## ABSTRACT

It has long been recognised that the alignment of fibrils of an extracellular matrix can guide cell displacement along an axis. However, bidirectional guidance alone is insufficient to explain the directed translocation of cell populations in an embryo. Evidence is presented here that matrix fibrils can also be arranged to confer a unidirectional bias on cell displacement.

When chick heart fibroblasts were cultured between two collagen matrices pretreated by shearing, the dis-placements of these cells were biased in the direction opposite to that of pre-shear. A possible explanation is that cells detect the directional arrangement of fibrils linked to a rigid surface. Results of a second experiment suggested that cells can indeed respond directionally to the linkage of fibrils to rigid surfaces. Cells spreading on the surface of matrices were aligned perpendicular to the edge of a rigid body embedded just beneath the surface. For cells close to this body, the effect of linkage was able to override guidance as the more important orienting cue.

‘DESMOTAXIS’ is suggested as a suitable name for the unidirectional movement of cells in response to the arrangement of fibrils relative to a rigid, anchoring surface. In the embryo, several factors could generate such arrangements of extracellular matrices around relatively solid structures. These possibilities are discussed with reference to directed cell migrations *in vivo*.

## Introduction

Many cell types migrate considerable distances in the early embryo, along highly specific pathways which in some cases influence their subsequent differentiation (Le Douarin and Teillet, 1974; Noden, 1983). Cell-marking and grafting experiments have shown that migratory pathways are in general specified by surrounding tissues, not by the migratory cells themselves (De Haan, 1963; Weston and Butler, 1966; Le Douarin and Teillet, 1974; Erickson *et al*. 1980). However, despite numerous experimental approaches, the factors directing migration remain in most cases poorly under-stood.

Alignment of migrating cells with their direction of migration, and their close associations with similarly aligned extracellular matrix fibrils, suggest a process resembling contact guidance (Ebendal, 1977; LÖfberg *et al*. 1980; Fitzharris and Markwald, 1982; Nakatsuji *et al*. 1982; Newgreen, 1989). Contact guidance describes the tendency of cells to move bidirectionally along an axis determined by some property of their substratum (Dunn, 1982). The specific case of a bidirectional response to oriented fibrillar matrices has been termed ‘strain guidance’ (Harris *et al*. 1984). However, since a guidance cue alone does not specify a preferred direction along the axis, it cannot cause any net displacement of a population (Dunn, 1981).

This limitation has frequently led to the assumption that structural properties of the extracellular environment cannot account for unidirectional migration. Many other factors, frequently in combination with contact guidance, have been invoked to explain cell migrations in the embryo, but most suffer from objections and counterexamples. Mutual contact inhibition of movement (Erickson, 1985), for instance, does not explain the directed movement of axolotl melanocytes, which occurs without cell-cell contact (Keller and Spieth, 1984). Neither does it account for the clearing from the neural crest pathway of the ‘tail end’ of the population (Trinkaus, 1984). It has been proposed that neural crest cell migration is initiated by changes in composition of the extracellular environment (Weston *et al*. 1978; Newgreen *et al*. 1982; Tucker, 1986; LÖfberg *et al*. 1989) and that physical barriers limit the space available for invasion (Erickson *et al*. 1980; Tosney, 1982). However, neural crest cells *in vitro* readily penetrate filter pores smaller than the openings in these barriers (Newgreen, 1989). Initiation of neural crest dispersal is preceded by localised production of hyaluronic acid (Pratt *et al*. 1975), causing enlargement of extracellular spaces (LÖfberg *et al*. 1980; Erickson and Weston, 1983), but is not prevented by injection of hyaluronidase, causing collapse of these spaces (Anderson and Meier, 1982). Another possible mechanism of unidirectional movement through fibrillar matrices depends on the preferred movement of cells up a gradient of matrix density and hence of potential sites for adhesion (Harris *et al*. 1984). Over certain ranges of matrix density, however, increasing density seems to inhibit rather than promote motility of several cell types (Brown, 1982; Schor *et al*. 1982; Tucker and Erickson, 1984).

This paper presents evidence for an alternative mechanism whereby structural properties of a fibrillar matrix can cause unidirectional displacement of cells. Cells embedded between two matrices pretreated by shearing tend to move in the direction opposite to that of preshear. Since shear forces sufficient to organise extra-cellular matrices are likely to be generated by morpho-genetic movements of the embryo, such an effect may be important to migrating cells *in vivo*. A possible explanation of this effect is that cells detect an asym-metrical pattern of linkage of matrix fibrils to the underlying, rigid surface. To further investigate this possibility, a second experiment examines the directional behaviour of cells close to rigid bodies to which matrix fibrils are linked.

## Materials and methods

### Preparation of substrata

#### Collagen solutions

Components in the following proportions were mixed on ice immediately before preparation of collagen matrices: Vitrogen (bovine dermal collagen at 3 mg ml, Collagen Corporation, Palo Alto, CA) 500/4, 10× medium 199 (Flow Laboratories, Rickmansworth) 100/4, foetal calf serum (Flow laboratories) 100 μl, 50mM-NaOH 130/4, 89.3 mM-NaHCO_{3} 46.7/4, 4mM-L-glutamine, penicillin and streptomycin (both at 2000i.u. ml^{1}) 50 /4, deionised water 73.3 /4. This mixture, diluted with an equal volume of medium 199, was used to coat supporting surfaces, which were then allowed to dry, rinsed in deionised water and re-dried. For gelled matrices, the mixture was used undiluted and allowed to precipitate for 2h at 37 °C in a humid atmosphere of 5 % CO_{2} in air. All matrices were soaked for 24 h in complete medium before use.

### Sheared matrices

For each culture, two matrices about 75μm deep were prepared separately then assembled together as shown in Fig. 1. The upper matrix was prepared using 43 /4 of collagen solution on an acid-washed coverslip (24 × 24 mm), which was first exposed to corona discharge and precoated with collagen. The lower matrix was prepared using 32/4 of collagen solution, on the central portion of a modified Petriperm dish (Heraeus). Dishes were supplied with the membrane inverted so that its hydrophobic surface formed the floor of the dish. A central rectangle (24×18 mm) was rendered hydrophilic by corona discharge and precoated with collagen. A glass strip, attached with nail lacquer across one end of the treated rectangle, formed a guide for positioning the upper matrix (Fig. 1B). Shear was introduced by tilting matrices 1.5° from horizontal during their precipitation.

### Matrices containing rigid bodies

Strips (10 × 1 mm) cut from cellulose filters (pore size 8μm, thickness 200 μ m, Millipore Corporation, Bedford, MA) were attached with nail lacquer to acid-washed coverslips which had been exposed to corona discharge and precoated with collagen. Circular matrices (diameter 18 mm, depth 250μm) were prepared using 50 μl of collagen solution to cover each strip. Matrices visibly distorted around the filter strip or not covering it with a depth of 30 to 80μm were discarded. To modify their mechanical properties, some matrices were fixed before use as follows. These were first rinsed in phosphate-buffered saline (PBS), fixed for 5 mins in 1% glutaraldehyde/PBS, then rinsed extensively in PBS. To quench residual aldehyde, fixed matrices were treated for 20 min with 250mM-glycine in PBS, then further rinsed in PBS and conditioned in complete medium before use. At 1 mm intervals around the filter strip, 500μm from its edge, the axis of any local alignment of matrix fibrils was identified as the principal axis of birefringence.

### Cell culture

#### Media and cells

Fibroblast outgrowths from 7 day embryo chick ventricular explants were harvested using 0.5% (w/v) trypsin in 10mM-EDTA/PBS and grown in Medium 199 (Flow Laboratories) supplemented with 10% (v/v) foetal calf serum, 0.2mM-t-glutamine, 4.17mM-NaHCC>3 and 100i.u.ml^{−1} each of penicillin and streptomycin, in a humid atmosphere of 5 % CO_{2} in air.

#### Cell culture between matrices pretreated by shearing

Cells at 1000 cm^{−2} were allowed to settle for 10 min on the lower matrix, prepared on a Petriperm dish. The upper matrix was then lowered into place (Fig. IB), using the glass strip as a guide to accurately superimpose the shearing directions of both matrices. Glass spacers alongside the lower matrix prevented compression of matrices. The Petriperm dish was positioned (Fig. 1C) over a coverslip sealed with dental wax over a window cut in the base of a 10 cm plastic Petri dish. This chamber was sealed with silicone grease and transferred to the stage of a Zeiss IM35 inverted microscope equipped for phase contrast with a 25 × plan objective, where it was gassed with warmed, humidified 5 % CO_{2} in air. Pieces of moistened filter paper maintained humidity and a warm air-curtain kept the chamber at 37 °C.

A series of cells was recorded in timelapse using a Falcon SIT video camera with uniformity and selective contrast expansion controls (Custom Camera Designs Ltd., Wells, Somerset) linked to a reel-to-reel video timelapse recorder (National, model NV-8030). Cells were selected at random, excluding only those within 200 μm of their nearest neighbour, and recorded at a lapse-rate of 1:72 (recording interval 1.44s).

#### Cell culture on matrices containing rigid bodies

Cells at 1000 cm^{−2} were allowed to settle on prepared matrices. Cultures were incubated for 3 h at 37°C, then rinsed in warm PBS, fixed for 5 min in 1 % glutaraldehyde in PBS, rinsed and mounted in PBS for microscopic analysis.

To determine whether chemoattractant properties of the filter itself, adsorbed medium components or the nail lacquer, used as adhesive, could influence cell alignment, four replicate control experiments were performed as follows. Cells were allowed to adhere at IODO cm^{−2} to collagen-coated coverslips, then covered with collagen solution, which was allowed to precipitate, forming a matrix 100 *gm* deep. Millipore filter strips, painted with nail lacquer and presoaked in medium, were added in a second layer of collagen solution, which was allowed to precipitate for a further 30 min. Cultures were immersed in fresh medium, incubated for 12 h at 37°C, then fixed for microscopic analysis.

### Analysis

#### Cell movement between sheared matrices

At 30 min recording intervals, the outline of the cell and the positions of 2- to 3-matrix irregularities within 100 μ*m* of its edge were traced from video recordings of each cell (final magnification × 870), indicating on each tracing the direction of matrix shearing and the centre of the monitor screen. Tracings were digitised at a resolution of 2.0mm using a Summagraphics Bitpad 2 linked to a PDP 11/44 minicomputer, aligning the centre of the monitor screen with that of the Bitpad and the direction of shear with its positive y-axis. From Cartesian coordinates for the geometrical centroid of each cell at the beginning and end of each 30 min interval was calculated a vector describing its displacement. This was corrected for movement of the matrix by subtracting from it the mean of the vectors describing the corresponding dis-placements of the 2- or 3-matrix irregularities recorded as markers with each cell.

#### Cell alignment on matrices containing rigid bodies

Using a Zeiss Photomicroscope II equipped for differential interference contrast with a 40x water immersion objective, camera lucida drawings (x971) were made of all cells within 1800 μ*m* of each filter strip, excluding those in contact with their neighbours. On each drawing was marked the axis normal to the edge of the filter strip (henceforth called the ‘normal axis’), the axis of local matrix alignment, determined before cell culture (henceforth called the ‘matrix alignment axis’), and the distance of the cell from the filter strip. Drawings were digitised at a resolution of 2.4mm, orienting each to align the normal axis with the y-axis of the bitpad.

Measures of cell shape and alignment were derived by generating a video image from each digitised outline. The size-invariant measures, orientation, elongation and paraxial elongation, described by Dunn and Brown (1986), are based on the zeroth to second-order, normalised, central moments of a shape. Briefly, a unique long axis can usually be defined from the second-order moments of any shape. **Orientation** is defined as the angle, measured in degrees, from a chosen reference axis to this long axis. **Elongation** is independent of orientation. It takes a value of zero for an unelongated shape and increasing, positive values for increasingly elongated shapes. **Paraxial elongation** measures how much a cell is elongated along the y-axis. It takes a maximum positive value equal to the value of elongation for a cell oriented along the y-axis and takes the negative of this value for a cell oriented along the x-axis. Its value is zero for a cell oriented at 45° to the coordinate axes or if a cell is not elongated.

#### Directional statistics

Vectors representing cell displacements between sheared matrices were first tested for any directional bias using Hotelling’s one-sample T^{2} test (described by Batschelet, 1978). In this test, a confidence ellipse for the mean vector is calculated, assuming normal distribution of both x- and y-components but without presupposing any relation between them or their variances. A significant directional bias is indicated if this confidence ellipse excludes the origin. Secondly, the y-components of sample vectors were tested for directional bias along the axis of shear.

To analyse by standard methods of directional statistics the alignment of cells on matrices containing rigid bodies, each sample of cell elongations and orientations was first converted to a sample of vectors. The length of each vector was given by the elongation of the cell and its direction was obtained by doubling the orientation angle. Thus, a sample of orientations (distributed between —90° and +90°) became a sample of directions (distributed around a full circle) and the chosen reference axis became a reference direction. Two statistical tests were used to determine firstly whether matrix alignment or the rigid body was the more important orienting cue, and secondly whether the less important orienting cue had any additional influence.

*V*test described by Batschelet (1972). This was used to test the clustering of directions representing the orientation of each cell. For each sample of vectors was calculated the resultant of corresponding unit vectors, the length

*V*of its component in the reference direction, and the test statistic

*u*, defined

*u* was then compared with confidence limits for the value expected given uniformly distributed sample directions.

The second test, to detect any influence of the less important orienting cue, was simply a two-tailed t-test performed on the sum S of vector components perpendicular to the reference direction. Because it uses both orientation and elongation, this test would detect an asymmetrical distribution of cell elongations even if cell orientations were unbiased.

## Results

### Cells between sheared matrices

Cells cultured between two matrices pretreated by shearing tend to move in the direction opposite to that of pre-shear. This unidirectional tendency is illustrated in Fig. 2. Cell displacements over 30 min intervals are drawn as vectors with a common origin, the positive y-axis representing the direction of shearing. Ellipses represent the 95 % confidence areas for the tip of the mean vector and for that of a new sample vector. Both are derived using the method of Hotelling’s one-sample *T*^{2} test (Batschelet, 1978). The shape and position of these ellipses suggest firstly that x-components (perpendicular to the direction of shear) are unbiased, and secondly that y-components (along the axis of shear) tend to be longer than x-components and are biased in the negative direction. The confidence ellipse for the mean vector excludes the x-axis and covers the negative y-axis, confirming that cells moved predominantly in the direction opposite to that of shearing.

The mean y-component of displacements is significantly (P<0.005) negative in a two-tailed i-test. Because of the slight positive kurtosis of the distribution, a non-parametric test was also performed on the median. 99% confidence limits for the median y-component, derived by the method of Nair (described by Colquhoun, 1971), indicate that this too is significantly positive. Results of both tests are given in Table 1.

### Cells on matrices containing rigid bodies

### Appearance of cultures

Cells close to filter strips are noticeably aligned with axes normal to the edge of the strip (‘normal axes’). This tendency is less noticeable in cells further from the strip. Within 3h, unfixed matrices become visibly distorted around cells, especially on the side directed toward the filter strip, and in many cases a bundle of matrix fibrils, realigned with the long axis of the cell, extends to the edge of the strip. Distortion of pre-fixed matrices is less marked but, sometimes from an early stage of spreading, cells are linked to the filter strip by a few realigned fibrils. These effects are illustrated in Fig. 3.

#### Paraxial elongation

The alignment measure, paraxial elongation (Dunn and Brown, 1986), increases with both the proportion and the elongation of cells oriented close to a reference axis. In Fig. 4, the paraxial elongation of each cell with respect to the normal axis is plotted against its distance from the filter strip. The significantly positive y-axis intercepts of regression lines fitted to these data confirm that cells close to filter strips embedded in either fixed or unfixed matrices are aligned with axes normal to the edge of the strip.

If alignment were influenced by a rigid body, it would be expected that this influence would decay assymptotically with distance and that paraxial elongation would decay similarly with distance from the filter strip to some background value determined by other orienting influences. Since no basis exists for predicting this background value, any influence of the filter strip is better indicated by the decay of paraxial elongation with distance than by its absolute value close to the strip.

Confidence limits for the parameters *A, B* and *C* were obtained using the Jackknife procedure described by Mosteller and Tukey (1977) and showed that the y-axis intercept is significantly (P<0.005) positive and that the gradient is significantly (P<0.1) negative up to 1mm from the filter strip. Curves fitted to data for cells on unfixed matrices resembled a straight line, making parameters *A* and *C* unstable to testing by the Jackknife procedure. Instead, a least squares linear regression was used to fit to the data the equation y=0.415-0.165*. Both the negative slope and the positive value of its y-axis intercept are significant (P<0.001 and 0.05 respectively).

The above results suggest some influence of the filter strip on cell alignment. The following controls allow rejection of two alternative explanations. Firstly, measuring angles between normal axes and matrix alignment axes at various distances from filter strips, no overall trend with distance was found in any of the matrices used in these experiments. Thus systematic variation in matrix alignment with distance from filter strips could not account for the observed cell alignment behaviour. Secondly, filter strips, painted with nail lacquer and pre-soaked in medium, were added, in a second layer of collagen mixture, to matrices 100 μ m deep covering cells adhering to collagen-coated coverslips. For 150 cells within 200 μ m of these filter strips, the mean value of paraxial elongation (– 0.064±0.086) did not differ significantly from zero, suggesting that neither the filter itself, adsorbed medium components, nor the nail lacquer, used as adhesive, oriented cells by chemoattractant influences.

#### Vector representation of cell alignment

To analyse separately the orienting effect of the rigid body and of matrix alignment, cells are represented (Fig. 5) by vectors of two types. In each case, the length **r**_{i} of the vector is equal to the elongation of the cell. For A-vectors **(r**_{i}, **a**,**)**, angle **a**_{1} is given by twice the orientation of cell i relative to the matrix alignment axis and takes a positive value when orientation deviates toward the normal axis. For B-vectors **(r**_{i}, **b**_{i}**)**, angle **b**_{i} is given by twice the orientation of cell i relative to the normal axis and takes a positive value when orientation deviates toward the matrix alignment axis.

For cells sampled close to filter strips in both fixed and unfixed matrices, B-vectors (Fig. 5A and B) are more clustered around the reference direction than are A-vectors (Fig. 5C and D), suggesting that the axis normal to the filter strip is a more important orienting influence than the initial alignment of the matrix. For cells sampled further from filter strips in matrices of both types (Fig. 5E and F), A-vectors are clustered around the reference direction, suggesting that preexisting matrix alignment is the principal orienting influence. Tables 2 and 3 give the results of two statistical tests, based on these samples of vectors, which examine the importance of each putative orienting cue.

Test 1 uses only the orientation of each cell to identify the more important orienting cue. The test statistic *u* (Batschelet, 1972) increases with the clustering of sample directions around the reference direction. Cells sampled close to filter strips in both fixed and unfixed matrices are significantly oriented along normal axes (P<0.0001 and 0.01, respectively). Cells further from filter strips in fixed and unfixed matrices are significantly oriented along local matrix alignment axes (P<0.0001 and 0.001, respectively).

Test 2 uses both the orientation and the elongation of each cell to identify any additional influence of the less important orienting cue. For each sample of vectors is calculated the sum 5 of components perpendicular to the reference direction. *S* takes a positive value for A-vectors which are biased toward the direction representing the normal axis, and for B-vectors which are biased toward the direction representing the matrix alignment axis. Two-tailed i-tests indicate that, close to filter strips in fixed but not in unfixed matrices, cell alignment is significantly (P<0.001) biased from the normal axis toward the matrix alignment axis. On neither fixed nor unfixed matrices is alignment of cells further from the filter strip biased from the matrix alignment axis toward the normal axis.

## Discussion

I have demonstrated by video timelapse analysis a significant unidirectional tendency of cells migrating between fibrillar collagen matrices pretreated by shearing. Chemotaxis is an unlikely explanation for this behaviour, since presoaking all matrices in complete medium before use would disperse any gradients of diffusible substances. Another explanation is a directional-response to a gradient of matrix density, caused by localised collapse of the matrix due to fluid drainage from the ‘upstream’ end. However, the uniform depth of matrices over the regions where cells were recorded eliminates this possibility. A third explanation is that cells were responding to some structural asymmetry of the matrix, introduced by shearing.

Phase contrast microscopy revealed alignment of matrix fibrils with the axis of shear. However, an axis of matrix alignment can specify only a bidirectional movement of cells (Dunn, 1981). A unidirectional movement requires a quite distinct influence. It is likely that shearing caused a unidirectional displacement of the exposed portions of matrix fibrils relative to the portions linked to the supporting surface. The resulting arrangement would have a built-in polarity, like an animal’s fur, which lies flat in one direction. I suggest the term ‘linkage’ to describe the arrangement of matrix fibrils relative to a rigid anchoring surface. Unlike gradients of chemical concentration or substratum adhesiveness, in which direction is specified by the uneven distribution of a scalar property, linkage is a vector property which can itself specify direction, even if it is uniformly distributed. A spreading or locomoting cell exerts centripetally directed tractive forces. Where linkage is polarised by shearing, it is clearly easier for cellular traction to displace fibrils in the direction opposite to that of pre-shear than to extend them any further in the direction of shearing. Thus fibrils on the ‘upstream’ side of a cell are more able to withstand cellular traction and therefore to support cell locomotion. The requirement of spreading and locomoting cells for a substratum which withstands their traction was discussed by Harris (1973, 1982), who noted that cells of lower tractive strength were able to spread on the surfaces of fluids of lower viscosity. Unidirectional movement of cells in response to linkage is a direct consequence of this requirement.

The results of a second experiment suggest that cells can indeed respond directionally to linkage. In this case, the anchoring surface consisted of a rigid body, embedded just beneath the surface of a matrix. This experimental environment differs from the first in two important respects. First, it is non-uniform: clearly, fibrils are more easily displaced toward than away from their attachments to a rigid body and this mechanical asymmetry must decay with distance from the anchoring surface. Second, the axis of any preexisting matrix alignment is unrelated to the direction specified by linkage, permitting independent testing of both putative orienting cues. Cell alignment with axes normal to the edge of the rigid body was not only independent of the axis of initial matrix alignment but also, in the immediate vicinity of this body, able to override the orienting influence of the slight alignment of the matrix. Analysis of cell shapes rather than displacements permitted sampling of more cells at various distances from the rigid body, but could not directly indicate unidirectional movement. However, a unidirectional response was suggested by the asymmetrical distortion of the matrix by individual cells.

Most embryonic cell migrations precede the formation of rigid skeletal elements but may be directionally influenced by linkage where basement membranes and other locally stiffened or compacted regions of extra-cellular matrix are able to anchor matrix fibrils. Indeed, sclerotome cells, condensing toward the notochord, become aligned with matrix fibrils radiating from and apparently attached to the notochord basement membrane (Ebendal, 1977). Physical changes in the embryonic environment seem important in initiating and directing cell migrations in embryos (Bard *et al*. 1975; Pratt *et al*. 1975; Markwald *et al*. 1978; Weston *et al*. 1978; Lofberg *et al*. 1980; Tucker, 1986; Newgreen, 1989) and cell responses to linkage appear to be sensitive to physical differences between fixed and unfixed matrices used in these experiments.

Shear, generated by morphogenetic movements, may also organise extracellular matrices in such a way that linkage could help to specify cell migration routes *in vivo*. Shearing could arise from folding of cell sheets, from relative sliding of tissue masses during differential or overall growth, or from fluid displacement caused by local swelling of extracellular matrices. Production of hyaluronic acid, which locally swells extracellular spaces, precedes several embryonic cell migrations (Bard *et al*. 1975; Pratt *et al*. 1975; Markwald *et al*. 1978; Lôfberg *et al*. 1980; Erickson and Weston, 1983). Displaced fluid, chanelled between tissue masses, may reorganise the matrix by shear. Ventrad sliding of the avian head ectoderm (Noden, 1984) could help to specify the ventrad migration routes of cranial neural crest cells by shearing the subectodermal matrix which forms their substratum. Migration terminates at a ridge that transiently forms on the midbrain but does not proceed even when this ridge subsides (Newgreen, 1989). Possibly, this ridge acts, not as a barrier to migrating cells (Tosney, 1982), but as a boundary between zones where the extracellular matrix is differently reorganised by sliding and by fluid flow. The unidirectional tendency of cells cultured between matrices pretreated by shearing was comparable with rates of population movement observed in, for example, migration of avian neural crest cells *in vivo* (Noden, 1975; Thiery *et al*. 1982; Erickson, 1985).

Since the effects of supposed fields of linkage on cell movement and alignment were statistically significant even in small samples, linkage may be an important factor during migrations of small cell populations such as those of the neural crest, sclerotome, endocardial cushion cells and primordial germ cells. The mechanisms proposed to explain these effects, and the ways in which they could arise *in vivo*, are speculative. However, the novel implication of the present results is that the structural arrangement of fibrillar matrices linked to rigid surfaces may confer a unidirectional tendency or taxis on cell movement. I have tentatively attributed this to linkage and suggest the name **DESMOT AXIS** for such a response (Gk. DESMO=chain/link).

## ACKNOWLEDGEMENTS

I am indebted to G. A. Dunn for pointing out the possibility of this type of response, and for frequent advice and discussion throughout this work. I wish to thank G. A. Dunn and A. F. Brown for the shape analysis and statistical software. This work was supported by an MRC research studentship.

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