Mechanisms of Epidermal Repair in Embryos

Epidermal wound healing in embryonic mammalian skin is very different from that in adult epidermal skin. Although not explicitly stated above, our modelling there is for adult re-epithelialisation. When adult skin is wounded, the epidermal cells surrounding the lesion move inwards to close the defect and the fairly well-established mechanism for closure is by lamellipodial crawling of the cells near the wound edge. Also almost all aspects of adult epidermal wound healing are regulated by biochemical growth factors. Although there is still controversy about some of the details the key elements seem fairly well established and it is these we incorporated in our models. Embryonic epidermal wound healing is very much less documented and very different. A brief review of the two processes is given by Sherratt et al. (1992).

Experimental work by Martin and Lewis (1991, 1992) suggests that embryonic epidermal wound healing may be caused by a completely different mechanism. Using a tungsten needle they made lesions on the dorsal surface of four-day embryonic chick wing buds, by dissecting away a patch of skin approximately 0.5 mm square and 0.1 mm thick. The epidermis, its basal lamina, and a thin layer of underlying mesenchyme were removed. The wounds healed perfectly and rapidly, typically in about 20 hours. Although mesenchymal contraction played some role in healing, the epidermis also moved actively across the mesenchyme. However, unlike adult epidermal cells, there was no evidence of lamellipodia at the wound front of the epidermis as shown in Figure 9.16(a). This absence of lamellipodia was consistent with a second important observation in a related study, namely, when a small island of embryonic skin was grafted onto a denuded region of the limb bud surface, the grafted epidermis, instead of expanding over the adjacent exposed mesenchyme, actually contracted, leaving its own mesenchyme exposed. This phenomenon suggested that the mechanism underlying epidermal movement might be a circumferential tension at the free edge, acting like a purse string that pulls the edges inwards. Such a mechanism would cause shrinkage of both an epidermal island and a hole in the epidermis.

Searching for the cause of such a purse string effect, Martin and Lewis (1991,1992) examined the distribution of filamentous actin in the healing wounds, by staining specimens with fluorescently tagged phalloidin, which binds selectively to filamentous actin. This revealed a thick cable of actin around the epidermal wound margin as shown in Figures 9.16(b) and (c) localized within the leading row of basal cells: it is a very narrow band. The cable appeared to be continuous from cell to cell, presumably via adherens junctions, except at a very few points; it was present within an hour of wounding, and persisted until the wound was closed. Preliminary evidence suggests that an actin cable may also form at the periphery of the contracting epidermis in the skin grafts mentioned above. Simple incisional wounds made by a slash, Figure 9.17, along the proximodistal axis of the limb take only seconds to make, as opposed to the 5-10 minutes required to dissect a square of skin from the limb bud. As described in the review article by Sherratt et al. (1992) the slash lesion data indicate that the cells at the wound edge begin to organize their actin into a cable within minutes of wounding, although the cable takes an hour or more to attain its full thickness. Below we discuss models which incorporate the concept of an actin cable and its role in embryonic wounds.

Figure 9.16. (a) Scanning electron micrograph of a wound edge in chick embryonic epidermis 12 hours after the operation. The wound was made by removing a square patch of embryonic skin from the dorsal surface of a chick wing bud at 4 days of incubation. The epidermis is above, with the flattened surface of the exposed mesenchyme below. Note the smooth edge of the epidermis and the absence of finger-like lamellipodia. Scale bar = 10 //m. (b) and (c) The epidermal wound front on the dorsum of a chick wing bud after 12 hours of healing, as seen in optical section by confocal scanning laser microscopy. The tissue has been stained with rhodamine-labelled phalloidin, which binds to filamentous actin, and the sections are parallel to the plane of the epidermis. The epidermis is at the lower left, with the exposed mesenchyme (largely below the plane of section) at the upper right. (b) Superficial section, in the plane of the periderm, whose broad flat cells are outlined by their cortical actin. (c) Section about 4 /m deeper, in the plane of the basal epidermal cells, showing the acting cable at the wound front. Scale bar for (b) and (c), = 50 /m. (From Sherratt et al. 1992, originally presented in Martin and Lewis 1991)

Figure 9.16. (a) Scanning electron micrograph of a wound edge in chick embryonic epidermis 12 hours after the operation. The wound was made by removing a square patch of embryonic skin from the dorsal surface of a chick wing bud at 4 days of incubation. The epidermis is above, with the flattened surface of the exposed mesenchyme below. Note the smooth edge of the epidermis and the absence of finger-like lamellipodia. Scale bar = 10 //m. (b) and (c) The epidermal wound front on the dorsum of a chick wing bud after 12 hours of healing, as seen in optical section by confocal scanning laser microscopy. The tissue has been stained with rhodamine-labelled phalloidin, which binds to filamentous actin, and the sections are parallel to the plane of the epidermis. The epidermis is at the lower left, with the exposed mesenchyme (largely below the plane of section) at the upper right. (b) Superficial section, in the plane of the periderm, whose broad flat cells are outlined by their cortical actin. (c) Section about 4 /m deeper, in the plane of the basal epidermal cells, showing the acting cable at the wound front. Scale bar for (b) and (c), = 50 /m. (From Sherratt et al. 1992, originally presented in Martin and Lewis 1991)

Figure 9.17. Scanning electron micrograph of a linear slash wound in chick embryonic epidermis, immediately after the operation. The wound was made on the dorsal surface of the wing bud at 4 days of incubation (stage 22/23). The thin arrows indicate the epidermal wound edge, while the thicker arrows denote the edge of the underlying mesenchyme. The epidermis has retracted over the underlying mesenchyme by about 3040 /m. Scale bar = 100 /m. (From Sherratt et al. 1992)

Figure 9.17. Scanning electron micrograph of a linear slash wound in chick embryonic epidermis, immediately after the operation. The wound was made on the dorsal surface of the wing bud at 4 days of incubation (stage 22/23). The thin arrows indicate the epidermal wound edge, while the thicker arrows denote the edge of the underlying mesenchyme. The epidermis has retracted over the underlying mesenchyme by about 3040 /m. Scale bar = 100 /m. (From Sherratt et al. 1992)

The different mechanisms of healing in adult and embryonic epidermis raise many problems that call for mathematical modelling. Perhaps the most important aspect of embryonic wound healing is that they heal without scarring, and not only epithelial wounds. An understanding of how the processes differ could have far-reaching implications for clinical wound management (see, for example, Martin 1997). Fetal surgery is a high-stakes field, has many attractions and dangers and is highly controversial with many complex ethical issues. It has already been used to treat spina bifida (since 1998) and this is only the beginning. There are many advocates for treating nonlethal conditions such as facial deformities and other defects. We have already mentioned the potential for cleft palate repair in Chapter 4. The review article by Longaker and Adzick (1991) and their edited book of contributed articles specifically on fetal wound healing (Adzick and Longaker 1991) is a good place to start. The article in this collection by Ferguson and Howarth (1991) specifically discusses scarless wound healing with marsupials and lists the many features which distinguish fetal from adult wound healing. A reason for studying marsupials is that unlike most mammals their young are very immature at birth. The article by Martin (1997) is also particularly relevant; he discusses wound healing from the point of view of perfect (scarless) skin regeneration. There is a large literature in the area with an abundance of data.

Another aspect of wound healing associated with the skin are the techniques now available for making cell layers from suspensions of disassociated cells which proliferate rapidly and form confluent monolayers for treatment of burns, plastic surgery and so on. For a view of the general picture, see the Scientific American article by Green

(1991). Again there is an increasing body of knowledge in this area with many modelling problems associated with the formation of these monolayers of cells.

9.9 Actin Alignment in Embryonic Wounds: A Mechanical Model

The experimental results of Martin and Lewis (1991, 1992) raise two major questions: first, how does the actin cable form, and, second, how does it cause the wound to close, if in fact it has this function? Here we consider the first of these questions. The actin cable forms in response to the creation of a free boundary at the wound edge. In this section we consider possible explanations for the aggregation and pronounced alignment of filamentous actin at the wound edge, which give rise to the actin cable, in terms of a mechanical response to this free boundary.

At the developmental stages we consider, the embryonic epidermis is two cell layers thick, consisting of a superficial, pavement-like peridermal layer and a cuboidal basal layer. The actin cable develops in the basal layer, and it is to this layer that our modelling considerations apply; refer also to Figure 9.16. The basal cells form a confluent sheet, attached to the underlying basal lamina. Following wounding, the cytoskeleton of these cells undergoes rapid changes, on the timescale of a few minutes, and reaches a new quasi-equilibrium state with a cable of actin at the wound margin. It is this state that we try to analyse. Of course, as the healing proceeds, this new 'equilibrium' state will change but over a timescale of hours; we do not consider here the processes taking place over this longer timescale.

Since forces clearly play a crucial role in the whole process we model the initial response to wounding by amending the mechanochemical model for the deformation of epithelial sheets initally proposed by Murray and Oster (1984). They considered the epithelium as linear, isotropic, viscoelastic continuum and derived a force balance equation for the various forces present; this basic model was discussed in Chapter 6. In their model the cell traction is mediated by calcium and so they included an equation for the calcium. Here we modify this model to investigate the new equilibrium reached by the basal cell sheet after wounding. Viscous effects can be neglected since we are only interested here in the short term 'equilibrium' state, and this simplifies the model considerably. However, an important addition to the Murray-Oster model, introduced by Sherratt (1991), are the effects of a microfilament anisotropy, which, as we shall see, plays a crucial role in our system and the wound healing process.

The mechanical properties of confluent cell sheets are largely determined by the intracellular actin filaments (Pollard 1990). In epithelial sheets, cell-cell adherens junctions serve as connection sites for actin filaments, and so the intracellular actin filaments are linked, via transmembrane proteins at these junctions, in an effectively two-dimensional transcellular network. Our model addresses the equilibrium state of this network. The forces exerted on an epidermal cell by the epidermal cells around it, via this actin filament network, can be divided into two types: elastic forces and active contraction forces; we include any effects of osmotic pressure within 'contraction forces.' The elasticity of the actin filament network arises from the extensive interpenetration of the long actin filaments, which tends to immobilize them (Janmey et al. 1988). As we discussed at length in Chapter 6 cell traction forces have been observed in a range of cell types and they play a major role in pattern formation processes. There we discussed in detail the form of elastic forces in the pattern generating mechanisms.

At equilibrium, these elastic and traction forces balance the elastic restoring forces that arise from attachment to the underlying mesenchyme. Let us recap the force balance scenario in the basal cell sheet. Following wounding, the epidermis retracts relative to the underlying mesenchyme, until a mechanical equilibrium is reached. Elastic and traction stresses are exerted by the surrounding cells at each point in the sheet, and in the postwounding equilibrium; these elastic and traction forces balance the restoring forces due to substratum attachments. The movement of the 'springs' represents local deformation of the superficial mesenchyme due to tension in the epidermis. In reality, the mesenchyme and epidermis are separated by a basal lamina, and our modelling assumes that the attachments are fixed in the basal lamina, and that this becomes wrinkled (so that the attachments are compressed) in response to wounding, to an extent reflecting the compaction of the cell sheet. Thus, the model equation, which predicts the new equilibrium configuration attained by the actin filament network of the epidermis after wounding, has the following general form,

Elastic forces within the actin filament network + Traction forces exerted by actin filaments = Elastic restoring forces due to substratum attachment.

We now have to quantify the various terms in this equation; it is helpful to review the relevant discussion in Section 6.2 in Chapter 6.

At equilibrium we model the stress tensor a by a = G[Ee + TV ■ uI] + tGI , (9.32)

elastic stresses active contraction stress where u is the displacement of the material point which was initially at position r, the strain tensor e = (1/2)(Vu + Vur), G (r) is the density of the intracellular actin filaments at the material point initially at r, E and T are positive (elastic) parameters and I is the unit tensor. In general, as we discuss below, the traction t is a function of the local compaction of the tissue. Unlike the general form used in Chapter 6 we have no viscous terms here since we are only dealing with the equilibrium situation.

We now consider the restoring forces due to the underlying substratum, via the cellular attachments, the importance of which has been demonstrated experimentally by Hergott et al. (1989). Following the concepts in Chapter 6 (and also Murray and Oster 1984a,b), we model these restoring forces by XGu, where X is a measure of the strength of the attachments. The proportionality factor, G, reflects the actin filament density and, as we shall see, in effect their filament orientation. So, the new equilibrium equation to be solved is

where a is given by (9.32). Since, in comparison with the experimental wound size, the cell sheet is infinite, the boundary conditions are u(ro) = 0, a ■ n = 0 on a free edge, (9.34)

where n is the unit vector normal to the wound edge. Initially we assume the boundary condition in the unwounded state is u = 0 everywhere. In a developing embryo this last assumption is not a totally trivial one. It is based on the exeprimental fact that the cell density is uniform and the substratum attachments are forming sufficiently fast so that the restoring forces are essentially negligible.

A crucial feature of the modelling is how to relate the density of microfilaments, G, at a point and the amount of expansion or compaction of the tissue resulting from the displacements, u, of that and neighbouring points, from their initial positions; we denote this compaction by A. There could, for example, be some actin polymerization at the edge of the wound. There does not seem to be any evidence of this, so we assume that in reponse to wounding there is no such polymerization and so we assume that the amount of filamentous actin is constant in a given region as it is deformed as a consequence of the wound injury. This implies that the actin density function G satisfies G(r)(1 — A) = k, where k is a constant. As a first approximation we take A « — V- u and so conservation of actin becomes

where k is a constant. The term V - u is the dilation, denoted by 0.

There is abundant experimental evidence, such as the seminal work by Kolega (1986) and the earlier study by Chen (1981), that actin filaments tend to align themselves parallel to the maximum applied stress. The former showed that fish epidermal cells when subjected to a tension aligned themselves in a matter of seconds while the latter showed that chick fibroblasts reoriented their actin filaments on the order of 15 seconds. If we think of a network of unstrained actin fibres (intuitively something like steel wool) and then subject it to an applied tension the effect of alignment is to concentrate the actin density by alignment along the tension lines (think again of a bundle of steel wool stretched: the strands tend to align themselves in the direction of the applied pull).

When actin filaments are compacted the sum of the traction forces exerted individually is less than the total force when acting together because of the formation of myosin cross-bridges (see, for example, the book by Alberts et al. 1994). Following the models of Oster (1984), Oster and Odell (1984) and Oster et al. (1985a) we take the specific form t = to/(1 — 3 A) to quantify the effect of compacting the actin filaments where 3 is a parameter. With this form a decrease in dilation (that is, an increase in compaction) results in an increase in the cell traction stress because of the increase in actin fibre density and, because of the synergy phenomenon, an increase in the traction stress per filament. Since we intuitively expect the former effect to be the larger effect we therefore require the parameter 3 < 1. With this restriction, t is bounded since A < 1 because a region cannot be compressed to point. In our analysis below we consider 0 < 3 < 1. Murray and Oster (1984a,b), who first proposed a continuum model for epithelial morphogenesis, took 3 = 0. Here we again approximate the compaction by A V ■ u and hence take the active traction term t to be a function of the dilation and modelled by

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