MULTISCALE PHENOMENA IN BIOLOGY: Proceedings of the 2nd Conference on Mathematics and Biology
1167(2009); http://dx.doi.org/10.1063/1.3246413View Description Hide Description
The collective movements of unicellular organisms such as bacteria or amoeboid (crawling) cells are often modeled by partial differential equations (PDEs) that describe the time evolution of cell density. In particular, chemotaxis equations have been used to model the movement towards various kinds of extracellular cues. Well‐developed analytical and numerical methods for analyzing the time‐dependent and time‐independent properties of solutions make this approach attractive. However, these models are often based on phenomenological descriptions of cell fluxes with no direct correspondence to individual cell processes such signal transduction and cell movement. This leads to the question of how to justify these macroscopic PDEs from microscopic descriptions of cells, and how to relate the macroscopic quantities in these PDEs to individual‐level parameters. Here we summarize recent progress on this question in the context of bacterial and amoeboid chemotaxis, and formulate several open problems.
1167(2009); http://dx.doi.org/10.1063/1.3246614View Description Hide Description
In this study, we describe efforts at modeling the electrophysiological dynamics of cortical networks in a multi‐scale manner. Specifically, we describe the implementation of a network model composed of simple single‐compartmental neuron models, in which a single complex multi‐compartmental model of a pyramidal neuron is embedded. The network is capable of generating Δ (2 Hz, observed during deep sleep states) and γ (40 Hz, observed during wakefulness) oscillations, which are then imposed onto the multi‐compartmental model, thus providing realistic, dynamic boundary conditions. We furthermore discuss the challenges and chances involved in multi‐scale modeling of neural function.
1167(2009); http://dx.doi.org/10.1063/1.3246412View Description Hide Description
Multi‐Scale Simulator for the Geoenvironment (MSSG), which is a coupled non‐hydrostatic atmosphere‐ocean‐land model, has been developed in the Earth simulator Center. Out line of MSSG is introduced and characteristics are presented. Computational performance analysis has been performed on the Earth Simulator. As the results of optimization, ultra high performance with MSSG achieved. Its computational performance on the Earth Simulator attained 52–55% of theoretical peak performance. In addition, results from preliminary validations including forecasting experiments are presented.
1167(2009); http://dx.doi.org/10.1063/1.3246414View Description Hide Description
Evo‐Devo, the science that puts together in a common framework the dynamics of evolution with the processes of embryonic development is inherently multiscale. The hierarchical organization of life phenomena also contributes to the possibility of reducing its complexity to workable modules. However, the emphasis on a compositional, or blocks‐within‐blocks kind of hierarchy, implies a reductionistic perspective on multiscaling that ignores the irreducibility of some levels. The notion of generative hierarchies tackles this problem, introducing an organicist perspective that, while keeping levels of organization, acknowledges the existence of breaks in the hierarchy at the genomic, cellular, individual, and species levels. Whereas independent modeling in development or evolution has been done at each scale of organization, no multiscale approaches have so far been worked out that can account for the relationship between these two fundamental mechanisms that have shaped biodiversity throughout the history of life on Earth.
1167(2009); http://dx.doi.org/10.1063/1.3246415View Description Hide Description
This paper is a plea for considering scientific perspectivism as the appropriate philosophical stance to deal with a number of epistemological, methodological, and ontological challenges modelers of complex, multi‐scale phenomena are facing. Broadly speaking, perspectivism is the philosophical position that one’s access to the world through perception, experience, and reason is possible only through one’s own perspective and interpretation. Scientific perspectivism extends this position to scientific.