A numerical model for durotaxis

Stefanoni, Filippo; Ventre, Maurizio; Mollica, Francesco; Netti, Paolo A.

doi:10.1016/j.jtbi.2011.04.001

Cited by 25 publications

(28 citation statements)

References 51 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…We find that soft-to-stiff durotaxis is a necessary consequence of stiffness-dependent persistence, with or without a rigidity-dependent crawling speed. The mechanism we uncover is fundamentally different from those reported in earlier theoretical works on durotaxis [20,21]: the cells take no directional cues from the gradient re- Simulated trajectories (2D model) of 50 cells, departing from the origin at t = 0 with a linear velocity of 50 µm/hr on a persistence gradient, increasing linearly from 0.2 to 2 hrs over the x-range [−0.1, 0.1] mm (i.e., ∆τp/∆x = 9 hrs/mm). The cells were tracked for 12 hrs, their positions recorded at 6-minute intervals.…”

contrasting

confidence: 99%

Persistence-Driven Durotaxis: Generic, Directed Motility in Rigidity Gradients

et al. 2017

View full text Add to dashboard Cite

Cells move differently on substrates with different elasticities. In particular, the persistence time of their motion is higher on stiffer substrates. We show that this behavior will result in a net transport of cells directed up a soft-to-stiff gradient. Using simple random walk models with controlled persistence and stochastic simulations, we characterize this propensity to move in terms of the durotactic index measured in experiments. A one-dimensional model captures the essential features of this motion and highlights the competition between diffusive spreading and linear, wavelike propagation. Since the directed motion is rooted in a non-directional change in the behavior of individual cells, the motility is a kinesis rather than a taxis. Persistence-driven durokinesis is generic and may be of use in the design of instructive environments for cells and other motile, mechanosensitive objects.

show abstract

contrasting

confidence: 99%

Persistence-Driven Durotaxis: Generic, Directed Motility in Rigidity Gradients

et al. 2017

View full text Add to dashboard Cite

show abstract

“…In both cases, it has been observed that mesenchymal cells migrate preferentially toward the regions of higher stiffness. Several models have been proposed to explain and describe durotaxis [16,17,18]. In Ref.…”

Section: Introductionmentioning

confidence: 99%

Cell migration driven by substrate deformation gradients

Márquez¹,

Reig²,

Concha³

et al. 2019

Phys. Biol.

View full text Add to dashboard Cite

Identifying the cues followed by cells is key to understand processes as embryonic development, tissue homeostasis, or several pathological conditions. Based on a durotaxis model, it is shown that cells moving on predeformed thin elastic membrane follow the direction of increasing strain of the substrate. This mechanism, straintaxis, does not distinguish the origin of the strain, but the active stresses produce large strains on cells or tissues being used as substrates. Hence, straintaxis is the natural realization of duratoaxis in vivo. Considering a circular geometry for the substrate cells, it is shown that if the annular component of the active stress component increases with the radial distance, cells migrate toward the substrate cell borders. With appropriate estimation for the different parameters, the migration speeds are similar to those obtained in recent experiments [Reig et al. Nat. Comm. 2017, 8, 15431]. In these, during the annual killifish epiboly, deep cells that move in contact with the epithelial enveloping cell layer (EVL), migrate toward the EVL cell borders with speeds of microns per minute.

show abstract

“…In the general case the cell migration can be also affected by external forces F , which can cause for instance chemotaxis [1], durotaxis [2,3], etc. In this case the existing gradient of the surface properties forces the cells to migrate along to.…”

mentioning

confidence: 99%

Brownian Motion and the Temperament of Living Cells

Tsekov

Lensen

2013

Chinese Phys. Lett.

View full text Add to dashboard Cite

The migration of living cells obeys usually the laws of Brownian motion. While the latter is due to the thermal motion of surrounding matter, the cells locomotion is generally associated to their vitality. In the present paper the concept of cell temperament is introduced, being analogous to thermodynamic temperature and related to the cell entropy production. A heuristic expression for the diffusion coefficient of cell on structured surfaces is derived as well. The cell locomemory is also studied via the generalized Langevin equation.Tissue cells (e.g. fibroblasts) are anchorage dependent, implying that they need an interface to adhere to. If a substrate with a sufficient rigidity is not available, those cells are not viable, even in the presence of extracellular matrix proteins. Successful initial adhesion is followed by cell spreading and eventually active migration, involving intricate mechano-transduction and biochemical signalling processes. Consequently, the cell migration is dependent on physical, chemical and mechanical cues, among others. This has inspired many researchers over the years to predict and control the cell migration, for example by administering increasing concentrations of nutrients to lure cells in a certain direction, which is denoted chemotaxis [1], or directing them to move up a gradient of substrate elasticity, a process called durotaxis [2,3].Controlling cell migration is a very important task in the biomedical field and in tissue engineering, since it determines for example the eventual integration of implants and plays an important role in cancer metastasis, where individual cells come loose from the tumour tissue and go out to settle at another suitable interface (e.g. in arteries). We have analysed the motility of single cells cultured on polymeric gel substrates, i.e. hydrogels, with variable rigidities. Our preliminary unpublished results show that both the mean square displacement and the average speed are larger on stiffer gels, while the mean square displacement scaled linearly with time, implying Brownian motion. Finally the persistence (angle of directional movement between subsequent steps) appeared larger on the softest gel, an observation that could however be affected inherently by the slower speed. Thus, it seems that cell motility and active migration are correlated to the substrate stiffness [2,3], besides other factors such as the ones mentioned above. Nevertheless, from single cell observations it becomes clear that cells are individual entities and do not behave all identically, whereas the chemical or mechanical cues are supposedly homogeneous and act upon all cells similarly. We are interested to unravel other driving forces that dictate cellular behaviour and wish to find out more about cell individual characteristics. In a sense, we are searching for biophysical factors besides the well-known chemical and mechanical pa-

show abstract

A numerical model for durotaxis

Cited by 25 publications

References 51 publications

Persistence-Driven Durotaxis: Generic, Directed Motility in Rigidity Gradients

Persistence-Driven Durotaxis: Generic, Directed Motility in Rigidity Gradients

Cell migration driven by substrate deformation gradients

Brownian Motion and the Temperament of Living Cells

Contact Info

Product

Resources

About