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Center for Nonlinear Studies |
The articulated architecture of the structure of matter in wide classes of materials, like biological tissues, requires often multi-scale and multi-field descriptions. Resulting continuum models rely first on the picture of the material element, that is on the description of the geometry of a body: the gross shape and its inner morphology. Material elements are commonly selected at a scale where statistical homogeneity of the material can be presumed reasonably. This way, when a geometric description of a material element is chosen, the element itself is considered as a canonical system, that is a system just in energetic contact with the neighboring fellows. Standard and microscopic actions arise. The former are due to the standard deformation, that is to the crowding and shearing of material elements, each one considered as a whole. The latter are produced by the microstructural rearrangements: these actions are subdivided into an inner family (inner meaning ‘inside’ the material element) and a contact family (contact exerted between neighboring material elements). The picture becomes more articulated when there is the possibility of migration of microstructures in a body because in this case material elements should more realistically be considered as grand canonical systems, that is systems able to exchange mass with the neighboring fellows. This case, information on the local microstructure numerosity seems to be necessary as well as an evolution equation of continuity type supplements the balances of macroscopic and microscopic actions. The case of a single macromolecule running in a body is in between. Distinction has to be made, in fact, between the case where the macromolecule can be considered as an inclusion in a different environment and the case that the environment be made by other macromolecules connected only one with the other up to forming a tissue, or embedded in a ground melt. In both cases, molecular dynamics based numerical simulations furnish information that can be compared with and/or included in a coarse grained representation of the molecular transport at continuum level. Here, we choose to focus our attention on the transport of a single macromolecule across a membrane, precisely, we consider protein translocation. We perform simulations based on molecular dynamics where a coarse-grained model for the protein is implemented. Lennard-Jones potential is considered between the atoms composing the molecule. In this way we are able to model chemical denatured states and thus study the relavant transport. The standard one-dimensional interpretation of numerical data or experiments is usually based on a Langevin equation describing the motion of the center of mass of the molecule itself. We propose a richer representation of the molecular motion including information on the shape of the protein. Finally, we interpret the two coarse grained representations of the molecular motion in terms of competition between microstructural actions from place to place, above all when such a motion is inside a complex fluid as the biological ones are in general.
Host: S. Gnanakaran, 5-1923, ghana@lanl.gov