Structural polymorphism of the cytoskeleton: a model of linker-assisted filament aggregation

Evolution of growth modes for polyelectrolyte bundles

Multivalent ions induce attractions between polyelectrolytes, but lead to finite-sized bundles rather than macroscopic phase separation. The kinetics of aggregation and bundle formation of actin is tracked using two different fluorescently labeled populations of F-actin. It is found that the growth mode of these bundles evolves with time and salt concentration, varying from an initial lateral growth to a longitudinal one at later stages. The results suggest that kinetics play a role in bundle growth, but not in the lateral size of bundles, which is constant for linear and branched topologies.

Structural polymorphism of the actin-espin system: a prototypical system of filaments and linkers in stereocilia

We examine the interaction between cytoskeletal F-actin and espin 3A, a prototypical actin bundling protein found in sensory cell microvilli, including ear cell stereocilia. Espin induces twist distortions in F-actin as well as facilitates bundle formation. Mutations in one of the two F-actin binding sites of espin, which have been implicated in deafness, can tune espin-actin interactions and radically transform the system's phase behavior. These results are compared to recent theoretical work on the general phase behavior linker-rod systems.

Molecular dynamics simulations of polyelectrolyte-polyampholyte complexes. Effect of solvent quality and salt concentration

Complexation between polyelectrolyte and polyampholyte chains in poor solvent conditions for the polyelectrolyte backbone has been studied by molecular dynamics simulations. In a poor solvent a polyelectrolyte forms a necklace-like structure consisting of polymeric globules (beads) connected by strings of monomers. The simulation results can be explained by assuming the existence of two different mechanisms leading to the necklace formation. In the case of weak electrostatic interactions, the necklace formation is driven by optimization of short-range monomer-monomer attraction and electrostatic repulsion between charged monomers on the polymer backbone. In the case of strong electrostatic interactions, the necklace structure appears as a result of counterion condensation. While the short-range attractions between monomers are still important, the correlation-induced attraction between condensed counterions and charged monomers and electrostatic repulsion between uncompensated charges provide significant contribution to optimization of the necklace structure. Upon forming a complex with both random and diblock polyampholytes, a polyelectrolyte chain changes its necklace conformation by forming one huge bead. The collapse of the polyelectrolyte chain occurs due to the neutralization of the polyelectrolyte charge by polyampholytes. In the case of the random polyampholyte, the more positively charged sections of the chain mix with negatively charged polyelectrolyte forming the globular bead while more negatively charged chain sections form loops surrounding the collapsed core of the aggregate. In the case of diblock polyampholyte, the positively charged block, a part of the negatively charged block, and a polyelectrolyte chain form a core of the aggregate with a substantial section of the negatively charged block sticking out from the collapsed core of the aggregate. In both cases the core of the aggregate has a layered structure that is characterized by the variations in the excess of concentration of monomers belonging to polyampholyte and polyelectrolyte chains throughout the core radius. These structures appear as a result of optimization of the net electrostatic energy of the complex and short-range attractive interactions between monomers of the polyelectrolyte chain.

Role of architecture in the elastic response of semiflexible polymer and fiber networks

We study the elasticity of cross-linked networks of thermally fluctuating stiff polymers. As compared to their purely mechanical counterparts, it is shown that these thermal networks have a qualitatively different elastic response. By accounting for the entropic origin of the single-polymer elasticity, the networks acquire a strong susceptibility to polydispersity and structural randomness that is completely absent in athermal models. In extensive numerical studies we systematically vary the architecture of the networks and identify a wealth of phenomena that clearly show the strong dependence of the emergent macroscopic moduli on the underlying mesoscopic network structure. In particular, we highlight the importance of the polymer length, which to a large extent controls the elastic response of the network, surprisingly, even in parameter regions where it does not enter the macroscopic moduli explicitly. Understanding these subtle effects is only possible by going beyond the conventional approach that considers the response of typical polymer segments only. Instead, we propose to describe the elasticity in terms of a typical polymer filament and the spatial distribution of cross-links along its backbone. We provide theoretical scaling arguments to relate the observed macroscopic elasticity to the physical mechanisms on the microscopic and mesoscopic scales.

Cytoskeletal polymer networks: the molecular structure of cross-linkers determines macroscopic properties

In living cells the mechanical properties of the actin cytoskeleton are defined by the local activation of different actin cross-linking proteins. These proteins consist of actin-binding domains that are separated and geometrically organized by different numbers of rod domains. The detailed molecular structure of the cross-linking molecules determines the structural and mechanical properties of actin networks in vivo. In this study, we systematically investigate the impact of the length of the spacing unit between two actin-binding domains on in vitro actin networks. Such synthetic cross-linkers reveal that the shorter the constructs are, the greater the elastic modulus changes in the linear response regime. Because the same binding domains are used in all constructs, only the differences in the number of rod domains determine their mechanical effectiveness. Structural rearrangements of the networks show that bundling propensity is highest for the shortest construct. The nonlinear mechanical response is affected by the molecular structure of the cross-linker molecules, and the observed critical strains and fracture stress increase proportional to the length of the spacing unit.

Counterions between charged polymers exhibit liquid-like organization and dynamics

Current understanding of electrostatics in water is based on mean-field theories like the Poisson-Boltzmann formalism and its approximations, which are routinely used in colloid science and computational biology. This approach, however, breaks down for highly charged systems, which exhibit counterintuitive phenomena such as overcharging and like-charge attraction. Models of counterion correlations have been proposed as possible explanations, but no experimental comparisons are available. Here, collective dynamics of counterions that mediate like-charge attraction between F-actin filaments have been directly observed in aqueous solution using high-resolution inelastic x-ray scattering down to molecular length-scales. We find a previously undescribed acoustic-like phonon mode associated with correlated counterions. The excitation spectra at high wave-vector Q reveal unexpected dynamics due to ions interacting with their "cages" of nearest neighbors. We examine this behavior in the context of intrinsic charge density variations on F-actin. The measured speed of sound and collective relaxation rates in this liquid agree surprisingly well with simple model calculations.

Spontaneous assembly of viruses on multilayered polymer surfaces

The idea that randomly arranged supermolecular species incorporated in a network medium can ultimately create ordered structures at the surface may be counterintuitive. However, such order can be accommodated by regulating dynamic and equilibrium driving forces. Here, we present the ordering of M13 viruses, highly complex biomacromolecules, driven by competitive electrostatic binding, preferential macromolecular interactions and the rigid-rod nature of the virus systems during alternating electrostatic assembly. The steric constraints inherent to the competitive charge binding between M13 viruses and two oppositely charged weak polyelectrolytes leads to interdiffusion and the virtual 'floating' of viruses to the surface. The result is the spontaneous formation of a two-dimensional monolayer structure of viruses atop a cohesive polyelectrolyte multilayer. We demonstrate that this viral-assembled monolayer can be a biologically tunable scaffold to nucleate, grow and align nanoparticles or nanowires over multiple length scales. This system represents an interface that provides a general platform for the systematic incorporation and assembly of organic, biological and inorganic materials.

Morphological transitions during the formation of templated mesoporous materials: theoretical modeling

We put forward a theoretical model for the morphological transitions of templated mesoporous materials. These materials consist of a mixture of surfactant molecules and inorganic compounds which evolve dynamically upon mixing to form different morphologies depending on the composition and conditions at which mixing occurs. Our theoretical analysis is based on the assumption that adsorption of the inorganic compounds onto mesoscopic assemblies of surfactant molecules changes the effective interactions between the surfactant molecules, consequently lowering the spontaneous curvature of the surfactant layer and inducing morphological changes in the system. On the basis of a mean field phase diagram, we are able to follow the trajectories of the system starting with different initial conditions, and predict the final morphology of the product. In a typical scenario, the reduction in the spontaneous curvature leads first to a smooth transition from compact spherical micelles to elongated worm-like micelles. In the second stage, the layer of inorganic material coating the micelles gives rise to attractive inter-micellar interactions that eventually induce a collapse of the system into a closely packed hexagonal array of coated cylinders. Other pathways may lead to different structures including disordered bicontinuous and ordered cubic phases. The model is in good qualitative agreement with experimental observations.

Micro- and macrorheological properties of actin networks effectively cross-linked by depletion forces

The structure and rheology of cytoskeletal networks are regulated by actin binding proteins. Aside from these specific interactions, depletion forces can also alter the properties of cytoskeletal networks. Here we demonstrate that the addition of poly(ethylene glycol) (PEG) as a depletion agent results not only in severe structural changes, but also in alterations in mechanical properties of actin solutions. In the plateau of the elastic modulus two regimes can be distinguished by micro and macrorheological methods. In the first, the elastic modulus increases only slightly with increasing depletion agent, whereas above a critical concentration c*, a strong increase of cPEG6k3.5 is observed in a distinct second regime. Microrheological data and electron microscopy images show a homogenous network of actin filaments in the first regime, whereas at higher PEG concentrations a network of actin bundles is observed. The concentration dependence of the plateau modulus G0, the shift in entanglement time taue, and the nonlinear response indicate that below c* the network becomes effectively cross-linked, whereas above c* G0(cPEG6k) is primarily determined by the network of bundles that exhibits a linearly increasing bundle thickness.

Morphology of Actin Assemblies in Response to Polycation and Salts

F-actins are semi-flexible polyelectrolytes and can be assembled into a large polymer-actin complex with polymorphism through electrostatic interaction with polycations. This study investigates the structural phase behavior and the growth of polymer-actin complexes in terms of its longitudinal and lateral sizes in various polycation and KCl concentrations for a constant actin concentration. Our results show that the longitudinal growth and lateral growth of polymer-actin complexes, initiated by a common nucleation process, are dominated by different factors in subsequent growth process. This induces the structural polymorphism of polymer-actin complexes. Major factors to influence the polymorphism of polymer-actin complexes in polyelectrolyte systems have been discussed. Our results indicate that the semiflexible polyelectrolyte nature of F-actins is important for controlling the morphology and growth of actin architectures in cells.