Stochastic Automata Networks in Cell Biology -- Modeling, Computation and Analysis

Mathias在数值线性代数和矩阵分析方面有着广泛的工作。 大约一年前，他开始与格雷戈里D。史密斯，一个理论细胞生物学家，在建模细胞内钙离子通道。 他们开发和使用的随机自动机网络（SAN）模型能够重现观察到的细胞内钙离子浓度的兴奋性。SAN方法的使用允许在比以前大得多的规模上进行建模。 马蒂亚斯将花一年的时间学习数学生物学，学习离子通道建模所需的生物学背景知识和数学生物学中的其他问题。数学生物学是一个相对较新的领域。 它将数学建模方法应用于广泛的生物学问题，从细胞内水平，例如模拟细胞内钙浓度随时间的变化，到整个器官水平，例如模拟心脏的活动。 除了实验之外，通过数学模型来研究物理现象是科学总趋势的一部分。 可靠的数学模型可以更快地提供科学见解，并且比传统的科学实验更有效。 马蒂亚斯将沉浸在数学生物学一年，以便在未来，他将能够利用他在数学方面的训练，使数学生物学的研究贡献-与社会明显的好处。

Mathias has worked extensively in numerical linear algebra and matrix analysis. About a year ago he started collaborative work with Gregory D. Smith, a theoretical cell biologist, on modeling intra-cellular calcium ion channels. The stochastic automaton network (SAN) model that they developled and used was able to recreate the observed excitability of the intra-cellular calcium ion concentration. The use of the SAN approach allowed modelling on a much larger scale than had previously ben done. Mathias will spend animmersion year in mathematical biology learning the biological background required for the modeling of ion channels and other problems in mathematical biology. Mathematical biology is a relatively new field. It brings mathematical modeling methods to bear on a wide range of biological problems from the intra-cellular level, for example modeling the variation of the concentration of calcium over time within a cell, to the whole organ level, for example, modeling the action of the heart. It is part of a general trend in science to investigate physical phenomena through mathematical models in addition to experiments. A reliable mathematical model can provide scientific insights more quickly, and is more effectively than a traditional scientific experiment. Mathias will immerse himself in mathematical biology for one year, so that in the future he will be able to use his training in mathematics to make research contributions in mathematical biology--with obvious benefits to society.