion flow lies in the membranes, the internal potential, - -V and potassium concentration, K i are practically uniform.

The steady state flux across either membrane is obtained from one of the Goldman constant field equations as given by H o d g k i n and K a t z (1949):

F2/RT Ko--Ki" e - V F / R T = P K " V " " 1-- e - -VF/RT (2)

Induction of Polarity in Fucus Eggs by Potassium Ion Gradients 265

where d is the cur rent densi ty or flux, PK is the pe rmeab i l i t y constant, K o is the outside potass ium concentrat ion. A p p l y (2) to both membranes and equate the fo rward fluxes. One

obtains:

K1 - - Ki" exp ( - - V_F/RT) = - - [ K 2 - - K i �9 exp ( VF/RT)]

�9 . K,: = (K1 +KQ2 exp(VF/RT) (3)

Pu t (5) in (2) for ei ther membrane :

~. F" PK" A K" VF/RT 2 [1 - - exp ( - - VF/RT)]

~ - o c F . P K . A K

(4)

VF/R~' where ~ --~

2 [1 - - exl o ( - - VF/RT)]

a is a dimensionless t e rm which at 15 ~ C varies f rom 2.1 for a membrane potent ia l of 100 mill ivolt to 0.5 for a zero potential . For most purposes, then, it should suffice to t ake a as two.

Final ly , if one sets a equal to two, and expresses d in amperes /em e, PK in cm/sec and A K in mill imoles pe r liter, one obtains:

~ 0 . 2 . P K . A K. (4a)

Summary

Establ i shment of s teady differences of 20 to 40 mil l imolar potass ium ion across Fucus eggs induces about 53% orientat ion of the rhizoidal poles toward the high potass ium end.

We argue tha t the potass ium gradient acts b y w a y of a t r ansey top lasmie voltage gradient .

We describe a method for establishing known and s teady concentrat ion gradients across each of large numbers of developing cells.

Es tab l i shment of s teady hydrogen ion gradients across Fucus eggs induces an or ientat ion of the rhizoidal poles toward the more acid end. Per cent or ientat ion equals ~.5 times per cent hydrogen ion gradient.

References

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Authors ' addresses: Dr .F . B e n t r u p, Insti tute of Botany, Universi ty of Erlangen- Niirnberg, D-852 Erlangen. Dr. T. S a n d a n, Kyoto Gakugei University, Japan. Dr. L. J a f f e, Biology Dept., Purdue University, Lafayette, Indiana, U.S.A.