A methodology for the systematic and quantitative study of cell contact guidance in oriented collagen gels Correlation of fibroblast orientation and gel birefringence

The movement of a cell exhibiting contact guidance is characterized as ‘bi-directional’, a cell having the maximum probability of migrating in opposite directions. These preferred directions are associated with chemical, structural and/or mechanical anisotropies of the substratum (Dunn, 1982). The most relevant example of contact guidance involves the bi-directional migration of cells along an axis of oriented extracellular matrix fibers. It is generally believed that contact guidance is an important morphogenetic mechanism, where traction forces exerted by cells might even create the fiber orientation that then serves to guide their migration (Stopak and Harris, 1982). Contact guidance is also implicated as an important component of several homeostatic processes (Katz and Lasek, 1980), such as wound healing, where retraction of the fibrin clot by platelets and contraction of the wound site by fibroblasts could cause radial orientation of extracellular matrix fibers and thereby guide cells to the wound (Lackie, 1986).

Despite the likely role of contact guidance in every physiological process involving cell migration (since tissue fiber orientation is either inherent or cell traction-induced), while there are several published studies of contact guidance based on artificial surfaces, such as grooved glass, plastic or quartz (e.g. see Dunn and Brown, 1986; Matthes and Gruler, 1988), there are only a few based on a biological substratum: specifically, collagen films (Dunn and Ebendal, 1978; Haston et al., 1983; Wilkinson et al., 1982; Boocock, 1987). Further, there are none, to date, that have systematically and quantitatively examined contact guidance of cells migrating within a biological three-dimensional environment, for example, reconstituted ‘tissue-equivalent’ collagen gels. This unsatisfactory situation exists because of the relative ease of preparing well-defined contact guidance fields and observing the resultant cell migration microscopically on the two-dimensional substrata, as compared to three-dimensional collagen gels^*. Clearly, a method that facilitates the systematic and quantitative study of contact guidance in the physiologically relevant environment of an oriented collagen gel is highly desirable.

There has been considerable study of fibroblasts in collagen gels recently, reflecting a growing consensus on the use of tissue-equivalent environments instead of tissue culture plastic and glass surfaces; the differences can be significant. For example, the proliferation (Sarber et al., 1981; Kono et al., 1990) and biosynthetic activity (Paye et al., 1987) of fibroblasts is suppressed for cells cultured in collagen gels as compared to those cultured on plastic. Improvments in imaging technology have given a particular impetus to the study of cell behavior in collagen gels, and again the differences can be significant. For example, the polarized morphology exhibited by fibroblasts cultured in collagen gels resembles the bipolar or stellate morphology observed in vivo rather than the morphology observed on planar glass or plastic, i.e. a single broad lamella (Heath and Hedlund, 1984; Heath and Peachy, 1989).

In this study, we continue the trend towards study of cell behavior in the tissue-equivalent environment of a collagen gel by characterizing fibroblast contact guidance in oriented collagen gels. Further, we describe a novel means of controlling contact guidance by controlling the directionality and extent of magnetically induced collagen fibril orientation. Ultimately, we seek to develop a quantitative relationship between an index of biased cell migration and an index of fibril orientation. Our approach towards this goal involves the following steps: (1) developing a method for systematically and reproducibly preparing simply (i.e. axially) oriented collagen gels; (2) measuring birefringence to characterize the fibril orientation; (3) measuring the biased migration response of the cells to characterize contact guidance; and (4) developing a correlation between birefringence and fibril orientation. In this paper, we describe our results for steps (1) to (3), and the automation of steps (2) and (3) via computer-controlled staging and image analysis. For step (3), we present here contact guidance results in terms of cell orientation measured from static images. We present elsewhere results in terms of biased cell migration obtained from three-dimensional cell tracking (Dickinson et al., 1993).

The key to step (1) is the use of a magnetic field to induce orientation of collagen fibrils during fibrillogenesis of a cell-containing collagen solution, apparently novel for the purpose of creating a contact guidance field. The methods used by previous investigators include drainage-induced orientation, when the collagen solution undergoes fibrillo-genesis on an inclined surface (Elsdale and Bard, 1972; Dunn and Ebendal, 1978; Kono et al., 1990), and stretch-induced orientation by absorption of free medium into pieces of filter paper placed at the ends of a slab of collagen gel (Wilkinson et al., 1982). Other methods of generating fibril orientation that have been reported are ordered convection driven by a collagen concentration gradient (Ghosh and Comper, 1988) or temperature gradient (Hughes et al., 1988) and weak electric currents (Becker et al., 1964). However, the fibril orientation in each of the latter methods was very nonuniform throughout the chamber.

Compared to drainage- and stretch-induced fibril orientation, magnetically induced orientation offers a unique combination of simplicity, systematizing and reproducibility. The orienting effect of a high magnetic field during fibrillogenesis has been applied to several biological systems (Yamagishi, 1990). The effect of magnetic fields on the self-assembly of lathyritic rat skin collagen was studied for samples contained in quartz cells with a 1 or 2 mm thickness maintained at 27.5°C during fibrillogenesis (Torbet and Ronziere, 1984). The development of fibril orientation was followed by monitoring birefringence as a function of time for magnetic field strengths of 1.9 T and 5.6 T. Examination of optical micrographs of the samples taken between crossed polars revealed that fibrils were highly oriented along the long axis of the chambers^*. Since a magnetic field will theoretically induce isotropic orientation of collagen fibrils in the plane normal to the field direction (see below), additional ordering induced by interactions of the growing fibrils with the long walls of the cuvette was inferred. This was supported by the observation of smaller birefringence for thicker samples.

Although unnecessary for exploiting a magnetic field to induce orientation of collagen fibrils, knowledge of the mechanism is of fundamental interest. It is known that a collagen molecule exhibits negative diamagnetic anisotropy, Δχ. In a magnetic field of strength H, a collagen molecule experiences a torque that tends to orient the molecule normal to the field direction. However, the ratio of orienting energy, ΔχH²/2, to randomizing thermal energy (Brownian motion), κT, is only 5×10⁻³ for a single collagen molecule at room temperature in the highest magnetic field available (about 20 T). It has been proposed that this ratio should exceed 6 in order to have more than 75% of the maximum magnetic orientation (Torbet and Ronziere, 1984). It was therefore concluded that the high orientation observed is due to the summation of diamagnetic anisotropies of the collagen molecules (monomers) that comprise the fibril (polymer). If N monomers assemble into a rotationally symmetric rigid polymer with their symmetry axes parallel, the diamagnetic anisotropy of the polymer can be considered to a good approximation as the sum of the diamagnetic anisotropies of the monomers, NΔχ. Thus, N must be sufficiently large before the growing fibrils become physically constrained in the developing collagen network such that the ratio NΔχH²/2κT is large enough to allow a high degree of fibril orientation. The effect of varying the fibrillogenesis time on fibrin filament orientation has been discussed by Torbet (1986) for fibrin assembly in a magnetic field: slow self-assembly at lower temperatures results in a large magnetically induced orientation, as growing fibrin filaments have enough time to orient into their equilibrium positions; for fast self-assembly at higher temperatures the time required for orientation is greater than that for filament growth and network formation, leading to a small orientation.

Following Torbet and Ronziere, we show here, on the basis of birefringence measurements, that collagen fibril orientation induced by magnetic fields in our observation chambers can be biased along the long axis of the chamber uniformly throughout the chamber and that the bias can be varied systematically by varying the magnetic field strength or temperature during fibrillogenesis. Further, we show that contact guidance of cells entrapped in the collagen gel that is elicited by collagen fibril orientation can thereby be varied systematically. Following a description and validation of our methods, we report the first correlation of fibroblast contact guidance (based on cell orientation) with collagen fibril orientation (based on gel birefringence) for cells cultured within oriented collagen gels.

Human foreskin fibroblasts (HFF) are obtained using a primary explant technique (Freshney, 1987) and kept in liquid nitrogen after slow freezing. A cell line is initiated for culture by thawing the contents of a vial and centrifuging at 1000 r.p.m. for 10 min at room temperature. The resulting pellet is resuspended in fresh Dulbecco’s modified Eagle’s medium (DMEM) supplemented with Fungizone, penicillin-streptomycin (P/S) and L-glutamine. Cells are plated out in 75 cm² culture flasks using 12 ml of DMEM with 20% fetal bovine serum (FBS) and kept in a humidified 10% CO₂ incubator at 37°C. At confluency cells are passed using trypsin and plated out 1:4 in flasks. Cells are discarded after the 15th passage and a new cell line is initiated.

Chambers suitable for observations in the light microscope of living cells dispersed in a collagen gel have to meet a number of requirements, for both maintaining cells and ensuring good optical quality (McKenna and Wang, 1989). The chambers used in this work consist of a U-shaped glass plate of nominal thickness 3 mm (Fig. 1), sealed between two cut microscope slides that are glued to the glass with silicone adhesive (Raumedic SI 2000) (after being cut to size, the microslides are preselected for minimal strain birefringence by examination between crossed polars). The rectangular space so formed has a length of 4 cm and a width of 1 cm. The adhesive is allowed to cure for 24 h and then the chamber is soaked in distilled water for 12 h. To minimize drying and ensure sterility, a Teflon cap is placed at the open end of the chamber after filling and a strip of Parafilm is wrapped around the cap. The chamber is inexpensive, autoclavable, easy to fabricate and handle, and proves to be satisfactory with respect to optical quality and maintenance of cells over the typical 24-48 h observation period. An additional criterion considered in the choice of aspect ratio and thickness of the rectangular space is to maximize the orienting effect of the magnetic field, which appears to be influenced by bounding surfaces (see Introduction), and by free convection effects (see Discussion). We observe that cell viability is compromised by using a thickness smaller than 2 mm.

The inverted microscope used in this work is a Zeiss Axiovert 10 equipped with a halogen lamp for transmitted light. For observations in polarized light the following optical components are used: (1) two polarizing filters as polarizer and analyzer (transmission for natural unpolarized light with filters crossed relative to filters parallel approx. 5×10⁻⁶); (2) a long working distance (70 mm) ‘LD’ condenser, with numerical aperture (NA) = 0.3, used for both brightfield and phase-contrast; (3) a ×10/0.3 NA Plan-Neofluar objective; (4) a ×40/0.6 NA LD Achroplan objective; (5) a ×25 Optovar lens; (6) a telescopic eyepiece; (7) a monochromatic interference green filter with nominal wavelength of 546 nm; (8) a λ/30 Brace-Kohler compensator (American Optical Instruments) consisting of a slide carrying a calibrated mica plate with retardation of 23 nm; (9) a first-order red plate (American Optical Instruments); (10) a λ/4 wave plate (American Optical Instruments). Neither the LD condenser nor the ×10 objective are manufactured to be strain-free. Although any strain-birefringence in the LD condenser is irrelevant, since the polarizer is placed beneath it, it is necessary to consider the strain-birefringence in the ×10 objective (see below).

For birefringence measurements, the analyzer is placed in a slot of fixed orientation located below the objective. The rotatable polarizer is mounted at the bottom of the LD condenser, and the compensator is inserted into a slot on the LD condenser mount immediately after the polarizer, taking advantage of the large free working distance available. Another slot, located immediately above the analyzer, allows insertion of the λ/4 wave plate or first-order red plate oriented 45° with respect to the analyzer. For birefringence measurements, the ×10 objective in combination with the LD condenser is employed between crossed polarizer and analyzer. For imaging cells within the gel for orientation measurement, the same combination is employed in brightfield. For imaging collagen fibrils within the gel, the ×40 objective in combination with the ×2.5 Optovar lens and LD condenser is employed in phase-contrast microscopy.

Observations using the microscope are performed through the eyepiece or by sending all the light with a beam-splitting prism to a Hamamatsu CD 2400-07 Newvicon video camera system for cell and fibril imaging or a Pulnix TM-745 CCD video camera system for birefringence measurement, both provided with independent controls of gain and offset for contrast enhancement (see below). By imposing a high offset (threshold level) on the video signal and amplifying with the gain, the contrast in the video signal above the offset is enhanced (Inoue, 1987).

The video cameras are interfaced to a Kontron IBAS image processing and analysis system (386-based MIAP-2). A schematic representation of the system is shown in Fig. 2. The analog signal coming from the video camera is converted by an 8-bit digitizer into an array of digital values, ranging from 0 to 255, which are displayed on an image monitor as gray levels. The IBAS system includes a number of routines for image enhancement and image analysis that are accessible at a programming level, which we incorporate into structured macros for automatic execution. A Panasonic TQ-2028F optical disk recorder is used to store images for subsequent verification of macro execution.

An important feature of our workstation that is exploited for automated birefringence and cell orientation measurements is the Zeiss 3-axis motorized translating microscope stage, which allows the sample to be moved in three dimensions under computer control (Zeiss Microscope System Processor (MSP) 65 controller). The optically encoded motors of the translating stage allow high precision movement in 0.25 μm increments in the x- and y-axes and 0.05 μm increments in the z-axis (< 1 μm repeatability). Further, in order to fully automate birefringence measurements, an encoded motorized rotating stage (Oriel) connecting to a chamber holder is mounted on top of the translating stage (Fig. 3). The rotating stage is also interfaced to and controlled by the IBAS macros via the MSP 65. It has a 36 mm diameter through-hole that makes it suitable for imaging the samples in the chamber suspended below it and is rotatable through 360° (0.5 arc/s resolution, ± 25 arc/s unidirectional repeatability, 6 min backlash). The chamber is set in the rectangular recess of a circular brass plate also having a 36 mm diameter through-hole. This plate rotates on the ledge of a recessed hole in a supporting brass base, which itself is mounted on top of the translating stage.

First, the center of rotation of the stage is determined by the following procedure. A point on a microslide is focused and centered in the field of view. The microslide is then rotated 180°and the same point is recentered in the field of view. The coordinates of the center of rotation are calculated as the mean values of the coordinates of the point before and after the rotation. The coordinates of the center of rotation are assigned as the origin for the translating stage. The rotating polarizer and fixed-orientation analyzer are inserted into the light path and crossed by rotating the polarizer to the position of maximum extinction.

Then, a chamber is mounted on the rotating stage with its long dimension, approximately the slow axis of the sample if the chamber was oriented properly in the magnetic field, parallel to the axis of the polarizer. Five points are user-selected, four defining the midpoints of the sides of a 15 mm × 6 mm rectangle centered with respect to the chamber, and the fifth at the center of the rectangle (points are user-selected to ensure that measurements are not made in the vicinity of any air bubbles).

The chamber is then rotated by 5° increments over a 180° range. At each orientation, the translating stage sequentially moves to center each user-selected point in the field of view, for which the mean gray level (MGL) in the IBAS measurement window (displayed on the image monitor) is measured and stored in a data array. The window is an ellipse, with principle axes in a ratio equal to the pixel aspect ratio of the CCD camera (1.27). The long axis of the elliptical window is set at 100 μm, so that the MGL corresponds to a measured area of 6.18×10³ μm². When the 180° rotation is complete, the compensator is inserted into the light path (centered over the specimen in the LD condenser mount) with the slow axis of the mica plate, as determined using a first-order red plate (Bennett, 1950), oriented at a prescribed angle relative to the axis of the analyzer. The chamber is then rotated again over a 180° range at 5° increments following the same procedure as described above. The prescribed angle is usually 4°, as we have determined that with our oriented gels using typical light levels and typical CCD video camera gain and offset settings, the output video signal from the CCD camera is within its linear range over the rotation. The importance of staying within the linear range is discussed next.

where MGL₀ is the MGL of the light leaving the polarizer and δ is the retardation of the sample (Fuller, 1990). MGL values as a function of θ are thus measured values and χ, B and A are fitted parameters (in principle, MGL₀ could be determined and then δ derived from A using equation (2), which is the transmission method as opposed to the null method that we employ, as described subsequently, but in practice the accurate determination of MGL₀ using the transmission method is very difficult (Allen et al., 1981)). Fig. 4A shows the MGL as a function of θ for one point of an oriented gel sample between crossed polarizer and analyzer and the least squares fit to equation (1).

MGL values as a function of β, the angle between the axis of the polarizer and the fast axis of the sample (β = θ + 90° − χ for that point), are measured values, α is the angle between the axis of the polarizer and the fast axis of the compensator (86°), δ′ is the retardation of the compensator expressed in degrees (23 μm/546 μm.360°), and MGL₀ and δ, the retardation of the sample expressed in degrees, are fitted parameters. Fig. 4B shows the MGL as a function of β with the compensator inserted for the same oriented gel sample point as in Fig. 4A and the least squares fit to equation (3).

Since the objective is not strain-free, it is necessary to account for the contribution of its strain birefringence, since it can be significant given the relatively small changes in measured MGL values with the compensator placed at a prescribed angle of 4°. A procedure that we have derived to do this is described in the Appendix. Fig. 5 shows the improved least squares fit to the extended forms of equations (1) and (3) stated therein. In this case, the corrected value of δ differs by only 2% (15.2° versus 14.9°).

However, as seen in Table 1, corrections to δ among those presented range up to 22.4%.

where λ is the wavelength of light (546 nm) and L is the sample thickness (3.2 mm average for our chambers). We use the convention for collagen that, since the slow axis of transmission is parallel to the long axis of the fibril, the fibril is said to exhibit positive birefringence with respect to its long axis (Bennett, 1950).

As noted above, we assume that the video output signal from the CCD camera is a linear function of the input light intensity. In order to verify this, we conducted the following test: using only the LD condenser and ×10 objective, we measured the MGL with (MGL₅₀) and without (MGL₁₀₀) a 50% neutral density filter in the light path over a series of light levels for our typical gain and offset camera control values. After subtracting the (small) measured MGL at zero light level from each value, we plotted MGL₁₀₀ versus MGL₅₀ (Fig. 6), which should be linear with slope = 2 if MGL = c I, since the 50% neutral density filter causes I → I/2 at each light level. As can be seen, the linear range is defined over some initial range of light levels. Accordingly, we adjust the light level to ensure that measured MGL values fall within this linear range in the birefringence measurements.

In order to assess the accuracy of birefringence measurements, the λ/4 wave plate (calibrated for a wavelength of 546 nm) and the compensator were placed between crossed polarizer and analyzer. The λ/4 wave plate was oriented with its slow axis parallel to the axis of the polarizer. The compensator was inserted between the λ/4 wave plate and the analyzer with its slow axis oriented 45°to the axis of the polarizer and then rotated to obtain MGL as a function of θ. By fitting these data with equation (3), a value of 22.17 nm is obtained for the retardation of the compensator, as compared to the value of 23 nm reported by the manufacturer. The discrepancy may be due to the fact that while the λ/4 wave plate was factory-calibrated for a wavelength of 546 nm, it is not known whether the compensator was also. As one further check, we created an oriented gel having relatively small birefringence within the range of the compensator when used in the conventional way (Bear and Schmitt, 1936), with a retardation of 8.7° read directly from the compensator (the gel was oriented under the conditions suggested in the Discussion). This value compares very well with the value of 8.63 (^± 0.15)° obtained using our automated birefringence method described above.

A predefined volume within the gel is prescribed to be automatically scanned for imaging cells and measuring their orientation with respect to the long axis of the chamber. This volume is chosen to be contained in the volume within which birefringence measurements are made. The automatic scanning is accomplished with the IBAS-controlled translating stage by defining a two-dimensional x-y meander across a plane in the upper portion of the gel, involving a series of adjacent fields (1160 μm × 870 μm). For each field, the gel beneath is ‘optically sectioned’ by acquiring images for a series of prescribed z-depths (100 μm increments). A deblurring algorithm based on using a high-pass filter to remove ‘out-of-focus’ information (Dickinson et al., 1993b) is used to develop a composite image of the projected cell images for all cells in the thickness of gel optically sectioned. A standard IBAS function is used for measuring the orientation of an object based on the orientation of its maximum Feret diameter (32 directions separated by 5.6° increments being sampled) with respect to the x-axis, which corresponds to the long axis of the chamber and the axis of fibril orientation (see Results). Since the cells are typically quite elongated in the gel with a large aspect ratio (Fig. 7), the orientation measurement of the projected cell morphology is quite accurate. A comparison of the orientation measurement obtained from our automated image analysis with that inferred from the cell morphology can be made in Fig. 8. Given such a favorable comparison, adaptation of the more complicated determination of orientation proposed for cells on planar substrata based on cell shape analysis (Dunn and Brown, 1986) was not pursued. Since we confine our region of interest to be within the gel and do not include cells within approx. 200 μm of the microslides, the possibility of ‘desmotaxis’ should not complicate our cell orientation measurement. Desmotaxis refers to the directed movement of cells in response to the cell traction-induced outward orientation of fibrils that are anchored to a proximal rigid surface, and was shown to be important for primary chick heart fibroblasts in Vitrogen 100 gels up to 100 μm from a surface (Boocock, 1989).

which varies between 0 and 1 as the cell orientation with respect to the axis of fibril orientation (θ_c) varies from random to perfect orientation. The x-y meander in the automated scan is continued until a minimum of 300 cells are measured for computing O_c.

Collagen gels are prepared with the following composition (volume basis): HEPES (2%), 0.1 M NaOH (13.2%), 10× minimum essential medium (10%), FBS (6.7%), P/S (0.1%), L-glutamine (1%), and Vitrogen 100 collagen solution (67%) (Celtrix Laboratories). The components and the final mixtures are kept on ice to avoid gellation of the sample before exposure to the magnetic field. Cells suspended in DMEM with 20% FBS are added to the mixture in such a way that the initial cell concentration is between 10³ and 10⁴ cells/ml. A low cell concentration is desired in order to minimize cell restructuring of the fibril orientation induced by the magnetic field and to minimize change in the medium composition, since it is not possible to change the medium in our chambers.

The chambers, previously sterilized in an autoclave, are loaded, capped, and kept on ice before being exposed to the magnetic field. Because none of the super-conducting magnets used are equipped with a system for temperature control, the chambers are placed in polystyrene insulating boxes containing water warmed to a temperature in the range 31°C to 35°C (see below) during the exposure to the magnetic field. Measurements performed outside the magnets show that the temperature inside the boxes drops about 1.5 deg. C in one hour. The chambers are oriented with their long axis normal to the direction of the magnetic field in order to have the orientation of the collagen fibrils along the long axis, i.e. their long axis is oriented normal to the bore of the magnet (Torbet and Ronziere, 1984). In order to minimize cell settling effects, chambers are inverted immediately before exposure to the magnetic field. The samples are exposed to the magnetic field for 2 h. Independent tests show that the majority of fibrillogenesis occurs well within this time at 31°C to 35°C. The tests are performed by measuring MGL versus time for a chamber filled with collagen solution (data not shown). The increase in turbidity (i.e. MGL) that occurs during gellation is correlated to the extent of fibrillogenesis (Gross and Kirk, 1958). The appearance of the collagen fibril network that we observe under high magnification at the light microscope level (Fig. 9) is consistent with that previously reported by others (Grinnell and Lamke, 1984; Allen et al., 1984)

After removal from the magnets, the chambers are placed on the microscope stage and maintained at 37°C with an air stream incubator. The first set of birefringence and cell orientation measurements is performed after the initial cell spreading period (6-12 h following gellation) and again after a subsequent 50 h incubation. To assess further any time-dependent contact guidance, orientation measurements are made for selected specimens at 45- min intervals during the incubation period (in this case, less than 300 cells could be measured, as indicated subsequently).

An important issue concerning our methodology is whether the fibril orientation is biased along the long axis of the chamber, since this is the simplest contact guidance field that can be created, and therefore the desired one at this juncture (in this case, contact guidance can be characterized most simply as cell orientation with respect to the long axis of the chamber, see eqn (5)). Specifically, when viewing the gel from the chamber top, we want the projections of the fibrils into the plane to be, on average, biased along the long axis of the chamber with symmetry about the axis, which we will refer to as ‘axially oriented’. Notice that this places no requirements on what the distribution must be when viewing from the side (see Discussion). The fact that the fibrils are axially oriented is demonstrated by our finding that the measured extinction angle is very close to 0°, the angle with respect to the long axis of the chamber (Table 1). Since a collagen fibril exhibits positive birefringence with respect to its long axis (Bennett, 1950), i.e. the slow axis of transmission is parallel to the long axis of the fibril, a 0° extinction angle implies that the mean orientation of the fibrils is along the long axis of the chamber.

Another important issue is whether the fibril orientation is uniform as well as axial, since the low cell concentration used to minimize cell-cell interactions and cell traction-induced changes of the imposed fibril orientation requires a large region to be scanned in order to measure a statistically significant number of cells. The fit at all five points defining the 15 mm × 6 mm rectangle centered within the chamber (see Materials and Methods) is comparable to that illustrated in Fig. 5 for one point. This is reflected in the small standard deviations for the measured values for χ and δ stated in Table 1. Thus, it appears valid to characterize contact guidance based on all cells contained within the sampling volume defined by the rectangle and 3 mm chamber thickness (2700 cells at 10⁴cells/ml if the entire volume is measured).

A more subtle issue is whether the HFF contribute significantly to the birefringence measurement, since a cell is birefringent when elongated because of the alignment of its cytoskeletal filaments and fibers, as is evident in Fig. 7. The total cell contribution is an increasing function of cell concentration (the same is true for the collagen fibrils). As seen in Table 2, there is no statistically significant difference in birefringence between HFF-populated and HFF-free gels made under identical conditions at the cell concentration used (retardation values following the initial cell spreading period are used for comparison to avoid the potential complication of time-dependent birefringence in the HFF-populated gels due to extensive fibril reorganization associated with the cells’ tractional structuring activity; see below).

Table 1 presents measured values for collagen fibril orientation (i.e. χ and corrected δ) for duplicate 4.0 T/35°C samples, a 3.6 T/32°C sample, duplicate 4.7 T/34°C samples, and a 4.0 T/31°C sample. The values for both pairs of duplicate samples are very similar, attesting to reproducibility. The ability to vary the extent of fibril orientation by varying the magnetic field strength and/or temperature during fibrillogenesis is demonstrated by comparing the conditions for which greater values for δ are obtained. A significantly greater value is obtained for the lower 31°C fibrillogenesis temperature at 4.0 T as compared to the 35°C samples at 4.0 T. In fact, a somewhat greater value is even obtained for a somewhat smaller and greater magnetic field strength (3.6 T/32°C and 4.7 T/34°C samples) when the fib-rillogenesis temperature is also lower. These results appear to be due to the orienting effect of the magnetic field acting over an extended fibrillogenesis period associated with a lower temperature (see Introduction).

Another important issue of our methodology, especially in view of the extended time-lapse observation necessary for the cell tracking required to assess biased migration in contact guidance, is whether the uniform axial fibril orientation remains so. This is a nontrivial issue, especially for fibroblasts, which have been reported to significantly restructure (Stopak and Harris, 1982) and even grossly compact (Bell et al., 1979) collagen gels due to traction exerted on local fibrils. Even though the HFF locally restructure the fibrils in our oriented gels, as seen in the polarized light micrograph of Fig. 7, Fig. 10 shows that under the conditions employed, HFF contact guidance, as characterized by the cell orientation parameter, O_c, is relatively constant over at least the initial 20 h incubation period (fluctuations in O_c reflect imprecision in the orientation measurements and the fact that less than 300 cells were measured in obtaining this time-dependent data). This is consistent with our finding that the retardation, δ, is not statistically different between the beginning and end of the 50 h incubation period (as seen in Table 3), and that O_c is essentially constant, except for a decrease in the least magnetically oriented 4.0 T/35°C sample. (The trend we observe is that O_c is more variable in time for samples with even less fibril orientation, which, however, are also not uniformly axial as oriented under our present conditions (see Discussion) and are thus not reported here). It is also consistent with the finding of a threshold cell concentration for cell orientation to develop in a rectangular collagen film that, like the gel in our chambers, is restrained from macroscopically compacting (see Klebe et al., 1989).

For the different combinations of magnetic field strength and temperature during fibrillogenesis (Table 1) that generated samples possessing different collagen fibril orientations (i.e. Δn values, obtained from the corrected δ values and eqn (4)), we quantified the resultant cell orientation (O_c). Although the plot of Fig. 11 correlating O_c to Δn does not characterize the complete range of O_c values, it is consistent with the expectation that O_c increases monotonically with Δn, i.e. HFF orientation increases monotonically with fibril orientation from random to perfect. This correlation can be visualized in the videomicrographs of composite cell images presented in Fig. 12 and in the cell orientation distributions presented in Fig. 13 (from which the O_c values are derived via eqn (5)), which clearly show the increase in cell orientation along the axis of collagen fibril orientation as Δn increases. Table 4 presents the probability that any two of the distributions in Fig. 13 are identical, based on a two-sided Komolgorov-Smirnov test (e.g. see Hogg and Tanis, 1983). We conclude with reasonably high probability that the contact guidance responses, based on the cell orientation distributions, are different among the collagen gels oriented under different conditions.

The main purpose of this paper is to describe the basis for a complete methodology to quantify systematically the correlation between biased cell migration and collagen fibril orientation for cells cultured in an oriented collagen gel, a model for cell contact guidance in a tissue with oriented ECM fibers. We validate the various methods and demonstrate their implementation here by developing the first quantitative correlation for cell contact guidance in an oriented collagen gel, using human foreskin fibroblasts (Fig. 11). The merits of our methodology are obvious: (1) the simple, systematic and reproducible method of creating a uniform axially oriented contact guidance field, which can be varied as a function of the magnetic field strength and temperature during fibrillogenesis; (2) the quantification of the contact guidance field (i.e. extent of collagen fibril orientation) by measuring birefringence using automated sample positioning and rotation and image analysis; and (3) the quantification of contact guidance by measuring cell orientation, again using automated sample positioning and image analysis. Since fibroblasts were reported to exert the most traction among several differentiated blood and tissue cells (Harris et al., 1980), in our demonstration that we can adjust our assay conditions and measurement methods so as to circumvent significant HFF-induced tractional restructuring of the magnetically induced collagen fibril orientation, which although an interesting phenomenon would make interpretation of the data for our stated goal difficult, we have successfully handled the most demanding case.

Before discussing our ongoing development of this methodology and its possible applications, it is appropriate to discuss some of its limitations. In fact, seeking to remove the limitations constitutes our ongoing development.

One limitation is that of obtaining less-oriented collagen gels that are still uniformly axial, in order to define the lower range of the contact guidance correlation presented in Fig. 11. We observe, with our present chambers, that the orientation of samples created in 1.0 or 1.5 T at 30°C to 35°C is not reproducibly uniform and axial. This is indicated by large variations in regression values for χ and δ as a function of position, e.g. χ = 9.5° ± 38.5° for a 1.5 T/30°C sample, and by a bimodal cell orientation distribution, with a second preferred direction being the short axis of the chamber, as seen for the 0 T/37°C sample in Fig. 13A. (Curiously, Matthes and Gruler (1988) report, in their Fig. 4A, bimodal orientation distributions for neutrophils on planar substrata that are perfectly uniformly axial, with the orientation in the second preferred direction, which is normal to the principle axis, being almost as high; this is in contrast to our results where we observe bimodal orientation distributions for HFF in the oriented collagen gels that are not uniformly axial but unimodal distributions in the oriented gels that are so.) This also shows that some collagen fibril orientation occurs in the chambers even in the absence of a magnetic field, probably due to recirculation zones of the collagen solution in the chamber that we can observe prior to gellation, in combination with surface effects. We speculate that the effects of free convection on the orientation of growing collagen fibrils during gellation may dominate the orienting effects of the magnetic field at lower field strengths leading to gels that are not uniformly axially oriented. We are investigating the use of higher fib-rillogenesis temperatures (36°C to 40°C) and collagen concentrations (75%) at a higher field strength (5.0 T). With these conditions, the dominating effects of the magnetic field act over a much shorter gellation time, which may yield a uniform axially oriented gel but with less orientation (as desired) in our present chamber. It may also be worthwhile investigating the use of chambers with a larger aspect ratio (long axis/short axis) to minimize or eliminate free convection and determining if uniformly axial orientation can then be obtained at 1.0 and 1.5 T.

While on the subject of fibril orientation in our samples, it is worth noting that although equations (A2) and (A4) in the Appendix fit the MGL versus rotation angle data very well, as illustrated in Fig. 5, a good fit, while demonstrating that the birefringence measurements are valid, implies only that the gel is birefringent in the direction tested (i.e. through the thickness). It implies nothing about the nature of the fibril orientation distribution, although we can infer from the extinction angles that the fibrils are axially aligned as noted previously (this is also the impression gleaned from direct microscopical observation of the fibrils, e.g. see Fig. 9). However, our birefringence measurements through the gel thickness imply nothing, in particular, about the orientation distribution of the fibril projections in the plane when viewing from the chamber side. Any assessment would require birefringence measurements in that direction (i.e. through the gel width). This has proven logistically difficult, although our impression when viewing from the side of a chamber (with side walls made from microslides) in polarized light is that, across most of the thickness, fibril orientation does not appear to be biased along the long axis of the chamber with symmetry about the axis. Rather, fibrils appear to be oriented diagonally, which is possibly a consequence of the recirculation pattern of the solution during fibrillogenesis (in contrast, fibrils within approx. 100 μm of the microslides appear highly oriented in the plane parallel with the microslides). This, however, does not have an impact on the validity of characterizing contact guidance with respect to the long axis of the chamber when viewing from above, for which we have documented the uniform axial orientation of fibrils.

Another limitation of our present methodology is due to the form birefringence inherent in a collagen gel, so that measured birefringence cannot be theoretically related to the collagen fibril orientation distribution via molecular optics theory (e.g. Lorentz-Lorenz equation; Fuller, 1990). Theory can only relate intrinsic birefringence to orientation distribution except for a few idealized cases. Intrinsic birefringence arises from the inherent anisotropy in the polarizability (e.g. nonuniform distribution of transition moments) of the molecules in the sample. When molecules with such anisotropic properties are also arranged in an anisotropic way, macro-scopic quantities such as refractive index will be dependent on the orientation of the incident polarized light. Form bire-fringence is present when molecules of anisotropic shape dissolved or suspended in a medium are arranged in an anisotropic way and the refractive index of the molecules is different from that of the medium (it is present even if the molecules are isotropic in their polarizability but are anisotropically arranged; it vanishes when the refractive index of the particles is equal to that of the surrounding medium irrespective of arrangement). Although form birefringence, if it exists, will always be a positive contribution to the measured birefringence, there is no complete theory that can predict the magnitude of its contribution and thereby the magnitude of intrinsic birefringence (Fuller, 1990). Since the refractive index of collagen has been reported in the range 1.46-1.52 (Yarker et al., 1983) and we have measured that for our tissue culture medium to be 1.335 (using an Abbe refractometer), form birefringence occurs in collagen gels. Fortunately, we find that many collagen fibrils are optically resolvable with the light microscope at high power (Fig. 9), so we can develop an empirical correlation in the following way: after measuring the birefringence (Δn) at a point, morphometric analysis of the collagen network image (e.g. see Liu et al., 1990) can be conducted to determine a collagen fibril orientation parameter, O_p (e.g. defined analogously to O_c). The correlation can thus be developed from applying this procedure to gels oriented to various degrees using different conditions and should be valid for constant contact guidance assay conditions (collagen concentration, tissue culture medium composition, chamber thickness). Once this correlation is available, we can convert all the Δn values reported here into O_p values.

As stated in the Introduction, our ultimate goal is to develop a quantitative correlation between an index of biased cell migration and an index of fibril orientation. As the next step in that direction, we will present elsewhere a preliminary correlation for biased cell migration and birefringence for the same fibroblasts used here by extending our methodology to employ 3-D cell tracking algorithms along with automated image analysis (R. B. Dickinson, S. Guido and R. T. Tranquillo, unpublished). We are currently developing similar correlations for a variety of blood and tissue cell types in addition to fibroblasts, and in oriented fibrin gels as well as collagen gels.

Our methodology may prove useful in determining the dominant cellular mechanism underlying contact guidance among those proposed by Dunn (1982): (1) focal adhesions are confined to fibrils, which, since aligned (chemical anisotropy), will orient the adhesions, hence locomotion (i.e. haptotaxis); (2) the cell distorts differently when migrating in different directions, less so when oriented with fibrils, due to the structural anisotropy, and hence favors locomotion oriented along fibrils; and (3), as elaborated by Haston et al. (1983), since exertion of cell traction on the substratum is necessary for locomotion, pseudopods pulling in the direction of maximum elasticity modulus (i.e. along fibrils) are more efficient, because the displacement of fibrils towards the cell is much less than for pseudopods pulling in the direction of minimum elasticity (i.e. across fibrils); the result of this mechanical anisotropy again being locomotion oriented along the fibrils.

A potentially significant application of our use of a magnetic field to create a contact guidance field is for engineering the fibril orientation of bioartificial organs and tissues so as to control the infiltration of host cells and/or the distribution of graft cells (Doillon et al., 1988, Greisler, 1990). We observe that fibroblasts directionally invade a highly oriented collagen gel relative to a control gel, i.e. one not oriented with a magnetic field (unpublished).

The ultimate challenge in the understanding of contact guidance in fibrillar networks like collagen gels, fibrin gels and tissues is to predict a priori how cells will redistribute in response to the contact guidance field that they create themselves by deforming, thereby orienting, the fibrillar network in the course of exerting traction. This potentially significant morphogenetic mechanism in development and homeostasis (e.g. wound contraction) has been documented in vitro (Harris et al., 1981, 1984; Stopak et al., 1982). The correlations obtained by the methodology described here, based on contact guidance in response to an imposed (magnetically induced) fibril orientation, will serve as the basis for developing and refining mathematical theories relating cell traction, network deformation, fibril orientation and contact guidance, i.e. contact guidance in response to cell traction-induced fibril orientation (Tranquillo et al., 1992).

This work has been supported by a National Science Foundation Presidential Young Investigator Award (BCS-8957736) to RTT. Valuable technical assistance by Alina Ruta, the generous provision of laboratory facilities by Drs David Knighton and Michael Caldwell (Department of Surgery), and the use of the magnets in the Center for Magnetic Resonance Research of the Medical School, the MRI Department at the University of Minnesota Hospital, and the laboratory of Prof. Bruce Hammer (Department of Radiology) are all gratefully acknowledged.

where, as in equation (3) in the main text, β and δ are the angle between the fast axis of the sample and the axis of the polarizer, and the retardation of the sample, respectively, and β = θ − χ.

The system of equations composed of (A2) and (A4) is solved for δ, taking advantage of the fact that γ and δ′′ appear only as the product (sin2γsinδ′′), as follows. First, since the extinction angle of the sample, χ, is observed not to be significantly affected by the objective, equation (1) is used to determine χ (i.e. values of χ determined from the more complicated equation (A1) do not differ significantly from those determined by equation (1) for the estimated values of γ and δ′′ and typical values of δ). The first set of MGL versus β data (without compensator in place) is fit with equation (A2) using the value of δ determined from equation (3). The fit parameters are the product (sin2γsinδ′′), MGL₀ and B. The value of (sin2γsinδ′′) so determined is substituted into equation (A4), and by fitting the second set of MGL versus β data (with compensator in place) a new value of δ is calculated. This value is substituted into equation (A2) and the procedure is repeated iteratively until convergence is attained.