Optogenetic control of intracellular flows and cell migration: A comprehensive mathematical analysis with a minimal active gel model

Optogenetic switching of migration of contractile cells

“…The parameters of the model can be estimated from experimental data for crawling cells. Following earlier work [16], one obtains L 2 = 1.25 and P = 0.1. A can be determined from k = 10 4 Pa [13,16,24,25], ξ = 2 • 10 14 Pa s /m 2 [16,26] and D = 0.7 • 10 −12 m 2 / s to be A ≈ 1/70.…”

“…Following earlier work [16], one obtains L 2 = 1.25 and P = 0.1. A can be determined from k = 10 4 Pa [13,16,24,25], ξ = 2 • 10 14 Pa s /m 2 [16,26] and D = 0.7 • 10 −12 m 2 / s to be A ≈ 1/70. A rough estimate for the volume of one (unclustered) myosin motor is 10 2 nm 2 • 100 nm and the myosin concentration in cells is of the order of c 0 ≈ µM [27].…”

“…We finally assume that the flow fields at the boundaries agree with cell movement (v(l ± ) = l± ). This implies that we disregard the effect of actin polymerization, which could be incorporated as a modified boundary condition [16].…”

“…We consider no-flux boundary conditions at the edges, i.e., ∂ x c(l ± ) = 0. Following earlier work along these lines [13,16], we non-dimensionalize length by L 0 , time by L 2 0 /D, stress by k, and concentration by c 0 = c dx/L 0 . We then map the problem on the interval [0, 1] using u = (x − l − )/L and get three dimensionless model parameters: the hydrodynamic damping length L = η/(ξL 2 0 ) arising from the competition between viscous and frictional dissipation; the Péclet number Pe = k/ξD describing the importance of advection versus diffusion; and myosin contractility P = χc 0 /k.…”

“…An alternative way has been described very recently: there a chemotaxis receptor was optogenetically activated in neutrophils, which promotes Rac/Cdc42-activity and decreases contractility. Both optogenetic strategies can be implemented in our model by introducing an optogenetic contribution to contraction, P → P + EΞ, with a shape function Ξ encoding the spatio-temporal activation and E the activation strength [16]. E is positive (negative), depending on whether one activates (inhibits) myosin II contractility.…”