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The Mechanics and Thermodynamics of Tubule Formation in Biological Membranes

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Abstract

Membrane tubulation is a ubiquitous process that occurs both at the plasma membrane and on the membranes of intracellular organelles. These tubulation events are known to be mediated by forces applied on the membrane either due to motor proteins, by polymerization of the cytoskeleton, or due to the interactions between membrane proteins binding onto the membrane. The numerous experimental observations of tube formation have been amply supported by mathematical modeling of the associated membrane mechanics and have provided insights into the force-displacement relationships of membrane tubes. Recent advances in quantitative biophysical measurements of membrane-protein interactions and tubule formation have necessitated the need for advances in modeling that will account for the interplay of multiple aspects of physics that occur simultaneously. Here, we present a comprehensive review of experimental observations of tubule formation and provide context from the framework of continuum modeling. Finally, we explore the scope for future research in this area with an emphasis on iterative modeling and experimental measurements that will enable us to expand our mechanistic understanding of tubulation processes in cells.

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Abbreviations

AC:

Anterograde carriers

BAR:

Bin/Amphiphysin/Rvs

BDP:

BAR domain protein

BFA:

Brefeldin A

BIN1:

Bridging Integrator 1

CICR:

Calcium-induced calcium release

ER:

Endoplasmic reticulum

ERES:

ER exit site

ERGIC:

ER-Golgi intermediate compartment

GFP:

Green Fluorescent Protein

GUV:

Giant unilamellar vesicle

iPALM:

Interferometric photoactivated localization microscopy

LTCC:

yL-type calcium channel

PEC:

Protrusion, engorgement, and consolidation

RyRs:

Ryanodine receptors

SR:

Sarcoplasmic reticulum

TC:

Transport carrier

T-tubules:

Transverse tubules

wtENTH:

Wild-type epsin N-terminal homology

References

  • Adams I, Jones D (1982) Quantitative ultrastructural changes in rat cortical synapses during early-, mid-and late-adulthood. Brain Res 239(2):349–363

    Article  CAS  PubMed  Google Scholar 

  • Alimohamadi H, Rangamani P (2018) Modeling membrane curvature generation due to membrane-protein interactions. Biomolecules 8(4):120

    Article  PubMed Central  Google Scholar 

  • Alimohamadi H, Vasan R, Hassinger JE, Stachowiak JC, Rangamani P (2018) The role of traction in membrane curvature generation. Mol Biol Cell 29(16):2024–2035

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  • Alimohamadi H, Bell M, Halpain S, Rangamani P (2020) Mechanical principles governing the shapes of dendritic spines.bioRxiv

  • Argudo D, Bethel NP, Marcoline FV, Grabe M (2016) Continuum descriptions of membranes and their interaction with proteins: towards chemically accurate models. Biochim Biophys Acta Biomembr 1858(7):1619–1634

    Article  CAS  Google Scholar 

  • Aridor M, Bannykh SI, Rowe T, Balch WE (1995) Sequential coupling between copii and copi vesicle coats in endoplasmic reticulum to golgi transport. J Cell Biol 131(4):875–893

    Article  CAS  PubMed  Google Scholar 

  • Arroyo M, DeSimone A (2009) Relaxation dynamics of fluid membranes. Phys Rev E 79(3):031915

    Article  Google Scholar 

  • Barbosa J, Stein H, Martinez RL, Galan-Gadea A, Li S, Dalmau J, Adam KC, Valls-Solé J, Constantinidis C, Compte A (2020) Interplay between persistent activity and activity-silent dynamics in the prefrontal cortex underlies serial biases in working memory. Nat Neurosci. 1–9

  • Bassereau P, Jin R, Baumgart T, Deserno M, Dimova R, Frolov VA, Bashkirov PV, Grubmüller H, Jahn R, Risselada HJ et al (2018) The 2018 biomembrane curvature and remodeling roadmap. J Phys D Appl Phys 51(34):343001

    Article  PubMed  PubMed Central  Google Scholar 

  • Baumgart T, Hess ST, Webb WW (2003) Imaging coexisting fluid domains in biomembrane models coupling curvature and line tension. Nature 425(6960):821–824

    Article  CAS  PubMed  Google Scholar 

  • Ben-Tekaya H, Miura K, Pepperkok R, Hauri H-P (2005) Live imaging of bidirectional traffic from the ergic. J Cell Sci 118(2):357–367

    Article  CAS  PubMed  Google Scholar 

  • Bielli A, Haney CJ, Gabreski G, Watkins SC, Bannykh SI, Aridor M (2005) Regulation of sar1 nh2 terminus by gtp binding and hydrolysis promotes membrane deformation to control copii vesicle fission. J Cell Biol 171(6):919–924

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  • Bobrovska N, Gozdz W, Kralj-Iglic V, Iglic A (2013) On the role of anisotropy of membrane components in formation and stabilization of tubular structures in multicomponent membranes. PLoS ONE 8(9):e73941

    Article  PubMed  PubMed Central  Google Scholar 

  • Bobrovska N, Góźdź W, Kralj-Iglič V, Iglič A (2013) On the role of anisotropy of membrane components in formation and stabilization of tubular structures in multicomponent membranes. PLoS ONE 8(9):e73941

    Article  PubMed  PubMed Central  Google Scholar 

  • Bornschlögl T, Romero S, Vestergaard CL, Joanny J-F, Van Nhieu GT, Bassereau P (2013) Filopodial retraction force is generated by cortical actin dynamics and controlled by reversible tethering at the tip. Proc Nat Acad Sci 110(47):18928–18933

    Article  PubMed  Google Scholar 

  • Brochard F, Lennon J (1975) Frequency spectrum of the flicker phenomenon in erythrocytes. J Phys 36(11):1035–1047

    Article  Google Scholar 

  • Busch DJ, Houser JR, Hayden CC, Sherman MB, Lafer EM, Stachowiak JC (2015) Intrinsically disordered proteins drive membrane curvature. Nat Commun 6(1):1–11

    Article  Google Scholar 

  • Butler MH, David C, Ochoa G-C, Freyberg Z, Daniell L, Grabs D, Cremona O, Camilli PD (1997) Amphiphysin ii (sh3p9; bin1), a member of the amphiphysin/rvs family, is concentrated in the cortical cytomatrix of axon initial segments and nodes of ranvier in brain and around t tubules in skeletal muscle. J Cell Biol 137(6):1355–1367

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  • Campas O, Leduc C, Bassereau P, Joanny J-F, Prost J (2009) Collective oscillations of processive molecular motors. Biophys Rev Lett 4(01n02):163–178

    Article  CAS  Google Scholar 

  • Campelo F, Hernández-Machado A (2008) Polymer-induced tubulation in lipid vesicles. Phys Rev Lett 100(15):158103

    Article  CAS  PubMed  Google Scholar 

  • Canham PB (1970) The minimum energy of bending as a possible explanation of the biconcave shape of the human red blood cell. J Theor Biol 26(1):61–81

    Article  CAS  PubMed  Google Scholar 

  • Chabanon M, Ho JC, Liedberg B, Parikh AN, Rangamani P (2017) Pulsatile lipid vesicles under osmotic stress. Biophys J 112(8):1682–1691

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  • Choi J, Ko J, Racz B, Burette A, Lee J-R, Kim S, Na M, Lee HW, Kim K, Weinberg RJ et al (2005) Regulation of dendritic spine morphogenesis by insulin receptor substrate 53, a downstream effector of rac1 and cdc42 small gtpases. J Neurosci 25(4):869–879

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  • Co C, Wong DT, Gierke S, Chang V, Taunton J (2007) Mechanism of actin network attachment to moving membranes: barbed end capture by n-wasp wh2 domains. Cell 128(5):901–913

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  • Cullen PJ (2008) Endosomal sorting and signalling: an emerging role for sorting nexins. Nat Rev Mol Cell Biol 9(7):574–582

    Article  CAS  PubMed  Google Scholar 

  • De Gennes P, Taupin C (1982) Microemulsions and the flexibility of oil/water interfaces. J Phys Chem 86(13):2294–2304

    Article  Google Scholar 

  • Dai J, Sheetz MP (1995) Mechanical properties of neuronal growth cone membranes studied by tether formation with laser optical tweezers. Biophys J 68(3):988–996

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  • Dailey ME, Smith SJ (1996) The dynamics of dendritic structure in developing hippocampal slices. J Neurosci 16(9):2983–2994

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  • Dent EW, Kwiatkowski AV, Mebane LM, Philippar U, Barzik M, Rubinson DA, Gupton S, Van Veen JE, Furman C, Zhang J et al (2007) Filopodia are required for cortical neurite initiation. Nat Cell Biol 9(12):1347–1359

    Article  CAS  PubMed  Google Scholar 

  • Derganc J, Čopič A (2016) Membrane bending by protein crowding is affected by protein lateral confinement. Biochim Biophys Acta Biomembr 1858(6):1152–1159

    Article  CAS  Google Scholar 

  • Derényi I, Jülicher F, Prost J (2002) Formation and interaction of membrane tubes. Phys Rev Lett 88(23):238101

    Article  PubMed  Google Scholar 

  • Deserno M (2005) The influence of thermal fluctuations on the bending rigidity of fluid membranes. Max-Planck-Institut für Polymerforschung, Ackermannweg 10:55128 Mainz

  • Dotti CG, Sullivan CA, Banker GA (1988) The establishment of polarity by hippocampal neurons in culture. J Neurosci 8(4):1454–1468

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  • Farsad K, Ringstad N, Takei K, Floyd SR, Rose K, De Camilli P (2001) Generation of high curvature membranes mediated by direct endophilin bilayer interactions. J Cell Biol 155(2):193–200

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  • Fiala JC, Feinberg M, Popov V, Harris KM (1998) Synaptogenesis via dendritic filopodia in developing hippocampal area ca1. J Neurosci 18(21):8900–8911

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  • Figard L, Sokac AM (2014) A membrane reservoir at the cell surface: unfolding the plasma membrane to fuel cell shape change. Bioarchitecture 4(2):39–46

    Article  PubMed  PubMed Central  Google Scholar 

  • Figard L, Xu H, Garcia HG, Golding I, Sokac AM (2013) The plasma membrane flattens out to fuel cell-surface growth during drosophila cellularization. Dev Cell 27(6):648–655

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  • Ford MG, Mills IG, Peter BJ, Vallis Y, Praefcke GJ, Evans PR, McMahon HT (2002) Curvature of clathrin-coated pits driven by epsin. Nature 419(6905):361–366

    Article  CAS  PubMed  Google Scholar 

  • Forssmann W, Girardier L (1970) A study of the t system in rat heart. J Cell Biol 44(1):1–19

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  • Fournier J (1996) Nontopological saddle-splay and curvature instabilities from anisotropic membrane inclusions. Phys Rev Lett 76(23):4436

    Article  CAS  PubMed  Google Scholar 

  • Fournier JB, Galatola P (1997) Tubular vesicles and effective fourth-order membrane elastic theories. Europhys Lett 39(2):225–230

    Article  CAS  Google Scholar 

  • Frankel T (2011) The geometry of physics: an introduction. Cambridge University Press, Cambridge

    Book  Google Scholar 

  • Fricke K, Sackmann E (1984) Variation of frequency spectrum of the erythrocyte flickering caused by aging, osmolarity, temperature and pathological changes. Biochim Biophys Acta Mol Cell Res 803(3):145–152

    Article  CAS  Google Scholar 

  • Fricke K, Wirthensohn K, Laxhuber R, Sackmann E (1986) Flicker spectroscopy of erythrocytes. Eur Biophys J 14(2):67–81

    Article  CAS  PubMed  Google Scholar 

  • Frost A, Perera R, Roux A, Spasov K, Destaing O, Egelman EH, De Camilli P, Unger VM (2008) Structural basis of membrane invagination by f-bar domains. Cell 132(5):807–817

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  • Fu Y, Shaw SA, Naami R, Vuong CL, Basheer WA, Guo X, Hong T (2016) Isoproterenol promotes rapid ryanodine receptor movement to bridging integrator 1 (bin1)-organized dyads. Circulation 133(4):388–397

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  • Fygenson DK, Marko JF, Libchaber A (1997) Mechanics of microtubule-based membrane extension. Phys Rev Lett 79(22):4497

    Article  CAS  Google Scholar 

  • Föster D (1986) On the scale dependence, due to thermal fluctuations, of the elastic properties of membranes. Phys Lett A 114(3):115–120

    Article  Google Scholar 

  • García-Sáez AJ, Chiantia S, Schwille P (2007) Effect of line tension on the lateral organization of lipid membranes. J Biol Chem 282(46):33537–33544

    Article  PubMed  Google Scholar 

  • Gez LS, Hagalili Y, Shainberg A, Atlas D (2012) Voltage-driven ca2+ binding at the l-type ca2+ channel triggers cardiac excitation-contraction coupling prior to ca2+ influx. Biochemistry 51(48):9658–9666

    Article  CAS  PubMed  Google Scholar 

  • Gillingham AK, Munro S (2003) Long coiled-coil proteins and membrane traffic. Biochim Biophys Acta Mol Cell Res 1641(2–3):71–85

    Article  CAS  Google Scholar 

  • Girard P, Prost J, Bassereau P (2005) Passive or active fluctuations in membranes containing proteins. Phys Rev Lett 94(8):088102

    Article  CAS  PubMed  Google Scholar 

  • Girard P, Pécréaux J, Lenoir G, Falson P, Rigaud J-L, Bassereau P (2004) A new method for the reconstitution of membrane proteins into giant unilamellar vesicles. Biophys J 87(1):419–429

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  • Globus A, Scheibel AB (1966) Loss of dendrite spines as an index of pre-synaptic terminal patterns. Nature 212(5061):463–465

    Article  CAS  PubMed  Google Scholar 

  • Gompper G, Kroll D (1996) Random surface discretizations and the renormalization of the bending rigidity. J Phys I 6(10):1305–1320

    Google Scholar 

  • Gov N (2018) Guided by curvature: shaping cells by coupling curved membrane proteins and cytoskeletal forces. Philos Trans R Soc London Ser B 373(1747):20170115

    Article  Google Scholar 

  • Hassinger JE, Oster G, Drubin DG, Rangamani P (2017) Design principles for robust vesiculation in clathrin-mediated endocytosis. Proc Natl Acad Sci USA 114(7):E1118–E1127

    Article  CAS  PubMed  Google Scholar 

  • Hauri H-P, Schweizer A (1992) The endoplasmic reticulum-golgi intermediate compartment. Curr Opin Cell Biol 4(4):600–608

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  • Heberle FA, Feigenson GW (2011) Phase separation in lipid membranes. Cold Spring Harb Perspect Biol 3(4):a004630

    Article  PubMed  PubMed Central  Google Scholar 

  • Heinrich MC, Capraro BR, Tian A, Isas JM, Langen R, Baumgart T (2010) Quantifying membrane curvature generation of drosophila amphiphysin n-bar domains. J Phys Chem Lett 1(23):3401–3406

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  • Helfrich W (1973) Elastic properties of lipid bilayers: theory and possible experiments. Z Nat C 28(11–12):693–703

    CAS  Google Scholar 

  • Helfrich W (1985) Effect of thermal undulations on the rigidity of fluid membranes and interfaces. J Phys 46(7):1263–1268

    Article  CAS  Google Scholar 

  • Hirokawa N (1998) Kinesin and dynein superfamily proteins and the mechanism of organelle transport. Science 279(5350):519–526

    Article  CAS  PubMed  Google Scholar 

  • Hirschberg K, Miller CM, Ellenberg J, Presley JF, Siggia ED, Phair RD, Lippincott-Schwartz J (1998) Kinetic analysis of secretory protein traffic and characterization of golgi to plasma membrane transport intermediates in living cells. J Cell Biol 143(6):1485–1503

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  • Hochmuth R, Evans C, Wiles H, McCown J (1983) Mechanical measurement of red cell membrane thickness. Science 220(4592):101–102

    Article  CAS  PubMed  Google Scholar 

  • Hochmuth F, Shao J-Y, Dai J, Sheetz MP (1996) Deformation and flow of membrane into tethers extracted from neuronal growth cones. Biophys J 70(1):358–369

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  • Hochmuth R, Wiles H, Evans E, McCown J (1982) Extensional flow of erythrocyte membrane from cell body to elastic tether. ii. experiment. Biophys J 39(1):83–89

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  • Hong T, Shaw RM (2017) Cardiac t-tubule microanatomy and function. Physiol Rev 97(1):227–252

    Article  PubMed  Google Scholar 

  • Hong T, Yang H, Zhang S-S, Cho HC, Kalashnikova M, Sun B, Zhang H, Bhargava A, Grabe M, Olgin J et al (2014) Cardiac bin1 folds t-tubule membrane, controlling ion flux and limiting arrhythmia. Nat Med 20(6):624

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  • Horstmann H, Ng CP, Tang BL, Hong W (2002) Ultrastructural characterization of endoplasmic reticulum-golgi transport containers (egtc). J Cell Sci 115(22):4263–4273

    Article  CAS  PubMed  Google Scholar 

  • Hu M, Briguglio JJ, Deserno M (2012) Determining the gaussian curvature modulus of lipid membranes in simulations. Biophys J 102(6):1403–1410

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  • Iglič A, Babnik B, Gimsa U, Kralj-Iglič V (2005) On the role of membrane anisotropy in the beading transition of undulated tubular membrane structures. J Phys A 38(40):8527

    Article  Google Scholar 

  • Iglič A, Hägerstrand H, Veranič P, Plemenitaš A, Kralj-Iglič V (2006) Curvature-induced accumulation of anisotropic membrane components and raft formation in cylindrical membrane protrusions. J Theor Biol 240(3):368–373

    Article  PubMed  Google Scholar 

  • Jenkins JT (1977) The equations of mechanical equilibrium of a model membrane. SIAM J Appl Math 32(4):755–764

    Article  Google Scholar 

  • Jülicher F, Lipowsky R (1993) Domain-induced budding of vesicles. Phys Rev Lett 70:2964–2967

    Article  PubMed  Google Scholar 

  • Kabaso D, Bobrovska N, Góźdź W, Gov N, Kralj-Iglič V, Veranič P, Iglič A (2012) On the role of membrane anisotropy and bar proteins in the stability of tubular membrane structures. J Biomech 45(2):231–238

    Article  PubMed  Google Scholar 

  • Kabaso D, Gongadze E, Jorgačevski J, Kreft M, Van Rienen U, Zorec R, Iglič A (2011) Exploring the binding dynamics of bar proteins. Cell Mol Biol Lett 16(3):398–411

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  • Kaech S, Banker G (2006) Culturing hippocampal neurons. Nat Protoc 1(5):2406

    Article  CAS  PubMed  Google Scholar 

  • Karatekin E, Sandre O, Guitouni H, Borghi N, Puech P-H, Brochard-Wyart F (2003) Cascades of transient pores in giant vesicles: line tension and transport. Biophys J 84(3):1734–1749

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  • Klopfenstein DR, Tomishige M, Stuurman N, Vale RD (2002) Role of phosphatidylinositol (4, 5) bisphosphate organization in membrane transport by the unc104 kinesin motor. Cell 109(3):347–358

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  • Koster G, Cacciuto A, Derényi I, Frenkel D, Dogterom M (2005) Force barriers for membrane tube formation. Phys Rev Lett 94(6):068101

    Article  PubMed  Google Scholar 

  • Koster G, VanDuijn M, Hofs B, Dogterom M (2003) Membrane tube formation from giant vesicles by dynamic association of motor proteins. Proc Natl Acad Sci USA 100(26):15583–15588

    Article  CAS  PubMed  Google Scholar 

  • Kralj-Iglic V, Hagerstrand H, Veranic P, Jezernik K, Babnik B, Gauger DR, Iglic A (2005) Amphiphile-induced tubular budding of the bilayer membrane. Eur Biophys J 34:1066–1070

    Article  CAS  PubMed  Google Scholar 

  • Kralj-Iglič V, Remškar M, Vidmar G, Fošnarič M, Iglič A (2002) Deviatoric elasticity as a possible physical mechanism explaining collapse of inorganic micro and nanotubes. Phys Lett A 296(2–3):151–155

    Article  Google Scholar 

  • Kwok R, Evans E (1981) Thermoelasticity of large lecithin bilayer vesicles. Biophys J 35(3):637–652

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  • Leduc C, Campàs O, Zeldovich KB, Roux A, Jolimaitre P, Bourel-Bonnet L, Goud B, Joanny J-F, Bassereau P, Prost J (2004) Cooperative extraction of membrane nanotubes by molecular motors. Proc Natl Acad Sci USA 101(49):17096–17101

    Article  CAS  PubMed  Google Scholar 

  • Lee C, Chen LB (1988) Dynamic behavior of endoplasmic reticulum in living cells. Cell 54(1):37–46

    Article  CAS  PubMed  Google Scholar 

  • Lee I-H, Imanaka MY, Modahl EH, Torres-Ocampo AP (2019) Lipid raft phase modulation by membrane-anchored proteins with inherent phase separation properties. ACS Omega 4(4):6551–6559

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  • Leibler S (1986) Curvature instability in membranes. J Phys 47(3):507–516

    Article  CAS  Google Scholar 

  • Leibler S, Andelman D (1987) Ordered and curved meso-structures in membranes and amphiphilic films. J Phys 48(11):2013–2018

    Article  CAS  Google Scholar 

  • Li Z, Anvari B, Takashima M, Brecht P, Torres JH, Brownell WE (2002) Membrane tether formation from outer hair cells with optical tweezers. Biophys J 82(3):1386–1395

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  • Lieu DK, Liu J, Siu C-W, McNerney GP, Tse H-F, Abu-Khalil A, Huser T, Li RA (2009) Absence of transverse tubules contributes to non-uniform ca2+ wavefronts in mouse and human embryonic stem cell-derived cardiomyocytes. Stem Cells Dev 18(10):1493–1500

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  • Lim SK, Wong AS, de Hoog H-PM, Rangamani P, Parikh AN, Nallani M, Sandin S, Liedberg B (2017) Spontaneous formation of nanometer scale tubular vesicles in aqueous mixtures of lipid and block copolymer amphiphiles. Soft Matter 13(6):1107–1115

    Article  CAS  PubMed  Google Scholar 

  • Lipowsky R (1991) The conformation of membranes. Nature 349:475–481

    Article  CAS  PubMed  Google Scholar 

  • Lipowsky R (2013) Spontaneous tubulation of membranes and vesicles reveals membrane tension generated by spontaneous curvature. Faraday Discuss 161:305–331

    Article  CAS  PubMed  Google Scholar 

  • Lippincott-Schwartz J, Cole NB, Marotta A, Conrad PA, Bloom GS (1995) Kinesin is the motor for microtubule-mediated golgi-to-er membrane traffic. J Cell Biol 128(3):293–306

    Article  CAS  PubMed  Google Scholar 

  • Lyon AR, MacLeod KT, Zhang Y, Garcia E, Kanda GK, Korchev YE, Harding SE, Gorelik J et al (2009) Loss of t-tubules and other changes to surface topography in ventricular myocytes from failing human and rat heart. Proc Natl Acad Sci USA 106(16):6854–6859

    Article  CAS  PubMed  Google Scholar 

  • Mahapatra A, Saintillan D, Rangamani P (2020) Transport phenomena in fluid films with curvature elasticity. arXiv preprint arXiv:2001.07539

  • Di Maio A, Karko K, Snopko RM, Mejía-Alvarez R, Franzini-Armstrong C (2007) T-tubule formation in cardiacmyocytes: two possible mechanisms? J Muscle Res Cell Motil 28(4–5):231–241

    Article  PubMed  Google Scholar 

  • Marzban B, Yuan H (2017) The effect of thermal fluctuation on the receptor-mediated adhesion of a cell membrane to an elastic substrate. Membranes 7(2):24

    Article  PubMed Central  Google Scholar 

  • Mattila PK, Lappalainen P (2008) Filopodia: molecular architecture and cellular functions. Nat Rev Mol Cell Biol 9(6):446–454

    Article  CAS  PubMed  Google Scholar 

  • Miller JP, Jacobs GA (1984) Relationships between neuronal structure and function. J Exp Biol 112(1):129–145

    Article  CAS  PubMed  Google Scholar 

  • Mollenhauer H, Morré DJ (1998) The tubular network of the golgi apparatus. Histochem Cell Biol 109(5–6):533–543

    Article  CAS  PubMed  Google Scholar 

  • Nakata T, Terada S, Hirokawa N (1998) Visualization of the dynamics of synaptic vesicle and plasma membrane proteins in living axons. J Cell Biol 140(3):659–674

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  • Nelson DA, Benson ES (1963) On the structural continuities of the transverse tubular system of rabbit and human myocardial cells. J Cell Biol 16(2):297–313

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  • Odell GM, Oster G, Alberch P, Burnside B (1981) The mechanical basis of morphogenesis: I. epithelial folding and invagination. Dev Biol 85(2):446–462

    Article  CAS  PubMed  Google Scholar 

  • Oster GF, Perelson AS, Tilney LG (1982) A mechanical model for elongation of the acrosomal process in thyone sperm. J Math Biol 15(2):259–265

    Article  Google Scholar 

  • Özel MN, Langen M, Hassan BA, Hiesinger PR (2015) Filopodial dynamics and growth cone stabilization in drosophila visual circuit development. Elife 4:e10721

    Article  PubMed  PubMed Central  Google Scholar 

  • Pearce KM, Bell M, Linthicum WH, Wen Q, Srinivasan J, Rangamani P, Scarlata S (2020) G\(\alpha\)q-mediated calcium dynamics and membrane tension modulate neurite plasticity. Mol Biol Cell 31(7):683–694

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  • Peliti L, Leibler S (1985) Effects of thermal fluctuations on systems with small surface tension. Phys Rev Lett 54(15):1690

    Article  CAS  PubMed  Google Scholar 

  • Perutkova S, Kralji-Iglic V, Frank M, Iglic A (2010) Mechanical stability of membrane nanotubular protrusion influenced by attachment of flexible rod-like protein. J Biomech 43:1612–1617

    Article  PubMed  Google Scholar 

  • Peter BJ, Kent HM, Mills IG, Vallis Y, Butler PJG, Evans PR, McMahon HT (2004) Bar domains as sensors of membrane curvature: the amphiphysin bar structure. Science 303(5657):495–499

    Article  CAS  PubMed  Google Scholar 

  • Pezeshkian W, Gao H, Arumugam S, Becken U, Bassereau P, Florent J-C, Ipsen JH, Johannes L, Shillcock JC (2017) Mechanism of shiga toxin clustering on membranes. ACS Nano 11(1):314–324

    Article  CAS  PubMed  Google Scholar 

  • Polishchuk EV, Di Pentima A, Luini A, Polishchuk RS (2003) Mechanism of constitutive export from the golgi: bulk flow via the formation, protrusion, and en bloc cleavage of large trans-golgi network tubular domains. Mol Biol Cell 14(11):4470–4485

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  • Posey AD Jr, Swanson KE, Alvarez MG, Krishnan S, Earley JU, Band H, Pytel P, McNally EM, Demonbreun AR (2014) Ehd1 mediates vesicle trafficking required for normal muscle growth and transverse tubule development. Dev Biol 387(2):179–190

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  • Powers TR, Huber G, Goldstein RE (2002) Fluid-membrane tethers: minimal surfaces and elastic boundary layers. Phys Rev E 65(4):041901

    Article  Google Scholar 

  • Rangamani P, Agrawal A, Mandadapu KK, Oster G, Steigmann DJ (2013) Interaction between surface shape and intra-surface viscous flow on lipid membranes. Biomech Model Mechanobiol 12(4):833–845

    Article  PubMed  Google Scholar 

  • Rangamani P, Zhang D, Oster G, Shen AQ (2013) Lipid tubule growth by osmotic pressure. J R Soc Interface 10(88):20130637

    Article  PubMed  PubMed Central  Google Scholar 

  • Rangamani P, Behzadan A, Holst M (2020) Local sensitivity analysis of themembrane shape equation’derived from the helfrich energy. arXiv preprint arXiv:2005.12550

  • Raote I, Ernst AM, Campelo F, Rothman JE, Pincet F, Malhotra V (2020) Tango1 membrane helices create a lipid diffusion barrier at curved membranes. Elife 9:e57822

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  • Reynolds CH, Holloway MK (2011) Thermodynamics of ligand binding and efficiency. ACS Med Chem Lett 2(6):433–437

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  • Robertson AM, Allan VJ (2000) Brefeldin a-dependent membrane tubule formation reconstituted in vitro is driven by a cell cycle-regulated microtubule motor. Mol Biol Cell 11(3):941–955

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  • Rohatgi R, Ma L, Miki H, Lopez M, Kirchhausen T, Takenawa T, Kirschner MW (1999) The interaction between n-wasp and the arp2/3 complex links cdc42-dependent signals to actin assembly. Cell 97(2):221–231

    Article  CAS  PubMed  Google Scholar 

  • Roossien DH, Lamoureux P, Van Vactor D, Miller KE (2013) Drosophila growth cones advance by forward translocation of the neuronal cytoskeletal meshwork in vivo. PLoS ONE 8(11):e80136

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  • Roux A, Cappello G, Cartaud J, Prost J, Goud B, Bassereau P (2002) A minimal system allowing tubulation with molecular motors pulling on giant liposomes. Proc Natl Acad Sci USA 99(8):5394–5399

    Article  CAS  PubMed  Google Scholar 

  • Roux A, Koster G, Lenz M, Sorre B, Manneville J-B, Nassoy P, Bassereau P (2010) Membrane curvature controls dynamin polymerization. Proc Natl Acad Sci USA 107(9):4141–4146

    Article  CAS  PubMed  Google Scholar 

  • Sackmann E, Duwe HP, Engelhardt H (1986) Membrane bending elasticity and its role for shape fluctuations and shape transformations of cells and vesicles. Faraday Discuss Chem Soc 81:281–290

    Article  CAS  Google Scholar 

  • Safran S (2018) Statistical thermodynamics of surfaces, interfaces, and membranes. CRC Press, Boca Raton

    Book  Google Scholar 

  • Sanborn J, Oglecka K, Kraut RS, Parikh AN (2013) Transient pearling and vesiculation of membrane tubes under osmotic gradients. Faraday Discuss 161:167–176

    Article  CAS  PubMed  Google Scholar 

  • Sauer RA, Duong TX, Mandadapu KK, Steigmann DJ (2017) A stabilized finite element formulation for liquid shells and its application to lipid bilayers. J Comput Phys 330:436–466

    Article  CAS  Google Scholar 

  • Schuster BS, Reed EH, Parthasarathy R, Jahnke CN, Caldwell RM, Bermudez JG, Ramage H, Good MC, Hammer DA (2018) Controllable protein phase separation and modular recruitment to form responsive membraneless organelles. Nat Commun 9(1):1–12

    Article  CAS  Google Scholar 

  • Scriven DR, Dan P, Moore ED (2000) Distribution of proteins implicated in excitation-contraction coupling in rat ventricular myocytes. Biophys J 79(5):2682–2691

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  • Seifert U (1997) Configurations of fluid membranes and vesicles. Adv Phys 46(1):13–137

    Article  CAS  Google Scholar 

  • Sekino Y, Kojima N, Shirao T (2007) Role of actin cytoskeleton in dendritic spine morphogenesis. Neurochem Int 51(2–4):92–104

    Article  CAS  PubMed  Google Scholar 

  • Sens P, Johannes L, Bassereau P (2008) Biophysical approaches to protein-induced membrane deformations in trafficking. Curr Opin Cell Biol 20(4):476–482

    Article  CAS  PubMed  Google Scholar 

  • Sens P, Turner MS (2004) Theoretical model for the formation of caveolae and similar membrane invaginations. Biophys J 86(4):2049–2057

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  • Sens P, Turner MS (2006) Budded membrane microdomains as tension regulators. Phys Rev E 73(3):031918

    Article  Google Scholar 

  • Shao J-Y, Ting-Beall HP, Hochmuth RM (1998) Static and dynamic lengths of neutrophil microvilli. Proc Natl Acad Sci USA 95(12):6797–6802

    Article  CAS  PubMed  Google Scholar 

  • Shepherd N, McDonough HB (1998) Ionic diffusion in transverse tubules of cardiac ventricular myocytes. Am J Physiol Heart Circ Physiol 275(3):H852–H860

    Article  CAS  Google Scholar 

  • Shi Z, Baumgart T (2014) Dynamics and instabilities of lipid bilayer membrane shapes. Adv Colloid Interface Sci 208:76–88

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  • Shi Z, Graber ZT, Baumgart T, Stone HA, Cohen AE (2018) Cell membranes resist flow. Cell 175(7):1769–1779

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  • Shtengel G, Galbraith JA, Galbraith CG, Lippincott-Schwartz J, Gillette JM, Manley S, Sougrat R, Waterman CM, Kanchanawong P, Davidson MW et al (2009) Interferometric fluorescent super-resolution microscopy resolves 3d cellular ultrastructure. Proc Natl Acad Sci USA 106(9):3125–3130

    Article  CAS  PubMed  Google Scholar 

  • Simunovic M, Manneville J-B, Renard H-F, Evergren E, Raghunathan K, Bhatia D, Kenworthy AK, Voth GA, Prost J, McMahon HT et al (2017) Friction mediates scission of tubular membranes scaffolded by bar proteins. Cell 170(1):172–184

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  • Snead WT, Hayden CC, Gadok AK, Zhao C, Lafer EM, Rangamani P, Stachowiak JC (2017) Membrane fission by protein crowding. Proc Natl Acad Sci USA 114(16):E3258–E3267

    Article  CAS  PubMed  Google Scholar 

  • Snead WT, Zeno WF, Kago G, Perkins RW, Richter JB, Zhao C, Lafer EM, Stachowiak JC (2019) Bar scaffolds drive membrane fission by crowding disordered domains. J Cell Biol 218(2):664–682

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  • Soeller C, Cannell M (1999) Examination of the transverse tubular system in living cardiac rat myocytes by 2-photon microscopy and digital image-processing techniques. Circ Res 84(3):266–275

    Article  CAS  PubMed  Google Scholar 

  • Sokac AM, Wieschaus E (2008) Local actin-dependent endocytosis is zygotically controlled to initiate drosophila cellularization. Dev Cell 14(5):775–786

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  • Solon J, Pécréaux J, Girard P, Fauré M-C, Prost J, Bassereau P (2006) Negative tension induced by lipid uptake. Phys Rev Lett 97(9):098103

    Article  PubMed  Google Scholar 

  • Sorre B, Callan-Jones A, Manneville J-B, Nassoy P, Joanny J-F, Prost J, Goud B, Bassereau P (2009) Curvature-driven lipid sorting needs proximity to a demixing point and is aided by proteins. Proc Natl Acad Sci USA 106(14):5622–5626

    Article  CAS  PubMed  Google Scholar 

  • Stachowiak JC, Brodsky FM, Miller EA (2013) A cost-benefit analysis of the physical mechanisms of membrane curvature. Nat Cell Biol 15(9):1019–1027

    Article  CAS  PubMed  Google Scholar 

  • Stachowiak JC, Hayden CC, Sasaki DY (2010a) Steric confinement of proteins on lipid membranes can drive curvature and tubulation. Proc Natl Acad Sci USA 107(17):7781–7786

    Article  CAS  PubMed  Google Scholar 

  • Stachowiak JC, Schmid EM, Ryan CJ, Ann HS, Sasaki DY, Sherman MB, Geissler PL, Fletcher DA, Hayden CC (2012) Membrane bending by protein-protein crowding. Nat Cell Biol 14(9):944–949

    Article  CAS  PubMed  Google Scholar 

  • Stachowiak JC, Stevens MJ, Robinson DB, Branda SS,Zendejas F, Meagher RJ, Sasaki DY, Bachand GD,Hayden CC, Sinha A, et al. (2010b) Biomolecular transport and separationin nanotubular networks. In: tech. rep., Sandia NationalLaboratories

  • Stahelin RV, Long F, Peter BJ, Murray D, De Camilli P, McMahon HT, Cho W (2003) Contrasting membrane interaction mechanisms of ap180 n-terminal homology (anth) and epsin n-terminal homology (enth) domains. J Biol Chem 278(31):28993–28999

    Article  CAS  PubMed  Google Scholar 

  • Staykova M, Holmes DP, Read C, Stone HA (2011) Mechanics of surface area regulation in cells examined with confined lipid membranes. Proc Natl Acad Sci USA 108(22):9084–9088

    Article  CAS  PubMed  Google Scholar 

  • Steigmann D (1999) Fluid films with curvature elasticity. Arch Ration Mech Anal 150(2):127–152

    Article  Google Scholar 

  • Steinkühler J, Bhatia T, Zhao Z, Lipowsky R, Dimova R (2020)“Super-elasticity of plasma-and synthetic membranes by coupling of membraneasymmetry and liquid-liquid phase separation,”

  • Stephens DJ, Pepperkok R (2001) Illuminating the secretory pathway: when do we need vesicles? J Cell Sci 114(6):1053–1059

    Article  CAS  PubMed  Google Scholar 

  • Svitkina TM, Bulanova EA, Chaga OY, Vignjevic DM, Kojima SI, Vasiliev JM, Borisy GG (2003) Mechanism of filopodia initiation by reorganization of a dendritic network. J Cell Biol 160(3):409–421

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  • Takei K, Haucke V, Slepnev V, Farsad K, Salazar M, Chen H, De Camilli P (1998) Generation of coated intermediates of clathrin-mediated endocytosis on protein-free liposomes. Cell 94(1):131–141

    Article  CAS  PubMed  Google Scholar 

  • Takei K, McPherson PS, Schmid SL, De Camilli P (1995) Tubular membrane invaginations coated by dynamin rings are induced by gtp-\(\gamma\)s in nerve terminals. Nature 374(6518):186–190

    Article  CAS  PubMed  Google Scholar 

  • Takei K, Slepnev VI, Haucke V, De Camilli P (1999) Functional partnership between amphiphysin and dynamin in clathrin-mediated endocytosis. Nat Cell Biol 1(1):33–39

    Article  CAS  PubMed  Google Scholar 

  • Taylor KL, Taylor RJ, Richters KE, Huynh B, Carrington J, McDermott ME, Wilson RL, Dent EW (2019) Opposing functions of f-bar proteins in neuronal membrane protrusion, tubule formation, and neurite outgrowth. Life Sci Alliance 2(3)

  • Theriot JA, Mitchison TJ (1991) Actin microfilament dynamics in locomoting cells. Nature 352(6331):126–131

    Article  CAS  PubMed  Google Scholar 

  • Tian A, Baumgart T (2009) Sorting of lipids and proteins in membrane curvature gradients. Biophys J 96(7):2676–2688

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  • Tojima T, Hines JH, Henley JR, Kamiguchi H (2011) Second messengers and membrane trafficking direct and organize growth cone steering. Nat Rev Nerosci 12(4):191–203

    Article  CAS  Google Scholar 

  • Tozzi C, Walani N, Arroyo M (2019) Out-of-equilibrium mechanochemistry and self-organization of fluid membranes interacting with curved proteins. New J Phys 21:093004

    Article  CAS  Google Scholar 

  • Ursell TS, Klug WS, Phillips R (2009) Morphology and interaction between lipid domains. Proc Natl Acad Sci USA 106(32):13301–13306

    Article  CAS  PubMed  Google Scholar 

  • Vasan R, Rudraraju S, Akamatsu M, Garikipati K, Rangamani P (2020) A mechanical model reveals that non-axisymmetric buckling lowers the energy barrier associated with membrane neck constriction. Soft Matter 16:784–797

    Article  CAS  PubMed  Google Scholar 

  • Vasioukhin V, Bauer C, Yin M, Fuchs E (2000) Directed actin polymerization is the driving force for epithelial cell-cell adhesion. Cell 100(2):209–219

    Article  CAS  PubMed  Google Scholar 

  • Veksler A, Gov NS (2007) Phase transitions of the coupled membrane-cytoskeleton modify cellular shape. Biophys J 93(11):3798–3810

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  • Visscher K, Schnitzer MJ, Block SM (1999) Single kinesin molecules studied with a molecular force clamp. Nature 400(6740):184–189

    Article  CAS  PubMed  Google Scholar 

  • Wacker I, Kaether C, Kromer A, Migala A, Almers W, Gerdes H-H (1997) Microtubule-dependent transport of secretory vesicles visualized in real time with a gfp-tagged secretory protein. J Cell Sci 110(13):1453–1463

    Article  CAS  PubMed  Google Scholar 

  • Walani N, Torres J, Agrawal A (2014) Anisotropic spontaneous curvatures in lipid membranes. Phys Rev E 89(6):062715

    Article  Google Scholar 

  • Walani N, Torres J, Agrawal A (2015) Endocytic proteins drive vesicle growth via instability in high membrane tension environment. Proc Natl Acad Sci USA 112(12):E1423–E1432

    Article  CAS  PubMed  Google Scholar 

  • Warn R, Magrath R (1983) F-actin distribution during the cellularization of the drosophila embryo visualized with fl-phalloidin. Exp Cell Res 143(1):103–114

    Article  CAS  PubMed  Google Scholar 

  • Waugh RE (1982) Surface viscosity measurements from large bilayer vesicle tether formation. ii. experiments. Biophys J 38(1):29

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  • Weber C, Michaels T, Mahadevan L (2019) Spatial control of irreversible protein aggregation. Elife 8:e42315

    Article  PubMed  PubMed Central  Google Scholar 

  • Wu M, Huang B, Graham M, Raimondi A, Heuser JE, Zhuang X, De Camilli P (2010) Coupling between clathrin-dependent endocytic budding and f-bar-dependent tubulation in a cell-free system. Nat Cell Biol 12(9):902–908

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  • Xu G, Shao J-Y (2008) Human neutrophil surface protrusion under a point load: location independence and viscoelasticity. Am J Physiol Cell Physiol 295(5):C1434–C1444

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  • Yamagishi A, Masuda M, Ohki T, Onishi H, Mochizuki N (2004) A novel actin bundling/filopodium-forming domain conserved in insulin receptor tyrosine kinase substrate p53 and missing in metastasis protein. J Biol Chem 279(15):14929–14936

    Article  CAS  PubMed  Google Scholar 

  • Yuan F, Alimohamadi H, Bakka B, Trementozzi AN, Fawzi NL,Rangamani P, Stachowiak JC (2020) “Membrane bending by protein phaseseparation,”

  • Yuan F, Alimohamadi H, Bakka B, Trementozzi AN, Fawzi NL,Rangamani P, Stachowiak JC (2020) “Membrane bending by protein phaseseparation,” bioRxiv

  • Zhang T, Hong W (2001) Ykt6 forms a snare complex with syntaxin 5, gs28, and bet1 and participates in a late stage in endoplasmic reticulum-golgi transport. J Biol Chem 276(29):27480–27487

    Article  CAS  PubMed  Google Scholar 

  • Zhang F, Yim Y-I, Scarselletta S, Norton M, Eisenberg E, Greene LE (2007) Clathrin adaptor gga1 polymerizes clathrin into tubules. J Biol Chem 282(18):13282–13289

    Article  CAS  PubMed  Google Scholar 

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Acknowledgements

The authors would like to thank their many collaborators in the field of membrane mechanics for discussing ideas and the organizers of the International Symposium on Cell Surface Macromolecules 2020 for engaging discussions. They would also like to acknowledge Haleh Alimohamadi, Prof. Ali Behzadan, Miriam Bell, and Jennifer Fromm for providing their critical comments and feedback for the manuscript. This work was supported by NIH R01GM132106 to P.R.

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Mahapatra, A., Uysalel, C. & Rangamani, P. The Mechanics and Thermodynamics of Tubule Formation in Biological Membranes. J Membrane Biol 254, 273–291 (2021). https://doi.org/10.1007/s00232-020-00164-9

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