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Mathematical modeling of acto myosin contraction

De
26 pages
10 days Mathematical modeling of acto-myosin contraction in wound healing and regeneration Luís Almeida (CNRS, AGIM – Aging Imaging Modeling, FRE3405)

  • myosin contraction

  • no inflamatory

  • actin cable

  • contraction waves

  • embryonic wound

  • healing

  • regenerative repair

  • achieve regenerative


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Mathematical modeling of acto-myosin contraction
in wound healing and regeneration
Luís Almeida (CNRS, AGIM – Aging Imaging Modeling, FRE3405)
10 daysMathematical modeling of actin cable contraction in
embryonic wound healing and regeneration
Actin cable formation – actin wave
Actin cable contraction:
wound-healingEmbryo wound healing
No inflamatory response
Original tissue building machinery is reactivated to yield perfect (scarless) repair
Regenerative repair
Conserved mechanisms and regulatory pathways across species :
morphogenesis and wound healing in chick, mouse, zebrafish (…) embryos
Wound healing in zebrafish larvae
and even some small adult wounds (rabbit cornea)Regenerative or fibroctic repair
Gurtner, Werner, Barrandon & Longaker, Nature 2008
Re-activating morphogenetic and embryonic
repair mechanisms in adults to achieve
regenerative repair and avoid fibrosis
Stages of classic wound healing:
Remodeling
Inflammation Tissue formation and migrationPurse-string formation: actio-myosin and contraction wavesGlobal Process of Dorsal Closure
amnioserosa
ectoderm
A P
• actin cable tension
• amnioserosa contraction
• ectoderm resistance
• zipping
• head and tail elongationModeling a closure
 (1) quasi-static approach : succession of linear elastic equilibria
 (2) evolution of the boundary between two equilibriaModeling a closure
 (1) quasi-static approach : succession of equilibria
 (2) evolution of the boundary between two equilibria
Given a set of forces (parameters C ) and i
mechanical hypothesis + a boundary iiModeling a closure
 (1) quasi-static approach : succession of equilibria
 (2) evolution of the boundary between two equilibria
Given a set of forces (parameters C ) and i
mechanical hypothesis + a boundary i
(1) we compute the displacement field {u } i
outside the hole (and extend it inside)Modeling a closure
 (1) quasi-static approach : succession of equilibria
 (2) evolution of the boundary between two equilibria
Given a set of forces (parameters C ) and i
mechanical hypothesis + a boundary i
(1) we compute the displacement field {u }i
(2) we evolve based on {u }i i