Geometry-Sensitive Protrusion Growth Directs Confined Cell Migration

Johannes Flommersfeld, Stefan Stöberl, Omar Shah, Joachim O. Rädler, and Chase P. Broedersz

Phys. Rev. Lett. 132, 098401 – Published 27 February 2024

Abstract

The migratory dynamics of cells can be influenced by the complex microenvironment through which they move. It remains unclear how the motility machinery of confined cells responds and adapts to their microenvironment. Here, we propose a biophysical mechanism for a geometry-dependent coupling between cellular protrusions and the nucleus that leads to directed migration. We apply our model to geometry-guided cell migration to obtain insights into the origin of directed migration on asymmetric adhesive micropatterns and the polarization enhancement of cells observed under strong confinement. Remarkably, for cells that can choose between channels of different size, our model predicts an intricate dependence for cellular decision making as a function of the two channel widths, which we confirm experimentally.

Received 17 August 2023
Accepted 30 January 2024

DOI:https://doi.org/10.1103/PhysRevLett.132.098401

Physics Subject Headings (PhySH)

Cell migration Cell polarity

Cell membrane Cytoskeleton

Langevin equation Stochastic differential equations

Physics of Living Systems

Authors & Affiliations

Johannes Flommersfeld ^1,2, Stefan Stöberl ³, Omar Shah¹, Joachim O. Rädler ³, and Chase P. Broedersz ^1,2,*

¹Department of Physics and Astronomy, Vrije Universiteit Amsterdam, 1081HV Amsterdam, Netherlands
²Arnold Sommerfeld Center for Theoretical Physics and Center for NanoScience, Department of Physics, Ludwig-Maximilian-University Munich, Theresienstraße 37, D-80333 Munich, Germany
³Faculty of Physics and Center for NanoScience, Ludwig-Maximilian-University, Geschwister-Scholl-Platz 1, D-80539 Munich, Germany

^*c.p.broedersz@vu.nl

Article Text (Subscription Required)

Click to Expand

Supplemental Material (Subscription Required)

Click to Expand

References (Subscription Required)

Click to Expand

Issue

Vol. 132, Iss. 9 — 1 March 2024

Reuse & Permissions

Access Options

Author publication services for translation and copyediting assistance advertisement

Images

Figure 1
Components of the migration model. (a) Side view with key molecular components. The stochastic (un)binding of adhesion molecules with rates $k_{on / off}$ gives rise to effective friction coefficients of protrusion ( $ζ_{a}$ ) and nucleus ( $ζ_{n}$ ). Actin polymerizes at the edge of the protrusions (rate $r_{p}$ ) and depolymerizes near the nucleus (rate $r_{d}$ ). Polarity cues transiently bind to actin with rates $κ_{on}^{c}$ and $κ_{off}^{c}$ . (b) Top view on unisotropic substrate. The retrograde flow (velocity $v_{r}$ ) is driven by myosin contractility ( $f_{c}$ ) and membrane forces ( $f_{τ}$ ). Confinement-induced actin alignment (angle $ϑ$ ) stimulates protrusion growth, resulting in increased membrane tension and retrograde flow.
Reuse & Permissions
Figure 2
Cell migration on directed substrates (ratchetaxis). (a) In contrast to symmetric patterns (right), triangular patterns (left, center) lead to protrusions of different widths $w_{p}$ on both sides of the nucleus. If neighboring patterns are also asymmetric (center), this can result in different densities of adhesive bonds $ρ_{b}$ at the front of the protrusions. $x_{ℓ / r}$ denote the position of the left or right protrusion. These asymmetries in protrusion width and adhesiveness lead to biased migration. (b) The model reproduces the experimentally observed first-step migration biases on micropatterns shown in (a). (c) Effect of pattern spacing on the average long-term migration bias $\bar{p} = ⟨ (N_{+} - N_{-}) / (N_{+} + N_{-}) ⟩$ on periodic ratchetlike patterns [(a), center], with the number of steps in the $+ / -$ direction $N_{+ / -}$ . $⟨ L_{p} ⟩_{\exp}$ indicates the average experimentally determined protrusion length ( $27 μ m$ ). As observed experimentally, the bias increases with increasing pattern spacing (experimental data from [18]).
Reuse & Permissions
Figure 3
Cell migration in lateral confinement. (a) Lateral confinement of the protrusion leads to actin filament alignment. (b) Fit of expression for $α$ on dumbbell-shaped patterns to the values reported in [14]. (c),(d) Lateral confinement induces spontaneous polarization of the cell. For homogeneous confinement (c), both polarization directions are equally likely. For asymmetric confinement (d), polarization is biased in the direction of stronger confinement.
Reuse & Permissions
Figure 4
Cellular decision making in lateral confinement. (a) Time series of a cell migrating on a chain of adhesive islands that are connected by adhesive bridges of increasing width (scale bar, $35 μ m$ ). (b) The reduced phase space. The estimated position of the different experiments relative to the case of MDA-MB-231 cells on highly adhesive patterns ( $M +$ ) are indicated by the black markers (cross, MDA-MB-231, high adhesiveness; diamond, MDA-MB-231, low adhesiveness; star, HT-1080, high adhesiveness). (c) Experimentally observed migration biases together with model fits for MDA-MB-231 and HT-1080 cells, where $p_{r / ℓ}$ denotes the probability for a cell to choose the right or left channel. With increasing bridge widths, cells transition from a bias toward wider bridges to a bias toward narrower bridges. (d) Predicted migration biases of MDA-MB-231 cells on patterns of reduced adhesiveness together with experimental data.
Reuse & Permissions

Physical Review Letters