Modelling Collagen Alignment in Dermal Wounds

1. Modelling Collagen Alignment in Dermal Wounds John Dallon, Jonathan Sherratt, Mark Ferguson and Philip K. Maini

2. Key Players Fibroblasts degrade fibrin secrete collagen Collagen slows down fibroblasts Fibroblasts < ----------- > collagen alignment

3. Alignment problems occur in a wide variety of applications:crystals, ecology, developmental biology etcMathematical approaches: integro-partial-differential equations,discrete orientation �

4. The Orientation Model VariablesCells � discrete objects paths given by fCollagen � continuous vector field denoted by c (x, t)

15. The Tissue Regeneration Modelfibrin network is represented by b (x,t)

23. Altering the speed of fibroblasts: increasing the speed leads to greater alignment. Can be done using a chemoattractant (Knapp et al, 1999 � can increase speed 3-fold (Ware et al, 1998)) or altering the integrin expression levels of the fibroblasts (Palecek et al, 1997)

24. Reducing contact guidance: inhibit the formation of microtubules with colcemid (Oakley et al, 1997); treatment with colchicine (causes rounder morphology (Mercier et al, 1996)

25. Effects of initial collagen orientation: transplant pieces of tendon (Matsumoto et al, 1998); place pieces of oriented gel (Guido and Tranquillo, 1993)

27. Altering the profile of transforming growth factor beta can have profound effects on the healing process, including significantly increasing or decreasing the degree of scarring (Shah et al, 1992, 1994, 1995, 1999)

28. Effects of TGF-beta Cell proliferation � biphasic (depends on age) Cell motility � biphasic effect on directed cell movement (chemotaxis) Collagen production � increase collagen production and decrease collagenase production Cell reorientation � development of lamellipodia and filopodia depends on concentration levels

31. Model results Effects on cell proliferation, migration and extracellular matrix production influence collagen alignment in only a MINOR way Regulation of filopodial extensions by TGF-beta could be the CRUCIAL property

32. Interpretation Adding TGF-beta-3 causes more cell reorientation, leads to less alignment and scarring is reduced Antibodies to TGF-beta-1 and 2 would, in this interpretation, lead to more alignment and hence more scarring. CONTRADICTION Both these isoforms bind to cells competitively (Altomonte et al, 1996, Piek et al, 1999)

34. Model considered wound is isolation. If we embed it in tissue we find that the time taken for the cells to enter and �heal� the wound is too long.

35. McDougall and Sherratt Add a chemoattractant produced in the wound (PDGF, IL-Ibeta, TNF-alpha) Reaction-diffusion equation at steady state Cells velocity now depends on size of chemical gradient and is in the direction of the gradient

36. Fibroblast density is low at top and high at bottom (staining experiments)

37. RESULTS Wound heals in reasonable time Widely dispersed chemoattractant prolife leads to greater degree of interdigitation (better linked) Uniform cell distribution in the unwounded skin leads to parallel alignment rather than perpendicular alignment (w.r.t. bottom of wound)

38. Switching off the speed cue leads to fewer cells entering the wound. Orientation not altered Switching off the directional cue (but not speed) is worse Pattern of alignment depends crucially on the form taken for velocity dependence

39. Therapeutic aspects Decrease the sensitivity of fibroblast reorientation to chemoattractant gradients (add agent that binds competitively to receptors � mannose 6 phosphate acts in this way [Ferguson and O�Kane, 2004] have shown this reduces scarring)

40. References J.C. Dallon, J.A. Sherratt, P.K. Maini, J.theor.Biol., 199, 449-471 (1999) J.C. Dallon, J.A. Sherratt, P.K. Maini, M. Ferguson, IMA J.Math.Appl.Biol.Med, 17, 379-393 (2000) J.C. Dallon, J.A. Sherratt, P.K. Maini, Wound Repair and Regeneration, 9, 278-286 (2001) S. McDougall, J. Dallon, J. Sherratt, PKM, (submitted)