Laurent MacKay

Graduate Student
McGill Univ
Email author

Dynamics of Protrusive Oscillations in the Membranes of Fish Keratocyte Cells

Laurent MacKay, Etienne Lehman, Anmar Khadra

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The goal of this project was to understand how spatio-temporal dynamics in the fish keratocyte lamellipodium can produce a rough motiliy phenontype. We are interested in this phenonmenon as we work with chinese hampster ovary (CHO) cells which exhibit primarily the rough motility phenotype, and this phenotype was previously poorly understood.

With careful analysis of the mathematical model, we have been able to conclude that the rough motility phenotype is likely caused by a bistable configuration of equilibria where transitions between the two equilibria are driven by both noise (e.g., during wave initiation) and spatial dynamics (e.g., during wave propagation).

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Dynamics of Protrusive Oscillations in the Membranes of Fish Keratocyte Cells

Laurent MacKay, Etienne Lehman, Anmar Khadra

Motile cells depend on an intricate network of feedback loops that are essential in driving cell movement. Integrin-based focal adhesions (FAs) along with actin are the two key factors that mediate such motile behaviour. Together, they generate excitable dynamics that are essential in forming protrusions at the leading edge of the cell and, in certain cases, traveling waves along the membrane. A partial differential equation (PDE) model of a self-organizing lamellipodium in crawling keratocytes has been previously developed to understand how the three spatiotemporal patterns of activity observed in such cells, namely, stalling, waving and smooth motility are produced. The model consisted of three key variables: the density of barbed actin filaments, newly formed FAs called nascent adhesions (NAs) and VASP, an anti-capping protein that gets sequestered by NAs during maturation. Using parameter sweeping techniques, the distinct regimes of behaviour associated with the three activity patterns were identified. In this study, we convert the PDE model into an ordinary differential equation (ODE) model to examine its excitability properties and determine all the patterns of activity exhibited by this system. Our results reveal that there are two additional regimes not previously identified, including bistability and stochastic waving (generated by three steady states and their manifolds, rather than limit cycles). These regimes are also present in the PDE model. Applying slow-fast analysis on the ODE model shows that it exhibits a canard explosion through a folded-saddle and that rough motility seen in keratocytes are likely due to noise-dependent motility governed by bistability rather than stochastic waving. The two parameter bifurcation suggests that the increase in the proportion of rough motion is due to a shift in activity towards the bistable regime induced by a decrease in NA maturation rate. Our results thus provide important insight into how microscopic mechanical effects are integrated to produce the observed modes of motility.