/ . Embryol. exp. Morph. Vol. 26, 2, pp. 231-252, 1971
Printed in Great Britain
231
Transmission and spread of embryonic induction
I. Temporal relationships in transfilter induction
of kidney tubules in vitro
By STIG NORDLING, HEIKK1 MIETTINEN,
JORMA WARTIOVAARA AND LAURI SAXEN1
From the Third Department of Pathology and Department of
Zoology, University of Helsinki
SUMMARY
The question of whether inductive tissue interactions involve factors transmitted by longrange diffusion was investigated. In transfilter experiments with spinal cord as the inductor
and metanephric mesenchyme as the responding tissue it was established that interposition of
a second TA Millipore filter (pore size 0-8 /tm, thickness 25 /*m) prolongs the induction time
by about .12 h. The prolongation of the induction time was concluded to be due to the time
taken by the inductor to pass through the second filter. It was also demonstrated that metanephric mesenchyme partially lost its competence if precultivation lasted more than 12 h.
This explains why 100% induction never was achieved in the double-filter experiments.
In order to rule out the possibility that the filters, owing to their inhomogeneous structure
and negative surface charge, seriously restricted diffusion, the diffusion of several substances
through the filter was measured under conditions as closely similar as possible to those in the
transfilter experiments. Although there was some restriction of diffusion, the calculated
diffusion constants were of the same order of magnitude as those reported in the literature,
indicating that the filter is no major obstacle.
Calculations based on four different hypotheses that the inductor is transmitted by diffusion,
indicate that diffusion can hardly explain the long transmission time.
INTRODUCTION
The special form of intercellular communication known as embryonic
induction involves passage of morphogenetic 'messages' from one cell to another.
The nature of these messages and their carriers are practically unknown and so
is the mechanism of their transmission. To explain primary induction occurring
during gastrulation, two opposite theories have been put forward, one postulating free diffusion of the inductive components (Holtfreter, 1955; cf. Saxen &
Toivonen, 1962) and the other based on surface interactions of cells in close
contact (Weiss, 1958). Experiments showing that normal induction can be
imitated by chemical components and devitalized tissues seem to support the
former hypothesis {op. tit.), as do investigations employing membrane filters
between the interactants. In both amphibian and avian embryos, separation of
1
Authors' address: University of Helsinki, SF-00290 Helsinki 29, Finland.
232
S. NORDLING AND OTHERS
the ectoderm from its underlying mesoderm by thin membrane filters does not
prevent induction (Saxen, 1961, 1963; Gallera, 1967). Electron-microscope
examination of these filters does not reveal any cytoplasmic penetration into the
pores and thus suggests an interaction not mediated by cytoplasmic contacts
(Nyholm, Saxen, Toivonen & Vainio, 1962; Gallera,Nicolet & Baumann, 1968).
Similar data on other interactive processes, although available, are more
difficult to interpret. With the exception of cartilage induction (Lash, Hommes &
Zilliken, 1962; Strudel, 1962) and odontogenesis(Slavkine?tf/. 1969), attempts to
produce secondary induction with cell-free materials have been unsuccessful.
On the other hand, a variety of epithelial-mesenchymal interactions can occur
through membrane filters (Grobstein, 1956, 1957; cf. Saxen & Kohonen, 1969).
When filters with relatively large pores (0-8-0-45 jum) were used, the maximum
thickness still allowing induction was of the order of 60-70 ju,m for kidney tubule
and cartilage induction (Grobstein, 1957; Flower & Grobstein, 1967), but at
least twice that for transmission of the factor(s) controlling the behaviour of
epidermal basal cells (Wessells, 1962). Filters with average pores of 0-45 /im
allow the passage of inductive messages in practically all the interactive systems
so far explored (cf. Saxen & Kohonen, 1969), whereas filters with smaller pores
have only occasionally been used. In a study on dermal/epidermal interactions
definite orientation of the epidermal basal cells (although not histogenesis) was
still noticed when the dermis was separated by filters with an average pore size
of 0-1 jam (thickness 25 /«n) (Wessells, 1962). Saunders & Gasseling (1963)
obtained a weak 'maintenance' effect when the epidermal and mesenchymal
components of the wing bud were separated byfilters25 jam thick with an average
pore size of 0-05 jam. But these authors stress that the effect was definitely
weakened, which might be attributed to the slow or insufficient transmission of
the factor(s). Grobstein & Dalton (1957) explored the requirements of kidney
tubule induction in great detail and used filters with an average pore size of
0-1 ± 0-008 jam. The thickness of these filters revealed considerable variation,
and experimental results suggested that induction was not prevented as long
as the thickness was below 20 /an. But the effect of the inductor was again
definitely weaker than when filters with larger pores were used.
To summarize, the still somewhat inconsistent results suggest that transmission of inductive messages is definitely restricted by distance and by the pore
size of intervening materials. Therefore passage of materials by free diffusion is
unlikely to afford a full explanation of the transmission mechanism, and further
studies seemed necessary. Determination of the time factor appeared to be one
approach to the evaluation of the various possible transmission mechanisms.
This approach would require a model system in which the rate and distance of
transmission of the inductor could be measured. But until more is known about
the factors involved, their distribution in time and space can be determined only
by the response of the target tissue. With these facts in mind, a series of experiments was designed for measuring the parameters of transmission with the
Induction of kidney tubules in vitro
233
kidney model developed by Grobstein (1956) and subsequently used by our
group in a variety of experiments (Saxen et al. 1968; Saxen, 1971).
The minimum time required for the completion of tubule induction in
transfilter experiments has been shown to be of the order of 24 h (Grobstein,
1967; Saxen, 1970) (filter thickness, 25 /im, pore size 0-45-0-8 fim). After this,
the responding mesenchyme will continue its development and differentiation
even after contact with the inductor is broken. This 'minimum time' apparently
involves several time-consuming steps: Grobstein (1967) suggests the following
ones: 'production time' and 'transmission time' of the inductor and 'response
time' of the mesenchyme. To these must be added an 'adaptation time', during
which the separated and explanted tissue fragments recover and adapt to their
new, artificial environment (Vainio, Jainchill, Clement & Saxen, 1965). If the
distance between the interacting tissues is now increased by separating them with
an additional filter, it is likely that the time required for adaptation, production
andresponse will not be influenced. Any delay in induction would thenpresumably
reflect the actual transmission time of the 'inductor' through the second filter.
Then, knowing the time and distance of transmission of the hypothetical
factors, calculations of free diffusion versus other transmission mechanisms
could be made. A further condition for such evaluations would be knowledge
of the structural characteristics of the intervening material and the actual
rate of diffusion through it. Consequently, such studies will also be reported.
MATERIALS AND METHODS
Transfilter induction experiments
Eleven-day-old Fx hybrid mouse embryos obtained through mating of A/Sn
males with CBA/TeTG females were used throughout the work. Metanephrogenic
mesenchyme was separated from the still unbranched ureteric bud in Ca2+Mg2+-free saline (PBS) without enzyme treatment. The culture medium was
Eagle's minimum essential medium in Earle's balanced salt solution supplemented with 10% foetal calf serum (Vainio et al 1965).
Millipore-type TA filters were used in all experiments. The filters were sterilized by immersion in 70 % ethanol for 30 min, followed by thorough rinsing in
saline. According to the manufacturer, the average pore size is 0-8 ftm and its
thickness 25 + 5 /mi. When samples of the filters were measured with a
micrometer (10 measurements per 3 x 3 cm piece) their thickness in the dry state
ranged between 20 and 30 /tin, with a mean of 26 /on. The variation in the
thickness of the same 3 x 3 cm piece of filter was at most 3 fiva. After ethanol
treatment and rinsing in PBS the thickness of the filters (the same pieces as
above) ranged from 21 to 31 /.im, with a mean thickness of 27 ptm.
Instead of the natural inductor (ureteric bud), embryonic spinal cord - a
potent tubule inductor-was used (Grobstein, 1955; Lombard & Grobstein,
1969). The dorsal half of the spinal cord was cemented to the underside of the
234
S. NORDLING AND OTHERS
filter and six to eight mesenchymes were placed on the filter above the spinal
cord and coated with 1 % agar. The explants were subsequently cultured on a
Trowell-type screen for varying lengths of time, after which the spinal cord was
completely removed from the filter and the mesenchymes cultured for a further
48 h. When two filters were used, the components that were to interact were
placed on separate filters and thinly coated with agar, and the filters were
brought together. Inspection with a dissecting microscope in most instances
suggested close contacts between the filters. The few cases with interposed
material (agar, air bubbles) were discarded. The number of tubules in positive
explants was determined from serial sections of the explants, in which the
tubules were followed microscopically from section to section. Fig. 1 shows a
Kidney
mesenchyme
Filter(s)
Spinal cord
Single filter experiment
Double filter experiment
Fig. 1. Diagram of single- and double-filter explants, approximately to scale.
diagram of the explants, drawn approximately to scale, to demonstrate the
approximate dimensions of the explants. In the ageing experiments the agarcoated kidney mesenchymes were first precultivated on TA Millipore filters for
12, 18, 24 or 40 h. The spinal cord was cemented to the underside of the filter
and cultivated with the mesenchymes for a further 48 h.
Ultrastructural analysis of the Millipore filters
TA Millipore filters were analysed by electron microscopy, using the freezeetching technique. Small pieces of filter were sterilized as in the organ culture
experiments by immersion in 70 % ethanol for 30 min, followed by thorough
rinsing in PBS. After this they were frozen in Freon 22 and then transferred to
liquid nitrogen. Replicas of cleaved filters were made with a Balzers freezeetching apparatus using 1 min etching times at - 100 °C. Electron micrographs
of the replicas were taken with a Philips EM 300 microscope and enlarged as
desired.
The proportions of space and material in the filter were determined by tracing
outlines from the electron micrographs on paper of uniform thickness. The
filter tubules were then cut out and their weight compared with the initial weight
of the paper.
Induction of kidney tubules in vitro
235
Diffusion experiments
Molecules of different size, shape and electrical properties were chosen
for the diffusion experiments. These were: [3H]thymidine (New England Nuclear
Co., Boston, Mass.); trypan blue (Edward Gurr Ltd., London, England); blue
dextran 2000 (Pharmacia, Uppsala, Sweden); bovine serum albumin 'BSA'
(Bovine Albumin Powder, Fraction V, Armour Pharmaceutical Co., Eastbourne,
England); protamine sulphate (Medica Pharmaceutical Co., Helsinki, Finland);
[3H]protamine sulphate (Schwarz Bioresearch Inc., Orangeburg, N.Y.);
[14C]amino acid mixture (New England Nuclear Co., Boston, Mass.); [3H]polio
virus (by courtesy of Dr L. Kaariainen, Department of Virology, University of
Helsinki) - the virus was made radioactive by cultivation in the presence of
[3H]phenylalanine, and then purified by two successive isopycnic bandings
in caesium chloride; T2-phage (by courtesy of Dr O. Makela, Department of
Serology and Bacteriology, University of Helsinki). Their approximate molecular
weights are listed in Table 3 (p. 242).
Of these substances, blue dextran represents a molecule with a chain-like
structure, bovine serum albumin a close to sperhical molecule, and protamine
sulphate one with a strong positive charge.
The rates of diffusion of these substances were measured in an apparatus
(obtained from Dr S. Salminen) consisting of two chambers of equal volume
separated by one or two TA Millipore filters of known thickness and surface
area. The apparatus is similar to the one described by Fuchs & Gorin (1961) and
used for the same purpose. The filters had been treated in exactly the same way
as those in the induction experiments, i.e. a 30 min 70% ethanol treatment
followed by thorough rinsing in PBS and then in serum-containing tissue
culture medium.
At time 0 a small volume of the test substance is added to side A and simultaneously the same amount of medium to side B. Both sides are continuously
stirred. At intervals small samples (10-100 jttY) are taken simultaneously from
both sides with Hamilton syringes or Carlsberg pipettes and the concentration
of the substance determined. The concentration of the radioactively labelled
substances was determined by liquid scintillation spectrometry in Bray's
solution, trypan blue and blue dextran by spectrophotometry at their adsorption
maxima and BSA using Folin's reagent according to Lowry et al. (1951). The
T2-phage concentration was determined by seeding a sample of known
volume on an Escherichia coli culture and counting the number of plaqueforming units (by courtesy of Dr O. Makela). The diffusion of the radioactive
compounds and T2-phage was determined in culture medium containing serum,
whereas the diffusion of the other substances had to be determined in phosphatebuffered saline in order to avoid interference with the spectrophotometric
readings.
236
S. NORDLING AND OTHERS
Adsorption experiments
Only adsorption of radioactive substances was determined. In all experiments
the concentration of [3H]protamine sulphate was 1 /*g/ml (except in the
0-1 /*g/ml experiment) and non-labelled protamine sulphate was added to get
the stated final concentration. After completion of the diffusion experiment the
chambers were emptied, first side B, then side A, and the filter was therefore
filled with liquid from side A. Then the volume of liquid in the filter was
determined by weighing the wet filter and subtracting its dry weight. The filter
was cut in two: one half was not rinsed, the other half was thoroughly rinsed
in PBS and left in a beaker of PBS for 1 h, after which the radioactivity of the
rinsed and unrinsed half of the filter was determined by liquid scintillation
counting in Bray's solution.
RESULTS
Temporal relationships in transfilter induction
The results of the temporal relationships in the induction process through one
versus two Millipore filters are indicated in Table 1 and one typical doublefilter explant is illustrated in Fig. 2.
Table 1. Effect of transfilter contact time on tubule induction
Double filter
Single filter
A
r
Transfilter
contact(h)
Explants
12
18
24
30
36
42
48
11
13
20
—
—
—
—
Proportion Tubules per
of
positive
positives
Explants
explant
0
0-92
10
—
—
—
—
0
3-3
8-4
—
—
—
—
—
19
17
11
12
16
Proportion Tubules per
of
positive
positives
explant
—
005
0-35
0-64
0-67
0-69
—
10
4-3
2-9
80
81
— = Not determined.
The apparent conclusion to be drawn from these results is that in single-filter
experiments induction is completed in ca. 18 h, i.e. some 12 h before the onset of
morphogenesis is noted (Wartiovaara, 1966; Saxen et al. 1968). The interposition
of a second filter of the same thickness increases this ' minimum time' by some
12-18 h, but a more detailed and exact analysis seems difficult with the present
method (see Discussion). The quantitative estimate presented in Table 1
suggests, in addition, that we are not dealing with an all-or-none response, as
the number of induced tubules increases with increased transfilter contact.
Induction of kidney tubules in vitro
237
Ageing of the responding tissue
It is interesting to note that in the one-filter experiments all mesenchymes
showed tubule formation if the induction time was long enough, whereas in the
double-filter experiments a plateau was reached after 36 h when about 70 % of
the mesenchymes showed tubule formation. An increase in the induction time
did not increase the number of positive cases. A possible explanation for this
was that in the double-filter experiments the mesenchymes had to wait some
12-18 h longer for the inductor. This prolonged culture in vitro would then lead
to loss of responsiveness, i.e. 'competence', by the mesenchyme as in corresponding experiments with amphibian ectoderm, where reactivity to both normal
Fig. 2. Micrograph of double-filter explant cultured in vitro for 5 days. The arrows
indicate tubules in the kidney mesenchyme.
and heterologous inductors is lost in some 18-24 h (Leikola, 1963; Grunz, 1970).
This point was therefore investigated in experiments simulating the situation in
the double-filter series. At 12 h there was no loss of competence, whereas at 18 h
most of the mesenchymes had lost their competence, with a correspondingly
decreased induction percentage (and decreased number of tubules) as compared
16
EMB 26
238
S. N O R D L I N G AND OTHERS
•t^
^•flrVs:**
'£
*A*t
Fig. 3. Micrographs of explants in which the kidney mesenchyme was aged (cultivated
separately) for 18 h before addition of spinal cord. (A) Negative explant without any
tubule formation. (N.B. The explant shows no sign of decreased viability.)
(B) Positive explant in which tubules have formed (indictated by arrows) in the
kidney mesenchyme.
with those combined immediately after isolation (Table 2). An additional 6 h of
precultivation weakened the responsiveness of the mesenchyme somewhat
further, as only two out of nine cultures showed tubule formation (Fig. 3 B), and
again in reduced amount. The remaining negative explants showed good
viability and preservation of their original shape (Fig. 3 A), suggesting that loss
of competence rather than experimental conditions was the true cause of the
unresponsiveness. So far, nothing can be said of the mechanism of this in vitro
change or its metabolic background. Experiments on amphibian material suggest
Induction of kidney tubules in vitro
239
that inhibition of protein synthesis during the ageing process preserves the
competence, but corresponding information on the kidney material is still
lacking (Grunz, 1970).
Table 2. Effect of ageing of mesenchymes on tubule induction
Proportion
of
Precultivation
of mesenchymes (h)
Explants
positives
0
12
18
24
40
20
12
10
9
8
10
10
Tubules per positive
explant
8-4
4-9
20
30
—
0-30
0-22
0
The percentage induction in the double-filter experiments was therefore
corrected, on the assumption that ageing is a continuous process, by taking the
delay in induction in the double-filter experiments as 14 h and extrapolating the
loss of competence at this time from Table 2. The result thus obtained shows
that the corrected response is close to 100 % after 36 h, but that the slope of the
one-filter curve is steeper than that of the double-filter curve, suggesting a greater
variation in induction time in the latter conditions (Fig. 4).
100
r
80 -
JJ
o
"
0
-0
Double filter
corrected
60 -
ft
Single filter /
> 40 i
/
Double filter observed
/
20 i
i
i
12
/
i
r
i
18
24
30
Induction time (h)
i
i
36
42
48
Fig. 4. Percentage of tubule-positive explants in single- and double-filter experiments
as a function of contact time. In the corrected double-filter curve, loss of competence
due to ageing has been taken into account.
infrastructure of the filter
For evaluation of the above-explained results, information about the ultrastructure of the filters is important, especially as regards the transmission of
16-2
240
S. NORDLING AND OTHERS
substances through the filter. Because it has been reported that ethanol causes
Millipore niters to swell (England, 1969), the niters were treated in the same way
as in the induction experiments and furthermore a freeze-etching technique was
used; then no organic solvents which may alter the structure of the niters are
Fig. 5. Electron micrograph of TA Millipore filter, made by the freeze-etching
technique. Thefilterconsists of extremely tortuous channels with varying diameters.
The walls of the channels have a vermicular appearance and a relatively constant
diameter, in spite of their variation in shape, x 20000.
Induction of kidney tubules in vitro
241
necessary in processing the specimens for electron microscopy. The technique
produces three-dimensional replicas of cleaved planes through frozen filters for
electron-microscopy analysis.
As demonstrated in Fig. 5, the cleavage plane of a TA Millipore filter consists
of vermicular structures with uneven interspaces. There are distinct channels
and larger lacunae are noticeable in the filter. Consequently, the pore size of the
filter is a mean figure with x 3-4 variations between the individual pores. The
pores are extremely tortuous and branching channels are formed between walls
with uneven thickness.
The porosity of the filters was measured from the electron micrographs by a
paper-weighing method. The porosity thus determined was only 36 %, which is
less than half the porosity reported by the manufacturer (84 %).
Diffusion through the filter
The above-related ultrastructure of the filter and their relatively low porosity
as well as the net negative charge of the filter (unpublished) could considerably
restrict the diffusion, especially that of large and/or charged molecules compared
to their diffusion in a free space. Consequently we measured the diffusion of
such molecules across the filters under conditions similar to those in the induction experiments.
The equation for diffusion is
dm = -DS^-dt.
ax
(1)
The number of moles dm flowing through the cross-sectional area S in the short
time dt is proportional with the concentration gradient dcjdx at this time. D is
the diffusion constant. When equation (1) is solved for the appropriate boundary
conditions in the diffusion chamber:
In £• = D£ t,
(2)
Ac
Vh
where c0 is the concentration of the substance in chamber A when t = 0 (in the
protamine sulphate experiments, where there was substantial loss of substance
because of adsorption c0 = cA + cB, where cA and cB are the concentrations at
time / in chambers A and B respectively), Ac = cA-cB. S is the surface area and
/? the thickness of the filter. Kis the volume of each chamber. The rate constant
ln(co/Ac) will be termed b. Thus b increases linearly with time (the experimental
data has been plotted in Fig. 6, where the lines have been obtained by the method
of least squares). For small values of b (< 0-6), cBjcA « \b.
Table 3 shows the rate constants b for the various substances, and also the
diffusion constant calculated from equation (4) (see below), taking the effective
surface area as 0-84 (i.e. the porosity reported by the manufacturer) of the total
area. The diffusion across the filter is considerably smaller than anticipated, as
242
S. NORDLING AND OTHERS
shown by the fact that the diffusion constants found are usually only one-third
to one-quarter of the true diffusion constants. In order to exclude the possibility
that the negative charges on the filter partially or completely restrict the free
diffusion of positively charged compounds, the diffusion of an amino acid
mixture and protamine sulphate was studied (Fig. 7). In this instance no regression lines were calculated since there is a considerable scatter of the results and
the diffusion in PBS is concentration dependent. The results, however, indicate
that the diffusion is relatively fast and that the filter constitutes no major
obstacle.
i
0-5
I
1
1-5
I
I
i
2-5
3 0
05
Diffusion time (h)
Fig. 6. Diffusion of various substances through one or two filters in a diffusion
chamber as a function of time. O—0, 3 H-TdR; A—A, trypan blue; D—D, BSA;
O—O, blue dextran; y—V> [3H]polio virus; x — x , T2-phage. cA and cB are the
respective concentrations at time / in chambers A and B, between which the
filter(s) has been cemented. c0 = cA when t = 0; Ac = cA — cB.
Table 3. Permeability of TA Millipore filters
Rate constant ± S.E.
(h-1)
\Ar\1 £*/•*! ii o t*
Substance
Thymidine
Trypan blue
Protamine sulphate
Albumin
Blue dextran
Polio virus
To-Dhaee
IVlUlCLUlai
weight
242
960
5000
9x10*
2xlO 6
6-8 x 106
215xlOG
(
Diffusion constant
(xl0 G cm2 s"1)
A
^ Calculated
1 filter 2 filters
207 ±004 0-85 ±001
1-23
1-24 ±008 0-35 ±001
0-7
0-51 ±006
—
0-3
0-38 ±002 014 ±002
0-23
0-112±0003 0058±0002
007
0-132±0017 0103±0004
008
0104 ±0008
—
008
Literature*
4
2-5
1-5
0-6
0-15
018
006
S.E. = standard error of the mean.
— = not determined.
* In some instances the values have been extrapolated from those for similar substances.
Induction of kidney tubules in vitro
243
The double-filter experiments were done in order to determine whether the
liquid layers possibly present between the filters would restrict diffusion. The
rate constants in the double-filter experiments should be half the value of those
in the single-filter experiments (Table 3), but actually in some instances they are
only one-third. The reason is that in these instances no special precaution was
taken to avoid liquid between the filters and after completion of the experiment a
small amount of liquid was seen between the filters.
Medium
05 -
1
0-5
1
1
i
1-5 0
0-5
Diffusion time (h)
I
1
1-5
Fig. 7. Diffusion of an amino acid mixture ( • — • ) and various protamine
sulphate concentrations in a diffusion chamber, in PBS and in culture medium.
O — O , 1 mg/ml; V—V, JOO/tg/ml; • — • , 10/ig/ml; A—A, 1 /tg/mi; O ~ O ,
01 yug/ml protamine sulphate. c0 is the sum of cA and cB, which are the respective
concentrations in chambers A and B, between which the filter is cemented. Ac =
The porosity of the Millipore filters has been determined by a mercuryintrusion method (Honold & Skau, 1954) which only measures the ratio of
empty space volume to total volume of the filter and yet blind pockets were
demonstrated to exist in the filters. The freeze-etching electron micrographs
showed a considerably lower porosity of 0-36. Although these pockets may be
filled when mercury is forced into the filter under high pressure they will restrict
diffusion and the true porosity of the filter may be much smaller, thus explaining
the too low diffusion constants.
Fuchs & Gorin (1961) have determined the diffusion of various proteins
through 150 /em thick Millipore filters with various pore sizes and found that the
effective diffusion area was less than 10 % of the surface area of the filter, whereas
we find a considerably higher value (compare the diffusion constants in Table 3).
This discrepancy cannot be due to the fact that our filters were only 25 ju,m thick,
244
S. N O R D L I N G AND OTHERS
since in experiments with Millipore 150 /tm thick filters we have found that the
diffusion area is approximately 50 % of the surface area for filters with pore
sizes above 0-2 [im (unpublished).
Adsorption on the filter
Since the filters carry a net negative charge the adsorption of positively charged
substances and some other substances was studied. In culture medium only
protamine sulphate is adsorbed on the filter to a substantial degree (Table 4),
and the degree of adsorption is concentration-dependent. Within the range of
Table 4. Adsorption of different substances on TA Millipore
filters and the diffusion rate constant
Ratio filter concentration/final medium concentration
PBS adsorption
Substance
3
[ H]thymidine
Amino acid mixture
Protamine sulphate
0-1 /tg/ml
1 /tg/ml
10/tg/ml
100/ig/ml
.1 mg/ml
Unrinsed
filter
5-4 (0)
47-5 (1)
156(5)
365 (12)
368(12)
341 (11)
235 (8)
Rinsed
filter
0-94 (0)
36 (1)
134(4)
369 (12)
341 (11)
240(11)
235 (8)
Diffusion rate
constant! S.E.
(h-1)
2-36 ±005
0-32 ±003
0-60 ± 008
0-66 ±007
0-50 ±007
0-85 ±005
Medium adsorption
Unrinsed
filter
0-5 (0)
0-9 (0)
105 (3)
190(6)
222 (7)
103 (3)
41 (1)
Rinsed
filter
0-5 (0)
0-7 (0)
122(4)
148 (5)
194(6)
79(3)
37 (1)
Diffusion rate
constant + S.E.
(lr ] )
2-89 ±0-13
0-39 ±004
0 51 ±006
0-42 ± 004
0-51 ±002
0-52 ±007
Number in parentheses is the percentage of the added amount adsorbed to t he filter.
S.E. = standard error of the mean.
1-100 /tg/ml the ratio between the amount adsorbed and the concentration in
the medium was nearly constant, whereas this ratio was somewhat smaller at a
concentration of 1 mg/ml (Table 4). The ratios tabulated are: amount of
protamine sulphate per mg dry weight of the filter divided by the amount of
protamine sulphate per mg of medium in side A of the chamber at the end of
the diffusion experiment. In the case of unrinsed filters the amount of protamine
sulphate in the medium contained in the filter was subtracted before the ratios
were calculated.
A substantial proportion of the protamine sulphate was adsorbed (Table 4).
In some instances there was a considerable loss of substance (not found in the
medium nor in the filter) probably due to adsorption to the walls of the diffusion
chamber. This adsorption may partially account for the non-linearity of the
diffusion curves (Fig. 7).
The conclusions to be drawn from these experiments are apparently that
Induction of kidney tubules in vitro
245
certain substances are adsorbed in substantial quantities on the filter, but that
diffusion occurs even before saturation of the filter (which did not occur at all
in the experiments).
DISCUSSION
As mentioned in the Introduction, the total induction time consists or several
time-consuming events, whereas it is likely that the difference in total induction
time between single and double-filter experiments reflects the transmission time
through the second filter. The transfilter experiments show that this time is at
least 12 h. This fact permits calculations of the diffusion constant, size and
molecular weight of the hypothetical inductor, if some assumptions are made
about the induction process.
If diffusion plays a role in tubule induction, induction could be diffusiondependent in one of the following four ways: (1) induction takes place when a
threshold concentration of the inductor has been reached; (2) induction requires
the establishment of a linear gradient, as recently suggested by Crick (1970) in
another morphogenetic model; (3) induction takes place when a threshold flow
of substance is reached; (4) induction takes place when a threshold amount of
substance has reached the responding cell. In all these instances breakdown of
the substance, rate of release in the inducing tissue and utilization of the substance have to be considered. This makes mathematical formulation complicated
and therefore several simplifications have been introduced: the concentration of
the inductor at the source is constant and independent of the diffusion rate; the
diffusion constant is concentration-independent and the same in the filter as in
the tissues; the diffusion is one-dimensional. In the transfilter experiments this
last assumption seems reasonable, since the tissues are fairly sheet-like and the
spinal cord is wider than the metanephric mesenchyme (Fig. 1).
For diffusion, the following partial differential equation applies:
--£—
(S)
where D is the diffusion constant, x the distance and c the concentration. If the
concentration of the inductor at time 0 is instantaneously increased from 0 to c0
and then kept constant all the time, the diffusion along the x-axis can be calculated from equation (3), and according to Crank (1956)
Ci = c e r f c
°
^
where ct is the threshold concentration and erfc the complement of the error
function. By the first hypothesis, i.e. that a threshold concentration of the
inductor is required for induction, D can be calculated if ct is known. Theoretically, CJCQ can vary between 0 and 1. In the second case t approaches infinity,
since erfc (equation 4) is 1 when x\[2^(Dt)] = 0.
In the experiments it was not the total induction time but the increase in this
246
S. NORDLING AND OTHERS
time that was determined and the distance between the source and the responding cell is not exactly known. Therefore equation (4) has to be modified.
Let x be the distance between the source of the inductor and the responding
cell at the longest distance when one filter is interposed between spinal cord and
kidney mesenchyme and let x' be the thickness of the second filter. tx and t2 are
the induction times when one and two filters are interposed. Af = t2~t1. Then:
Ci = c erfc
which gives
» ymresp-c'
= c « erfc
xM
K }
* x'(2x + x'y
Biologically the most satisfactory result is obtained when the equations are
solved in such a way that the required concentration and the size of the molecule
are reasonably small (D reasonably large). Then x should be large and t small
(equation 4). As x increases, tx also increases (equation 5). x has a higher power
Table 5. Calculated effect of interposition of an additional filter
between the tissues on diffusion time and concentration
Prolongation of diffusion
time caused by interposed
filter
f
Substance
Thymidine
Trypan blue
Protamine sulphate
Albumin
Blue dextran
Polio virus
TVphaee
c, = 001 c0
c,. = 0-9c0
1 sec
1 sec
2 sec
6 sec
23 sec
19 sec
56 sec
6 min
9 min
15 min
38 min
2-5 h
20 h
6-3 h
^
Concentration ratio 12 h
after interposing filter
(c,/c0)
0-99
0-99
0-99
0-98
0-95
0-96
0-92
c0 = concentration at inductor-filter interface ( = constant), c( = concentration in
responding cell. In single-filter experiments the distance between the source of the inductor
and the responding cell has been taken as 75/mi and in the double-filter experiments as 100/im.
For the computations equation (4) and the diffusion constants in Table 3 have been used.
than t and has therefore a greater influence. The value assigned to x must both
be within the limits of the physical dimensions of the explants (Fig. 1) and fulfil
the condition that the transmission time in the single-filter experiments does not
exceed 18 h (cf. Table 1). According to the second condition, x can at most be
86 /mi (not taking into consideration the porosity of the filter). In the calculations
we have used a value of 75 jam, as this approximates to the distance between the
spinal cord-filter interface and the top of the kidney mesenchyme.
For the substances used in the diffusion experiments the increase in diffusion
time when the diffusion distance is increased from 75 to 100 jam has been calculated for c€ = 0-01c0 and ci = 0-9c0 (Table 5). One per cent of the initial
Induction of kidney tubules in vitro
247
concentration is rapidly obtained with all substances, even with the T2-phage.
A substance which requires 12 h increase in diffusion time to diffuse a further
25 /Mn would have a diffusion constant of 4-2 x 10~10 cm2 s - 1 (calculated from
equation (4) taking into consideration that D is inversely proportional to t).
When D is known, the size of the molecule can be calculated from the following
equation, which is valid for spherical particles:
L
(7)
where k is Boltzmann's entropy constant, T the absolute temperature, 7/ the
viscosity of the medium and r the radius of the molecule. If?; is 1 cP, r is 5-4^111.
It takes a considerable time for the concentration to reach 90 % of the initial
value (Table 5), but, even then, the diffusion of the T2-phage is faster than the
experimentally observed delay in induction time. An inductor that requires 12 h
to reach 90 % of the initial concentration would have a D of 3-2 x 10~8 cm2 s - 1
and a radius of 0041 /im (equation 7), a value which is rather large, corresponding to that of a virus. Table 5 also shows the concentration ratio between the
responding cell and the source if the additional diffusion time through the
second filter is 12 h. In all instances this ratio is above 0-9.
The second hypothesis recently suggested by Crick (1970) requires the establishment of a linear gradient between the source and the responding cell. The
development of such a gradient requires a constant concentration at the source
and at the responding cell. The steady state is achieved when Dt/x* = 0-45
approximately (Crank, 1956), in the simplest case when at the source c increases
from 0 to cQ and the most distant cell is at a 0 concentration. We will take a
value of 0-5. On analogy to the previous case:
0-5
D
=
As before and for the same reasons, x will be taken as 75 jam, in which case D is
5x 10-10cm2 s"1 and the radius of the inductor 4-5 jam (equation 7). The
porosity of the Millipore filter has not been taken into account. As this was
found by measurement to be 0-36, the calculated values will still be of the same
order of magnitude.
According to the third hypothesis a threshold flow through the tissue was
required. It is not easy to calculate the time at which the flow is maximal at a
given distance, but as the flow is proportional to the gradient, the result can be
obtained graphically. Therefore Fig. 8 was plotted using equation (4) and a
diffusion constant of 4 x 10~6 cm2 s - 1 for thymidine. The same curves can be
used for substances with other diffusion constants if the times are altered since
the time is inversely proportional to D, i.e. for polio virus the times should be
multiplied by approximately 20. At a distance of 100 fim the gradient reaches a
maximum when t is approximately 0-5 min (Fig. 8). A substance which at a
248
S. NORDLING AND OTHERS
distance of 100 /*m reaches its maximal flow 12 h later than at 75 /<.m must have
a diffusion constant of 1-1 x 10~9 cm2 s"1 and a radius of 2-0 fim (equation 7).
The fourth hypothesis states that induction takes place when a threshold
amount of substance has flowed through the responding tissue. This total flow
through a cross-sectional area can be obtained by integration of equation (4).
1
5h
1h
0-9
•
08
n-\\
^v\^^^^
"""
10 rriin
5 min
"—-
—
07
0-6
0-5
^
^
^
\
"•"-
1 min
0-4
- \
03
0-2 0-1
A
\J
-
\
\0-1 sec \
V
>y
1 sec N . 3 sec
Ns^
>^
25
i
30 sec
^^^>
^"^^^^
i ^ —
50
^ ^
^^^^
10 sec
~*T
75
100
Distance (urn)
I
125
150
Fig. 8. The diffusion of thymidine from a plane source kept at constant concentration
into a semi-infinite space. Concentration (c), expressed as a fraction of the concentration at the source (c,), has been plotted versus distance at different diffusion times.
Table 6. Calculated effect of additional filter on total
flow of substance
Flow through second filter
Substance
Thymidine
Trypan blue
Protamine sulphate
Albumin
Blue dextran
Polio virus
T2-phage
1-2
10
0-8
0-5
0-3
0-3
0-2
The table lists the total amount which at time tx has flowed through a cross-sectional area
of 500 x 500/^m at distance 75 /*m and the same amount 12 h later at distance .100/tm. The
size of the spinal cord is taken as 500 x 500 x 100 /mi, the concentration of the inductor
in the spinal cord is assumed to be constant at 1 mg/cm3 or 25 ng/spinal cord.
The effect of interposing an additional filter on the flow of substances used in
the diffusion experiments has been calculated (Table 6) from tabulated values
for the integral (Crank, 1956). The flow, especially of the small molecular weight
substances, is very high.
Induction of kidney tubules in vitro
249
tn the case of a positively charged molecule, protamine sulphate, there was
considerable adsorption on the filter. It might be argued that this slows down
diffusion through the filter, since, if the equilibrium of the reaction
free protamine sulphate + filter ^protamine filter + sulphate
is strongly towards the right side, little protamine sulphate diffuses through the
filter until all available adsorption sites are occupied, which may take a long
time. The experiments with various protamine sulphate concentrations showed
that the absolute amount retained in the filter was concentration-dependent, but
that the relative amount was constant, except at the lowest and highest concentration. Furthermore, diffusion was not substantially affected. But, in view
of the unknown nature of the active compound, adsorption on the filter cannot
yet be completely ruled out.
Until some clue is obtained to the way in which morphogenetic 'information'
is conveyed, conclusions about the mechanism of their transport will have to
wait. In experiments dealing with primary induction, differentiation has been
triggered by a variety of factors ranging from small inorganic ions (Barth and
Barth, 1969) to proteins with a molecular weight of the order of 30000 (Tiedemann, 1968), whereas nothing is known about the factors transmitting the
inductive stimulus in kidney tubule formation. Our experiments on the actual
passage of molecules through Millipore filters included compounds of varying
molecular weight (up to very large particles), molecules with a definitely nonspherical shape, and, finally, highly charged molecules. For all these the rate of
transmission exceeded that of the inductor determining the tubule-forming
field by several orders of magnitude when measured in a biological model
system. Hence, we would suggest that our results exclude the possibility that
induction in this case is determined by long-range diffusion of a stable substance.
Rapid destruction of the inductor substance in the filter(s) and the tissues must
be considered. This would also be a potential mechanism for restricting the depth
of a field. If the breakdown of the inductor is a first-order reaction c = cQ2IIT,
where c0 is the concentration at time 0, c the concentration at time t, and T the
half-life of the molecule. If the production is sufficiently rapid to ensure that
there is no exhaustion of inductor molecules, even rapid destruction will have
little effect, since the gradient will increase as molecules are destroyed. In
practice, production would probably be the limiting step in case of rapid firstorder breakdown. The main effect would be to limit the depth of the field and
not so much to increase the transmission time. A similar line of reasoning also
applies to the effect of adsorption on the filter. In several developing systems
this distance has been estimated to be of the order of 50-100 cells (Wolpert,
1969), and in transfilter experiments with spinal cord and metanephrogenic
mesenchyme the hypothetical substance is transmitted over a distance of
60-70 /an (Grobstein, 1957). In the spinal cord-metanephric mesenchyme
model system the depth of the inductive field exceeds 200 /.cm (Saxen & Saksela,
250
S. NORDLING AND OTHERS
1971). Although the possibility of breakdown cannot yet be completely ruled
out, we feel that mechanisms other than free diffusion and rapid, uniform
breakdown of the active compounds should be explored.
If long-range diffusion cannot explain the transmission of morphogenetic
messages, other modes of intercellular communication should be considered.
Interaction through cell contacts was already mentioned, and has, in fact, been
demonstrated to occur in certain model systems (Furshpan & Potter, 1968;
Loewenstein, 1968). Thus the lengthy transmission time observed in our experiments may be explained by relatively slow, active growth into the filter of
cytoplasmic processes seeking for contacts. Cytoplasmic material can, indeed, be
demonstrated in the relatively large pores of our filters. Further characterization
of this material and its accumulation might yield valuable information of the
carriers of the inductive messages.
The suggestion that actual cytoplasmic processes or materials from the cell
periphery are responsible for the transmission induction is still incompatible
with the findings of Grobstein & Dalton (1957) referred to in the Introduction.
In their filters, which had an average pore size of 0-1 jum, practically no material
was detected, but nevertheless a weak inductive effect crossed the membrane.
Our preliminary experiments, in which we employed the same filter material,
have shown short-range penetration of cell processes into the pores, but we
have neither been able to demonstrate such processes in the middle of the filter
nor to obtain tubule induction. In view of the previous observations on the
definitely restrictive conditions for induction (Introduction), the results presented here and our preliminary observations, the question of whether cell
processes transmit induction should obviously be re-examined.
The skilful technical assistance of Miss Monica Schoultz, Miss Ann-Kristin Thors and
Mrs Anja Tuomi is gratefully acknowledged. We wish to thank Dr S. Salminen, Mr A.
Ekman, Mr H. Laine and Dr M. Kekki for valuable suggestions and comments concerning
the diffusion experiments. The investigation has been aided by grants from the Sigrid Juselius
Foundation and the National Research Council for Medical Sciences.
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{Manuscript received 3 February 1971)