Near the onset of rigidity in living and nonliving matter

Syracuse University, Syracuse NY

Investigators

Abstract

NONTECHNICAL SUMMARY Have you ever played a game of "Pick up Sticks" and wondered how an entire structure of randomly arranged sticks can collapse with the removal of just one stick? And have you ever wondered how a skin cell changes shape to crawl towards a wound to heal it? The notion of the onset of mechanical rigidity in both living and nonliving matter will help answer both of these seemingly disparate questions. To explore the emergence (and destruction) of mechanical rigidity in nonliving matter, the proposed modeling will be based on a collection of frictionless, repulsive soft spheres; while in living matter, it will utilize a disordered spring network. The PI's group will test both models by investigating what properties - friction, particle/filament shape, type of crosslinking between filaments, local mechanical stability - affect the nature of the rigidity transition. These models will be used to describe mechanical stability of two- and three-dimensional systems including granular systems, filamentous cytoskeletal networks, and biological tissue in the brain. The proposed work, therefore, extends the reach of materials science to living systems to help drive the emerging field of quantitative biology. The results of the proposed research will be used for development of a new course material on rigidity in both living and nonliving systems at undergraduate and graduate levels. The proposed collaborations with Syracuse Museum of Science and Technology and the YWCA will educate the public about the intrigue of soft matter. The PI will use her knowledge and experience to recruit women to the physical sciences by presenting scientific advances used to decouple the biological clock and the tenure clock to senior graduate students and post-docs. TECHNICAL SUMMARY How does a collection of randomly packed frictional particles at the threshold of mechanical rigidity destabilize with the deletion of just one contact? And how does a collection of cytoskeletal filaments attain mechanical rigidity to extend the reach of a cell? In nonliving matter, the model will be based on a collection of frictionless, repulsive soft spheres; while in living matter, it will utilize a disordered spring network. The PI's group will test the robustness of both models by investigating what properties - friction, particle/filament shape, type of crosslinking between filaments, local mechanical stability - affect the nature of the rigidity transition. To test for this robustness in nonliving systems, the local properties of mechanical stability at the onset of rigidity for frictionless, repulsive soft discs in two dimensions will be studied by using concept of jamming graph. Armed with the information of constraint counting, geometry, and force-balance, the PI's group will develop a model for the onset of rigidity in frictionless, particulate matter. The emergence (and destruction) of rigidity abounds in living matter as well. The actin filament cytoskeletal network adjusts its morphology to support the cell structurally. The proposed research will narrow the existing theoretical gap between morphology and mechanics by building disordered spring network models that encode more of the network morphology, such as anisotropy and angle-constraining crosslinks, to determine which aspects are more relevant to the onset of rigidity than others. Moreover, quantitative modeling of biological tissue in the brain will be developed using vertex models, which are related to disordered spring networks. The PI's group will investigate the interplay between morphology and mechanics to determine how glial cells structurally support bundles of neurons. The results of the proposed research will be used for development of a new course material on rigidity in both living and nonliving systems at undergraduate and graduate levels. The proposed collaborations with Syracuse Museum of Science and Technology and the YWCA will educate the public about the intrigue of soft matter. The PI will be involved in the recruitment of women to the physical sciences by presenting scientific advances used to decouple the biological clock and the tenure clock to senior graduate students and post-docs.