We use mathematical, computational and theoretical biophysical modeling of cell biological phenomena to understand how subcellular machines work. Our approaches and modeling philosophy are described in these reviews:

Alex Mogilner, Jun Allard and Roy Wollman. Cell polarity: Quantitative modeling as a tool in cell biology. Science, 336, 175-179 (2012)
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A. Mogilner, R. Wollman, W. Marshall, Quantitative Modeling in Cell Biology: What Is It Good for? Dev. Cell , 11, 279-287 (2006)
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A. Mogilner, D. Odde, Modeling cellular processes in 3D. Trends Cell Biol., 21, 692-700 (2011)
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J. M. Scholey, I. Brust-Mascher, A. Mogilner, Cell division, Nature , 422 , 746-752 (2003).
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A. Mogilner, R. Wollman, G. Civelekoglu-Scholey, J. Scholey, Modeling Mitosis. Trends Cell Biol., 16, 88-96 (2006)
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A. Mogilner, E. Craig, Toward quantitative understanding of mitotic spindle assembly and mechanics J. Cell Science. , 123, 3435-3445 (2010)
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A. Mogilner, G. Oster, Polymer Motors: Pushing out the Front and Pulling up the Back. Curr. Biol., 13 , R721-R733 (2003)
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A. Mogilner, On the Edge: Modeling Protrusion. Cur. Opin. Cell Biol., 18, 32-39 (2006)
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A. Mogilner, Mathematics of Cell Motility: Have We Got Its Number?
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A. Mogilner, K. Keren, The shape of motile cells Curr. Biol. , 19, R762-R771 (2009)
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Jun Allard and Alex Mogilner. Traveling waves in actin dynamics and cell motility. Cur. Opin. Cell Biol., 25, 107-115 (2013)
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Gaudenz Danuser, Jun Allard and Alex Mogilner. Mathematical modeling of eukaryotic cell migration: insights beyond experiments. Ann. Rev. Cell Dev. Biol., 29: 501-528 (2013).
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A. Mogilner and A. Manhart. Intracellular fluid mechanics: coupling cytoplasmic flow with active cytoskeletal gel. Annu. Rev. Fluid Mech. , 50 : 347-370 (2018).
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Vikash Verma, Alex Mogilner, Thomas J. Maresca. Classical and Emerging Regulatory Mechanisms of Cytokinesis in Animal Cells. Biology , 8(3) : 55 (2019).
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Mogilner A, Barnhart EL, Keren K. Experiment, theory, and the keratocyte: An ode to a simple model for cell motility. Semin Cell Dev Biol., 100: 143-151 (2020). preprint in pdf format