The Role of Subunit Entropy in Cooperative Assembly. Nucleation of Microtubules and Other Two-dimensional Polymers

Overview

Journal Biophys J

Publisher Cell Press

Specialty Biophysics

Date 1981 May 1

PMID 7236853

Citations 42

Authors

H P Erickson

D Pantaloni

Affiliations

Soon will be listed here.

Abstract

The self-assembly and nucleation of two-dimensional polymers is described by a theory based on a model of rigid subunits and bonds and simple principles of thermodynamics. The key point in the theory is to separate as an explicit parameter the free energy, primarily attributed to the entropy of the free subunit, that is required to immobilize a subunit in the polymer. Quantitative relations for the association of a subunit forming a longitudinal bond, a lateral bone, or both together are obtained, which demonstrate the basis and magnitude of cooperativity. The same formalism leads to a quantitative estimate for th concentration of the small polymers that are important intermediates in nucleation. It is shown that, if the concentration of free subunits is below a certain "critical supersaturation," the concentration of some essential intermediates is too low to support any significant assembly and nucleation is blocked. If the subunit concentration is above the critical supersaturation, all of the small intermediates are sufficiently stable to form and grow spontaneously. The theory predicts a critical supersaturation of 3.5 to 7 (the ratio of subunit concentration to the equilibrium solubility) for parameters appropriate to assembly of the microtubule wall. Experimentally, nucleation and assembly of microtubules is obtained at somewhat lower concentrations, 1.5 to 3 times the equilibrium solubility. Special mechanisms that could stabilize small polymers and facilitate nucleation of microtubule assembly are suggested.

Citing Articles

Regulation of cytoskeleton dynamics and its interplay with force in plant cells.

Sun Z, Wang X, Peng C, Dai L, Wang T, Zhang Y Biophys Rev (Melville). 2024; 5(4):041307.

PMID: 39606182 PMC: 11596143. DOI: 10.1063/5.0201899.

Diverse cytomotive actins and tubulins share a polymerization switch mechanism conferring robust dynamics.

Wagstaff J, Planelles-Herrero V, Sharov G, Alnami A, Kozielski F, Derivery E Sci Adv. 2023; 9(13):eadf3021.

PMID: 36989372 PMC: 10058229. DOI: 10.1126/sciadv.adf3021.

CAMSAP2 organizes a γ-tubulin-independent microtubule nucleation centre through phase separation.

Imasaki T, Kikkawa S, Niwa S, Saijo-Hamano Y, Shigematsu H, Aoyama K Elife. 2022; 11.

PMID: 35762204 PMC: 9239687. DOI: 10.7554/eLife.77365.

Tunable, division-independent control of gene activation timing by a polycomb switch.

Pease N, Nguyen P, Woodworth M, Ng K, Irwin B, Vaughan J Cell Rep. 2021; 34(12):108888.

PMID: 33761349 PMC: 8024876. DOI: 10.1016/j.celrep.2021.108888.

Microtubules form by progressively faster tubulin accretion, not by nucleation-elongation.

Rice L, Moritz M, Agard D J Cell Biol. 2021; 220(5).

PMID: 33734292 PMC: 7980253. DOI: 10.1083/jcb.202012079.

References

Lee J, Timasheff S . The reconstitution of microtubules from purified calf brain tubulin. Biochemistry. 1975; 14(23):5183-7. DOI: 10.1021/bi00694a025. View

Ferrone F, Hofrichter J, Sunshine H, Eaton W . Kinetic studies on photolysis-induced gelation of sickle cell hemoglobin suggest a new mechanism. Biophys J. 1980; 32(1):361-80. PMC: 1327316. DOI: 10.1016/S0006-3495(80)84962-9. View

Chothia C, Janin J . Principles of protein-protein recognition. Nature. 1975; 256(5520):705-8. DOI: 10.1038/256705a0. View

Binder L, DENTLER W, Rosenbaum J . Assembly of chick brain tubulin onto flagellar microtubules from Chlamydomonas and sea urchin sperm. Proc Natl Acad Sci U S A. 1975; 72(3):1122-6. PMC: 432478. DOI: 10.1073/pnas.72.3.1122. View

Erickson H . Microtubule surface lattice and subunit structure and observations on reassembly. J Cell Biol. 1974; 60(1):153-67. PMC: 2109150. DOI: 10.1083/jcb.60.1.153. View

Steinberg I, Scheraga H . Entropy changes accompanying association reactions of proteins. J Biol Chem. 1963; 238:172-81. View

Oosawa F, Kasai M . A theory of linear and helical aggregations of macromolecules. J Mol Biol. 1962; 4:10-21. DOI: 10.1016/s0022-2836(62)80112-0. View

Koren R, Hammes G . A kinetic study of protein-protein interactions. Biochemistry. 1976; 15(5):1165-71. DOI: 10.1021/bi00650a032. View

Bryan J . A quantitative analysis of microtubule elongation. J Cell Biol. 1976; 71(3):749-67. PMC: 2109791. DOI: 10.1083/jcb.71.3.749. View

10.

Herzog W, Weber K . In vitro assembly of pure tubulin into microtubules in the absence of microtubule-associated proteins and glycerol. Proc Natl Acad Sci U S A. 1977; 74(5):1860-4. PMC: 431031. DOI: 10.1073/pnas.74.5.1860. View

11.

Himes R, Burton P, Gaito J . Dimethyl sulfoxide-induced self-assembly of tubulin lacking associated proteins. J Biol Chem. 1977; 252(17):6222-8. View

12.

Johnson K, Borisy G . Kinetic analysis of microtubule self-assembly in vitro. J Mol Biol. 1977; 117(1):1-31. DOI: 10.1016/0022-2836(77)90020-1. View

13.

Carlier M, Pantaloni D . Kinetic analysis of cooperativity in tubulin polymerization in the presence of guanosine di- or triphosphate nucleotides. Biochemistry. 1978; 17(10):1908-15. DOI: 10.1021/bi00603a017. View

14.

Caspar D . Movement and self-control in protein assemblies. Quasi-equivalence revisited. Biophys J. 1980; 32(1):103-38. PMC: 1327271. DOI: 10.1016/S0006-3495(80)84929-0. View

15.

Lesk A, Chothia C . Solvent accessibility, protein surfaces, and protein folding. Biophys J. 1980; 32(1):35-47. PMC: 1327253. DOI: 10.1016/S0006-3495(80)84914-9. View

16.

Wegner A, Engel J . Kinetics of the cooperative association of actin to actin filaments. Biophys Chem. 1975; 3(3):215-25. DOI: 10.1016/0301-4622(75)80013-5. View