The effects of internal forces and membrane heterogeneity on three-dimensional cell shapes

Research output: Contribution to journalArticlepeer-review


The shape of cells and the control thereof plays a central role in a variety of cellular processes, including endo- and exocytosis, cell division and cell movement. Intra- and extracellular forces control the shapes, and while the shape changes in some processes such as exocytosis are intracellularly-controlled and localized in the cell, movement requires force transmission to the environment, and the feedback from it can affect the cell shape and mode of movement used. The shape of a cell is determined by its cytoskeleton (CSK), and thus shape changes involved in various processes involve controlled remodeling of the CSK. While much is known about individual components involved in these processes, an integrated understanding of how intra- and extracellular signals are coupled to the control of the mechanical changes involved is not at hand for any of them. As a first step toward understanding the interaction between intracellular forces imposed on the membrane and cell shape, we investigate the role of distributed surrogates for cortical forces in producing the observed three-dimensional shapes. We show how different balances of applied forces lead to such shapes, that there are different routes to the same end state, and that state transitions between axisymmetric shapes need not all be axisymmetric. Examples of the force distributions that lead to protrusions are given, and the shape changes induced by adhesion of a cell to a surface are studied. The results provide a reference framework for developing detailed models of intracellular force distributions observed experimentally, and provide a basis for studying how movement of a cell in a tissue or fluid is influenced by its shape.

Original languageEnglish (US)
Article number1
JournalJournal of Mathematical Biology
Issue number1
StatePublished - Jan 2023

Bibliographical note

Funding Information:
This work was supported in part by NSF Grant DMS 1311974, and NIH Grant 54-CA-210190, the Newton Institute and the Simons Foundation.We thank a reviewer for a very thorough reading of the work that brought a number of minor errors to our attention.

Publisher Copyright:
© 2022, The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature.


  • Cell cortex
  • Helfrich energy
  • Surface finite element method

PubMed: MeSH publication types

  • Journal Article
  • Research Support, Non-U.S. Gov't
  • Research Support, N.I.H., Extramural
  • Research Support, U.S. Gov't, Non-P.H.S.


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