Abstract
A simple semi-empirical theory is developed for the ionic strength dependence of the flexible polymer-induced condensation of semiflexible polyelectrolytes such as DNA and F-actin filaments. Critical concentrations of flexible polymer needed for condensation are calculated by comparing the free energies of inserting the semiflexible polyelectrolytes in a solution of flexible polymers, respectively, in their free state, and in their condensed state. Predictions of the theory are compared to experimental data on the condensation of DNA and F-actin filaments induced by the flexible polymer poly(ethylene oxide). The theory also predicts that reentrant decollapse is possible at low ionic strength and high concentrations of flexible polymer, as observed for DNA.
Full Text
The Full Text of this article is available as a PDF (86.0 KB).
Selected References
These references are in PubMed. This may not be the complete list of references from this article.
- Adams M., Fraden S. Phase behavior of mixtures of rods (tobacco mosaic virus) and spheres (polyethylene oxide, bovine serum albumin). Biophys J. 1998 Jan;74(1):669–677. doi: 10.1016/S0006-3495(98)77826-9. [DOI] [PMC free article] [PubMed] [Google Scholar]
- Bloomfield V. A. DNA condensation. Curr Opin Struct Biol. 1996 Jun;6(3):334–341. doi: 10.1016/s0959-440x(96)80052-2. [DOI] [PubMed] [Google Scholar]
- Cuneo P., Magri E., Verzola A., Grazi E. 'Macromolecular crowding' is a primary factor in the organization of the cytoskeleton. Biochem J. 1992 Jan 15;281(Pt 2):507–512. doi: 10.1042/bj2810507. [DOI] [PMC free article] [PubMed] [Google Scholar]
- Eisenriegler E, Hanke A, Dietrich S. Polymers interacting with spherical and rodlike particles. Phys Rev E Stat Phys Plasmas Fluids Relat Interdiscip Topics. 1996 Aug;54(2):1134–1152. doi: 10.1103/physreve.54.1134. [DOI] [PubMed] [Google Scholar]
- Evdokimov Y. M., Pyatigorskaya T. L., Polyvtsev O. F., Akimenko N. M., Kadykov V. A., Tsvankin D. Y., Varshavsky Y. M. A comparative X-ray diffraction and circular dichroism study of DNA compact particles formed in water-salt solutions, containing poly(ethylene glycol). Nucleic Acids Res. 1976 Sep;3(9):2353–2366. doi: 10.1093/nar/3.9.2353. [DOI] [PMC free article] [PubMed] [Google Scholar]
- Goverman J., Schick L. A., Newman J. The bundling of actin with polyethylene glycol 8000 in the presence and absence of gelsolin. Biophys J. 1996 Sep;71(3):1485–1492. doi: 10.1016/S0006-3495(96)79349-9. [DOI] [PMC free article] [PubMed] [Google Scholar]
- Grosberg AYu, Zhestkov A. V. On the compact form of linear duplex DNA: globular states of the uniform elastic (persistent) macromolecule. J Biomol Struct Dyn. 1986 Apr;3(5):859–872. doi: 10.1080/07391102.1986.10508469. [DOI] [PubMed] [Google Scholar]
- Hagerman P. J. Flexibility of DNA. Annu Rev Biophys Biophys Chem. 1988;17:265–286. doi: 10.1146/annurev.bb.17.060188.001405. [DOI] [PubMed] [Google Scholar]
- Hanke A., Eisenriegler E., Dietrich S. Polymer depletion effects near mesoscopic particles. Phys Rev E Stat Phys Plasmas Fluids Relat Interdiscip Topics. 1999 Jun;59(6):6853–6878. doi: 10.1103/physreve.59.6853. [DOI] [PubMed] [Google Scholar]
- Kulp D. T., Herzfeld J. Crowding-induced organization of cytoskeletal elements. III. Spontaneous bundling and sorting of self-assembled filaments with different flexibilities. Biophys Chem. 1995 Dec;57(1):93–102. doi: 10.1016/0301-4622(95)00050-8. [DOI] [PubMed] [Google Scholar]
- Käs J., Strey H., Tang J. X., Finger D., Ezzell R., Sackmann E., Janmey P. A. F-actin, a model polymer for semiflexible chains in dilute, semidilute, and liquid crystalline solutions. Biophys J. 1996 Feb;70(2):609–625. doi: 10.1016/S0006-3495(96)79630-3. [DOI] [PMC free article] [PubMed] [Google Scholar]
- Laemmli U. K. Characterization of DNA condensates induced by poly(ethylene oxide) and polylysine. Proc Natl Acad Sci U S A. 1975 Nov;72(11):4288–4292. doi: 10.1073/pnas.72.11.4288. [DOI] [PMC free article] [PubMed] [Google Scholar]
- Lerman L. S. A transition to a compact form of DNA in polymer solutions. Proc Natl Acad Sci U S A. 1971 Aug;68(8):1886–1890. doi: 10.1073/pnas.68.8.1886. [DOI] [PMC free article] [PubMed] [Google Scholar]
- Madden T. L., Herzfeld J. Crowding-induced organization of cytoskeletal elements: I. Spontaneous demixing of cytosolic proteins and model filaments to form filament bundles. Biophys J. 1993 Sep;65(3):1147–1154. doi: 10.1016/S0006-3495(93)81144-5. [DOI] [PMC free article] [PubMed] [Google Scholar]
- Madden T. L., Herzfeld J. Crowding-induced organization of cytoskeletal elements: II. Dissolution of spontaneously formed filament bundles by capping proteins. J Cell Biol. 1994 Jul;126(1):169–174. doi: 10.1083/jcb.126.1.169. [DOI] [PMC free article] [PubMed] [Google Scholar]
- Maniatis T., Venable J. H., Jr, Lerman L. S. The structure of psi DNA. J Mol Biol. 1974 Mar 25;84(1):37–64. doi: 10.1016/0022-2836(74)90211-3. [DOI] [PubMed] [Google Scholar]
- Odijk T. Osmotic compaction of supercoiled DNA into a bacterial nucleoid. Biophys Chem. 1998 Jul 13;73(1-2):23–29. doi: 10.1016/s0301-4622(98)00115-x. [DOI] [PubMed] [Google Scholar]
- Parsegian V. A., Rand R. P., Fuller N. L., Rau D. C. Osmotic stress for the direct measurement of intermolecular forces. Methods Enzymol. 1986;127:400–416. doi: 10.1016/0076-6879(86)27032-9. [DOI] [PubMed] [Google Scholar]
- Podgornik R., Rau D. C., Parsegian V. A. Parametrization of direct and soft steric-undulatory forces between DNA double helical polyelectrolytes in solutions of several different anions and cations. Biophys J. 1994 Apr;66(4):962–971. doi: 10.1016/S0006-3495(94)80877-X. [DOI] [PMC free article] [PubMed] [Google Scholar]
- Post C. B., Zimm B. H. Theory of DNA condensation: collapse versus aggregation. Biopolymers. 1982 Nov;21(11):2123–2137. doi: 10.1002/bip.360211104. [DOI] [PubMed] [Google Scholar]
- Rau D. C., Lee B., Parsegian V. A. Measurement of the repulsive force between polyelectrolyte molecules in ionic solution: hydration forces between parallel DNA double helices. Proc Natl Acad Sci U S A. 1984 May;81(9):2621–2625. doi: 10.1073/pnas.81.9.2621. [DOI] [PMC free article] [PubMed] [Google Scholar]
- Suzuki A., Ito T. Polymorphism of F-actin assembly. 2. Effects of barbed end capping on F-actin assembly. Biochemistry. 1996 Apr 23;35(16):5245–5249. doi: 10.1021/bi9526948. [DOI] [PubMed] [Google Scholar]
- Suzuki A., Yamazaki M., Ito T. Osmoelastic coupling in biological structures: formation of parallel bundles of actin filaments in a crystalline-like structure caused by osmotic stress. Biochemistry. 1989 Jul 25;28(15):6513–6518. doi: 10.1021/bi00441a052. [DOI] [PubMed] [Google Scholar]
- Suzuki A., Yamazaki M., Ito T. Polymorphism of F-actin assembly. 1. A quantitative phase diagram of F-actin. Biochemistry. 1996 Apr 23;35(16):5238–5244. doi: 10.1021/bi952693f. [DOI] [PubMed] [Google Scholar]
- Tang J. X., Ito T., Tao T., Traub P., Janmey P. A. Opposite effects of electrostatics and steric exclusion on bundle formation by F-actin and other filamentous polyelectrolytes. Biochemistry. 1997 Oct 14;36(41):12600–12607. doi: 10.1021/bi9711386. [DOI] [PubMed] [Google Scholar]
- Tang J. X., Janmey P. A. The polyelectrolyte nature of F-actin and the mechanism of actin bundle formation. J Biol Chem. 1996 Apr 12;271(15):8556–8563. doi: 10.1074/jbc.271.15.8556. [DOI] [PubMed] [Google Scholar]
- Tang J. X., Janmey P. A. Two distinct mechanisms of actin bundle formation. Biol Bull. 1998 Jun;194(3):406–408. doi: 10.2307/1543126. [DOI] [PubMed] [Google Scholar]
- Ubbink J., Odijk T. Electrostatic-undulatory theory of plectonemically supercoiled DNA. Biophys J. 1999 May;76(5):2502–2519. doi: 10.1016/S0006-3495(99)77405-9. [DOI] [PMC free article] [PubMed] [Google Scholar]
- Ubbink J., Odijk T. Polymer- and salt-induced toroids of hexagonal DNA. Biophys J. 1995 Jan;68(1):54–61. doi: 10.1016/S0006-3495(95)80158-X. [DOI] [PMC free article] [PubMed] [Google Scholar]