Provided for non-commercial research and educational use only. Not for reproduction, distribution or commercial use. This chapter was originally published in the Comprehensive Biophysics, the copy attached is provided by Elsevier for the author’s benefit and for the benefit of the author’s institution, for non-commercial research and educational use. This includes without limitation use in instruction at your institution, distribution to specific colleagues, and providing a copy to your institution’s administrator. All other uses, reproduction and distribution, including without limitation commercial reprints, selling or licensing copies or access, or posting on open internet sites, your personal or institution’s website or repository, are prohibited. For exceptions, permission may be sought for such use through Elsevier’s permissions site at: http://www.elsevier.com/locate/permissionusematerial From D.N. Robinson, Y.-S. Kee, T. Luo and A. Surcel, Understanding How Dividing Cells Change Shape. In: Edward H. Egelman, editor: Comprehensive Biophysics, Vol 7, Cell Biophysics, Denis Wirtz. Oxford: Academic Press, 2012. pp. 48-72. ISBN: 978-0-12-374920-8 © Copyright 2012 Elsevier B.V. Academic Press. Author's personal copy 7.5 Understanding How Dividing Cells Change Shape DN Robinson, Y-S Kee, T Luo, and A Surcel, Johns Hopkins University, Baltimore, MD, USA r 2012 Elsevier B.V. All rights reserved. 7.5.1 Introduction 49 7.5.2 Physical Parameters 49 7.5.2.1 Membrane Surface Area and Membrane Remodeling 50 7.5.2.2 Cortical Tension and Cell Surface Curvature 50 7.5.3 The Mechanical Parts List 51 7.5.4 Mechanical Features of the Cortical Cytoskeletal Network 54 7.5.5 Dissecting Mechanics Across Variable Timescales and Length Scales 55 7.5.6 Mechanical Properties of Cytokinesis: Active vs. Passive 56 7.5.6.1 Active Stress Generation 56 7.5.7 Mechanical Interplay Between Myosin II and Actin Crosslinkers 57 7.5.8 Role of Cell Surface Interactions 58 7.5.9 Mechanosensing and Mechanical Feedback 59 7.5.10 Biochemical-Mechanical Feedback Loops 62 7.5.11 Cleavage Furrow Ingression Through Three Mechanical Transitions 64 7.5.12 Cylinder-Thinning Model 65 7.5.13 Contractile Rings: The Schizosaccharomyces pombe Case 66 7.5.14 Comparisons Between Systems 67 7.5.15 Conclusion 68 Acknowledgments 68 References 68 Abbreviations Lp length of cortex tether pulled into micropipette AFM atomic force microscopy (depending on the context of usage) BLCBS both light chain binding sites LCBS light chain binding site BTF bipolar thick filament LTM laser-tracking microrheology CM contractile meshwork MPA micropipette aspiration CR contractile ring MSD mean square displacement E elastic modulus R putative myosin II BTF receptor ELC essential light chain R radius ELCBS essential light chain binding site Rf radius of the furrow F force Rp radius of the pipette FRAP fluorescence recovery after photobleaching RLC regulatory light chain Lc contour length RLCBS regulatory light chain binding site Lp persistence length (depending on the context of T tension usage) Glossary antiparallel actin bundles organized in a circumferential Cleavage furrow The indentation at the center of a ring. dividing cell, which ingresses into a bridge that connects the Cortex The region of the cell underlying the plasma two daughter cells. membrane that is rich in actin cytoskeleton, including Compressive stress The net stress that acts against the myosin II. outward flow of cytoplasm from the cleavage furrow. It Cortical tension The force in the cell cortex that serves to comprises the Laplace-like pressure from the daughter cells, minimize the surface area to volume ratio. polar cortical contractions, and viscoelastic cytoplasm. Curvature A mathematical term that describes how the Contractile meshwork The contractile structure at the geometry of a surface deviates from being flat. The curvature cleavage furrow of a dividing cell composed of a k of a sphere is 2/R, where R is the radius of the sphere; k of noncircumferentially arrayed network of actin a flat surface is zero as it can be treated as a sphere with an polymers. infinite radius. Contractile ring The contractile structure at the Cytokinesis The physical separation of a mother cell into cleavage furrow of a dividing cell composed of two daughter cells. 48 Comprehensive Biophysics, Volume 7 doi:10.1016/B978-0-12-374920-8.00705-0 Author's personal copy Understanding How Dividing Cells Change Shape 49 Duty ratio The fraction of time a motor protein spends also transmits signals that initiate mechanical and bound to its track relative to the duration of its entire biochemical changes in the equatorial and global cortices of ATPase cycle. a dividing cell. Elastic deformation The deformation in which the Myosin II A motor protein that binds to and performs mechanical stress is linearly proportional to the resulting mechanical work on actin filaments. Myosin II forms the mechanical strain. basis of cellular contractility. Elastic modulus The proportionality constant describing Persistence length The persistence length (Lp)isa the amount of mechanical stress required to impose a parameter used to describe semiflexible polymers. When certain amount of strain on a material during elastic polymer length is longer than Lp, the polymer is flexible. For deformation. polymer lengths shorter than Lp, the polymer behaves like a Equatorial cortex The central region of the cell cortex that rigid rod. generally gives rise to the cleavage furrow. Radial stress These are the active stresses, thought to be Global cortex The region of the cortex outside of the generated primarily by myosin II, that act at the cleavage cleavage furrow. This is also referred to as the polar cortex. furrow. Laplace pressure The pressure generated at a curved fluid Sarcomere The repeating contractile unit, consisting of surface due to surface tension. It serves to minimize the actin polymers and myosin II bipolar thick filaments, found surface area to volume ratio. in muscle. Mechanical phase angle The relationship between the Stretch modulus The proportionality constant elastic and viscous components of a viscoelastic material. describing the viscoelasticity in the plane tangential to Mechanical stress The pressure (force per unit area) the surface. applied to a material. Viscoelasticity A property of a material held together by Mechanosensing The ability to sense and respond to dynamic interactions. These dynamic interactions lead to mechanical inputs. time-dependent responses to imposed stresses, leading to Mechanotransduction The conversion of a mechanical both viscous and elastic characteristics. input into a biochemical signaling pathway. Viscosity The resistive property of a fluid to flow in Mitotic spindle The microtubule structure that separates response to an external stress. the sister chromatids during mitosis. The mitotic spindle 7.5.1 Introduction cells with a plasma membrane (meaning no cell wall), the core principles will prove to be universal. Apparent differences Cell division is an amazing cellular process in which a mother will likely reflect either specific details of individual systems or cell divides into two daughter cells in as little as five minutes. identify where understanding between these systems is still Cytokinesis requires every cytoskeletal polymeric network to lacking. operate together to ensure that the nuclear and cytoplasmic contents are evenly segregated into the two hemispheres that give rise to the daughter cells. These cytoskeletal networks 7.5.2 Physical Parameters drive the remodeling of the cell cortex as the cell pinches into two. Cytokinesis is elegant and spectacular, and is critical for Cytokinesis is inherently a mechanical process in which the normal development and in disease.1 Many important devel- cell deforms until a thin bridge is formed and ultimately opmental processes are coupled to cytokinesis, including stem severed to produce two daughter cells. To quantitatively assess cell decisions. Cells can manipulate cytokinesis to create the mechanical features of cytokinesis, basic physical para- highly asymmetrical cell divisions, such as the meiotic divi- meters that govern the deformation of the surface of the cell sions during mammalian oocyte maturation and in embryo- must be defined. Two of these are the bending modulus (or nic cells.2–4 Cytokinesis can also be suppressed altogether to bending energy), which is the proportionality constant create specialized cells such as the highly polyploid mega- describing the resistance to bending deformation perpendi- karyocytes, which will spend the remainder of their lives cular to the cell surface, and the stretch modulus, which is the producing platelets, or polyploid cells like those found in the proportionality constant describing the viscoelasticity in the liver.5,6 Numerous disease-causing mutations disrupt func- plane tangential to the cell surface. To determine whether the tions of proteins whose primary roles are to orchestrate cell energy cost of bending (bending modulus, B) or stretching 7,8 division. A number of excellent reviews have been written (stretch modulus, Sc) is likely to dominate a particular cellular on cytokinesis already (e.g., Refs 9 and 10). Here, the focus deformation, one can determine a characteristic length scale will be on the current view of the physical aspects of cell (l) defined as l ¼ O(B/Sc). From the published values for a division. Known parameters will be defined, how the cell Dictyostelium cell, lE50–100 nm,11 which implies that for a manipulates