CAREER: Probing Multiscale Growth Dynamics in Filamentous Cell Walls

Various plants and fungi rely on filamentous growth to develop, reproduce, or survive under environmental stress. For example, the growth of root hairs with one-cell width effectively increases the surface area of the plant roots to absorb water and nutrients. Although experimental approaches have been able to track cell wall morphology and kinematics on the expanding cell wall surface for more than a century, the regulation of cell wall growth needs further elucidation.

This project will develop mathematical models and computational methods to simulate the cell wall expansion due to the spatial patterning of new cell wall materials and mechanical interaction with the cell interior. Further, inference methods will be devised to predict the spatial patterning of wall-material trafficking from the cell wall geometry and quantify how volume growth inside the cell wall is distributed and rearranged to sustain the cell wall geometry during expansion and under mechanical constraints.

The methods developed in this research can be applied to filamentous growth systems such as pollen tubes, root hairs, fungus hyphae, thus having significant implications in advancing agriculture and improving public health. Complementary to the research, the investigator will engage students, including K-12, undergraduate, and graduate students, in research mentorship, journal clubs, and a new interactive learning platform "Filaform”, to promote interest and transdisciplinary understanding of this biological process by leveraging geometry and other mathematics in conjunction with modern and emerging experimental techniques.

To reach the research and education goals, two complementary mathematical models at different scales will be developed. The first will be a thin-shell model approximating the cell wall surface as a growing elastic boundary inflated by turgor pressure from the cell interior. Cubic-spline solutions will be developed to simulate the evolution of surface growth under the influence of turgor pressure and the distribution of exocytosis, a process that distributes new cell wall material along the cell wall interior surface.

In addition, an inverse problem coupled with a subset of the model equations will be formulated to infer the distribution of exocytosis given the steady-state cell shape. Taking the exocytosis distribution as an input, the second model will be a three-dimensional model that describes the growth distribution and directionality (anisotropy) across the cell wall thickness.

An energy-based material-point method will be developed to simulate the dynamics of the moving cell-wall domain. The investigator will infer the spatial map of the volume growth and anisotropy in the cell-wall domain by formulating optimization problems constrained by the three-dimensional model. Theoretical predictions from both models will be validated by experiments tracking the cell wall morphology, signals of protein complexes involved in exocytosis, and new polymers in the cell wall.

The investigator will create an open-source interactive teaching and learning platform for outreach to K-12 educators and students based on the thin-shell model and its simulation.

This project is jointly funded by the Mathematical Biology program of the Division of Mathematical Science and by the Biomechanics and Mechanobiology (BMMB) program in the Division of Civil, Mechanical, and Manufacturing Innovation.

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.