A minimal mathematical model of neutrophil pseudopodium formation during chemotaxis

The directed movement of neutrophils is provided by the rapid polymerization of actin with the formation of a protrusion growing forward. In our previous work we observed impaired neutrophil movement for patients with Wiskott-Aldrich syndrome (WAS) compared to healthy donors.

In this work, we set out to explain the impairment of neutrophil chemotaxis in patients by observation and computer modeling of the linear growth rates of the anterior pseudopodia. The neutrophil chemotaxis was observed by means of low-angle fluorescent microscopy in parallel-plate flow chambers. The computational model was constructed as a network-like 2D stochastic polymerization of actin guided by the proximity of cell membrane with branching governed by Arp2/3 and WASP proteins.

The observed linear velocity of neutrophil pseudopodium formation was 0.22 ± 0.04 μm/s for healthy donors and 0.23 ± 0.08 μm/s for WAS patients. The model described the velocity of the pseudopodium formation for healthy donors well. For the description of WAS patients data, a variation of branching velocity (governed by WASP) by an order of magnitude was applied, which did not significantly alter the linear protrusion growth velocity.

We conclude that the proposed mathematical model of neutrophil pseudopodium formation could describe the experimental data well, but the data on overall neutrophil movement could not be explained by the velocities of the pseudopodium growth.

Scheme of the computational model. (A) The scheme of stochastic events and species included in the model. A single F-actin filament is assumed to be straight and to be divided into segments. Each segment can be considered to be an actin monomer. New G-actin molecules can attach to and detach from the filament “barbed” end. It is assumed that the child filament begins to grow from the middle between two segments of F-actin at the angle of 70o.  If there is a branch growing from the F-actin segments, they are considered occupied and no branching can occur there. (B) The spatial restrictions on the filament growth and branching. The filaments can branch if the distance from the cell membrane is lesser than D. Filaments can grow if the distance from the cell membrane is lesser than H, where H > D.
#cytoskeleton#neutrophils#actin#chemotaxis#Wiskott-Aldrich syndrome

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