Staff member

Alejandro Torres Sánchez

Postdoctoral Researcher
Integrative Cell and Tissue Dynamics

Staff member publications

Torres-Sánchez, A., Santos-Oliván, D., Arroyo, M., (2020). Approximation of tensor fields on surfaces of arbitrary topology based on local Monge parametrizations Journal of Computational Physics 405, 109168

We introduce a new method, the Local Monge Parametrizations (LMP) method, to approximate tensor fields on general surfaces given by a collection of local parametrizations, e.g. as in finite element or NURBS surface representations. Our goal is to use this method to solve numerically tensor-valued partial differential equations (PDEs) on surfaces. Previous methods use scalar potentials to numerically describe vector fields on surfaces, at the expense of requiring higher-order derivatives of the approximated fields and limited to simply connected surfaces, or represent tangential tensor fields as tensor fields in 3D subjected to constraints, thus increasing the essential number of degrees of freedom. In contrast, the LMP method uses an optimal number of degrees of freedom to represent a tensor, is general with regards to the topology of the surface, and does not increase the order of the PDEs governing the tensor fields. The main idea is to construct maps between the element parametrizations and a local Monge parametrization around each node. We test the LMP method by approximating in a least-squares sense different vector and tensor fields on simply connected and genus-1 surfaces. Furthermore, we apply the LMP method to two physical models on surfaces, involving a tension-driven flow (vector-valued PDE) and nematic ordering (tensor-valued PDE), on different topologies. The LMP method thus solves the long-standing problem of the interpolation of tensors on general surfaces with an optimal number of degrees of freedom.

Keywords: Approximation, Finite elements, Surface PDE, Tensor-valued PDE, Vector-valued PDE

Torres-Sanchez, A., Millan, D., Arroyo, M., (2019). Modelling fluid deformable surfaces with an emphasis on biological interfaces Journal of Fluid Mechanics 872, 218-271

Fluid deformable surfaces are ubiquitous in cell and tissue biology, including lipid bilayers, the actomyosin cortex or epithelial cell sheets. These interfaces exhibit a complex interplay between elasticity, low Reynolds number interfacial hydrodynamics, chemistry and geometry, and govern important biological processes such as cellular traffic, division, migration or tissue morphogenesis. To address the modelling challenges posed by this class of problems, in which interfacial phenomena tightly interact with the shape and dynamics of the surface, we develop a general continuum mechanics and computational framework for fluid deformable surfaces. The dual solid–fluid nature of fluid deformable surfaces challenges classical Lagrangian or Eulerian descriptions of deforming bodies. Here, we extend the notion of arbitrarily Lagrangian–Eulerian (ALE) formulations, well-established for bulk media, to deforming surfaces. To systematically develop models for fluid deformable surfaces, which consistently treat all couplings between fields and geometry, we follow a nonlinear Onsager formalism according to which the dynamics minimizes a Rayleighian functional where dissipation, power input and energy release rate compete. Finally, we propose new computational methods, which build on Onsager’s formalism and our ALE formulation, to deal with the resulting stiff system of higher-order partial differential equations. We apply our theoretical and computational methodology to classical models for lipid bilayers and the cell cortex. The methods developed here allow us to formulate/simulate these models in their full three-dimensional generality, accounting for finite curvatures and finite shape changes.

Keywords: Capsule/cell dynamics, Computational methods, Membranes

Torres-Sánchez, A., Vanegas, J. M., Purohit, P. K., Arroyo, M., (2019). Combined molecular/continuum modeling reveals the role of friction during fast unfolding of coiled-coil proteins Soft Matter 15, (24), 4961-4975

Coiled-coils are filamentous proteins that form the basic building block of important force-bearing cellular elements, such as intermediate filaments and myosin motors. In addition to their biological importance, coiled-coil proteins are increasingly used in new biomaterials including fibers, nanotubes, or hydrogels. Coiled-coils undergo a structural transition from an α-helical coil to an unfolded state upon extension, which allows them to sustain large strains and is critical for their biological function. By performing equilibrium and out-of-equilibrium all-atom molecular dynamics (MD) simulations of coiled-coils in explicit solvent, we show that two-state models based on Kramers' or Bell's theories fail to predict the rate of unfolding at high pulling rates. We further show that an atomistically informed continuum rod model accounting for phase transformations and for the hydrodynamic interactions with the solvent can reconcile two-state models with our MD results. Our results show that frictional forces, usually neglected in theories of fibrous protein unfolding, reduce the thermodynamic force acting on the interface, and thus control the dynamics of unfolding at different pulling rates. Our results may help interpret MD simulations at high pulling rates, and could be pertinent to cytoskeletal networks or protein-based artificial materials subjected to shocks or blasts.