DEVELOPMENTAL

145,266-276 (1991)

BIOLOGY

Quantitative Effects of Laminin Concentration on Neurite Outgrowth in Vitro H. M. BUETTNER~.~ Department

of

AND

R. N.

PITTMAN

Pharmacology, University of Pennsylvania School of Medicine, Philadelphia,

Pennsylvania 19104-6084

Accepted February 8, 1991 Recent studies indicate that mediation of neurite outgrowth by the glycoprotein laminin may be a significant factor in the outgrowth of neurites to their targets during embryogenesis. To further characterize the possible role of this extracellular matrix molecule during development, we have systematically measured several features of outgrowth by neonatal rat sympathetic neurons on different concentrations of laminin. Individual neurons, obtained by mechanical dissociation of superior cervical ganglia (SCG), were cultured at low density on laminin substrates ranging from 0.01 to 1.0 rg/cm*. Outgrowth characteristics were subsequently analyzed for noninteracting cells in both fixed and live cultures Data obtained from neurons fixed after 11 hr of culture showed approximately twofold increases in neurite initiation and outgrowth, and a twofold decrease in branching for a corresponding lOO-fold increase in adsorbed laminin concentration. In time-lapse videomicroscopy observations, the root-mean square speed of growth cone movement increased from 60 to 90 pm/hr over the same range in concentration, while the persistence time remained constant at 0.10 hr. In general, neurite outgrowth parameters were relatively insensitive to changes in laminin concentration, supporting the idea that laminin is a permissive rather than an “instructive” substrate during development. Data obtained from fixed cultures were examined in terms of probability models to suggest possible mechanisms contributing to the dose-dependent effects observed. 0 1991 Academic press, IIIC.

strate (Hammarback and Letourneau, 1986). In the latter two of these situations, outgrowth is oriented by the edge of the laminin, i.e., a step gradient in concentration, suggesting that the in vitro guidance of neurite outgrowth by laminin depends upon at least two stages of growth: (1) extension across uniform concentrations of laminin, and (2) extension across or deflection at the boundary of the second substrate. This paper represents a preliminary investigation of the first of these two steps for rat sympathetic neurons grown on laminin densities ranging from 0.01 to 1.0 pg/cm2. The results reported below focus on a variety of morphological aspects of the developing neuron in vitro. To facilitate inspection of a large number of characteristics, data were taken primarily from cultures that were fixed after a period of growth. However, videomicroscopy of growing neurites was used to estimate dynamic growth parameters and to compare with conclusions based on the data from fixed cultures. For the sake of organization, results are divided into two sections representing, respectively, the cell body and the neurite of the developing neuron. Where possible, data have been generalized in terms of statistical models to aid in interpretation.

INTRODUCTION

Extracellular matrix cues are believed to help guide growing neurites to their targets in the developing embryo. Attempts to pinpoint specific molecules and their contributions to the guidance process have recently focused considerable attention on the glycoprotein laminin, a major constituent of the pathways over which neurites develop (Rogers et ab, 1986; Riggott and Moody, 1987; Letourneau et ab, 1988). Early studies by Rogers et al. (1983) and Davis et al. (1985) demonstrated a dose-dependent response of many outgrowth characteristics, such as the number of neurites per neuron and the length of outgrowth, to uniform concentrations of laminin. To see whether this differential response to laminin concentration could provide directional guidance to the growing neurite, several subsequent studies have investigated the response to more complex distributions of laminin. Although gentle, continuous gradients of laminin at near maximal neurite-promoting activity levels failed to orient neurite outgrowth (McKenna and Raper, 1988), neurites are capable of tracking both narrow lanes of laminin (Hammarback et al, 1985,1988; Gunderson, 1987) and discrete regions of laminin separated by thin strips or regions of a nonpermissive sub-

MATERIALS

Copyright All rights

$3.00

0 1991 by Academic Press, Inc. of reproduction in any form reserved.

METHODS

a. Cell Culture

1 Present address: Department of Chemical and Biochemical Engineering, P.O. Box 909, Rutgers University, Piscataway, NJ 08855-0909. ’ To whom correspondence should be addressed. OOIZ-1606191

AND

Laminin was coated onto the tissue culture surface by placing 0.5 ml of laminin solution, diluted to the appro266

BUETTNER

Neurite Outgrocoth on Law

AND PITTMAN

priate concentration in Hank’s balanced salt solution, into each well (2 cm2 bottom surface area) of a 24-well culture chamber (Nunc) and allowing the laminin to adsorb to the surface of the well at room temperature for 2 hr. The solution was then removed and each well washed with 0.5 ml of PBS. A second wash of 0.5 ml of PBS was placed in each well and removed 4 hr later, immediately prior to plating the neurons for culture. Neurons from the SCGs3 of l-day-old neonatal rats were mechanically dissociated and plated in serum-free, L15C0, medium (Pittman, 1985) at low density in the laminin-coated wells. For static measurements, following an 11-hr culture period at 37°C in 5% CO,, neurons were fixed by gentle replacement of the culture medium with PBS containing 2.5% gluteraldehyde. Dynamic neurite outgrowth data were recorded during Hours 2-18 following plating.

b. Laminin

Adsorption

The amount of laminin adsorbed to the tissue culture plastic on which neurites were grown was quantitated by incorporating tracer amounts of [3H]laminin into the laminin solution initially applied to the wells of the tissue culture chamber. Laminin was tritiated using NaBH, according to the method of Daule and Karlin (1978). The radioactivity washed from the wells prior to plating the neurons was quantitated using a scintillation counter and compared to the amount in the original solution to find the fraction adsorbed. The radioactivity present in the medium when outgrowth was halted was also measured to determine the fraction of adsorbed laminin that leached off during the culture period. The surface density of laminin adsorbed was calculated by dividing the total amount of laminin added to each well by the total surface area to which the laminin was exposed, including both the bottom and the side wall of the chamber. For the case of an approximately cylindrical well, the surface area is given by rr2 + 27rrh, where r is the radius of the well and h is the height of the fluid volume in the well. The fluid height, h, is equal to the fluid volume divided by the cross-sectional area, 7rr2. The values of r and h in this case were equal to 0.80 and 0.25 cm, respectively.

267

ixin

camera, an IBM XT computer, a Hi-pad digitizing tablet, and a commercially available digitizing interface (Southern Micro Instruments, Atlanta, GA). The microscope image was projected (20X objective, 5X projection lens) through the camera onto the computer monitor and then hand-traced on the monitor with the aid of the digitizing tablet. Hard copies of these tracings were printed and transferred to an Apple Macintosh II where morphometry was analyzed with a BASIC program developed by the authors. Live cultures. Dynamic characteristics of outgrowth were measured from time-lapse videotapes of growing neurites recorded at 1 frame/see on a JVC BR 9OOOU time-lapse videocassette recorder. Images were projected to the video recorder using the same microscope and camera system described above for fixed cultures. To obtain the trajectory of a neurite tip, a given neurite was followed for a minimum of 90 min. At the higher concentrations of laminin, this required several field shifts through mechanical adjustment of the microscope stage, while at lower concentrations, the neurite tip typically remained in the same field of view for the entire period of filming. The trajectory of each neurite was plotted by digitizing video frames at 5 min intervals with a MaeVision digitizer (Koala) connected to an Apple Macintosh II and then measuring the x-14 coordinate of the tip on each of the digitized images using the Image morphometry program (Wayne Rasband, National Institutes of Health). Statistics. The distribution of a given measurement around its mean was evaluated using either the x2 test or the Kolmogorov-Smirnov test for goodness-of-fit to a hypothesized probability distribution (see Press et al., 1986). The former was applied to discrete distributions, while the latter was used to test continuous distributions. In both tests, goodness-of-fit is indicated by a parameter, P, which ranges in value from 0 to 1 and indicates the probability that the measured distribution matches the hypothesized one. The higher the value of P, the better the agreement. The actual value of P is reported below for the measurements in question; however, a value of P = 0.1 is typically accepted as a reasonable match between the model and the data. RESULTS

c. Aylalysis Fixed cultures. Morphological characteristics were analyzed from digitized images of fixed neurons. Images were obtained using a computer-based system consisting of a Nikon Diaphot microscope, a Dage newvicon

3 Abbreviations cal ganglion.

used: rms,

root-mean

square:

SCG,

superior

cervi-

The fraction of laminin adsorbed to the tissue culture plastic was essentially constant at all concentrations of applied laminin, the actual fraction ranging between 0.64 and 0.73, as shown in Table 1. The resulting surface density of laminin ranged from 0.011 to 1.00 pg/cm’. Ten percent of the adsorbed laminin desorbed from the surface during the 11-hr culture period, except at the highest concentration of laminin, where desorption was slightly higher at 15%.

268

DEVELOPMENTAL

LAMININ Applied laminin

ADSORPTION

TABLE 1 TO TISSUE CULTURE

Fraction adsorbed prior to culture

COnC.

(&ml) 0.10

Resulting laminin cont.

(&cm’)

BIOLOGY

SURFACE Fraction desorbed during culture

0.73 0.64

0.011

0.066

0.034

3.30

0.68 0.65

0.32

10.00

0.67

1.00

0.110 0.092 0.091 0.150

0.33

1.00

0.10

Cell Body a. Initiation sites. The average number of sites at which neurites (projections B 1.5 times the cell body diameter) initiated from the cell body increased with increasing laminin concentration, averaging 1.2 at the three concentrations clustered at the low end of the scale, and increasing to 1.9 at the highest concentration of 1.0 pg/cm2. Table 2 summarizes the distribution of initiation sites at the different concentrations of laminin. Of the 405 cells examined, none displayed more than three established primary neurites. The majority of the cells observed at each of the four lowest concentrations (>65%) had a single neurite projecting from the cell body. In contrast, 51% of the cells at the highest concentration of laminin were bipolar. Fewer than 21% exhibited three neurites at any concentration. An excellent fit to the data at the four lowest concentrations was obtained using a truncated Poisson distribution4 (see: Olkin ef al., 1980), given by p(n) = X”/(n!(d

- l)),

n=l,2,3...,

(1)

where v is the number of neurites initiated, h is related to the average number initiated through the relationship n a”g = Xd/(d

- 1).

and p(n) is the fraction of neurons expected to initiate n neurit,es (Fig. 1). However, this model becomes inadequate at the highest concentration of laminin. Probability values are given in Table 2. b. Angles of initiation. The average angle between neurites projecting from a cell body was approximately 360” divided by the number of neurites on the cell body.

4 A truncated Poisson distribution differs from the standard Poisson distribution in that the value 71 = 0 cannot occur in the former. In this case, since only cells with neurites were counted and cells with zero neurites were excluded, the truncated distribution is the appropriate form to use. The same assumptions of rare, independent, and equally probable events apply in both cases.

VOLUME

145. 1991

Actual values for n = 2 and r~ = 3 were 174.0 & 9.4 and 120.0 ? 8.7, respectively (mean t SE; sample numbers are given in Table 2). No significant effect of laminin concentration on the initiation angle was observed. c. Cell body size. Cell body size, as measured by the cell perimeter, was not significantly affected by laminin concentration (Fig. 2). Neurons with two neurites had a slight but significant increase in cell perimeter over those with only one neurite at 0.034, 0.10, and 0.32 pg/ cm’. This may simply reflect the slight “flattening” of the cell body around the area where the neurite exits the cell body. Overall, the cell perimeter ranged between 30 and 40 pm, yielding an “equivalent diameter” of 10 to 13 pm. Neurite a. Extensicm. The effect of laminin concentration on neurite extension was examined with respect to its effect on the (a) extent, (b) rate, and (c) directionality of neurite outgrowth. The extent of neurite outgrowth was characterized in terms of: (1) the total length of neurite outgrowth per cell, and (2) the length of neurite growing out from a single initiation site (referred to as an arbor). Both quantities followed qualitatively similar trends with changes in laminin concentration, increasing in length as the concentration increased to 0.32 pug/cm2 and then leveling off (Fig. 3). Further examination of the length distributions, however, suggests that the arbor length is a more fundamental characteristic than is the total length per cell. As shown in Fig. 4, the distribution of individual arbor lengths is described well by the gamma probability distribution, defined as p(L) = (urLrpleevL)/(r where

u is the average length divided

- l)!,

(2)

by the variance

Y = L,,,/& and T is the square of the average length variance

divided by the

7” = (L,,,)W. P values are given in Table 3. By contrast, the distribution of total length per cell exhibited a lack of smoothness and a multimodality that is characteristic of mixed distributions, from which little can usually be inferred (Fig. 5). The rate and directionality of neurite outgrowth were assessed by measuring the root-mean square speed and directional persistence time of growth cone movement as defined by Dunn (1983). These were estimated in two ways: (1) by tracking the position of a growth cone at 5-min intervals and analyzing the shape of the resulting

BUETTNER

AND PITTMAN

NUMBER No. of neurons

Laminin cone. (pg/cm2)

’ Probability

iI = 1

with

Poisson

269

orI Lu ,I! iti in

TABLE 2 OF NEURITES PER NEURON

v neurites

,1 = 2

of fit to truncated

Neu rite 014 tqrowth

r, = 3

Netmites/ neuron t S.D.

No. of neurons

Poisson parameter x

Pr0h. of Iit” 1’

distribution.

trajectory, and (2) by analyzing the shape of the neurite present after an 11-hr period of growth, under the assumption that the neurite represented an accurate history of growth cone movement. The “effective” speed and persistence time measured in the second way (Fig. 6) were up to l-2 orders of magnitude lower and higher, respectively, than the values measured from actual growth cone trajectories (Fig. ‘7), as seen in Table 4. There are several possible reasons for this difference. (1) Measurements on fixed cultures assumed the same growth period of 10 hr, preceded by a precise 1-hr period for cells to attach and initiate neurites. In reality, neurons can continue to initiate neurites for several hours after being plated. If a significant fraction of neurites are initiated after 1 hr, the rate of growth would be underestimated. (2) Root-mean square speed characterizes the total distance moved by the growth cone rather than its net progress in a given direction, so that retraction as well as extension is counted when tracking live grouth cones but would not be detected for fixed cells.

(3) A considerable straightening of neurites often occurs over time in culture, particularly at the high concentrations of laminin, leading to a much less tortuous appearance of the neurite and, therefore, extremely high apparent values of the persistence time when calculated for fixed neurites. Thus, evaluation of outgrowth rates and persistence times from static cultures does not provide an order of magnitude estimate under the conditions examined here. For the sake of comparison, two other measures that have been previously employed to characterize outgrowth rate and directionality are listed in Table 4. The net rate, commonly used to estimate the rate of outgrowth, is defined as the straight-line distance between the final and initial positions of the growth cone divided by the total time of observation. The fractal dimension, as suggested by Katz (1985b) and Katz and George (1985), represents a measure of the tortuosity of the growth path; values

40 Laminin Cone Wcm2)

t

A n 0 0 0

IOO 032 010 0034 0011

0.01 0

1

Number

2

of Primary

3

Neurites

4

per Cell

FIG. 1. Distribution of primary neurites per cell. The fraction of cells having 1,2, or 3 primary neurites is shown for each of the laminin concentrations tested. The solid lines represent the number predicted by a Poisson probability distribution. Excellent agreement is obtained for all but the highest concentration of laminin (1.0 &cm’).

Laminin

01

Concentration

10

(lg/cm*

100

)

FIG. 2. Effect of laminin concentration on cell body size. Cell hody size is not significantly affected by laminin concentration. A slight but significant increase in cell perimeter is seen for neuruns with two neurites relative to those with only one. The typical cell perimeter was in the range of 30 to 40 pm, with a corresponding “equivalent diarnc>ter” of 10 to 13 wrn. Data represent means + SE.

270

DEVELOPMENTALBIOLOGY 600

V0~~~~145.1991

ity that a given neurite will contain n branches. The fact that negative binomial distributions often arise in connection with “compound” random phenomena, i.e., phenomena that are themselves the result of several more fundamental random events, suggested looking for a more simply distributed parameter. A more basic description of branching was found in the distance between branch points, as approximated by the distance from the cell body to the first branch point and the distance between the first and second branch points, shown in Table 6 and Fig. 10. No significant difference was found between these two distances, which represented 80-90s of the branch segment lengths at any given laminin concentration. The distribution of lengths matched well to an exponential distribution, providing one possible explanation for the negative binomial distribution of branch point numbers observed above. The exponential distribution is written as

(3)

p(L) = WoL,

Laminin

Concentration

(pg/cm*)

FIG. 3. Effect of laminin concentration on the extent of neurite outgrowth. (a) Total outgrowth per cell increases with concentration up to 0.32 kg/cm’ then remains constant at 450 wrn (11 hr incubation). (b) The increase in the number of initiation sites with increasing concentration results in a decrease in the length of outgrowth per initiation site (neurite length per arbor) at 1.00 pg/cm’. Data represent the means f SE. The number of neurons, 11, observed at each concentration is listed in Table 2.

vary between 1 for a perfectly straight path and 2 for a perfectly random path. b. Branching. Branching of neurites changed by a factor of 2 over the range of laminin concentrations examined, decreasing from an average of 1.24 branch points per primary neurite at 0.011 pug/cm’ to 0.61 at 1.00 pg/ cm2 (Fig. 8). The distribution of branch points per neurite is shown in Fig. 9. The distributions at the three lowest concentrations were not significantly different (P > 0.32), and the data at all concentrations were fit with a high level of significance by a negative binomial probability distribution, indicated by the solid line in Fig. 9 (see also Table 5). The negative binomial distribution is defined by p(n) = (r(k + n)q”(l

- q)“)/r(n

+ l)I(k),

n Z 0,

where p(n) is the probability that an event occurs n times, k and q are parameters related to the mean nsvg and the standard deviation (J by and k = (n,,,)“/(g - navg) q = navg/g, and P is the gamma function. In this case, n is the number of branch points per neurite, and p(n) is the probabil-

n > 0,

(3)

where, for our purposes, L is the length of a branch segment, 8 is the number of branch points per unit length, and p(n) is the probability that a branch segment will be of length L. A well-known property of the exponential distribution is that it represents the waiting time between successive Poisson events. Thus, if the distribution of waiting times between successive occurrences of an event is given by p(t) = uepYt, where u is the probability per unit time of occurrence and t is time, then the probability that n events occur in time t is given by

02

00

I I

I, 0

I,

200

I

400 Neurite

600 Length

/

800

1000

I

1200

(pm)

FIG. 4. Cumulative distribution of outgrowth length per initiation site. Each data point represents the fraction of initiation sites having total outgrowth of less than or equal to the corresponding length on the horizontal axis. For example, 80% of the initiation sites at 0.011 @g/cm2 exhibited less than 200 pm of outgrowth. The solid curves represent the theoretical gamma distributions that best fit the data.

BUETTNER

Nazi rite On tgrowtli

AND PITTMAN

TABLE OF NEURITE

TOTAL LENGTH

3 PER INITIATION

Laminin

Avg. SE

(pm)

117.44

11.46

?I

105

Max Min

(gm) (Frn)

559.61 22.15

P

0.10

168.52 15.24

227.93

89 786.67

105 886.67

a Probability

of fit to gamma

p(n)

=

e-“t(

(&cm*) 0.32

24.20 0.400

0.719

1.00

352.45 24.45

17.82

18.82

0.554

SITE

concentration

0.034

0.011

271

on Ltr w in in

230.38 17.60

115

118

1144.71

879.22

18.33 0.279

12.88 0.615

distribution.

n = 0, 1, 2, . . .

ut)“h!,

DISCUSSION

By analogy, if the distribution of lengths between branch points is given by Eq. (3), then the expected probability of n branches occurring in a length L is given by the Poisson distribution p(n) = e-“L(BL)“/n!

n = 0, 1, 2, . . .

In short, an exponential distribution of distances between branch points suggests that branching is a Poisson event with a constant but small probability of occurrence at any point along a neurite. Thus, our results are consistent with the hypothesis that branching is a Poisson event whose probability increases as the laminin concentration decreases.

In this study, we have systematically measured a number of parameters reflecting the effect of laminin concentration on neurite outgrowth morphology. At the simplest level, our results indicate an increased tendency for neurite initiation and extension, and a decreased tendency for branching as the laminin concentration increases. Thus, at higher concentrations, one sees more and longer primary neurites with a less elaborate structure than at lower concentrations. These results are consistent with those previously noted by Rogers et al. (1983) for chick sympathetic and sensory neurons growing on laminin. In analyzing neurite initiation, elongation, and branching characteristics, we looked not only at the average values of the parameters measured, but also at their distributions around the mean, which were then fit to theoretical probability distributions where possible. Katz (1985a) has presented similar raw distributions of initiation and branching parameters for frog embryo neurons growing on acidrinsed glass substrates, but we were unsuccessful in matching these published distributions to any of the common theoretical ones (eg., normal, exponential, gamma, binomial) that fit our own data. Whether this represents a true disparity in behavior or the result of

lb) JllhA2

4

5

8

Neurite Length (x100 pm)

10

12

14

2

4

6

8

10

WI

12

Neurite Length (x100 pm)

FIG. 5. Representative histograms of outgrowth length. Outgrowth per initiation site at (a) 1.0 &cm2 and (b) 0.33 &cm’; total outgrowth per cell at (c) 1.0 Kg/cm’ and (d) 0.33 &cm2. The distribution of individual arbor lengths (a, b) matches a gamma distribution; the distribution of total length per cell (c, d) is more complex and cannot be adequately described by a single probability distribution.

JO

02

Laminin

04

Cone

06

08

(pg/cmz)

10

”

00

02

Laminin

FIG. 6. Estimates of dynamic outgrowth parameters morphometry data. (a) rms speed and (b) directional Data represent means k SE.

04

Cone

06

08

10

(pg/cm2)

based on static persistence time.

DEVELOPMENTAL

00

02

Laminin

04

Cone

06

08

10

(pgicm2)

FIG. 7. Effect of laminin rameters ia) rms speed, and ments were obtained from rites. Data represent means

i 005”~‘. 00

BIOLOGY

Ibl 02

04

Laminin

Cone

““j 06 08

10

(pg/cm2)

concentration on dynamic outgrowth pa(b) directional persistence time. Measurevideotaped observations of growing neuk SE.

some more “selective” procedure on our part is not clear. Measurements such as this obtained from fixed cultures are useful in suggesting possible behavior underlying the outgrowth process, as discussed below. However, we have also shown, through comparison of morphometry data with videomicroscopy observations of growing neurites, that the “static” data obtained from fixed cultures are not necessarily an accurate representation of the behavior observed in living cultures. For example, while static data may be useful for comparing total outgrowth in a given period of time, these data do not give an accurate picture of the rate at which growth cones move or the tortuosity of their trajectory of movement. In addition, although it is generally stated that once initiated, neurites grow in a straight line unless the growth cone encounters an obstacle (physical or molecular), it is clear from calculations of persistence times and fractal dimensions of actively growing neurites that neurite outgrowth is far from being in a straight line. Once initiated, a neurite typically grows in the general direction of initial outgrowth; however, growth cone movement encompasses a much larger area than would be encountered if outgrowth occurred along a straight line. This

RMS

Method Video

Fixed

cultures

Laminin cont. b4dcm2) 0.10 0.32 1.00 0.011 0.034 0.10 0.32 1 .oo

RMS speed s k SE (pm/hi-) 61.40 85.89 92.27 7.12 10.31 14.45 22.57 17.62

k * k -+ k t f i

5.65 5.66 8.42 0.46 0.68 0.97 0.96 1.28

VOLUME

behavior of the growth cone could be useful during development to increase the number of cellular contacts during pathfinding and target recognition. The main purpose of this study was to pinpoint key areas for future investigations of neurite outgrowth mechanisms and the effect that laminin has on these. As a starting point, we chose to examine limits in the characteristic morphometry of neurons grown on laminin as possible indications of intrinsic or extrinsic constraints on the outgrowth capacity of the cell. One such limit was observed in the length of neurite outgrowth, which exhibited a plateau at the two highest concentrations of laminin. Since outgrowth requires the transport of lipids and proteins from the cell body to the neurite tip, an attractive hypothesis is that the cells are unable to produce, transport, or assemble the necessary material for outgrowth more quickly than they do when axons are growing on 0.32 or 1.0 yg/cm’ of laminin. Further support for this notion is provided by the fact that the rate of outgrowth, reflected in the rms speed of growth cone movement, exhibited a similar plateau. The length of neurite segment between branch points exhibited the same qualitative behavior as the total length, increasing steadily as the concentration increased from 0.01 to 0.33 pg/cm’ and then leveling off above that. An additional effect of delayed initiation on lower concentrations of laminin is also possible. More mechanistic interpretations are possible if we consider the probability models suggested by the data. Although these models characterize aspects of fixed neuronal morphology, they are easily cast in terms of dpnamic events contributing to this morphology by invoking some of the physical aspects of the system. In the case of neurite initiation, described by a Poisson distribution of the number of neurites per neuron, if we assume that cell bodies have approximately the same circumference, L, then we can define a new parameter

TABLE 4 SPEED AND PERSISTENCE Persistence time T k SE (hr) 0.07 0.10 0.10 5.80 5.36 11.34 13.65 22.84

145, 1991

* + F f k k ?I k

0.01 0.08 0.02 0.83 0.51 1.60 0.94 5.70

TIME

Net rate k SE (m/hr) 21.72 -+ 4.04 32.30 + 2.90 40.87 2 5.34

No. of growth cones 71 10 17 13 105 84 101 110 115

Fractal dimension 1.32 L 0.05 1.34 t 0.07 1.25 _t 0.05

278

BUETTNERANDPITTMAN

I,/ ,L

1 0 oi Laminin

FIG. 8. Effect

of laminin

01

10

Concentration

1

100

(pg/cm2)

concentration

on neurite

branching.

/ 1\

p = )l~,,,&/L

141

representing the probability of initiation per unit length of cell body circumference. If we also assume, for the sake of mathematical simplicity, that the number of neurites per neuron is well described by a standard Poisson distribution when the fraction of neurons without neurites is included, then a particularly simple relationship is obtained5 between the events at the cell perimeter and neurite initiation

p(n) = e?ypLy/?1!,

)l = 0, 1, 2, .

.

This relationship gives rise to the following hypotheses, based on the characteristics of a Poisson-distributed phenomenon: (1) The number of neurites initiated by any cell body is small (rare event). (2) Initiation of a neurite at any point along the perimeter is unaffected by initiation at any other point (independence of events). (3) Initiation is equally likely at any point around the cell body (equal probability of events). Thus, our probability model suggests a scenario in which the potential for initiation exists uniformly around the cell body but is expressed at only a few random sites. Consistent with this idea, several intracellular or cell surface molecules/features have been reported whose redistribution to a few random sites from an initially uniform distribution correlates with the subsequent initiation of neurites there. These features include protrusive activity (Wessells et'ab, 1978; Collins, 1978), focal contacts, and the cytoskeletal protein vincu5 By substituting Eq. (4) into the expression for the standard Poisson distribution, p(v) = Q*~~(rQn/r/! ?L = 0, 1, 2, A similar but more complicated expression would be obtained by substituting Eq. (4) into Eq. (1).

lin (Halegoua, 1987), suggesting involvement of the actin cytoskeleton, which is probably linked to the cell surface integrin receptor for laminin (Buck and Horwitz, 198’7). All of these features exhibit an apparent continuum of distribution preceding initiation, in accord with the requirement of a uniform potential for initiation at any point around the cell body. Additionally, the site of initiation has been correlated with the appearance of a large center of microtubule polymerization into which smaller foci coalesce prior to initiation (Spiegelman et (II., 1979). In accord with the second hypothesis, that neurite initiation is an independent event, the angles of initiation that we measured were characterized by large standard deviations, indicating a broad variation in the distance separating initiation sites along the cell body perimeter. Effects of laminin concentration, which appear to be rather subtle, could presumably occur at a number of steps in the integrin receptor-mediated interaction. Recent results by Bixbg (1989) indicate that protein kinase C affects initiation on laminin, suggesting a possible regulatory step at the level of vinculin phosphorylation and the redistribution of focal contacts (Werth and Pastan, 1984; Halegoua, 1987). Another locus of intera,ction with laminin is the cell surface galactosyl transferase receptor. Enhancement or inhibition of galactosyl transferase interaction with laminin significantly increases or decreases the number of neurons with neurites, respectively (Begovac and Shur, 1990). The presence of a second receptor for laminin (galactosyl transferase or other molecule) introduces the possibility that the Poisson character of neurite initiation and the increase in the mean number

0

2 Number

4

of Branch

6

8

Points

FIG. 9. Representative fit of the negative binomial probability distribution to the number of branch points per neurite. The fits ohtaincd at the two highest concentrations (0.32 and 1.0 p&cm’; not shown) were similar in shape, but the curves were shifted to the left reflecting a lower average number of branch points per neurite.

274

DEVELOPMENTAL BIOLOGY

VOLUME 145, 1991

TABLE 5 NUMBER OF BRANCHES PER NEURITE Laminin concentration 0.011

0.034

N” (%,

N(%)

Number of branches 0 1 2

70 (60) 28(24) 13 (11)

3

4 (3)

4 5

2 (2)

6

7 Total No. neurites

1.00

0.32

N(s)

NC%)

N(S)

51(45) 37(33)

45 (42) 30(28)

40 (43)

12 (11)

14 (13) 11 (10)

31 (44) 23 (33) 10 (14)

19 (20) 21 (22) 8 (9)

1 (1) l(1)

113

3 (4)

2 (2) 2 (2) 2 (‘4

5 (5)

2 (3) l(l) -

117

Branches per neurites SE P

0.10

4 (4) 5 (4)

-

(&cm’)

1 (1) 2 (3)

-

107

-

94

70

1.24

1.22

1.15

1.08

0.61

0.13 0.66

0.15 0.28

0.13 0.52

0.14 0.41

0.08 0.58

’ Number of neurites. *Probability of fit to negative binomial distribution.

of neurites per neuron reflect separate influences from the two receptor systems. An increasing contribution from the second receptor with increasing laminin concentration could also help explain the lack of agreement with the Poisson model that we observed at the highest laminin concentration. The events of neurite extension leading to a gamma distribution of arbor lengths are somewhat more difficult to construe, owing to the complexity of the model. As with the negative binomial distribution noted above, the gamma distribution generally arises in connection with compound random events. An example, given by Olkin et al. (1980) involves a problem that is solved in r sequential and independent steps. If the length of time required to complete each step is exponentially distrib-

Laminin corm. (m/cm’) 0.011

37.33

0.032

44.18 61.32 74.02 73.88

0.10 0.32

1.00 a Probability

2 2.87 -+ 4.12 k 5.48 Z!I7.89 + 8.51

5 c E

m

Fraction of total branches present

P

0.80

0.662

96

0.84 0.85 0.84

66

0.89

0.280 0.520 0.413 0.585

Number of branches analyzed 109 97 104

of fit to exponential distribution

(x2 test).

“”

5 .-E 0”

TABLE 6 DISTANCE TO FIRST AND SECONDBRANCH POINTS Mean distance k SE b-4

uted with a parameter u, then the length of time needed to solve the complete problem follows a gamma distribution with parameters u and r, given by Eq. (2). An analogous interpretation can be constructed for neurite elongation by assuming that extension occurs through the sequential addition of small “building blocks” of material to the neurite. If the length of net neurite extension in a small time increment (one “building block”) is exponentially distributed, then the total length extended over the entire observation time will follow a gamma distribution. The assembly of both microtubules and the actin microfilaments, the two major compo-

80

-

70 60 -

Laminin

Concentration

(pg/cm*)

FIG. 10. Mean distance between branch points. The distance between branch points increased with increasing laminin concentrations corresponding to a decreased frequency of branching per unit neurite length.

nents of the neurite cytoskeleton, occurs through sequential addition of subunits (see Mitchison and Kirschner, 1988); polymerization of microtubules in particular exhibits a random growth rate consistent with this model (Sammak and Borisy, 1988; Schulze and Kirschner, 1988). Unfortunately, the large variances we measured relative to the mean yielded small values of r and u (indicating the addition of a small number of subunits, r, with a large mean length, l/v). Further investigation is required to determine whether our variances are artificially large due to a distribution of initiation times producing a wider range in arbor length, or whether the basic interpretation must be modified. Either intrinsic or extrinsic factors may be responsible for the Poisson distribution of distances between branch points. Previous studies indicate that the frequency of branching can be affected by internal factors such as the perturbation of normal cytoskeletal polymerization using taxol (Letourneau et aZ., 1986) and external factors such as the placement of a physical obstruction in the path of a growth cone that serves to loosen its attachment to the substrate on which it is moving (Wessells and Nuttall, 1978). In either case, the likelihood exists of a “triggering” event that is also Poisson in nature. One possible external mechanism involves the occurrence of a physical heterogeneity at the molecular level in the surface on which the neurite is growing, for example, a particularly dense or sparse concentration of laminin, or a micro-heterogeneity in the tissue-culture plastic. Since branch distance increases with laminin concentration, it is not likely that the point of branching coincides with aggregates of laminin, as these would appear at shorter distances with increasing concentration. Sparse regions, however, would occur less frequently as would heterogeneities in the plastic, since more of these would be covered by laminin; these would serve to loosen the growth cone attachment to the substrate. Another possibility is that the branching occurs in response to an intrinsic, structural irregularity occurring randomly within the growing neurite itself. Such irregularities are not unexpected in a polymerization process. More detailed information about the polymerization characteristics of the neurite cytoskeleton is needed to provide insight into the nature of such irregularities, however. Of course, neither possibility is mutually exclusive. The importance of measuring multiple characteristics at this stage and of doing follow up studies on live cells in culture is evident in our results. In the estimate of outgrowth length, we examined two characteristics: the total outgrowth per cell and the outgrowth per initiation site. While the outgrowth per initiation site displayed an increase with concentration as did total outgrowth at the lower concentrations of laminin, the plateau at the higher concentrations is absent for the

length of outgrowth per initiation site. This is due to a simultaneous increase in the number of initiation sites, which obscures the effect of the outgrowth rate. Similarly, the length between branch points conveys information that is not apparent in the number of branch points per neurite. One of the best examples of the need for measurements on dynamic cell behavior is provided by the comparison of outgrowth rates measured from both fixed and live cells. Values of the rms speed and persistence time differed by as much as two orders of magnitude for the two cases, refuting the notion t,hat the neurite observed in fixed culture is an accurate representation of the history of growth cone movement. In terms of neurite outgrowth in the developing nervous system, the results presented here indicate that: (1) growth cone movement encompasses a much larger area than would normally be contacted if outgrowth occurred along a straight line, and (2) while laminin concentration may have a significant effect on neurite outgrowth, the effect remains relatively small over wide ranges in concentration. Videomicroscopy data and calculations of persistence times clearly show that growth cones “sweep” through a much larger area than the rather straight path the neurite assumes. This could be a very important property of growth cones during development, allowing them to contact a wider range of substrates and cells during pathfinding and target recognition. It is somewhat surprising that only small changes in neurite outgrowth parameters occur with large changes in laminin concentration. For example, the rms speeds measured for neurites at the highest concentrations of laminin are only 1.5 times that at 30 to 100 times lower concentrations, while the persistence time, which measures the tortuosity of the outgrowth path, remains constant across all concentrations. The variations in initiation and branching frequencies are similarly small over the same concentration range; in addition, both initiation and branching fit the description of Poisson events, which are characterized as rare and random. Laminin is an ubiquitous molecule in the developmental environment. Because changes in neurite outgrowth parameters measured in the present study were relatively insensitive to changes in laminin concentration, it seems unlikely that laminin serves as an “information” containing molecule or as an “instructive” substrate during development (see also McKenna and Raper, 1988). Rather, laminin probably serves as a very good permissive substrate, leaving other transiently or more specifically expressed molecules to alter characteristics such as initiation and branching in more pronounced ways. This work was supported Whitaker foundation.

by a Biomedical

Research

Grant

from

the

276

DEVELOPMENTAL BIOLOGY REFERENCES

BEGOVAC, P. C., and SHUR, B. D. (1990). Cell surface galactosyltransferase mediates the initiation of neurite outgrowth from PC12 cells on Iaminin. J. Cell Biol. 110, 461-470. BIXBY, J. L. (1989). Protein kinase C is involved in laminin stimulation of neurite outgrowth. Neural 3,287-297. BUCK, C. A., and HORWITZ, A. F. (1987). Cell surface receptors for extracellular matrix molecules. A?~nu. Rev. Cell Bid. 3, 179-205. COLLINS, F. (1978). Axon initiation by ciliary neurons in culture. Dec. Bid.

65, 50-57.

DAULE, V. N., and KARLIN, A. (1978). Affinity labeling of one of two tu-neurotoxin binding sites in acetylcholine receptors from Torpedo Cd~fornica. Biochemistry 17, 2039-2045. DAVIS, G. E., MANTHORPE, M., and VARON, S. (1985). Parameters of neuritic growth from ciliary ganglion neurons in vitro: Influence of laminin, Schwannoma polyornithine-binding neurite promoting factor and ciliary neuronotrophic factor. Deu. Brain Res. 17, 75-84. DUNN, G. A. (1983). Characterizing a kinesis response: Time averaged measures of cell speed and directional persistence. Agents Actiono [Suppl] 12, 14-33. GUNDERSON, R. W. (1987). Response of sensory neurites and growth cones to patterned substrata of Iaminin and fibronectin j?~ 7rit~~. Deu. Bid 121, 423-431. HALEGOUA, S. (1987). Changes in the phosphorylation and distribution of vinculin during nerve growth factor induced neurite outgrowth. Dev. Biol. 121, 97-104. HAMMARBACK, J. A., and LETOURNEAU, P. C. (1986). Neurite extension across regions of low cell-substratum adhesivity: implications for the guidepost hypothesis of axonal pathfinding. Deu. Bid. 117,655662. HAMMARBACK, J. A., MCCARTHY, J. B., PALM, S. L., FURCHT, L. T., and LETOURNEAU, P. C. (1988). Growth cone guidance by substratebound laminin pathways is correlated with neuron-to-pathway adhesivity. Dev. Bid. 126, 29-39. HAMMARBACK, J. A., PALM, S. L., FURCHT, L. T., and LETOURNEAU, P. C. (1985). Guidance of neurite outgrowth by pathways of substratum-adsorbed laminin. J. Neurosc. Res. 13,213-220. KATZ, M. J. (1985a). Axonal branch shapes, Brain Res. 361, 70-76. KATZ, M. J. (198513). How straight do axons grow? J Neurosci. 5,589595.

KATZ, M. J., and GEORGE, E. B. (1985). Fractals and the analysis of growth paths. Bull. Math. Bid. 47, 273-266. LETOURNEAU, P. C., MADSEN, A. M., PALM, S. L., and FURCHT, L. T.

VOLUME 145,199I

(1988). Imtnunoreactivity for Iaminin in the developing ventral longitudinal pathway of the brain. Dev. Bid. 125, 135-144. LETOURNEAU, P. C., SHATTUCK, T. A., and RESSLER, A. H. (1986). Branching of sensory and sympathetic neurites in vitro is inhibited by treatment with taxol. J. Neurosci. 6, 1912-1917. MCKENNA, M. P., and RAPER, J. A. (1988). Growth cone behavior on gradients of substratum bound laminin. Dev. Bid. 130, 232-236. MITCHISON, T., and KIRSCHNER, M. (1988). Cytoskeletal dynamics and nerve growth. Neuron 1, 761-772. OLKIN, I., GLESER, L. J., and DERMAN, C. (1980). “Probability Models and Applications.” Macmillan Co., New York, NY. PITTMAN, R. N. (1985). Release of plasminogen activator and a calcium-dependent metalloprotease from cultured sympathetic and sensory neurons. Dec. Bid 110, 91-101. PRESS, W. H., FLANNERY, B. P., TEUKOLSKY, S. A., and VE’ITERLING, W. T. (1986). “Numerical Recipes: The Art of Scientific Computing.” Curnl?ridoc L+riv. Press, Cambridge. RIGGOTT, M. J., and MOODY, S. A. (1987). Distribution of laminin and fibronertin along peripheral trigeminal axon pathways in the developing chick. .I Camp Ne~rol. 258, 580-596. ROGERS, S. L., EDSON, K. J., LETOURNEAU, P. C., and MCCLOON, S. C. (1986). Distribution of laminin in the developing peripheral nervous system of the chick. Del). Biol. 113, 429-435. ROGERS, S. L., LETOURNEAU, P. C., PALM, S. L., MCCARTHY, J., and FIJRCHT, L. T. (1983). Neurite extension by peripheral and central nervous system neurons in response to substratum-bound fibronectin and laminin. Dw. Bid 98, 212-220. SAMMAK, P. J., and BORISY, G. G. (1988). Direct observation of microtubule dynamics in living cells. Nofrrre 332, 724-726. SCHULZE, E. S., and KIRSCHNER, M. W. (1988). Direct observation of microtubule dynamics in living cells. Nuture 334, 356-359. SPIEGELMAN, B. M., LOPATA, M. A., and KIRSCHNER, M. W. (1979). Aggregation of microtubule initiation sites preceding neurite outgrowth in mouse neuroblastoma cells. Cell 16,253-263. WERTH, D. K., and PASTAN, I. (1984). Vinculin phosphorylation in response to calcium and phorbol esters in intact cells. J. Bid. Char. 259,5264-5270.

WESSELS, N. K., JOHNSON,S. R., and NUITALL, R. P. (1978). Axon initiation and growth cone regeneration in cultured motor neurons. Exi). Cdl Rw WESSELS,

117,

335-345.

N. K., and NUTTALL, R. P. (1978). Normal branching, induced branching, and steering of cultured parasympathetic motor neurons. E.rp. Ml Res. 115, 111-122.