Complex and Chaotic Biological Dynamics

生物和生理系统显示出丰富的复杂动力学。以前的工作证明了如何 相对简单的理论模型解释了控制良好的模型实验中的复杂动力学 系统.尽管取得了这些成功，但对大多数自然发生的生物节律的深入理解还没有 办妥了一批多年想特别是在理解基因、心脏和神经系统的动力学方面出现了一些基本问题。 网络.在我的研究中，我开发了大量相互作用元素的理论模型，并研究 动力学如何取决于可修改的实验参数的变化，包括空间 异质性，噪声，时间延迟，网络结构。 近年来，实验数据收集的新模式的发展使我们能够 来收集大量的数据。这些新方法包括使用荧光染料的活组织光学成像、基因表达芯片、多电极记录、DNA测序。由于这些进步，人们越来越认识到数学分析和生物系统建模的必要性。目前的工作将集中在涉及复杂的动力学和几何结构之间的连接在不同领域的问题，包括：在心脏组织培养包含起搏器和兴奋细胞的节奏代;视觉信息处理的皮层网络;在无脊椎动物的发展过程中的基因控制。在我看来，这些领域是由基本的未解决的科学问题的存在而统一起来的，这些问题需要理论和实验相结合的跨学科方法。此外，所有这些系统都包含复杂的空间网络，其中基本的数学性质仍然需要阐明。通过提供对正常动态的新理解，这项工作可能为控制异常动态的方法提供新的见解。参与这些项目的学生将接受生物学和数学的跨学科培训，这将使他们处于新兴科学领域的最前沿。

Biological and physiological systems display a wealth of complex dynamics. Previous work demonstrated how comparatively simple theoretical models account for complex dynamics in well-controlled model experimental systems. Despite these successes, a deep understanding of most naturally occurring biological rhythms has not been achieved. In particular fundamental issues arise in understanding dynamics in gene, cardiac, and neural networks. In my research, I develop theoretical models for large numbers of interacting elements, and study how the dynamics depends on variations on modifiable experimental parameters including spatial heterogeneity, noise, time delays, network structure. Recent years have witnessed the development of new modalities of experimental data collection that enable us to gather large amounts of data. These new methods include optical imaging of living tissue using fluorescent dyes, gene expression chips, multielectrode recordings, DNA sequencing. As a consequence of these advances, there is growing recognition of the necessity of mathematical analysis and modeling of biological systems. The current work will focus on problems that involve connections between complex dynamics and geometric structures in diverse areas including: rhythm generation in cardiac tissue culture containing both pacemakers and excitable cells; visual information processing by cortical networks; gene control during development in invertebrates. These areas are united by the presence of fundamental unsolved scientific questions that will, in my opinion, require interdisciplinary approaches combining theory and experiment. Further, all these systems contain complex networks in space in which basic mathematical properties still need to be elucidated. By providing new understanding of normal dynamics, the work may provide new insights into methods to control abnormal dynamics. Students engaged in these projects will receive interdisciplinary training in both biology and mathematics that will place them at the forefront of emerging fields of science.