Abstract
Cell migration in 3D microenvironments is a complex process which depends on the coordinated activity of leading edge protrusive force and rear retraction in a push-pull mechanism. While the potentiation of protrusions has been widely studied, the precise signalling and mechanical events that lead to retraction of the cell rear are much less well understood, particularly in physiological 3D extra-cellular matrix (ECM). We previously discovered that rear retraction in fast moving cells is a highly dynamic process involving the precise spatiotemporal interplay of mechanosensing by caveolae and signalling through RhoA. To further interrogate the dynamics of rear retraction, we have adopted three distinct mathematical modelling approaches here based on (i) Boolean logic, (ii) deterministic kinetic ordinary differential equations (ODEs) and (iii) stochastic simulations. The aims of this multi-faceted approach are twofold: firstly to derive new biological insight into cell rear dynamics via generation of testable hypotheses and predictions; and secondly to compare and contrast the distinct modelling approaches when used to describe the same, relatively under-studied system. Overall, our modelling approaches complement each other, suggesting that such a multi-faceted approach is more informative than methods based on a single modelling technique to interrogate biological systems. Whilst Boolean logic was not able to fully recapitulate the complexity of rear retraction signalling, an ODE model could make plausible population level predictions. Stochastic simulations added a further level of complexity by accurately mimicking previous experimental findings and acting as a single cell simulator. Our approach highlighted the unanticipated role for CDK1 in rear retraction, a prediction we confirmed experimentally. Moreover, our models led to a novel prediction regarding the potential existence of a ‘set point’ in local stiffness gradients that promotes polarisation and rapid rear retraction.
Highlights
Cell migration is a key physiological process which underpins development, immune responses, wound healing, and the metastatic progression of diseases such as cancer
We have interrogated the signalling dynamics which lead to rapid, efficient retraction of the rear with three different mathematical modelling approaches with the aim to (i) derive new knowledge of how the rear retracts and (ii) compare and contrast models of different complexity in the same, relatively understudied area
The key instigator of cell rear contractility is the ‘switch-like’ small GTPase RhoA [9,10]: RhoA activity, via effector proteins Rho kinase (ROCK1/2) [6] and/or PKN-2 [11] leads to phosphorylation of the motor-protein non-muscle myosin II (NMMII), which provides the force required to retract the rear of the cell [12]; RhoA is further required to activate diaphanous related formins (DRFs) including mDia-1 [13], which are required to reorganise the actin cytoskeleton at the trailing edge in a polymerising capacity [14]
Summary
Cell migration is a key physiological process which underpins development, immune responses, wound healing, and the metastatic progression of diseases such as cancer. Archetypal mesenchymal motility has been conceptualised as a cyclic process depending on the regulated activity of four key stages [1,2]: polarisation to form distinct leading and trailing edges [3]; forward protrusion of the leading edge [4]; adhesion to the substratum [5]; and retraction and forward propulsion of the cell rear [6] Of these steps, the retraction of the rear remains the most neglected area of study, despite it being essential for fast movement [7,8]. We produced a detailed cell rear model during 3D migration, incorporating the temporal dynamics of both signalling and mechanical events Simulations using this model generated the hypothesis that efficient rear retraction is a positive feedback process, and predicted that perturbation of F-actin or contractility disrupts caveolae formation, despite appearing ‘upstream’ in the model (a prediction subsequently validated experimentally [8]). Since this was an early rendering of such detailed dynamics and there remain numerous unknowns at play within the network, it is an ideal system to interrogate using three distinct modelling approaches of varying complexity: Boolean logic, deterministic ordinary differential equations (ODEs) and stochastic simulations
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