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. 2016 Oct 6;6(5):20160036.
doi: 10.1098/rsfs.2016.0036.

Local modulation of chemoattractant concentrations by single cells: dissection using a bulk-surface computational model

J A Mackenzie  1 , M Nolan  1 , R H Insall  2
Affiliations

Local modulation of chemoattractant concentrations by single cells: dissection using a bulk-surface computational model

J A Mackenzie et al. Interface Focus. .

Abstract

Chemoattractant gradients are usually considered in terms of sources and sinks that are independent of the chemotactic cell. However, recent interest has focused on 'self-generated' gradients, in which cell populations create their own local gradients as they move. Here, we consider the interplay between chemoattractants and single cells. To achieve this, we extend a recently developed computational model to incorporate breakdown of extracellular attractants by membrane-bound enzymes. Model equations are parametrized, using the published estimates from Dictyostelium cells chemotaxing towards cyclic AMP. We find that individual cells can substantially modulate their local attractant field under physiologically appropriate conditions of attractant and enzymes. This means the attractant concentration perceived by receptors can be a small fraction of the ambient concentration. This allows efficient chemotaxis in chemoattractant concentrations that would be saturating without local breakdown. Similar interactions in which cells locally mould a stimulus could function in many types of directed cell motility, including haptotaxis, durotaxis and even electrotaxis.

Keywords: bulk-surface model; cell motility; chemotaxis; self-generated gradients; surface finite-elements.

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Figures

Figure 1.
Figure 1.
We consider the simulation of a motile cell through a fixed laboratory frame of reference Λ. The cell membrane is denoted by Γ(t) and the extracelluar region close to the cell is denoted by formula image with far-field boundary formula image. After a time interval of size Δt, the material point located at formula image on the cell membrane Γ(t) evolves to the new location formula image.
Figure 2.
Figure 2.
Simulated ligand concentration and receptor occupancy for a stationary circular cell with no breakdown. The far-field concentration corresponds to a saturating field on which is imposed a shallow 2% linear gradient in the ligand concentration from the back to the front of the cell.
Figure 3.
Figure 3.
Simulated ligand concentration and receptor occupancy for a stationary circular cell with membrane-bound enzyme breakdown.
Figure 4.
Figure 4.
(a) Cell migration in an initially saturating linear gradient ligand field. Five snapshots of the position of the cell membrane and ligand field in the extracellular region. Membrane-bound enzyme degradation results in a depletion zone close to the cell. The continuous black line shows the trajectory of the cell centroid and the ligand concentration has been plotted on a log scale. (b) Colour plot of the local activator level on the cell membrane.
Figure 5.
Figure 5.
Computed ligand concentration and receptor occupancy on the membrane of an evolving cell in a shallow linear chemotactic field.
Figure 6.
Figure 6.
(a) Cell trajectories for simulated cells migrating in a shallow linear ligand field. A total of 16 cells are simulated over a time period of 20 min. (b) Rose plot of distribution of direction data; the resultant vector is shown in red.
Figure 7.
Figure 7.
Boxplot of the chemotactic index of 16 simulated cells migrating in an initial saturating linear field of chemoattractant. The mean value formula image and the standard error of the mean formula image.
Figure 8.
Figure 8.
Cell migration in an initially saturating homogeneous ligand field. Four time frames show the position of the cell membrane and ligand field in the extracellular region. Membrane-bound enzyme degradation results in a depletion zone close to the cell. The dotted line shows the trajectory of the cell centroid and the ligand concentration has been plotted on a log scale.
Figure 9.
Figure 9.
(a) Cell trajectories for simulated cells migrating in an initially homogeneous ligand field. A total of 16 cells are simulated over a time period of 20 min. (b) Rose plot of distribution of direction data; the resultant vector is shown in red.
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