Differential and Integral Equations in Physiology and Cell Biology

Ermentrout 9972913 研究者继续研究非线性动力学在细胞生物学和生理学中的应用，特别是在神经生理学中的应用。 具体研究了以下问题：1. 突触双稳态分析两个（或多个）相互耦合的神经元在没有输入的情况下保持活动的动力学机制是什么？ 2. 适应如何增强兴奋性耦合神经振荡器的同步？ 3. 是什么决定了在与延迟耦合的神经元系统以及丘脑振荡模型中出现的“蹒跚”波的形式和性质？ 4. 抑制和慢兴奋突触对皮层切片中波的传播有什么影响？ 5. 游离和结合的肌动蛋白在细胞中的空间分布是怎样的？聚合分子的长度分布是否有非平凡的空间依赖性？ 研究者研究如何用数学方法来理解生物系统是如何工作的。 具体来说，他感兴趣的是神经细胞如何相互作用，产生与行为有关的活动。 例如，当一个人或动物在短期记忆中记住某件事（比如电话号码）时，相关的神经元群是如何保持活跃的，又是什么使其关闭的？ 建立数学模型，并使用数学技术来研究这些模型，以便提出新的实验。 在正常和不正常的行为过程中，神经系统的某些部分能够产生在大脑各个区域移动的波。 研究人员感兴趣的是什么因素决定了这些波的性质，如它们的速度和形状。 最后，他研究了细胞内负责细胞形状和如何移动的成分的模型。

Ermentrout9972913 The investigator continues work on the applications ofnonlinear dynamics to cell biology and physiology with particularemphasis in neurophysiology. Specifically, the following problemsare studied: 1. Analysis of synaptic bistability; what is thedynamic mechanism by which two (and more) mutually coupledneurons can maintain activity in absence of inputs? 2. How doesadaptation enhance the synchronization of excitatorily coupledneural oscillators? 3. What determines the form and propertiesof ``lurching'' waves that arise in systems of neurons that arecoupled with delays as well as in models of thalamicoscillations? 4. What is the effect of inhibition and slowexcitatory synapses on the propagation of waves in corticalslices? 5. How are free and bound actin spatially distributedin the cell; is there any nontrivial spatial dependence on thelength distribution of the polymerized molecule? The investigator studies how mathematical methods can beused to understand how biological systems work. Specifically, heis interested in how nerve cells interact with each other toproduce activity that is related to behavior. For example, when aperson or animal holds something in short-term memory (like aphone number) how does the relevant group of neurons stay on andwhat turns it off? Mathematical models are created andmathematical techniques are used to study these models in orderto suggest new experiments. During normal and abnormal behaviorparts of the nervous system are capable of producing waves thatmove across regions of the brain. The investigator is interestedin what factors determine the properties of these waves, such astheir speed and shape. Finally, he studies models of thecomponents inside the cell that are responsible for the cell'sshape and how it moves around.