Collaborative Research: Nonlocal Interfaces in Biological Systems

该奖项支持数学工具的发展，以理解由生物界面之间的相互作用引起的现象。界面是系统中区域之间的过渡，每个区域都表现出不同的生物特性。自然界展示了大量以复杂界面动力学为特征的有组织系统，包括生长的肿瘤或细菌菌落的边缘，生长的中空胚胎的表面，或跳动的心脏中高和低电活动之间的过渡区域。该项目将研究涉及长尺度相互作用的界面的生物系统；这些界面的行为具有纯粹局部动力学无法预测的特性，例如当一个气泡在远处破裂时，其他气泡会生长。开发的新工具将通过细菌生物膜和人体类器官的实验进行验证。本科生和研究生将参与加州州立大学长滩分校和蒙大拿州立大学的研究，美国原住民学生将通过蒙大拿州立大学现有的合作外展项目被招募。研究将集中于研究以相互作用曲线或曲面的集合为特征的复杂系统。这些非局部相互作用可以产生各种典型的在经典界面模型中不会发生的模式形成行为。例如，非局部界面模型表现出阻滞面，这是复杂系统中准均匀区域之间的平稳、动态稳定的界面。某些菌株之间的相互作用提供了这种前沿的具体实例。基因相同的兄弟姐妹群体的进化导致了这些群体之间的竞争，这种竞争产生了一系列相互作用的界面（即每个群体的边界），最终在兄弟姐妹竞争的区域停止。该项目将为非局部接口引入第一原理建模框架，从分析和计算的角度降低模型复杂性。尽管这一框架相对简单，但其具体实例仍然捕获了各种生物系统中基本模式形成机制。因此，该奖项下的研究将侧重于通过在几个生物系统中的实验预测来验证这种总体方法。这种理解非局部模式形成的方法在项目中引入的一般性层面上是新的，它为框架的数学行为及其在不同实验系统中的应用的大量探索打开了大门。主要目的是为研究人员提供一个相对灵活、简约的框架来研究受阻锋和其他界面现象。该奖项反映了美国国家科学基金会的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。

This award supports the development of mathematical tools for understanding phenomena caused by the interactions among biological interfaces. An interface is a transition between regions in a system, each exhibiting different biological properties. The natural world displays a vast gallery of organized systems characterized by complex interface dynamics, including the edges of growing tumors or bacterial colonies, the surface of a growing, hollow embryo, or the transition region between high and low electrical activity in a beating heart. This project will investigate biological systems that involve interfaces with interactions on long length-scales; the behaviors of these interfaces have properties which cannot be predicted by purely local dynamics, as when a bubble popping far away allows other bubbles to grow. The new tools developed will be validated through experimentation with bacterial biofilms and human organoids. Undergraduate and graduate students will be involved in the research at both California State University-Long Beach and Montana State University, and Native American students will be recruited using collaborative outreach programs in existence at Montana State University.The investigation will focus on studying complex systems characterized by a collection of mutually interacting curves or surfaces. These nonlocal mutual interactions can produce a variety of pattern forming behaviors that typically do not occur in classical interfacial models. For example, nonlocal interfacial models exhibit arrested fronts, which are stationary, dynamically stable interfaces between quasi-homogeneous regions in a complex system. The interactions between certain strains of bacteria provide a concrete instance of such fronts. The evolution of genetically identical sibling colonies lead to competition between these colonies, and this competition produces a collection of mutually interacting interfaces (i.e. the boundary of each colony) that eventually arrest in regions of sibling-sibling competition. The project will introduce a first-principle modeling framework for nonlocal interfaces that offers reduced model complexity from both an analytical and computational perspective. Despite the relative simplicity of this framework, its specific instances still capture the essential pattern forming mechanisms in a variety of biological systems. As a consequence, research under the award will focus on validating this overall approach via experimental predictions in several biological systems. This approach to understanding nonlocal pattern formation appears new at the level of generality introduced in the project, and it opens the door to numerous explorations of the mathematical behavior of the framework and of its applications for different experimental systems. The major aim is to provide researchers with a comparatively flexible, minimalistic framework to study arrested fronts and other interfacial phenomena.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.