On the cytomechanics and fluid dynamics of growth cone motility

The importance of the highly motile growth cone in axonal elongation has long been appreciated. Both Ramon Y Cajal (1890) and Ross Harrison (1910) thought it was primarily responsible for axonal elongation. The early 1980s saw nearly uniform agreement that the growth cone pulled on the axon causing it to elongate (Johnston and Wessells, 1980; Bray, 1982; Letourneau, 1983; Landis, 1983). Repeated observations of actin and myosin in growth cones (Yamada et al. 1970; Roisen et al. 1978; Kuczmarski and Rosenbaum, 1979; Letourneau, 1981; Bridgman and Dailey, 1989) suggested some muscle-like process allowed filopodia to produce tension (Yamada et al. 1970; Bray, 1982; Wessells, 1982). Some workers pointed out, however, that this model was based on little direct evidence (Landis, 1983; Trinkaus, 1985). Indeed, direct observations that filopodia exerted force were limited to brief anecdotal mention in papers on other topics (Nakai, 1960; Wessells et al. 1980).

This contractile filopodia model strongly influenced thinking about mechanisms of growth cone navigation. Growth cones in culture preferentially follow certain substrata, as shown by the classic studies of Letourneau (1975a,6). Because this preference correlated with the adhesiveness of the substratum (Letourneau, 1975a), one could explain guidance by filopodia that test the adhesiveness of the environment by exerting force. Filopodia with stronger adhesion could exert more force than those with weak adhesion. The resulting ‘tug of war’ between filopodia might cause the weaker adhesions to break, thus steering the growth cone in the direction of the stronger adhesion (Bray, 1982; Letourneau, 1983; Bunge et al. 1983; Lockerbie, 1987). Differential adhesion became a common explanation for in vivo guidance of neurons (Taghert et al. 1982; Nardi, 1983; Bastiani and Goodman, 1984; Caudy and Bentley, 1986).

The contractile filopodia/pulling growth cone model was challenged by observations that chick sensory neurons could elongate on highly adhesive substrata in presence of cytochalasin D, which poisoned growth cone and filopodial movements (Marsh and Letourneau, 1984). Despite the grossly abnormal configuration of these neurites, the results indicated that elongation could occur without filopodial or other growth cone motions. Doubt about a role for contractile filopodia in growth cone movement also came from high resolution observations of growth cones of Aplysia neurons (Goldberg and Burmeister, 1986) and PC12 cells (Aletta and Greene, 1988). Both laboratories observed that growth cone advance was most closely correlated with protrusion of growth cone cytoplasm, lamellipodial formation in particular. The appearance of the protrusive activity suggested pushing, rather than pulling, as the cause of forward advance. Further, neither group noted any shortening of filopodia. However, the lamellipodial ‘veil’ of cytoplasm often moved forward between two filopodia, a tendency also observed by Bray and Chapman (1985).

In addition to studies on growth cone behavior, studies of axonal elongation also support the importance of lamellipodial protrusion in growth cone advance. Both in culture and in situ, highly lamellipodial growth cones were found at the tips of the most rapidly extending axons (Argiro et al. 1984; Bovolenta and Mason, 1987; Kleitman and Johnson, 1989), generally at early times of development. Prominent filopodia were found on somewhat slower, older growth cones (ibid.). Since filopodial growth cones were observed in regions where axons make navigational ‘decisions’ (Tosney and Landmesser, 1985; Bovolenta and Mason, 1987; Raper et al. 1983), it seemed possible that lamellipodia are responsible for advance, while filopodia might be ‘sensory’ structures responsible for navigation (Mason, 1985; Goldberg and Burmeister, 1986). These challenges to a motile role for filopodia opened a debate concerning the nature (push or pull) of the force required for growth cone advance and on the role of the filopodia (Bray, 1987; Letourneau et al. 1987; Goldberg and Burmeister, 1988; Turner and Flier, 1989). Our own data were ambiguous. Our correlations between neurite tensions and growth were consistent with pulling growth cones (Dennerll et al. 1988, 1989). But, our (unpublished) observations of chick sensory growth cone behavior were similar to those of Goldberg and Burmeister (1986) and Aletta and Greene (1988); advance was accompanied by prominent protrusions of cytoplasm suggesting a pushing growth cone, without any obvious contractile behavior by filopodia.

Direct observations and measurements of force production by chick sensory growth cones confirmed the classic model of a pulling ‘engine’ dependent upon filopodial ‘contraction,’ i.e. tension-producing activity (Lamoureux et al. 1989; Heidemann et al. 1990). Glass needles of known bending modulus (spring constant) were used to measure the force in neurites as growth cones advanced (Lamoureux et al. 1989). The needle was attached to the cell body and only the growth cone remained attached to the dish. A pulling mechanism was demonstrated by the strong positive correlation between growth cone advance and tension increases. The average correlation coefficient was 0.94 for 16 experiments on untreated tissue culture plastic. Periods of rapid growth cone advance produced rapid tension increases, while during short or long periods with no advance no tension increases occurred (Lamoureux et al. 1989). Since that report, we have confirmed this result on polylysine-treated plastic (Fig. 1). This is the sort of very adhesive substratum that allowed axonal elongation of chick sensory neurons without growth cone activity (Marsh and Letourneau, 1984). Fig. 1 shows that the growth cone is pulling even under conditions of high adhesion. Fig. 1A,C show that tension increases occur only during periods of growth cone advance. Fig. 1B,D show the same strong correlation between advance and tension found in the previous study.

In contrast to Fig. 1, a pushing mechanism must produce periods of axonal tension decline, e.g. if the lamellipodium is pushed out from a growth cone adhesion region. Oster and Perelson’s suggestion that osmotic forces contribute to motile advance (Oster and Perelson, 1987) should produce periods of tension decline during the periods of osmotic swelling. Models for growth cone advance involving slow axonal transport and/or polymer assembly as driving forces should involve compressive neurites, at least during advance. This is not to say that axonal pushing never occurs; the results of Marsh and Letourneau (1984) and of Spero and Roisen (1985) match our expectation of axonal elongation by a pushing mechanism. Here, elongation appears to be driven by microtubule assembly, as shown by the abnormally curved growth; pushing on or within a flexible neurite causes it to bend, as does pushing on a rope.

The direct evidence for a pulling growth cone raised an intriguing question in the light of the observations of growth cone behavior outlined in the introduction. How do growth cones pull while appearing to push? Of course, it is difficult to make inferences about internal force from observations of a moving object. For example, simple observations will not distinguish an automobile pulling via front wheel drive or pushing via the rear wheels. Rather, one must arrange for a ‘movable’ environment, e.g. placing a car onto mud or sand to see which wheels dig in. With this in mind, we observed the movement of glass fibers and the elastic deformation of neurites from other neurons (obstacle neurites) when they interacted with advancing growth cones of 10-12 day old embryonic chick sensory neurons (Heidemann et al. 1990). We saw 136 instances of obstacle movements caused by 16 growth cones interacting with glass fibers and 17 interacting with neurites.

Surprisingly, growth cones produced just three, highly stereotyped obstacle movements. The first was the attachment of filopodia to obstacles with subsequent shortening of filopodia to move the obstacle (Fig. 2). The behavior of obstacle neurites was particularly informative here because the force exerted by a single filopodium could be estimated from the elastic neurite distension (Fig. 3).

In the second stereotyped movement, obstacles moved smoothly rearward on the dorsal surface of growth cones (Fig. 4) giving a strong visual impression of movement on an escalator. The growth cone did not extend during these movements, but these ‘escalator’ movements were clearly similar to the movement of particles on dorsal growth cone surfaces (Bray, 1970; Feldman et al. 1981) and to the retrograde movement of cortical actin so clearly seen by Forscher and Smith (1988) on the dorsal surface of growth cones.

In the third category of interaction, obstacles were pushed aside by lamellipodial ruffling, in which veils of cytoplasm moved up from the substratum and rearward. This ruffling is distinguished from the more common, planar lamellipodial extension typical of growth cone motility. Neither glass fibers nor neurites interacted in a concerted fashion with these lamellipodia and there were no distensions of obstacle neurites for measurable times. Instead these interactions seemed to be simple collisions between an obstacle and moving cytoplasm. Our observations indicate no role for lamellipodial ruffling in providing motive force for advance. A similar conclusion was drawn for lamellipodial ruffling in fibroblast movement despite their close temporal correlation (Abercrombie et al. 1970).

Both filopodial shortening and the rearward ‘escalator’ movements produced 50-90×10⁻⁵pN as estimated from the deflection of neurites. Given that growth cones typically have several filopodia and a broad attachment to the substratum (Letourneau, 1979; Gundersen, 1988), either mechanism could account for the magnitude of tension exerted by the advancing growth cone. However, our observations suggested to us that filopodial shortening is mostly responsible for the rearward force necessary for advance, at least in these highly filopodial growth cones. Firstly, filopodial shortenings (100 instances) were three times more frequent than ‘escalators’ (31 instances). More telling, the highly variable force output of filopodia (Fig. 3) was much more consistent with the highly variable advance of growth cones in culture (Argiro et al. 1984; Katz et al. 1984). What had once seemed like futile movements by filopodia now seem to be a characteristic of filopodial operation. One final indication was that the five growth cones whose ventral, substratum-opposed surface interacted with obstacle neurites (interactions that reproduced the usual geometry between growth cone and substratum) clearly produced their force by filopodial shortening (Heidemann et al. 1990). We saw no evidence of an ‘escalator’ on the ventral growth cone surface. Previous work on fibroblasts also indicated that retrograde, cortical actin movements occurred primarily, but not exclusively (Harris and Dunn, 1972), on the dorsal surface (Abercrombie, 1980; Heath, 1983).

Although cytomechanical data thus supports an older model of growth cone motility, it argues against one of the presumed consequences of the model: guidance of growth cones by a ‘tug of war’ mechanism (Bray, 1982; Letourneau 1983). As mentioned earlier, this guidance model postulates that filopodia pulling against weak adhesions are lost. This suggests that filopodial tension is limited by the strength of substratum adhesion, i.e. growth cones and/or filopodia function near their adhesive limit. Our force measurements indicate this is not so. Rapid plucking of neurites, like a guitar string, of both PC 12 cells and chick sensory neurons produces purely elastic behavior (because the deformations are too rapid to engage the fluid elements of the overall viscoelastic response). Plucking with calibrated glass needles reveals both the rest tension and spring constant relationship between force and distension for any particular neurite (Dennerll et al. 1988,, 1989). As shown by the high tension data points in Fig. 5, we can apply much greater tension to the neurite than its ‘rest’ (zero distension) tension (at the y-intercept) without causing loss of growth cone adhesion. Also, we have elongated neurites attached only at the growth cone using tensions much greater than normal rest tensions (Zheng et al. 1991). Apparently, growth cones do not function near their adhesive limit suggesting that substratum preference is not a ‘tug of war’ but some other mechanism. We are currently investigating the cytomechanics of axonal elongation on differing surfaces to learn more about possible substratum interactions.

What is the relevance of these findings to those studies showing that rapid axonal elongation correlates more with lammellipodial presence and activity than with filopodia (Argiro et al. 1984; Bovolenta and Mason, 1987; Kleitman and Johnson, 1989)? It may well be that these growth cones exert traction force via the escalator mechanism (Bray and White, 1988; Smith, 1988). This might explain why such growth cones move more rapidly; force production by the ‘escalator’ was quite concerted, not variable as for filopodial shortening (Heidemann et al. 1990). However, it is also possible that force is produced in these growth cones by activity very similar to that of filopodia. The aligned actin bundles within filopodia (Letourneau, 1981; Tosney and Wessells, 1983; Bridgman and Dailey, 1989) are also typically observed in lamellipodial growth cones but are obscured by the veil of cytoplasm (Goldberg and Burmeister, 1986; Bridgman and Dailey, 1989). We present a model later in the paper to account for lamellipodial advance via tension on these actin bundles. In this regard, Tosney and Wessells (1983) concluded that the alignment of actin within filopodia was indicative of tension on them; unattached filopodia had actin networks not bundles. Possibly, filopodial actin bundles within growth cones are diagnostic of a pulling mechanism, but other mechanisms may also exist. For example, Kleitman and Johnson (1989) found only actin networks, no bundles, in highly lamellipodial, superior cervical ganglion neurons.

Presumably, the basic mechanism(s) by which growth cones exert force to drive growth cone advance and axonal elongation is independent of the presence or absence of obstacles. Why then does obvious filopodial shortening occur only with movable obstacles and not on the immovable substratum of the culture dish (Goldberg and Burmeister, 1986; Aletta and Greene, 1988)? One possible answer involves the peculiar fluid properties of cytoplasm.

As outlined earlier, lamellipodial protrusion is an important aspect of growth cone advance. This process appears as a ‘filling in’ of regions of the distal growth cone by moving cytoplasm, suggesting fluid behaviors. Indeed, it has long been appreciated that crawling and/or amoeboid motion by animal cells involves cytoplasmic flow (Seifriz, 1942; Taylor and Condeelis, 1979). In recent years it has become apparent that suspensions of F-actin show fluid behavior very similar to cytoplasm and are more convenient for study (Elson, 1988). We have examined the behavior of F-actin suspensions and of microtubules in response to increasing shear rates (Buxbaum et al. 1987). We have also examined the gel-to-sol behavior, called thixotropy, of F-actin suspensions (Kerst et al. 1990).

In these experiments, F-actin and microtubules are suspended in their typical in vitro assembly buffers at various concentrations between 2-12 mg ml⁻¹. The fluid is then placed in a rheometer between a shallow cone and a flat plate; the bottom plate is driven to rotate and the force is transmitted through the fluid to the upper cone whose response is recorded. One measure of fluid flow, the shear rate, is the change in the velocity of the fluid perpendicular to the direction of flow, i.e. the velocity gradient between the upper and lower plate. Shear rate is a velocity (cm s⁻¹) per unit distance (cm); canceling the cm units that appear in both numerator and denominator gives the non- intuitive unit for shear rate, reciprocal seconds (s⁻¹). Fig. 6 shows an even less intuitive behavior: viscosities of both F-actin and microtubules are inversely proportional to shear rate over three orders of magnitude of low, physiological shear rates (Maruyama et al. 1974; Buxbaum et al. 1987). This very unusual behavior indicates that shear stress is constant and independent of shear rate, as shown in Fig. 7. We refer to this ‘perfect’ shearthinning behavior as ‘indeterminate flow,’ because force does not determine the shear rate and vice versa. Over the years, a number of measurements have been made of in vivo cytoplasmic viscosity at different shear rates (Crick and Hughes, 1950; Yagi, 1961; Hiramoto, 1969; Sung et al. 1982; Nemoto, 1982; Sato et al. 1983; Valberg and Albertini, 1985). Plotting these various results on the same scale as our shear thinning data (Fig. 8), clearly shows that cytoplasm shares indeterminate fluid behavior with cytoskeletal proteins.

Some forms of liquid crystals also show indeterminate fluid behavior (Wissbrun, 1981). Liquid crystals are a phase of matter in which molecular rods align in a fluid to produce a polymer ‘log jam’ (Fig. 9A). The structure is maintained by a combination of thermodynamics and molecular shape interaction producing correspondingly complex flow properties. As their name implies, liquid crystals have both fluid properties, such as flow, and crystalline properties, such as birefringence in polarized light. Birefringence in a fluid is diagnostic for liquid crystal structure (Collings, 1990). As shown in Fig. 9B, actin suspensions have long been known to be biréfringent (Szent-Gyorgi, 1945; Kasai et al. 1960; Buxbaum et al. 1987). Also using birefringence data, Hitt et al. (1990) report that microtubule suspensions are nematic liquid crystals. We exploited the birefrigence of the actin to observe directly the flow (Kerst et al. 1990). We observed F-actin at concentrations between 6—20 mg ml⁻¹ through crossed polarizers. The fluid was sheared by pushing down on the coverslip. At low shear rates, we observed that actin broke into irregular domains that flowed past one another; imagine the movement of biréfringent ‘ice floes.’ This is shown clearly in the videotape of the polarization images of this flow, but only poorly represented by videoscreen photographs which are not reproduced here (but see Kerst et al. 1990). The domains of actin behaved like solids moving in a stream. The flow was dominated by sliding, solid friction interactions among domains, not interactions among individual polymers as for typical polymer fluids. Possibly this sliding friction explains the rheology of actin and microtubles, because in sliding friction the force is a constant at any velocity.

Cytoplasm and most liquid crystals are thixotropic, undergoing a solid ‘gel’ to fluid ‘sol’ transition under shear (Mewis, 1979). As mentioned, this property has long been associated with cell motility (Seifriz, 1942). Fig. 10 illustrates this thixotropy in a sample of F-actin. At the onset of shear, stress rises rapidly as the gel state responds elastically. At some threshold stress the gel fluidizes and the stress overshoot decays to a steady state stress indicative of viscous fluid, sol-state behavior. As shown in Fig. 11, the stress overshoot in a sample of actin recovers proportionately with increasing ‘rest’ periods between bouts of shearing (at 0.2s⁻¹), with nearly complete recovery by five minutes. This thixotropic behavior is consistent with the ‘solid-like domain’ interactions proposed for the indeterminate behavior of F-actin: static friction within the gel state (peak overshoot) is greater than the sliding friction of the sol state (Kerst et al. 1990).

These rheological data on F-actin suspensions have three levels of significance for understanding cell motility.

Most speculatively, perhaps cytoplasm is liquid crystalline. Clear evidence has been reported for biréfringent cytoplasm in the amoeba Chaos carolinensis (Allen, 1972) and the plasmodium Physarum polycephalum (Nakajima and Allen, 1965, Ueda et al. 1990). The biréfringent appearance of Chaos endoplasm (Allen, 1972) was strikingly similar to the ‘polycrystalline texture’ (Wissbrun, 1981) we observed in flowing actin suspensions (Kerst et al. 1990). Less speculatively, perhaps cytoplasm flows as domains without being liquid crystalline. Cross-linking of cytoplasmic filaments may impose a network structure on cytoplasm, which nevertheless breaks up into domains when sheared, like Jell-0 which is a network of collagen protein. Least controversially, cytoplasm is well known to be thixotropic. At times, growth cone cytoplasm behaves like a solid as in the shortening of filopodia to move obstacles. At other times, it behaves like a fluid as in the protrusion of lamellipodial veils. Perhaps these transitions are due to tension alone, exerted by filopodia. Recent models for growth cone advance have concentrated on purely elastic, solid behaviors (Mitchison and Kirschner, 1988; Smith, 1988). In order to reconcile much recent data on growth cone motility, we think fluid cytoplasmic responses must also be considered.

Our model is shown in Fig. 12. When filopodia attach to the environment at their distal ends, they produce or transmit force. Generally, this filopodial force is transmitted as tension along the underlying actin bundle, Fig. 12A. We postulate that solid, gel cytoplasm accommodates this tension by elastic deformation. Unless the filopodial tension overcomes some threshold, no shortening of filopodia nor forward movement of the growth cone is observed. However, as shown in Fig. 12B, cytoplasmic advance occurs when tension in the actin bundle is sufficiently great to overcome a threshold tension (similar to the stress overshoot shown in Fig. 10) causing the liquifaction of the cytoplasmic meshwork surrounding the filopodial actin bundle. That is, a sufficient stress exerted on/by the filopodial actin bundle causes a gel-to-sol transition. The newly solated cytoplasm flows in the direction of the force, and is observed as a forward movement of cytoplasmic veils along filopodial ‘tracks,’ i.e. the ‘protrusion’ step of Goldberg and Burmeister (1986, 1988), as has also been observed by others (Bray and Chapman, 1985; Aletta and Greene, 1988). This outflow could also contribute to the movement of cytoplasm seen during the ‘engorgement’ step of advance (Goldberg and Burmeister, 1986), orienting microtubules for vesicle transport. Microtubule orientation could also occur in response to elastic cytoplasmic responses before solation. In this model, lamellipodial protrusion and filopodial ‘contraction’ are not alternative mechanisms but are causally related.

Recent evidence from growth cone behavior in situ is consistent with a fluid outflow mechanism. O’Connor et al. (1990) investigated growth cone advance in identified pioneer neurons in developing grasshopper limb buds. They discerned three different steering events, shown in Fig. 6 of their paper. All three suggest the fluid flow of axoplasm into ‘new’ regions of the growth cone involving recruitment of axoplasm from previously established regions.

Note that this cytoplasmic outflow model for lamellipodial advance runs against ordinary experience; one normally observes outflow caused by fluid compression, i.e. a push. For example, higher hydrostatic pressure within an overturned glass drives the advancing spill. This is the reason, we think, that observations of fluid-like lamellipodial advance had intuitively suggested pushing.

We think it unlikely that the actin bundle itself behaves as an actomyosin motor-like muscle. This would require that the bundle physically shorten when the cytoplasm liquifies; no such shortening is observed (Goldberg and Burmeister, 1986; Aletta and Greene, 1988). Rather, as shown in Fig. 12C, it seems likely that the force producer (the surfer of Fig. 12C), possibly myosin, is found in the meshwork cytoplasm surrounding the actin bundle. In fact, growth cone myosin is found in areas outside the filament bundles (Bridgman and Dailey, 1989).

When the filopodium is attached to a movable obstacle, the force producer would exert tension that ‘reels in’ the obstacle. Under these conditions, the filopodium (but not the internal bundle) shortens, as shown in Fig. 2. If, however, the filopodium is attached to the substratum, the stress exerted on the actin bundle by the ‘motors’ could be transmitted to the cytoplasm either by cross-links or, more simply by viscous interaction. Again, when this force reaches some threshold tension, cytoplasm solation causes lamellipodial advance, as shown in Fig. 12C. This scenario produces no shortening of filopodia during normal motility, in agreement with recent observations (Goldberg and Burmeister, 1986; Aletta and Greene, 1988).

The authors would like to thank Tim Dennerll, Craig Chmielewski, Jim Steffe and many others in the Physiology and Chemical Engineering Departments for their contributions to the work described here. This work was supported by NIH grant GM 36894 and NSF grant BNS 8807920.