Evidence is presented that (a) the growth cone of cultured neurons can exert mechanical tension, and (b) that the direction of advance of the growth cone is determined by the tension existing between it and the rest of the cell.
(a) The evidence that growth cones can pull comes from a vectorial analysis of the outlines of individually isolated sensory neurons. The angles formed in these outgrowths are very close to those of tension-generated networks anchored at their free ends and these values are restored shortly after an experimental displacement. The relative mechanical tension on each segment of an outgrowth can be calculated by standard methods and is found to decrease at each branch point. It appears to be correlated with the diameter of the fibre so that thicker fibres maintain more tension than thinner ones.
(b) The influence of tension on the direction of advance of the growth cone is shown by 2 kinds of experiment. If a growing neurite is pulled to one side with a microelectrode then the direction of its advance is changed immediately according to the new stress. If the mechanical tension on the growth cone of a neurite is released by amputation or displacement the growth cone is found to have a high probability of branching shortly afterwards.
The ability of the growth cone to exert tension is discussed in relation to evidence that microspikes have contractile properties and in terms of the distribution of microfilaments within the neurite. It is suggested that the exertion of tension by a growth cone could serve to guide the neurite along paths of high adhesivity both in vitro and in vivo.
Single neurons from embryonic sympathetic or sensory ganglia will extend long branching processes, called neurites, on a plain glass or plastic surface in culture medium supplemented with nerve growth factor (Levi-Montalcini & Angeletti, 1963). Such outgrowths resemble those in the embryo in many respects: in the form and movement of their terminal growth cones (Ludueña & Wessells, 1973; Bray, 1973); in the fine structure of their extended neurites (Bunge, 1973; Yamada, Spooner & Wessells, 1971); and in their ability to generate action potentials, and, eventually, to form synapses (Mains & Patterson, 1973; Rees & Bunge, 1974). Their overall form is strongly influenced by the conditions of culture and is not, in general, close to that of normal axons and dendrites. However, their isolated condition enables observations to be made and experiments to be performed that are not possible in a complex intact tissue. If these are interpreted with care then they can provide information on the intrinsic mechanisms by which the neuron can grow and form branches.
Cultures of sensory neurons were prepared from chick dorsal root ganglia by methods previously described (Shaw & Bray, 1977). Cells were plated at a sufficiently low density that single neurons could be easily found and no attempt was made to reduce the number of non-neuronal cells. The cells were grown either on plastic or on glass, and were examined in an inverted phase microscope either in the living state or after fixation and drying. In order to photograph the extensive outgrowths a low-magnification objective (3.2 ×) was necessary.
Experimental amputations and displacements were carried out on cells from 14-day embryos growing in medium with 10% foetal calf serum. Microelectrodes broken to a tip size of about 10μm were used to cut the fibres, while for displacements, glass needles with a smooth tip of about 5-10 μm were prepared in a Fonbrune microforge apparatus (Beaudouin, Paris).
Scanning electron microscopy
Cells were seeded onto small pieces of glass each 9 mm by about 5 mm (prepared from 9 × 22 mm coverslips) contained in a 3-cm plastic culture dish. After growth they were fixed by the introduction of warm Vaughn-Peters aldehyde (Vaughn & Peters, 1967) into the bottom of the dish with the removal of the upper layers. Fresh aldehyde at room temperature was introduced into the dish after approximately 30 and 60 min, and the culture finally transferred, still in fixative, into the refrigerator and left there for 2–3 days.
After this period the liquid in the culture dish was slowly and gently changed for water and then into increasing concentrations of acetone, up to 50%. At this point the small glass fragments were transferred without allowing them to dry into specially prepared metal clips which could hold 3 or 4 fragments with their culture surface exposed.
Up to 4 metal clips were then transferred to the chamber of a critical-point apparatus (Polaron, Watford) containing 50% acetone. The bathing fluid was changed in stages over a period of 2–3 h into dry (redistilled) acetone and dried by the procedure recommended by the manufacturers.
The dried specimens were mounted for inspection on glass slides. Suitable cells were located and photographed and their positions marked by scribing a circle around the cell with a Leitz specimen marker. The specimens were mounted on metal stubs and sputter-coated with gold-palladium and examined in a JEOL-35 scanning electron microscope. The previously identified cells were located by the position of the scribed circle and then examined at nominal magnifications from 1000 to 5000. Estimates of the mean diameter of a segment were made over an appreciable length (about 5 μm) and occasional protuberances and dilations were not included. A standard grid was photographed at each session on the microscope and used to calibrate the magnifications.
It must be emphasized that the diameters measured in this way will be inaccurate. They are subject to an unavoidable shrinkage during the dehydration and an increase in diameter due to the metal coating procedure. No attempt to correct for these has been made and the values used throughout this work were measured directly from the micrographs. In defence of this it may be said that the 2 errors are in the opposite sense and so will tend to cancel each other out and there is in any case no obvious way in which the amount of shrinkage could be measured. Furthermore, the relative diameters within a given cell, which are the most important values in the present context, will be less subject to error than the absolute ones.
The orientation, θ, of each terminal segment was taken as the angle between it and an arbitrary axis, measured at the point at which it joined the rest of the cell. It does not, therefore, take account of any curvature in the fibre. Polygons of forces were constructed (Fig. 2, p. 395) by drawing a unit vector for each terminal segment with the same orientation as that segment.
The resultant force, f, on an individual cell (Tables 1, 2, p. 396) was calculated on the assumption that each growth cone exerts an equal pull. The values of f, in growth cone units, are then given by the formula,
Branching angles ϕ, were measured by drawing tangents to the intersecting fibres at a branch point. If these fibres are called a, b, c, then ϕab is the angle less than 180° between a and b, and so on. The relationship between the tension on segment a and that on b is given by tension b = tension a (sin ϕac/sinϕbc).
An arbitrary value of 1.00 was assigned to a segment (usually one close to the centre of the network) and the values of adjoining segments calculated from the above formula. This procedure was applied iteratively until the whole network had been computed. The cell soma was, for these purposes, regarded as either an unbranched neurite or as a branch point. If junctions of more than 3 fibres were present it was necessary to assign an additional arbitrary value, again taken as 1.00.
The segmental tensions of each cell were calculated in this way and then, for convenience, normalized to give an average value of 1.18. This was chosen so that the average tension of the terminal segments, taken separately, was 100; the tension may, therefore, be said to be in growth cone units. The value f/N was calculated for each network and gave a useful measure of the closeness to equilibrium. It is equivalent to the gap in the polygon of forces expressed as a fraction of the total contour length. The maximum value of f/N is 10 and its minimum, at equilibrium, is 0.00.
Values of n that minimized this function for each branch point were calculated on a Nova 800 computer and then averaged. The same procedure was used for the diameters measured at branch points.
The general features of the growth of sensory neurons in culture are well established (Levi-Montalcini & Angeletti, 1963; Ludueña & Wessells, 1973). The outgrowths in the present study were very similar to those of individually isolated rat sympathetic neurons described before (Bray, 1973) except that the sensory neurons were larger. In other respects the 2 were morphologically indistinguishable. In both kinds of culture the extent of branching was very variable and it was possible to find, in the same dish, cells with 2 straight processes as well as those whose processes branched repeatedly.
Many of these outgrowths had a symmetrical appearance. This was seen in the orientation of primary neurites from the cell soma; the tendency of these primary neurites to support similar numbers of branches; and in the similar branching angles exhibited at different parts of an outgrowth (Fig. 1). Although at first sight this could indicate a cellular coordination in the formation of branches, upon closer examination it appears to be capable of a simpler interpretation, since the orientations of different segments of an outgrowth are frequently close to those expected if they were governed by mechanical tension exerted from the growth cones. This is obvious in bipolar neurons where the 2 processes almost always emerge from diametrically opposite positions on the soma, and accounts in a simple way for the absence of unipolar neurons.
An attempt was made to test this explanation quantitatively by statical methods. If a neuronal outgrowth is subject to the same forces as a system of ropes pulled at the free ends then it should meet the same conditions of equilibrium. If each force-generating element is represented by a vector then the whole set of vectors should form a closed polygon. These principles were applied to the outlines of a number of individual cells traced from photographs such as those in Fig. 1. The transition from a single neuron to a system of ropes under tension involved, understandably, a number of simplifying assumptions. In particular, it was assumed that the segments of the outgrowth are perfectly straight - so that the direction of pull is taken as the orientation of the terminal branch at its last junction with the cell - and that each growth cone is able to pull the cell to the same extent. When this was done then the cell could be represented by a set of vectors (Fig. 2). In many cells but not all these came close to forming a closed polygon. The results of an equivalent algebraic test carried out on 21 isolated networks are given in Table 1. These are expressed in terms of a factor, f /N, that represents the amount by which the network deviates from apparent equilibrium. This can take values between zero (at equilibrium) and 1. The cells of Fig. 2, for example, have f/N values of 0.05, 0.00 and 0.26 (the largest value observed in normal cultures). Fourteen of the 21 cells examined in this way were found to have f/N values of less than 0.10 and were therefore very close to apparent equilibrium (Table 1).
It was also obvious from observations of living cells that many departures from equilibrium were transient. If a fibre retracted or came into contact with another cell then the neuron would adjust to the change by movements of its outgrowth or the formation of new branches. This is illustrated in Table 2 where vectorial analysis has been carried out on a cell that was deliberately displaced from equilibrium by micromanipulation. The f/N value of the cell, which was 0.51 immediately after the operation, fell to less than o-io within 30 min. Presumably, cells that display large values of f/N spontaneously (Table 1), are in a similar way only transiently displaced from equilibrium - although this has not been directly tested.
If the outgrowths are assumed to be at tensional equilibrium then the relative tension on each segment - that is, unbranched length of neurite - may be calculated. The value on one segment is chosen arbitrarily and then the tension on the 2 adjoining segments calculated from the branching angles as described in Methods. In most networks this procedure may be applied iteratively to give a complete solution; in the occasional cell with a fourfold junction it is necessary to assign two arbitrary values before this can be achieved.
Each cell had an average value of 1.18 and values for 12 cells ranged around this with a standard deviation of 0.42 (134 values). The terminal segments, bearing growth cones, had a slightly lower tension which had an average value of 1.00 and a standard deviation of 0.26: the assumption of a constant unitary pull by each growth cone is clearly not precisely true. The f/N values for the networks calculated on the basis of these tensions are necessarily very close to zero. They are not exactly zero because of the slight curvature of some of the longer segments.
The calculated tensions were usually higher near the cell soma than peripherally. This was most pronounced in highly branched outgrowths (Fig. 3) and arises because the tension of a daughter segment is almost always lower than its parent branch. Examination of 39 branch points show that the 2 daughter branches have average tensions (taking larger and smaller values separately) that are 76% (±13%) and 53% (± 17%) the value of the parent branch. These correspond to bifurcation angles of 131°and 149° respectively. The relationship between the tension on a parent branch (T) and the tension on the 2 daughter branches (tt and t2) could be represented by a relationship of the form:
Measurement of diameters
In the previous study of sympathetic neurons it was observed that the diameters of the segments appeared to be uniform between branch points and to decrease with each bifurcation. It seemed possible that this decrease would occur in a regular manner and that it might reveal the principal constraints in branch formation. A convenient way to measure the diameters was found with scanning electron microscopy and images of convenient size and extent could be obtained in this way, as illustrated in Fig. 4. The fibres were found to be not perfectly regular in diameter and it was necessary to take the mean value over an appreciable length, and to ignore occasional protuberances and dilations. Values for each of the segments of 8 cells were measured; 7 of these cells were also used for the measurement of branching angles. Diameters ranged between 0.13 and 0.92 μm with an average value over 54 segments of 0.355 μm (S.D=0.037) (Table 3). The diameters decreased with each branch and the largest values were found adjacent to the soma. The diameters were used to test for a possible power function relating parent and daughter branch diametersjust as for their tensions. A range of values of ‘n’ in the formula (see Table 3) were tested and the best fit obtained with n = 1.73 ± 0.10 (S.E.).
The measurements made so far gave 2 values for each neuronal segment: its diameter and its relative tension. The possibility that these were related was next examined. Values for the segments of 7 isolated neurons were plotted against each other and the result is given in Fig. 5. A positive correlation between the 2 measurements exists with a correlation coefficient of 0.63 (95% confidence limits 0.46 to 0.79).
In a previous study of growing sympathetic neurons it was seen that the growth cones advanced in straight lines and adopted their direction immediately upon their formation by the division of an existing growth cone (Bray, 1973). Since it appeared from the above results that the direction taken was also that appropriate to tension equilibrium it seemed possible that the growth cone was in some way constrained to grow in the direction away from the tension on its neurite. Support for this was obtained by examining cells in which, either by spontaneous retraction or by deliberate mechanical intervention, the direction of pull was changed. Wherever this was examined the growth cone in question changed its direction of advance to accommodate the altered mechanical stress. An experiment in which a growing neurite was deliberately made to change its direction by displacement with a microelectrode is shown in Figs. 6 and 7. The growth cone altered its direction 3 times in this experiment: twice in response to a displacement and once when the microelectrode was removed.
Further evidence for tension guidance came from experiments in which the tension on a fibre was released. This could be done in 2 ways: either by cutting a fibre or by displacing it to such an extent that a considerable amount of free ‘slack’ was produced. Both kinds of manipulation were performed and in each situation the neurite showed a high probability of branching soon afterwards. Two typical time courses of a displacement are given in Figs. 8 and 9 while the consequence of an amputation is shown in Fig. 10. A summary of the experiments performed in a series of amputations and displacements is given in Table 4.
The displacements were less effective than the amputations in inducing a permanent branch and in a number of cases a small branch that was formed immediately after the operation later retracted. It was apparent that the displaced fibre could shorten and restore tension following the operation so that the growth cone might be without tension for only a short time period. By contrast, the amputation in almost every case (87 compared to 4% in an unoperated control - Table 3) produced a branch, provided the fibre survived the operation. The 2 daughter growth cones in such a situation usually grew in diametrically opposite directions while the cut stump retracted into a central region between the two (Fig. 10).
Growth cones can pull
Even a casual examination of these cultured neurons is sufficient to show that they are anchored principally at their ends and that their fibres are probably under mechanical stress. These features, which have been noted in a number of recent studies (Bray, 1973; Letourneau, 1975 a, b; Ludueña, 1973), are reflected in the straightness of the individual neuronal branches, which is soon restored after a mechanical displacement; the way in which the outgrowth will adjust itself to spontaneous changes such as the retraction of a branch; and in the retraction of neurites that have been cut.
These impressions are given quantitative support by the measurement of branching angles (Fig. 2; Table 1). If the cells are treated as though they were systems of ropes pulled by equal amounts at their free ends then, in the majority of the cells examined, statical methods show that this network is close to equilibrium. Further-more, if a cell is deliberately displaced then it will return to an equilibrium position within a short time (Table 2). This treatment involves a number of assumptions that are clearly not precisely true. The fibres are not perfectly straight; the growth cones are not all of the same size, and probably do not pull to the same extent; not every network will be at equilibrium at any given time. The fact that many cells, nevertheless, appear so close to apparent equilibrium with this simple treatment is therefore especially striking. Tension appears to be a major factor in producing the often symmetrical appearance of such networks.
Tension and diameter are related
The diameter of the branches of a number of individual neurons was measured by S.E.M. This technique was chosen because the fibres are below the size at which accurate measurements can be made by light microscopy and their considerable lateral extent would make conventional electron microscopy prohibitively timeconsuming. Even so, as discussed above (Methods), the diameters measured by S.E.M. are subject to several inaccuracies and can be regarded only as approximations to the true values.
The diameters measured were in the range of 0.9 down to 0.05 μm - values which are in the range of those measured in sectioned specimens. The diameter fell at each branch point so that, for a given cell, the largest values were found next to the soma. This decrease was not linear and, for every branch point measured, the sum of the daughter branches was greater than that of the parent (Table 3). The best fit to a power law for this decrease was given by an exponent of 1.73. It is noteworthy that the only other examination of dendritic diameters that has been made showed a three-half power law (Rail, 1959). The latter values were from silver-stained preparations of the dendritic trees of spinal motoneurons and the sesquiplicate relationship was explained in terms of the cable properties of the dendrites. A law of this kind allows electrical impedances to be matched within a ramifying dendritic tree (Rail, 1962).
It was possible to calculate the relative tensions on each segment of a cell provided that cell was assumed to be at equilibrium. These tensions were also found to be reduced at each branch point and the best fit to a power law for tensions had an exponent of 1.66-very close to that for diameters (1.73). A correlation between diameter and tension was also apparent from those cells in which both were measured on the same segments (Fig. 6). This is an indication that thicker fibres sustain a greater tension; and could arise, for example, if a thicker fibre produces a larger growth cone, which in turn, exerts a greater pull.
Another factor which should be mentioned here is the possibility that the neurites themselves are contractile and able to exert tension. There are suggestions that this might be so from the reactions of cut segments and from the ability of displaced segments to shorten in length. This would in no way remove the need for the growth cones to pull - since in order to advance they must generate a tension equal to that in the fibre - but it could have consequences for the diameter. In particular, if the data are taken at face value, the fact that the tension is linearly related to the diameter rather than to its square might be an indication that the contractile element is not evenly distributed within the cytoplasm. The most simple geometrical arrangement to give a linear relationship would be circumferential and it is noteworthy that a cortical layer of microfilaments has been seen in certain neuronal processes (Chang & Goldman, 1973).
Growth cones are guided by tension
The neurites in these cultures normally extend in straight lines. The growth cone progresses in the direction of the neurite that bears it even though the latter is neither rigid nor unmovable. When changes occur in the orientation of the neurite, for example when a sister fibre retracts, then the direction of advance of the growth cone is changed accordingly. A similar effect may be produced deliberately by pushing a neurite to one side. Provided that the operation is gentle enough to permit growth to continue the growth cone will change its direction almost immediately.
This is illustrated by the experiment shown in Figs. 6 and 7 in which a single neurite was twice pulled to one side and twice released. This growth cone was observed to undergo a total of 3 changes in direction in the course of these experiments, in each case adopting the path that was directly against the tension (Fig. 11).
More direct evidence comes from cells in which the tension has been deliberately released by manipulation. In a recent study of the effects of cutting neurites in culture it was observed, in passing, that when single fibres were cut they were likely to branch shortly afterwards (Shaw & Bray, 1977). In the present work it was found that in essentially every case in which an effective cut was made, the growth cone branched shortly afterwards (Fig. 10, Table 4).
Nor was it necessary to cut the fibre. The tension on the neurite could be slackened by pulling the fibre or by lifting an adjacent branch and, here again, it was found that the growth cone of such neurites was likely to branch soon afterwards. Displacement was less effective than amputation in this regard, and an appreciable proportion of the branches that were initially formed retracted in the subsequent 10–20 min. Presumably this was due to the fact that the tension on a neurite in such a situation is soon restored by the shortening of the neurite. Nevertheless, the frequency of branching after such a displacement is many times that of spontaneous branch formation (Table 4) and it seems difficult to avoid the conclusion that the release of tension has been directly responsible for the bifurcation of the growth cones. They have divided, it seems, in order to grow once again against a mechanical force - even if, as in the case of the amputated fragment, this must be provided by the sister growth cone (Fig. 11).
Relevance to nerve growth in vivo
It could be that the behaviour shown by the neurons in this study is unique to a situation in which adhesivity is a limiting factor. The increased opportunity for adhesion in vivo may make this mode of shape control of limited importance. Nevertheless, there are indications - for example, from the responses of axotomized nerves (Cajal, 1958) - that axons in the animal may be under mechanical stress. Moreover, there is no obvious reason why the ability of a growth cone to pull, which is manifest in tissue culture, should not be present in a developing tissue. Even though developing neurons do not have the taut guy-rope appearance of these cells in culture - and experience a greater lateral association with neighbouring cells - an effective tension could still be developed between the leading tip of the growth cone and the most adjacent region of the neurite.
Of what value would this be? One answer is that it would provide a simple way to guide the growth cone along paths of high adhesivity. It is widely thought that a major mechanism by which neurons in developing tissue are guided to their targets is by paths of preferential adhesion. Direct evidence that neurons in culture will select regions of high adhesivity has been given by Letourneau (1975 a) who has also shown the importance of adhesion in promoting the growth of neurites (Letourneau, 1975b). In principle there are many kinds of signal, ionic and other, that would enable the leading margin of the growth cone to select regions to which it can form a good attachment. But probably the simplest way would be to test the potential contacts mechanically: to apply ‘weight’ to them just as a mountaineer would test a hand-hold. If the adhesion is sufficient, then the growth cone can contract against it and advance in that direction. If the hold is not secure then the leading edge of the growth cone will be retracted.
Very little can be said about the mechanism of tension guidance except that it is likely to involve the filopodia of the growth cone. Letourneau (1975 b) showed that the initial detection of adhesive tracks on a culture substratum is made by filopodia and that this is followed by growth in that direction. Nakai (1960) observed that lateral filopodia are able to shorten and exert force. Albrecht-Buehler & Goldman (1976) showed that the filopodial-like extensions put out by fibroblasts as they settle onto a culture dish will contract after they have made contact with their surroundings; while Gustafson & Wolpert (1963) have discussed the way in which the extension and retraction of pseudopods could guide cellular locomotion. It seems possible that an isometric contraction of filopodia could align the cytoplasm of the growth cone as it does in the cytoplasm of Physarum (Fleischer & Wohlfarth-Bottermann, 1975), and may also do in cultured fibroblasts (Heath & Dunn, 1978). And this could, in turn, channel the supply of precursors for the elongation of the neurite.
I wish to thank G. Shaw for many valuable suggestions throughout the course of this work. I am also grateful to W. Lieb for computations and D. Gilbert for criticism; and to T. Schroeder, S. Villanueva and the Microscopy Laboratory of Queen Elizabeth College, London, for their help with the scanning electron microscope.