OCCAM Wednesday Morning Event
|
Wed, 12/10/2011 10:10 |
Hans Othmer |
OCCAM Wednesday Morning Event  |
OCCAM Common Room (RI2.28) |
| Cell locomotion is essential for early development, angiogenesis, tissue regeneration, the immune response, and wound healing in multicellular organisms, and plays a very deleterious role in cancer metastasis in humans. Locomotion involves the detection and transduction of extracellular chemical and mechanical signals, integration of the signals into an intracellular signal, and the spatio-temporal control of the intracellular biochemical and mechanical responses that lead to force generation, morphological changes and directed movement. While many single-celled organisms use flagella or cilia to swim, there are two basic modes of movement used by eukaryotic cells that lack such structures – mesenchymal and amoeboid. The former, which can be characterized as `crawling' in fibroblasts or `gliding' in keratocytes, involves the extension of finger-like filopodia or pseudopodia and/or broad flat lamellipodia, whose protrusion is driven by actin polymerization at the leading edge. This mode dominates in cells such as fibroblasts when moving on a 2D substrate. In the amoeboid mode, which does not rely on strong adhesion, cells are more rounded and employ shape changes to move – in effect 'jostling through the crowd' or `swimming'. Here force generation relies more heavily on actin bundles and on the control of myosin contractility. Leukocytes use this mode for movement through the extracellular matrix in the absence of adhesion sites, as does Dictyostelium discoideum when cells sort in the slug. However, recent experiments have shown that numerous cell types display enormous plasticity in locomotion in that they sense the mechanical properties of their environment and adjust the balance between the modes accordingly by altering the balance between parallel signal transduction pathways. Thus pure crawling and pure swimming are the extremes on a continuum of locomotion strategies, but many cells can sense their environment and use the most efficient strategy in a given context. We will discuss some of the mathematical and computational challenges that this diversity poses. | |||
|
Wed, 19/10/2011 10:10 |
Kevin Painter |
OCCAM Wednesday Morning Event |
OCCAM Common Room (RI2.28) |
| Successful navigation through a complicated and evolving environment is a fundamental task carried out by an enormous range of organisms, with migration paths staggering in their length and intricacy. Selecting a path requires the detection, processing and integration of a myriad of cues drawn from the surrounding environment and in many instances it is the intrinsic orientation of the environment that provides a valuable navigational aid. In this talk I will describe the use of transport models to describe migration in oriented environments, and demonstrate the scaling approaches that allow us to derive macroscopic models for movement. I will illustrate the methods through a number of apposite examples, including the migration of cells in the extracellular matrix, the macroscopic growth of brain tumours and the movement of wolves in boreal forest. | |||
|
Wed, 26/10/2011 10:15 |
Marc Fivel (Grenoble INP) |
OCCAM Wednesday Morning Event |
OCCAM Common Room (RI2.28) |
|
Wed, 02/11/2011 10:15 |
Per Lotstedt |
OCCAM Wednesday Morning Event |
OCCAM Common Room (RI2.28) |
| In biological cells, molecules are transported actively or by diffusion and react with each other when they are close. The reactions occur with certain probability and there are few molecules of some chemical species. Therefore, a stochastic model is more accurate compared to a deterministic, macroscopic model for the concentrations based on partial differential equations. At the mesoscopic level, the domain is partitioned into voxels or compartments. The molecules may react with other molecules in the same voxel and move between voxels by diffusion or active transport. At a finer, microscopic level, each individual molecule is tracked, it moves by Brownian motion and reacts with other molecules according to the Smoluchowski equation. The accuracy and efficiency of the simulations are improved by coupling the two levels and only using the micro model when it is necessary for the accuracy or when a meso description is unknown. Algorithms for simulations with the mesoscopic, microscopic and meso-micro models will be described and applied to systems in molecular biology in three space dimensions. | |||
|
Wed, 09/11/2011 10:15 |
Simon Tavener (Colorado State University) |
OCCAM Wednesday Morning Event |
OCCAM Common Room (RI2.28) |
|
Diffusive process with discontinuous coefficients provide significant computational challenges. We consider the solution of a diffusive process in a domain where the diffusion coefficient changes discontinuously across a curved interface. Rather than seeking to construct discretizations that match the interface, we consider the use of regularly-shaped meshes so that the interface "cuts'' through the cells (elements or volumes). Consequently, the discontinuity in the diffusion coefficients has a strong impact on the accuracy and convergence of the numerical method. We develop an adjoint based a posteriori error analysis technique to estimate the error in a given quantity of interest (functional of the solution). In order to employ this method, we first construct a systematic approach to discretizing a cut-cell problem that handles complex geometry in the interface in a natural fashion yet reduces to the well-known Ghost Fluid Method in simple cases. We test the accuracy of the estimates in a series of examples. |
|||
|
Wed, 16/11/2011 10:10 |
Min Chen |
OCCAM Wednesday Morning Event |
OCCAM Common Room (RI2.28) |
|
Wed, 23/11/2011 10:15 |
Nick Hale (OCCAM) |
OCCAM Wednesday Morning Event |
OCCAM Common Room (RI2.28) |
|
Fractional differential equations are becoming increasingly used as a modelling tool for processes associated with anomalous diffusion or spatial heterogeneity. However, the presence of a fractional differential operator causes memory (time fractional) or nonlocality (space fractional) issues that impose a number of computational constraints. In this talk we discuss efficient, scalable techniques for solving fractional-in-space reaction diffusion equations combining the finite element method with robust techniques for computing the fractional power of a matrix times a vector. We shall demonstrate the methods on a number examples which show the qualitative difference in solution profiles between standard and fractional diffusion models. |
|||
