A coupled model of transport-reaction-mechanics with trapping. Part I – Small strain analysis

Salvadori, Alberto; McMeeking, Robert M.; Grazioli, Davide; Magri, M.

doi:10.1016/j.jmps.2018.02.006

Cited by 60 publications

(56 citation statements)

References 65 publications

(149 reference statements)

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“…For in vitro experiments [17,18,28], ligands are prevented to flow onto the substrate: given that complex molecules result from the interaction with immobile ligands, they are macroscopically steady as well. Since receptors move along the membrane, reaction (17) traps mobile receptors and vice-versa [29]. In this work, analogously to [30], ligands and complex are assumed to be motionless, i.e.…”

Section: Relocation and Reactionmentioning

confidence: 99%

“…Following [29], receptors motion on the lipid membrane is thermodynamically described by energy and entropy balances, imposing as usual that the internal production of entropy cannot be negative. After the definition of the referential specific Helmholtz free energy per unit volume ψ R , taken as a function of temperature and concentrations, ψ R T , c R R , c L R , c C R the entropy imbalance in the Clausius-Duhem form is derived.…”

Section: Thermodynamics Of Receptors Motion On the Membranementioning

confidence: 99%

“…Following again [29], the thermo-chemo-mechanics of endothelial cells can be stated stemming from energy and entropy balances. The referential specific Helmholtz free energy per unit volume ψ R T , c G R , c F R , C, ξ is taken as a function of temperature, strains (either C or E), concentrations c G R , c F R , and of some kinematic internal variables ξ that compare with the usual meaning in inelastic constitutive laws [6,22,[64][65][66][67].…”

Section: Thermo-chemo-mechanics Of Cellsmentioning

confidence: 99%

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Modeling cells spreading, motility, and receptors dynamics: a general framework

et al. 2021

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The response of cells during spreading and motility is dictated by several multi-physics events, which are triggered by extracellular cues and occur at different time-scales. For this sake, it is not completely appropriate to provide a cell with classical notions of the mechanics of materials, as for “rheology” or “mechanical response”. Rather, a cell is an alive system with constituents that show a reproducible response, as for the contractility for single stress fibers or for the mechanical response of a biopolymer actin network, but that reorganize in response to external cues in a non-exactly-predictable and reproducible way. Aware of such complexity, in this note we aim at formulating a multi-physics framework for modeling cells spreading and motility, accounting for the relocation of proteins on advecting lipid membranes. Graphic Abstract We study the mechanical response under compression/extension of an assembly composed of 8 helical rods, pin-jointed and arranged in pairs with opposite chirality. In compression we find that, whereas a single rod buckles (a), the rods of the assembly deform as stable helical shapes (b). We investigate the effect of different boundary conditions and elastic properties on the mechanical response, and find that the deformed geometries exhibit a common central region where rods remain circular helices. Our findings highlight the key role of mutual interactions in the ensemble response and shed some light on the reasons why tubular helical assemblies are so common and persistent.

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Section: Relocation and Reactionmentioning

confidence: 99%

Section: Thermodynamics Of Receptors Motion On the Membranementioning

confidence: 99%

Section: Thermo-chemo-mechanics Of Cellsmentioning

confidence: 99%

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Modeling cells spreading, motility, and receptors dynamics: a general framework

et al. 2021

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“…The mathematical model here proposed accounts for diffusion of VEGFR2 along the cellular membrane and for ligands-receptors chemical reactions. It is framed in the mechanics and thermodynamics of continua, following a general description proposed in [8], and takes advantage of successful descriptions of physically similar systems [9,10]. The effect of the cell deformation on the diffusionreaction process on the membrane is here strongly simplified, surrogating the effects of the change in geometry on the chemodiffusive equations with a fictitious source term of ligands, detailed in Section 2.2.…”

Section: Introductionmentioning

confidence: 99%

Modeling and Simulation of VEGF Receptors Recruitment in Angiogenesis

Salvadori

Damioli

Ravelli

et al. 2018

Mathematical Problems in Engineering

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Angiogenesis, the process of new blood vessel formation from preexisting ones, plays a pivotal role in tumor growth. Vascular endothelial growth factor receptor-2 (VEGFR2) is the main proangiogenic tyrosine kinase receptor expressed by endothelial cells (ECs). VEGFR2 binds different ligands triggering vascular permeability and growth. VEGFR2-ligands accumulate in the extracellular matrix (ECM) and induce the polarization of ECs as well as the relocation of VEGFR2 in the basal cell membrane in contact with ECM. We propose here a multiphysical model to describe the dynamic of VEGFR2 on the plasma membrane. The governing equations for the relocation of VEGFR2 on the membrane stem from a rigorous thermodynamic setting, whereby strong simplifying assumptions are here taken and discussed. The multiphysics model is validated against experimental investigations.

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“…This is not the only possible choice, as discussed in[19]. Focusing on the functional dependence on the strain only, the Helmholtz free energy could be written as a function of the whole strain tensor and its inelastic counterpart ψ = ψ ε, ε dif f , ...(21)…”

mentioning

confidence: 99%

A coupled model of diffusional creep of polycrystalline solids based on climb of dislocations at grain boundaries

Magri

Lemoine²,

Adam³

et al. 2020

Journal of the Mechanics and Physics of Solids

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A continuum theory based on thermodynamics has been developed for modeling diffusional creep of polycrystalline solids. It consists of a coupled problem of vacancy diffusion and mechanics where the vacancy generation/absorption at grain boundaries is driven by grain boundary dislocations climb. The model is stated in terms of general balance laws and completed by the choice of constitutive equations consistent with classical non-equilibrium thermodynamics. The kinetics of diffusional creep is derived from physically-based mechanisms of climb of dislocations at grain boundaries, thus introducing a dependence of diffusional creep on the density and mobility of boundary dislocations. Several representative examples have been solved using the finite element method and assuming representative volume elements made up of an array of regular-shaped crystals. The effect of stress, temperature, grain size, and grain boundary dislocation mobility is analyzed and compared with classical theories of diffusional creep. The simulation results demonstrate the ability of the present model to reproduce the macroscopic stress and grain size dependence observed under both diffusion and interface controlled regimes as well the evolution of this dependency with the temperature. In addition, the numerical implementation of the model allows to predict the evolution of microscopic fields through the microstructure. arXiv:1911.06802v1 [cond-mat.mtrl-sci]

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A coupled model of transport-reaction-mechanics with trapping. Part I – Small strain analysis

Cited by 60 publications

References 65 publications

Modeling cells spreading, motility, and receptors dynamics: a general framework

Modeling cells spreading, motility, and receptors dynamics: a general framework

Modeling and Simulation of VEGF Receptors Recruitment in Angiogenesis

A coupled model of diffusional creep of polycrystalline solids based on climb of dislocations at grain boundaries

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