BIOCttlMICA ET BIOPHYSICA ACTA
I43
BBA 45 O9I
AMINO ACID U P T A K E BY E S C H E R I C H I A COLI GROWN IN P R E S E N C E OF
AMINO ACIDS
E V I D E N C E F O R R E P R E S S I B I L I T Y OF AMINO ACID U P T A K E
YUKIHARU
I N U I AND H I T O S H I
AKEDO
Department of Biological Chemistry, The Center for Adult Diseases, Osaka (Japan)
(Received M a r c h 3rd, 1964)
SUMMARY
I. The nature of the reduced uptake of amino acids b y Escherichia coli K10, grown
in the presence of amino acids was investigated. The uptake of cycloleucine and
L-leucine was reduced when cells were grown in a medium containing synthetic
cycloleucine, L-leucine or L-methionine. Such inhibition of uptake was not observed
when the cells were grown in the presence of L-tyrosine or ~-aminoisobutyrate, nor
demonstrated when cells were incubated in a nitrogen-free medium or in a medium
containing added chloramphenicol even in the presence of the above inhibitory amino
acids. Mitomycin C, in contrast to chloramphenicol, allowed the inhibitory effect
to develop.
2. The inhibition resulting from the preincubation with cycloleucine was reversed by further growth in a medium not containing cycloleucine.
3. 2,4-Dinitrophenol inhibited the uptake of cycloleucine both by the normal
cells and by cells maximally inhibited by cycloleucine.
4. The uptake of ~-methylglucoside and D-galactose was not inhibited by the
prior presence of cycloleucine in the growth medium.
5. Kinetic studies of the inhibition indicated that both the influx and the efflux
were changed.
INTRODUCTION
i-Aminocyclopentanecarboxylic acid (cycloleucine) has recently been used as
a model amino acid in studying transport 1-3. This synthetic amino acid was found to
be insignificantly metabolized in various animal tissues as well as to be a good model
for naturally occuring neutral amino acids. Therefore, we used this amino acid to.
investigate the mechanism of amino acid transport in Escherichia coli. During the
course of our experiments, we found that preincubation of the bacterial cells in a
growth medium with cycloleucine strongly inhibited the subsequent uptake of this
amino acid. This paper deals with the nature of the persisting inhibition on amino acid
uptake resulting from such preincubation.
Biochim. Biophys. Acta, 94 (1965) 143 I5~
144
Y. INU[, H. AKEDO
MATERIALS AND METHODS
Bacteria, culture media and compounds
The strain of bacteria used throughout these experiments was E. coli I(-IO.
The salt medium (medium I) with glucose used for bacterial growth contained per 1:
2.5 g (NH4),SO4, 3.0 g Na, HPO4, 2.0 g N a H , P O , , I.O g NaC1, o.I g MgSO 4 and 3.0 g
glucose. The nitrogen-free medium (medium II) for uptake experiments contained
per 1:12.6 g KH~PO4, 5.4 g K~HP04, 2 g Na~SO~, 0. 4 g MgSO 4, and 0.oi g CaCI~.
This medium was adjusted to p H 7.0 with NaOH. IOO/~g/ml of glucose was added
for amino acid-uptake experiments. To test the effect of the prior presence of cycloleucine on the uptake of sugars, no glucose was added to the uptake medium. To test
the uptake of D-galactose, the cells were grown on medium I with D-galactose instead
of D-glucose. L- [14Ce]Leucine was purchased from Daiichi Pure Chemicals Co. ; ~-methylD-E14C~]glucoside, D-[14C6]galactose, ~-aminoEIA4C]isobutyric acid and [I-14C]cycloleucine, from California Corporation for Biochemical Research. A part of the EI-14Cicycloleucine used was a gift of Dr. H. N. CHRISTENSEN.
uptake experiments
The uptake experiments were carried out by a slight modification of the method
of HAGIHIRA et al. 4. The exponentially grown cells were centrifuged, washed and
resuspended in medium I I for the uptake experiments. The concentrations of the test
radioactive compounds were 0.2-0.26 mM (7" lO3-3 . lO4 counts/min, ml unless otherwise stated). The concentrated cell suspension was introduced at time zero into the
uptake medium so as to give a final absorbancy of 0.2 at 660 my. This absorbancy was
preliminarily found to correspond to IOO tzg dry weight of cells per ml. The uptake
experiments were carried out at 15 °. The samples were filtered through a Millipore
filter (pore size, 0.45 ~) at intervals, and were washed 3 times with medium II. The
filters were dried and counted with a gas-flow counter. The recovery of radioactivity
of the cells on the filter was found to be in very good agreement with that obtained
b y the centrifugation-extraction method usually employed in the uptake experiments
on animal cells.
Preincubation with amino acids
The exponentially grown cells were inoculated into fresh growth medium (medium
I containing glucose or galactose), or resting medium (medium n), with or without
a test amino acid at a level of 0.23 mM. The cell suspension was further incubated
at 37 ° for 1-3 h, then centrifuged, washed and used for the uptake experiments.
In the kinetic studies of the inhibitory effects of preincubation the cells, preincubated with or without cycloleucine in the growth medium, were introduced into
two different uptake media, one containing labelled and the other containing nonlabelled cycloleucine (0.23 mM). The first batch of cells was used for determination
of the equilibrium level of the amino acid. This was done by counting the cellular
level of labelled cycloleucine. After equilibrium was reached, the tracer amount of
radioactive cycloleucine was added to the second batch of cell suspension. No significant change occurred in total concentration of the amino acid in the medium. The
radioactivity found with time in the second batch of cells was used for the kinetic
treatment shown in the APPENDIX.
.Biochim. Biophys. Acta, 94 (1965) 143-152
145
AMINO ACID UPTAKE BY E. coli
RESULTS
Cycloleucine as a non-metabolizable amino acid in E. coli K - z •
E. coli K - i • grown on medium I, containing glucose as carbon source, was
inoculated into the same medium with cycloleucine at the same concentration instead
of glucose. The bacteria failed to grow on such a medium. Paper chromatograms
(tert.-butanol-formic a c i d - w a t e r ; 7o:15:15, v/v) of cell extracts made with water
at IOO° for 5 min after incubation of the cells with [i-14Clcycloleucine, demonstrated
only one radioactive spot corresponding to cycloleucine itself. The radioactivity found
in the protein fraction was negligible.
Preincubation with cycloleucine
The uptake of 0.23 mM [I-14Clcycloleucine was measured with the cells grown
for I or 3 h in the presence or absence of 0.23 mM non-radioactive cycloleucine.
During preincubation with cycloleucine cell growth was somewhat depressed compared to that of the control (i.e. without cycloleucine). This will be discussed later.
As shown in Fig. I, the uptake of cycloleucine b y the cells preincubated with cycloleucine was markedly depressed as compared with that of control cells. This inhibitory
effect of cycloleucine was about 7 ° % after I h and about 9 ° % after 3 h of preincubation. One m a y explain this behaviour as resulting from the irreversible binding of
the sites b y cycloleucine or from the occupation of a slightly exchangeable compartment 5-7 b y the non-radioactive cycloleucine during preincubation. To eliminate this
possibility the cells were grown in the presence of radioactive cycloleucine of the
same specific activity as used in the uptake medium, and it was observed that the
radioactivity found in the cells during the uptake was markedly less than that of the
control (Fig. 2).
oo /
iI
1o0
--o
50
~E
t./
oy
.~
Time (rain)
Time ( mi• )
Fig. I. Effect of p r e i n c u b a t i o n w i t h cycloleucine on the s u b s e q u e n t u p t a k e of cycloleucine. The
cells were first i n c u b a t e d w i t h 0.23 mM unlabelled cycloleucine at 37 ° for I h in g r o w t h m e d i u m .
The u p t a k e of labelled cycloleucine (o.23 mM) was m e a s u r e d at 15 °. The control cells were h a n d l e d
in the same w a y except t h a t cycloleucine was o m i t t e d from the p r e i n c u b a t i o n m e d i u m . × - - × ,
the cells p r e i n c u b a t e d w i t h cycloleucine; 0 - - 0 ,
the cells p r e i n c u b a t e d w i t h o u t cycloleucine.
B o t h curves continue in the indicated direction to 19o m i n of incubation.
Fig. 2. Effect of p r e i n c u b a t i o n w i t h labelled cycloleucine on the s u b s e q u e n t u p t a k e of cycloleucine.
The procedure was the same as t h a t for Fig. i except t h a t the p r e i n c u b a t i o n was carried o u t w i t h
labelled cycloleucine at the same specific a c t i v i t y as was used for the u p t a k e experiment. × - - × ,
the cells p r e i n c u b a t e d w i t h labelled cycloleucine; • - - O ,
the cells p r e i n c u b a t e d w i t h o u t cycloleucine.
Biochim. Biophys. Acta, 94 (1965) I 4 3 - I 5 2
146
¥ . INUI, H. AKEDO
Preincubation of the resting cells with cydoleucine
The inhibitory effect was not observed when cells were preincubated with the
amino acid in a nitrogen-free medium (medium II). In this medium the absorbancy
of cell suspension did not increase. Moreover, the presence of IOO ~g/ml of chloramphenicol in t h e growth medium inhibited the appearance of the usual effect of
preincubation with cycloleucine (Fig. 3). Mitomycin C added during preincubation,
~5C
5 -
3C
o
"~
6(2
.J
"3
2C
l
o
/1/"
6
£
"8
20
°o ~b
Time (rain)
Q
/
e
" " "~ " " " "
3;
60
~o
Time (rain)
Fig. 3. Effect of chloramphenicol on the appearance of inhibition by cycloleucine. Chloramphenicol
(IOO/,g/ml) was added to the preincubation medium (growth medium containing cycloleucine).
Other experimental details as for Fig. i. x - - ×, the cells preincubated with cycloleucine; 0 - - 0 ,
the cells preincubated without cycloleucine.
Fig. 4- Reversibility of the inhibitory effect of preincubation. The cells were preincubated with
o.23 mM cycloleucine in growth medium for 15o min at 37 ° (ist preincubation), washed, inoculated
into fresh growth medium not containing cycloleucine and grown overnight. The uptake of cycloleucine was then measured ( O - - O ) . The control cells ( O - - O ) were handled in the same way
except t h a t cycloleucine was omitted from the Ist preincubation medium. Part of the cells, both
from the control and from those preincubated with cycloleucine, were again incubated for i h with
cycloleucine, and the uptake of the amino acid then measured. • - - • ,
preincubation with cycloleucine of the control cells; A - - A , 2nd preincubation of the recovered cells.
on the other hand, allowed the inhibitory effect to develop. Mitomycin C at a level
of IO/~g/ml was reported to block DNA synthesis without interfering with the synthesis of protein or RNA 8. These results strongly indicate that cell growth is necessary
for the inhibitory effect of the preincubation. This effect may be localized in protein
or RNA synthesis or both.
Reversibility of the effect of preincubation with cycloleucine
To test for reversibility of the inhibitory effect, cells preincubated with cycloleucine were inoculated into a fresh medium without cycloleucine and were permitted
to multiply overnight. The uptake of cycloleucine was almost normal (Fig. 4). Sensitivity of the recovered cells to a second preincubation with cycloleucine is also shown
in Fig. 4.
Effect of preincubation with o~-aminoisobutyrate on the uptake of amino acids
The uptake of a-aminoisobutyrate was measured in the cells preincubated with
cycloleucine, with the finding that ~-aminoisobutyrate uptake was also diminished.
Preliminary tests showed that a-aminoisobutyrate was hardly metabolized b y this
bacterial strain.
~iochim. Biophys. Acta, 94 (I965) 143-152
AMINO ACID UPTAKE BY
E. coli
147
T h e u p t a k e of = - a m i n o i s o b u t y r a t e w a s s l i g h t l y i n h i b i t e d , b u t t h a t of c y c l o l e u c i n e w a s n o t i n h i b i t e d , b y p r e i n c u b a t i o n w i t h = - a m i n o i s o b u t y r a t e (Fig. 5). T h e s e
t w o a m i n o a c i d s w e r e f o u n d t o c o m p e t e w i t h e a c h o t h e r f o r u p t a k e b y cells n o t p r e i n c u b a t e d w i t h e i t h e r of t h e s e a m i n o acids.
Effect of preincubation with naturally occurring amino acids
The above results indicate that preincubation with certain amino acids during
cell g r o w t h c h a n g e s t h e m e c h a n i s m of a m i n o a c i d t r a n s p o r t . A l t h o u g h t h e s e m o d e l
.•30
°
J
°
~
°
o~
,,,VL
o~
Eo
10
30
60
Time(min)
go
c
'<5
10
30
Time(rain)
Fig. 5- Effect of preincubation with a-aminoisobutyrate on the uptake of cycloleucine and a-aminoisobutyrate. The cells were preincubated with o.26 mM ~-aminoisobutyrate for I h, then the uptake
of ~-aminoisobutyrate (0.26 raM) a n d cycloleucine (0.23 raM) was measured. The control cells
were handled in the same way b u t without a-aminoisobutyrate. The upper group of curves indicates
the uptake of cycloleucine; the lower, t h a t of a-aminoisobutyrate. × - - ×, cells preincubated with
c~-aminoisobutyrate; • - - • ,
cells preincubated without a-aminoisobutyrate.
Fig. 6. Effect of preincubation with L-leucine on the subsequent uptake of L-leucine. The cells were
preincubated with 0.23 mM L-leucine for I h, then the uptake of o.23 mM L-leucine was measured
in the presence of chloramphenicol (ioo/tg/ml). × - - x , preincubation with L-leucine; • - - O ,
preincubation without L-leucine.
"3
"2.
b~3o
"0
~
b
°
.J'-
6o
oE
~E 40
o~
~,
2c
--lit
10
30
60
Time(rain)
9b
"0 ~
100
E:z
o~
50
g~
o c
•
/
I .#
o
a
1o
30
-----~
. . . . . .
60
go
Time(rnin)
Fig. 7- Effect of preincubation with L-leucine on the uptake of cycloleucine. The cells were preincubated with o.23 mM L-leucine, then the uptake of 0.23 mM cycloleucine was measured. × - - ×,
preincubation with L-leucine; • - - O , preincubation without L-leucine.
Fig. 8. Effect of 2,4-dinitrophenol on the uptake of cycloleucine. The cells were first incubated with
0.23 mM cycloleucine for 2. 5 h, then the uptake of 0.23 mM cycloleucine was measured in the
presence or absence of i mM 2,4-dinitrophenol. • - - • , control; 0 - - O, control plus dinitrophenol;
• --•,
preincubation with cycloleucine; / k - A, preincubation plus dinitrophenol.
Biochim. Biophys. Acta, 94 (I965) I43-[52
148
Y. INUI, H. AKEDO
amino acids are not significantly incorporated into protein of this bacterial cell, they
are analogous with naturally occurring amino acids. Considering the possibility that
these model amino acids might act by antagonizing the synthesis of protein molecules
participating closely in amino acid transport, we tested the effect of preincubation
with a naturally occurring amino acid, L-leucine, on subsequent L-leucine uptake.
In Fig. 6, where the cells were preincubated with L-leucine, the uptake of L-leucine
was depressed. The cycloleucine uptake by these cells was also markedly inhibited
(Fig. 7). When the cells were preincubated in a nitrogen-free medium (medium II)
with chloramphenicol no inhibition by L-leucine was observed. Preincubation with
L-methionine was also found to show the same inhibitory effect on cycloleucine uptake.
L-Tyrosine, on the other hand, showed no effect. These results indicate that the effect
of preincubation with the model amino acids did not result from any specific antagonistic action on protein synthesis. Since L-leucine and L-methionine also showed
the same effect on amino acid uptake, this action may well be an effect caused by
the excess amount of any of a number of amino acids introduced into the growth
medium.
Effect of 2,4-dinitrophenol o~ the uptake of cycloleucine by cells preincubate~t with this
amino acid
The effect of 2,4-dinitrophenol on the uptake of cycloleucine was investigated
(Fig. 8) in cells preincubated with and without cycloleucine. 2,4-Dinitrophenol, at
a concentration of I mM, strongly inhibited the uptake of cycloleucine by the cells
not preincubated with the amino acid. The same inhibitory effect of dinitrophenol was
also observed with cells which had previously been incubated with 0.23 mM cycloleucine for 2.5 h, during which time the inhibitory effect of cycloleucine reached a
maximum. The results indicated that the diminished uptake of cycloleucine was still
dinitrophenol sensitive. Under our conditions the uptake still appeared to proceed
against a concentration gradient.
60[
9'o
Time ( rain )
o.1
2b
i;
s'o
t (rain)
Fig. 9. Effect of p r e i n c u b a t i o n w i t h cycloleucine on t h e s u b s e q u e n t u p t a k e of o~-methylglucoside.
T h e cells were i n c u b a t e d w i t h or w i t h o u t cycloleucine in t h e s a m e w a y as for Fig. i, t h e n t h e u p t a k e
of o.2 m M a - m e t h y l g l u c o s i d e w a s m e a s u r e d . × - - × , p r e i n c u b a t i o n w i t h cycloleucine; @ - - @ ,
control.
Fig. IO. U p t a k e of r a d i o a c t i v e cycloleucine a t e q u i l i b r i u m . T h e results s h o w n in Table I were
p l o t t e d a c c o r d i n g to E q n . 3 in t h e APPENDIX. L n v a l u e s were c o n v e r t e d to logt0 v a l u e s for t h e
plot. × - - × , p r e i n c u b a t i o n w i t h cycloleucine; O - - O , control.
Biochim. Biophys. Acta, 94 (1965) I 4 3 - 1 5 2
149
AMINO ACID UPTAKE BY E . coli
Uptake of e-methylglucoside and D-galactose by cells preincubated with cycloleucine
In order to test whether the effect of preincubation with amino acid extends
to the transport of sugar the uptake of ~-methylglucoside was investigated. Fig. 9
shows that there was no difference in the uptake of this sugar between the cells preincubated with cycloleucine and those without. This sugar has been reported not to
be a carbon source of E. coli K-IO but only to be phosphorylated 4,°. The uptake of
n-galactose was also not affected by be preincubation.
Kinetic study of the inhibition
We investigated whether the preincubation with cycloleucine changed the
influx or the efflux or both in the transport of this amino acid. The mathematical
basis of the analysis m a y be seen in the APPENDIX. The value of K at different
equilibrium levels of intracellular cycloleucine reached at various concentrations of
the amino acid in the medium was found to be independent of the intracellular concentration. This indicates that the efltux is proportional to the cellular level of cycloleucine under the experimental condition. Therefore, if the inhibition b y the preincubation is only caused by the increase in efflux, the per cent decrease of the equilibrium
level ( y J should be the same as the per cent increase in the efflux coefficient, K.
In Table I typical experimental results are shown. The cells, preincubated for
I h with and without cycloleucine in the growth medium, were transferred into the
uptake medium containing 0.23 mM non-labelled cycloleucine and incubated at 15 °
for IOO miD during which time the equilibrium was reached. Then a tracer amount of
radioactive cycloleucine was added and the cellular level of radioactivity with time
was measured. In Fig. IO the values of log (I --Y/Yoo), shown in Table I, were plotted
against time with the result that the efflux coefficient, K, was found to be 0.03 per
TABLE I
UPTAKE OF RADIOACTIVE CYCLOLEUCINE AT EQUILIBRIUM
See METHODS a n d APPENDIX for details of e x p e r i m e n t a l procedures. The cells were first i n c u b a t e d
for ioo miD w i t h o.23 mM non-labelled cycloleucine d u r i n g which t i m e equilibrium was reached.
T h e n a tracer a m o u n t of radioactive cycloleueine was added to the m e d i u m a n d the cellular level
of [x4C]cycloleucine was measured. Concentrations of r a d i o a c t i v i t y in the m e d i a were 2.2. IOacounts/miD, ml for the control a n d 13. 5. lO4 counts/miD, ml for the cells p r e i n c u b a t e d w i t h cycloleucine. Cellular r a d i o a c t i v i t y is expressed as counts/miD per lOO/~g dry weight.
Time
(miD)
Control
Preincubated with cycloleucine
Cellular
radioactivity
(counts/miD
per zoo i~g)
z -- y ]y oo
Cellular
radioactivity
(counts/miD
per zoo #g)
z -- Y/Yo~
3
6
IO
15
20
25
3°
85
142
200
296
326
368
433
0.887
0.809
0.730
0.599
0.558
o.5o2
o.41o
200
235
325
411
444
45 °
5°8
0.700
o.531
0.350
o.184
o.ii8
O.lO 5
I2O
130
717
746
I
Y~ = 734
461
536
496
ym
=
5 O1
Biochim. Biophys. Aeta, 94 (1965) I 4 3 - I 5 2
15 0
Y. INUI, H. AKEDO
min for the cells inhibited by the preincubation and o.oi per min with the control
cells. This indicates that a considerable decrease in the influx should have occurred,
since the equilibrium level of intracellular cycloleucine (Yo~) of the inhibited cells was
almost one-tenth that of the control cells, while the increase in K was found to be
only 3 fold. The ratio of influx of the inhibited to that of the control cells was threetenth calculated as follows:
V"I/VI = V"B/VE
=
K'. Y'/K" Y = 0.0 3" Y.o.I/O.OI. Y = 3/lO.
DISCUSSION
The above results indicate that an excess of a single amino acid provided during
cell growth interferes with the subsequent uptake of the same and other amino acids.
The reversibility of the effect of preincubation and the absence of any change in sugar
transport, as well as in If+-Na+ balance 1°, strongly suggest a rather specific modification of the amino acid-transport system rather than an overall damage or change in
the cell membrane. Our kinetic study indicates that the inhibition b y preincubation
cannot be simply explained as an induction of a transport system, mediating exodus n,
but rather involves a change in the transport system as a whole including both the
influx and the efflux. In 196o, VOGEL12 reported results which he suggested as indicating a repression of N-acetylornithine uptake by added arginine in the growth
medium. In our system an amino acid inhibited the uptake of the same amino acid
or that of the structurally related ones, although no s u b s t r a t e - p r o d u c t relationship
exists between them. The transport of solute, nevertheless, has m a n y times been
proved to be a chemical reaction involving transport sites and closely to resemble an
enzyme reaction. Although we recognize transport as the movement of solute from
one phase to the other without a persisting change in its chemical structure, some
chemical reactions must be involved in the movement. Therefore, an amino acid taken
up b y cells can be taken to be an end-product of the transport reaction, whereas that
in the medium m a y be considered to be the substrate.
Such considerations lead us to suggest a controlling mechanism working at the
transport level under our experimental conditions. In fact, the growth rate of E. coli
Bi-IO in the presence of cycloleucine (0.23 mM) was significantly depressed for about
i h of incubation and showed a duplication time of 9 ° min. I t later tended to recover
and approach the control rate with a duplication time of 60 min. The same tendency
was shown in the preincubation with L-leucine. Since the inhibitory effect of preincubation with amino acid reached a m a x i m u m in about 2 h of incubation, our findings
could indicate a cellular regulation of amino acid transport b y which the cells maintain
a suitable intracellular condition for cellular metabolism and growth in an unfavourable environment. Some investigators t3-1~ have suggested a decreased uptake of
antibiotics or of growth inhibitory amino acids b y resistant strains of bacteria or b y
tumour cells. JACQUEZ AND HUTCHINSON 16, however, failed to explain the difference in
tumour susceptibility of antibiotic amino acids b y reduced uptake of these drugs.
IZAKI et al. ~ found almost the same inhibitory effect of preincubation with
tetracycline on the uptake of this antibiotic using a tetracycline-resistant m u t a n t of
E. coll. His results are similar to ours in m a n y respects. One of the authors while
working with Dr. H. N. CIIRISTENSEN at the University of Michigan (Ann Arbor,
Mich., U.S.A.), found that a tryptophan-less m u t a n t of Bacillus subtilis 168 showed
Biochim. Biophys. Acta, 94 (1965) 143-152
_AMINO ACID UPTAKE BY E . c o l i
151
:a prolonged lag phase when an excess amount of L-tryptophan was added to the growth
medium TM. This demonstrates, after a long lag phase, the same duplication time as
that obtained at more normal levels of L-tryptophan. The effect m a y well be explained
by the similar regulation of uptake of tryptophan as that discussed here.
Tt~e broad specificity implied for the inhibition of the amino acid-transport
system is noteworthy since cycloleucine uptake was inhibited by preincubation with
L-leucine or L-methionine as well as cycloleucine itself but was not inhibited by preincubation with =-aminoisobutyrate or L-tyrosine. Although there have been reported
individually specific transport systems for each amino acid in bacteria 19-~2, our findings
suggest the presence of a repressible mediation shared, at least partly, by more than
one amino acid.
APPENDIX
In general, a solute taken up by the cell reaches an equilibrium at which the
influx and the efltux are considered to be the same. At such an equilibrium, if one
adds a tracer amount of radioisotope of this solute into the medium without changing
the total concentration of solute, the isotope starts to enter the cell and reaches an
isotopic equilibrium. At time t, the intracellular amount of the isotope, y, is expressed
as follows :
y=i
--e
Here, the term i indicates the total amount of isotope taken in by the cell and
the term e the total amount of isotope released from the cell during time t. Since these
terms y, i and e, are functions of incubation time t, the following differential equation
is valid:
d y / d / = d i / d t - - de~dr
In this formula, dy/dt illustrates the rate of increase in the intracellular level of the
isotope; di/dt, the rate of entry of the isotope; de/dt, that of exit. If the equilibrium
of solute is maintained during the incubation, the intracellular amount of solute, Y,
should be constant with time. Then the term, de/dt, is given by the following equation:
de/dr = VE(y/Y)
The term VE represents the rate of exit of the solute. Therefore,
dy/dt = di/dt -- VE(y/Y)
(l)
When isotopic equilibrium is reached,
(di/dt)t~
-- VE(y~/Y)
dy/dt
becomes zero:
= o
(di/dl)t~oo = VE(yoo/Y)
(2)
The term Yoo indicates the intracellular amount of isotope at isotopic equilibrium.
Since the equilibrium of solute is maintained during incubation, the rate of isotope
entry at isotopic equilibrium, (di/dt)t+,, is equal to that at time t, namely di/dt.
By substitution of the Eqn. 2 into Eqn. I we obtain
dy/dt = VE(ym/Y)
-- VE(y/Y)
B i o c h i m . B i o p h y s . A c t a , 94 (1965) 143-152
152
Y. INUI, H. AKEDO
B y integration, we further obtain
In (I -- Y/Yoo) = -- K t
(3}
K = VE/Y
Because the terms VE and Y are constant with time, the ratio of Vw to Y or K is
also independent of time t. Therefore, the correlation of the term, In (I --Y/Yoo) with
time t should result in a straight line giving a slope equal to K. From the value of
K and Y one can calculate VE, which under the experimental conditions should be
equal to VI, the influx of solute. The calculation of VE and VI at various equilibrium
levels allows us to determine the formulation of efflux and influx. If the value of K
is constant with various equilibrium levels, that is independent of intercellular concentration, the effiux VE is proportional to the intracellular concentration.
ACKNOWLEDGEMENTS
The
authors
are grateful
to Dr. H. HAGIHIRA at our laboratory
and
to Dr.
H . N . CHRISTENSEN f o r h e l p f u l d i s c u s s i o n a n d a d v i c e .
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