Deciphering the dynamics of lamellipodium in a fish keratocytes model

MacKay, L. A.; Lehman, Etienne; Khadra, Anmar

doi:10.1016/j.jtbi.2020.110534

Cited by 8 publications

(9 citation statements)

References 53 publications

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“…Much experimental evidence has repeatedly demonstrated the importance of shape oscillations in cell migration [31]. Several mathematical studies have attempted to understand how these oscillations are generated at the cell membrane level using a spatiotemporal model with multiple timescales [32, 33]. Existing mathematical models involving the Rac-Rho system typically accounted for polarized cells with a leading front and a stable back [26, 34, 35].…”

Section: Introductionmentioning

confidence: 99%

Polarity and mixed-mode oscillations may underlie different patterns of cellular migration

Plazen

Rahbani

Brown

et al. 2022

Preprint

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In mesenchymal cell motility, several migration patterns have been observed, including directional, exploratory and stationary. Two key members of the Rho-family of GTPases, Rac and Rho, along with an adaptor protein called paxillin, have been particularly implicated in the formation of such migration patterns and in regulating adhesion dynamics. Together, they form a key regulatory network that involves the mutual inhibition exerted by Rac and Rho on each other and the promotion of Rac activation by phosphorylated paxillin. Although this interaction is sufficient to generating wave-pinning that underscores cellular polarization comprised of cellular front (high active Rac) and back (high active Rho), it remains unclear how they interact collectively to induce other modes of migration detected in Chinese hamster Ovary (CHO-K1) cells. We previously developed a 6D reaction-diffusion model describing the interactions of these three proteins (in their active/phosphorylated and inactive/unphosphorylated forms) along with other auxiliary proteins, to decipher their role in generating wave-pinning. In this study, we explored, through computational modeling and image analysis, how differences in timescales within this molecular network can potentially produce the migration patterns in CHO-K1 cells and how switching between them could occur. To do so, the 6D model was reduced to an excitable 4D spatiotemporal model possessing three different timescales. The model produced not only wave-pinning in the presence of diffusion, but also mixed-mode oscillations (MMOs) and relaxation oscillations (ROs). Implementing the model using the Cellular Potts Model (CPM) produced outcomes in which protrusions in cell membrane changed Rac-Rho localization, resulting in membrane oscillations and fast directionality variations similar to those seen in CHO-K1 cells. The latter was assessed by comparing the migration patterns of CHO-K1 cells with CPM cells using four metrics: instantaneous cell speed, exponent of mean square-displacement (called α-value), directionality ratio and protrusion rate. Variations in migration patterns induced by mutating paxillin's serine 273 residue was also captured by the model and detected by a machine classifier, revealing that this mutation alters the dynamics of the system from MMOs to ROs or nonoscillatory behaviour through variation in the concentration of an active form of an adhesion protein called p21-Activated Kinase 1 (PAK). These results thus suggest that MMOs and adhesion dynamics are the key ingredients underlying CHO-K1 cell motility.

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Section: Introductionmentioning

confidence: 99%

Polarity and mixed-mode oscillations may underlie different patterns of cellular migration

Plazen

Rahbani

Brown

et al. 2022

Preprint

Self Cite

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“…Our study clarifies the contributions of lamellipodium actin polymerization and nascent adhesions to overall edge motion. Previous models have indicated both that actin polymerization is sufficient to drive edge protrusion and that adhesion promotes protrusion [28,31,[56][57][58][59]. In the recent model by Garner et al, filament polymerization alone generated stable protrusion [60],…”

Section: Discussionmentioning

confidence: 99%

“…Prior models of lamellipodial protrusion at the sub micrometer length scale probed the role of actin polymerization using the Brownian ratchet force-velocity relationship of actin filament elongation pushing the membrane [60,63,64], or probed actin and adhesion interactions by representing the actin as a gel with the molecular clutch adhesion lifetimetraction force relationship [27,28,30]. However, none of the previous models [28,56,57,[65][66][67], to the best of our knowledge, simultaneously incorporated the Brownian ratchet and molecular clutch mechanisms without predetermined relations between membrane motion and actin filament concentration or actomyosin contractility. In our model, lamellipodium dynamics emerge spontaneously from interactions and force balance between actin filaments, membrane, and adhesions.…”

Section: Discussionmentioning

confidence: 99%

Nascent adhesions differentially regulate lamellipodium velocity and persistence

Carney

Khan

Samson

et al. 2021

Preprint

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Cell migration is essential to physiological and pathological biology. Migration is driven by the motion of a leading edge, in which actin polymerization pushes against the edge and adhesions transmit traction to the substrate while membrane tension increases. How the actin and adhesions synergistically control edge protrusion remains elusive. We addressed this question by developing a computational model in which the Brownian ratchet mechanism governs actin filament polymerization against the membrane and the molecular clutch mechanism governs adhesion to the substrate (BR-MC model). Our model predicted that actin polymerization is the most significant driver of protrusion, as actin had a greater effect on protrusion than adhesion assembly. Increasing the lifetime of nascent adhesions also enhanced velocity, but decreased the protrusion’s motional persistence, because filaments maintained against the cell edge ceased polymerizing as membrane tension increased. We confirmed the model predictions with measurement of adhesion lifetime and edge motion in migrating cells. Adhesions with longer lifetime were associated with faster protrusion velocity and shorter persistence. Experimentally increasing adhesion lifetime increased velocity but decreased persistence. We propose a mechanism for actin polymerization-driven, adhesion-dependent protrusion in which balanced nascent adhesion assembly and lifetime generates protrusions with the power and persistence to drive migration.

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“…Besides the two 3D smooth subsystems S + and S − , one may find that the Filippov fast subsystem (4) also has one 2D sliding subsystem (9) in Σ S . Modulated by the slow variable w, attractors such as equilibria and cycles of smooth subsystems may collide with a sliding boundary in (8), behaving in nonconventional bifurcations. In other words, nonconventional bifurcations in (4) generally occur on sliding boundaries.…”

Section: Nonsmooth Dynamics Analysesmentioning

confidence: 99%

“…In the past decades, many research groups and scholars have studied slow-fast dynamical systems via experiments and computations based on extensive applications across many practical problems. For instance, neuronal activities and neural networks [1][2][3], calcium-ion oscillations in cells [4,5], catalytic oxidation reactions [6,7], and other applications [8][9][10].…”

Section: Introductionmentioning

confidence: 99%

Slow–Fast Dynamics Behaviors under the Comprehensive Effect of Rest Spike Bistability and Timescale Difference in a Filippov Slow–Fast Modified Chua’s Circuit Model

Chen

et al. 2022

Mathematics

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Since the famous slow–fast dynamical system referred to as the Hodgkin–Huxley model was proposed to describe the threshold behaviors of neuronal axons, the study of various slow–fast dynamical behaviors and their generation mechanisms has remained a popular topic in modern nonlinear science. The primary purpose of this paper is to introduce a novel transition route induced by the comprehensive effect of special rest spike bistability and timescale difference rather than a common bifurcation via a modified Chua’s circuit model with an external low-frequency excitation. In this paper, we attempt to explain the dynamical mechanism behind this novel transition route through quantitative calculations and qualitative analyses of the nonsmooth dynamics on the discontinuity boundary. Our work shows that the whole system responses may tend to be various and complicated when this transition route is triggered, exhibiting rich slow–fast dynamics behaviors even with a very slight change in excitation frequency, which is described well by using Poincaré maps in numerical simulations.

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Deciphering the dynamics of lamellipodium in a fish keratocytes model

Cited by 8 publications

References 53 publications

Polarity and mixed-mode oscillations may underlie different patterns of cellular migration

Polarity and mixed-mode oscillations may underlie different patterns of cellular migration

Nascent adhesions differentially regulate lamellipodium velocity and persistence

Slow–Fast Dynamics Behaviors under the Comprehensive Effect of Rest Spike Bistability and Timescale Difference in a Filippov Slow–Fast Modified Chua’s Circuit Model

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