Chirality and Equilibrium Biopolymer Bundles

Abstract

We use continuum theory to show that chirality is a key thermodynamic control parameter for the aggregation of biopolymers: chirality produces a stable disperse phase of hexagonal bundles under moderately poor solvent conditions, as has been observed in in-vitro studies of F-actin [O. Pelletier et al., Phys. Rev. Lett. 91, 148102 (2003)]. The large characteristic radius of these chiral bundles is not determined by a mysterious long-range molecular interaction but by in-plane shear elastic stresses generated by the interplay between a chiral torque and an unusual, but universal, non-linear gauge term in the strain tensor of ordered chains that is imposed by rotational invariance.PACS numbers: 87.16. Ka, 64.75.+g, 61.30.Dk The structural integrity of cells depends on long, semiflexible biopolymers-such as filamentous actin (F-actin), microtubules, and intermediate filaments-that make up the cytoskeleton. The controlled assembly and disassembly of these polymers is central to the division, development, and locomotion of cells [1]. In-vitro studies of their thermodynamic, structural, and elastic properties have contributed importantly to our understanding of the physical mechanisms that underlie the functioning of the cytoskeleton. For example, F-actin filaments adopt characteristic structural motifs inside cells: open, branched networks and filament bundles [2]. Growing networks play an important role during cell spreading while dense bundles are a necessary component of cellular force generation (stress fibers) and cell protrusions (e.g. microvilli and stereocilia). Networks and bundles appear as separate regions in the phase diagram of solutions of actin proteins and linkers under in-vitro conditions, [3,4,5,6] and much is now understood about the function of specialized linker proteins in the structural organization of actin filaments. Interestingly, even nonstructural biopolymers like DNA [7] can exhibit these morphologies in solutions with generic linker units, such as polyvalent ions.The observation of stable biopolymer bundle aggregates poses an interesting puzzle. Equilibrium solutions of (charged) rods of fixed length are predicted to form networks at low linker concentrations [8]. Beyond a critical linker concentration, cylindrical aggregates should form without a limit on their diameter: bundles can grow in size until the supply of free rods is depleted. Explanations for the observed finite size of the bundles have focused on the possibility of long-range interactions [9], on kinetic limitations to the bundle size [10], and on assembly defects of toroidal-shaped biopolymer aggregates [11]. A recent study [12] of fluorescently labeled F-actin mixtures has cast doubt on these explanations: non-toroidal bundles were found to maintain a well-defined, fixed diameter-in the range of 40-100 nmthat was greatly in excess of the electrostatic screening length even when filament exchange between and along different bundles was rapid.It is the aim of this Letter to argue that chirality is a key thermodynamic con...

Aggregation kinetics of stiff polyelectrolytes in the presence of multivalent salt

“…an infinitely large bundle [6], experiments always find finite-sized bundles [2,3]. To explain this, it has been suggested that the theoretically expected phase separation may be hindered by kinetic barriers [7], steric effects [8], or frustration of the local structure with energy penalty [3,9]. The phenomenon of bundle formation has also been studied using computer simulation, which indicated a tendency towards a well defined finite size [10,11].…”

Responsive biomimetic networks from polyisocyanopeptide hydrogels

“…This self-limiting behaviour of bundle formation is thought to be related to the chirality (i.e. the helical pitch) and the intrinsic stiffness of the polymer molecules 18 . As a consequence of a fixed bundle size the average pore size in the gel is directly controlled by the polymer concentration.…”

Non-Euclidean geometry of twisted filament bundle packing

“…Fibers of extracellular proteins like collagen (10) and fibrin (11) are well-known to organize into twisted assemblies, and the helical twist of multifiber cables has been implicated in the assembly thermodynamics of sickle-hemoglobin macrofibers (12). Whereas the helical twist of human-made ropes is built in to optimize mechanical properties-such as bending compliance (13) and tensile strength (14)-the twist of selfassembled ropes of biomacromolecules derives from torques generated by interactions between helical (i.e., chiral) molecules (15,16).…”

“…Fibers of extracellular proteins like collagen (10) and fibrin (11) are well-known to organize into twisted assemblies, and the helical twist of multifiber cables has been implicated in the assembly thermodynamics of sickle-hemoglobin macrofibers (12). Whereas the helical twist of human-made ropes is built in to optimize mechanical properties-such as bending compliance (13) and tensile strength (14)-the twist of selfassembled ropes of biomacromolecules derives from torques generated by interactions between helical (i.e., chiral) molecules (15,16).The complexity of cross-sectional packing in this archetypal material geometry has long been a subject of study, particularly from the viewpoint of the mechanical properties of manufactured textiles (14, 17) and wire ropes (13). The problem is best visualized from the perspective of the planar cross-section of a twisted bundle, as shown in Fig.…”