Structural reorganization of parallel actin bundles by crosslinking proteins: incommensurate states of twist.

We construct a coarse-grained model of parallel actin bundles crosslinked by compact globular bundling proteins, such as fascin and espin, necessary components of filopodial and mechanosensory bundles. Consistent with structural observations of bundles, we find that the optimal geometry for crosslinking is overtwisted, requiring a coherent structural change of the helical geometry of the filaments. We study the linker-dependent thermodynamic transition of bundled actin filaments from their native state to the overtwisted state and map out the "twist-state" phase diagram in terms of the availability as well as the flexibility of crosslinker proteins. We predict that the transition from the uncrosslinked to fully crosslinked state is highly sensitive to linker flexibility: flexible crosslinking smoothly distorts the twist state of bundled filaments, while rigidly crosslinked bundles undergo a phase transition, rapidly overtwisting filaments over a narrow range of free crosslinker concentrations. Additionally, we predict a rich spectrum of intermediate structures, composed of alternating domains of sparsely bound (untwisted) and strongly bound (overtwisted) filaments. This model reveals that subtle differences in crosslinking agents themselves modify not only the detailed structure of parallel actin bundles, but also the thermodynamic pathway by which they form.

[1]  Thomas E. Schaus,et al.  Intrinsic dynamic behavior of fascin in filopodia. , 2007, Molecular biology of the cell.

[2]  P. Matsudaira,et al.  Bending stiffness of a crystalline actin bundle. , 2004, Journal of molecular biology.

[3]  J. Howard,et al.  Mechanics of Motor Proteins and the Cytoskeleton , 2001 .

[4]  T D Pollard,et al.  Actin and actin-binding proteins. A critical evaluation of mechanisms and functions. , 1986, Annual review of biochemistry.

[5]  M. Hagan,et al.  Self-limited self-assembly of chiral filaments. , 2010, Physical review letters.

[6]  Céline Revenu,et al.  The co-workers of actin filaments: from cell structures to signals , 2004, Nature Reviews Molecular Cell Biology.

[7]  J. Saunders,et al.  Actin filaments, stereocilia, and hair cells of the bird cochlea. I. Length, number, width, and distribution of stereocilia of each hair cell are related to the position of the hair cell on the cochlea , 1983, The Journal of cell biology.

[8]  Gerard C L Wong,et al.  Cooperativity and frustration in protein-mediated parallel actin bundles. , 2009, Physical review letters.

[9]  J. Bartles.  Parallel actin bundles and their multiple actin-bundling proteins. , 2000, Current opinion in cell biology.

[10]  A. Kornyshev,et al.  Structure and interactions of biological helices , 2007 .

[11]  S. Neukirch,et al.  Chirality of coiled coils: elasticity matters. , 2008, Physical review letters.

[12]  M J Mulroy,et al.  The organization of actin filaments in the stereocilia of cochlear hair cells , 1980, The Journal of cell biology.

[13]  W. Kabsch,et al.  Atomic model of the actin filament , 1990, Nature.

[14]  Gary G. Borisy,et al.  Role of fascin in filopodial protrusion , 2006, The Journal of cell biology.

[15]  Mark Bathe,et al.  Structure, evolutionary conservation, and conformational dynamics of Homo sapiens fascin-1, an F-actin crosslinking protein. , 2010, Journal of molecular biology.

[16]  G. Wong,et al.  Structural polymorphism of the actin-espin system: a prototypical system of filaments and linkers in stereocilia. , 2007, Physical review letters.

[17]  R. Bruinsma,et al.  Phase diagram of chiral biopolymer Wigner crystals. , 2007, Physical review. E, Statistical, nonlinear, and soft matter physics.

[18]  W. Wriggers,et al.  Direct observation of counterion organization in F-actin polyelectrolyte bundles , 2005, The European physical journal. E, Soft matter.

[19]  N. Gov,et al.  Thickness distribution of actin bundles in vitro , 2008, European Biophysics Journal.

[20]  A. Kornyshev,et al.  Phase behavior of columnar DNA assemblies. , 2001, Physical review letters.

[21]  Anli Li,et al.  Small Espin: A Third Actin-bundling Protein and Potential Forked Protein Ortholog in Brush Border Microvilli , 1998, The Journal of cell biology.

[22]  M S Turner,et al.  Twisted protein aggregates and disease: the stability of sickle hemoglobin fibers. , 2003, Physical review letters.

[23]  D. DeRosier,et al.  How actin filaments pack into bundles. , 1982, Cold Spring Harbor symposia on quantitative biology.

[24]  Gregory M Grason,et al.  Braided bundles and compact coils: the structure and thermodynamics of hexagonally packed chiral filament assemblies. , 2008, Physical review. E, Statistical, nonlinear, and soft matter physics.

[25]  Per Bak,et al.  Commensurate phases, incommensurate phases and the devil's staircase , 1982 .

[26]  T. Yanagida,et al.  Torsional rigidity of single actin filaments and actin-actin bond breaking force under torsion measured directly by in vitro micromanipulation. , 1996, Proceedings of the National Academy of Sciences of the United States of America.

[27]  J. Howard.  Molecular Mechanics of Cells and Tissues , 2008 .

[28]  J. Bryan,et al.  Separation and interaction of the major components of sea urchin actin gel. , 1978, Journal of molecular biology.

[29]  Erwin Frey,et al.  Actin-binding proteins sensitively mediate F-actin bundle stiffness. , 2006, Nature materials.

[30]  Willy Wriggers,et al.  Like-charge attraction between polyelectrolytes induced by counterion charge density waves , 2003, Proceedings of the National Academy of Sciences of the United States of America.

[31]  Gregory M Grason,et al.  Chirality and equilibrium biopolymer bundles. , 2007, Physical review letters.

[32]  A. Bausch,et al.  Helical twist controls the thickness of F-actin bundles , 2008, Proceedings of the National Academy of Sciences.

[33]  D. DeRosier,et al.  Structure of F-actin needles from extracts of sea urchin oocytes. , 1981, Journal of molecular biology.

[34]  E. Mugnaini,et al.  The Deaf Jerker Mouse Has a Mutation in the Gene Encoding the Espin Actin-Bundling Proteins of Hair Cell Stereocilia and Lacks Espins , 2000, Cell.

[35]  Roger D Kamm,et al.  Measuring molecular rupture forces between single actin filaments and actin-binding proteins , 2008, Proceedings of the National Academy of Sciences.

[36]  Erwin Frey,et al.  Statistical mechanics of semiflexible bundles of wormlike polymer chains. , 2007, Physical review letters.

[37]  Structural Transitions and Soft Modes in Frustrated DNA Crystals , 2008, 0805.2868.

[38]  E. Mugnaini,et al.  Espin cross-links cause the elongation of microvillus-type parallel actin bundles in vivo , 2003, The Journal of cell biology.

[39]  K. Rottner,et al.  The making of filopodia. , 2006, Current opinion in cell biology.

[40]  Frustrated polyelectrolyte bundles and T= 0 Josephson-junction arrays. , 2006, Physical review letters.

[41]  J. Weisel,et al.  Twisting of fibrin fibers limits their radial growth. , 1987, Proceedings of the National Academy of Sciences of the United States of America.