Elastically driven linker aggregation between two semiflexible polyelectrolytes

Hydrogels based on methylated-alginates as a platform to investigate the effect of material properties on cell activity. The role of material compliance

Alginate-based hydrogels with tunable mechanical properties are developed by chemical methylation of the polysaccharide backbone, which was performed either in homogeneous phase (in solution) or in heterogeneous phase (on hydrogels). Nuclear Magnetic Resonance (NMR) and Size Exclusion Chromatography (SEC-MALS) analyses of methylated alginates allow to identify the presence and location of methyl groups on the polysaccharide, and to investigate the influence of methylation on the stiffness of the polymer chains. The methylated polysaccharides are employed for the manufacturing of calcium-reticulated hydrogels for cell growth in 3D. The rheological characterization shows that the shear modulus of hydrogels is dependent on the amount of cross-linker used. Methylated alginates represent a platform to explore the effect of mechanical properties on cell activity. As an example, the effect of compliance is investigated using hydrogels displaying similar shear modulus. An osteosarcoma cell line (MG-63) was encapsulated in the alginate hydrogels and the effect of material compliance on cell proliferation and localization of YAP/TAZ protein complex is investigated by flow cytometry and immunohistochemistry, respectively. The results point out that an increase of material compliance leads to an increase of the proliferative rate of cells and correlates with the translocation of YAP/TAZ inside the cell nucleus.

Sliding Contact Dynamic Force Spectroscopy Method for Interrogating Slowly Forming Polymer Cross-Links

Dynamic single-molecule force spectroscopy (SMFS), conducted most commonly using AFM, has become a widespread and valuable tool for understanding the kinetics and thermodynamics of fundamental molecular processes such as ligand-receptor interactions and protein unfolding. Where slowly forming bonds are responsible for the primary characteristics of a material, as is the case in cross-links in some polymer gels, care must be taken to ensure that a fully equilibrated bond has first formed before its rupture can be interpreted. Here we introduce a method, sliding contact force spectroscopy (SCFS), that effectively eliminates the kinetics of bond formation from the measurement of bond rupture. In addition, it permits bond rupture measurements in systems where one of the binding partners may be introduced into solution prior to binding without tethering to a surface. Taking as an example of a slowly forming bond, the "eggbox" junction cross-links between oligoguluronic acid chains (oligoGs) in the commercially important polysaccharide alginate, we show that SCFS accurately measures the equilibrated bond strength of the cross-link when one chain is introduced into the sample solution without tethering to a surface. The results validate the SCFS technique for performing single-molecule force spectroscopy experiments and show that it has advantages in cases where the bond to be studied forms slowly and where tethering of one of the binding partners is impractical.

Discontinuous bundling transition in semiflexible polymer networks induced by Casimir interactions

Fluctuation-induced interactions are an important organizing principle in a variety of soft matter systems. We investigate the role of fluctuation-based or thermal Casimir interactions between cross linkers in a semiflexible network. One finds that, by integrating out the polymer degrees of freedom, there is an attractive logarithmic potential between nearest-neighbor cross linkers in a bundle, with a significantly weaker next-nearest-neighbor interaction. Here we show that a one-dimensional gas of these strongly interacting linkers in equilibrium with a source of unbound ones admits a discontinuous phase transition between a sparsely and a densely bound bundle. This discontinuous transition induced by the long-ranged nature of the Casimir interaction allows for a similarly abrupt structural transition in semiflexible filament networks between a low cross linker density isotropic phase and a higher cross link density bundle network. We support these calculations with the results of finite element Brownian dynamics simulations of semiflexible filaments and transient cross linkers.

Many-body effect in ion binding to RNA

Ion-mediated electrostatic interactions play an important role in RNA folding stability. For a RNA in a solution with higher Mg(2+) ion concentration, more counterions in the solution can bind to the RNA, causing a strong many-body coupling between the bound ions. The many-body effect can change the effective potential of mean force between the tightly bound ions. This effect tends to dampen ion binding and lower RNA folding stability. Neglecting the many-body effect leads to a systematic error (over-estimation) of RNA folding stability at high Mg(2+) ion concentrations. Using the tightly bound ion model combined with a conformational ensemble model, we investigate the influence of the many-body effect on the ion-dependent RNA folding stability. Comparisons with the experimental data indicate that including the many-body effect led to much improved predictions for RNA folding stability at high Mg(2+) ion concentrations. The results suggest that the many-body effect can be important for RNA folding in high concentrations of multivalent ions. Further investigation showed that the many-body effect can influence the spatial distribution of the tightly bound ions and the effect is more pronounced for compact RNA structures and structures prone to the formation of local clustering of ions.

Polyamine-induced bundling of F-actin

To better understand the mechanism of actin filament (F-actin) bundling by polyamines, we have measured the onset of bundling as a function of polyamine concentration. Samples were centrifuged at low speeds to separate bundles from unbundled actin, and the relative amounts of actin in the pellet and supernatant were determined via gel electrophoresis, yielding a description of the bundling transition as a function of actin and polyamine concentrations. These experiments were carried out for two different polyamines, spermine (tetravalent) and spermidine (trivalent). We found that the threshold concentration of polyamine needed to bundle actin is independent of both actin concentration and Mg2+ concentration over a wide range in Mg2+ concentration. We also find that spermine in F-actin bundles is essentially invisible in solution-phase proton NMR, suggesting that it is bound so tightly to F-actin that it is immobilized.

Nucleoprotein assemblies at the nanoscale: medical implications

Bionanotechnology is exploiting the rich structural knowledge now available on DNA and DNA-protein interactions to construct nucleoprotein-based devices that have the potential not only to contribute to our understanding of the structure and function of the proteins and nucleic acids involved but also to new approaches to problems in medicine. Assemblies under development currently are poised to contribute to diagnosis and therapy. Here, I discuss recent work in this emerging field.

Magnetization of circular DNA

We investigate the orbital magnetization of DNA molecules in the relaxed circular structure. It is shown that DNA of homogeneous sequence exhibits paramagnetic responses to external magnetic fields and, surprisingly, the magnetism of circular DNA is equivalent to that of linear DNA. This turns out to result from the fact that the electron population is localized largely on one of the strands. More intriguingly, the magnetic susceptibility is observed to depend on the ring topology defined by the linking number. We also consider sequence heterogeneity and find that the magnetization displays characteristic oscillations, the pattern of which depends crucially on the sequence and the base content.

Condensation of DNA-actin polyelectrolyte mixtures driven by ions of different valences

Multivalent ions can induce condensation of like-charged polyelectrolytes into compact states, a process that requires different ion valences for different polyelectrolyte species. In this work we examine the condensation behavior in binary anionic polyelectrolyte mixtures consisting of DNA coils and F-actin rods in the presence of monovalent, divalent, and trivalent ions. As expected, monovalent ions do not condense either component and divalent ions selectively condense F-actin rods out of the polyelectrolyte mixture. For trivalent ions, however, we observe a microphase separation between the two polyelectrolytes into coexisting finite-sized F-actin bundles and DNA toroids. Further, by increasing the DNA volume fraction in the mixture, condensed F-actin bundles can be completely destabilized, leading to only DNA condensation within the mixture. We examine a number of possible causes and propose a model based on polyelectrolyte competition for ions.

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.

Discontinuous unbinding transitions of filament bundles

Bundles of semiflexible polymers such as actin filaments are studied theoretically. The bundle formation is governed by attractive filament interactions mediated by cross-linking sticker molecules. Using a combination of analytical arguments and Monte Carlo simulations, it is shown that the formation of bundles of parallel filaments requires a threshold concentration of linkers which becomes independent of the filament number for large bundles. The unbinding of bundles happens in a single, discontinuous transition. We discuss the behavior of the bundle thickness at and below the transition. In the bound phase, large bundles tend to segregate into sub-bundles due to slow kinetics. Our results are in qualitative agreement with experiments on F-actin in the presence of the cross-linking protein alpha-actinin.

Intermolecular adhesion in conducting polymers

We analyze the interaction of two conducting, charged polymer chains in solution using a minimal model for their electronic degrees of freedom. We show that a crossing of the two chains in which the polymers pass within angstroms of each other leads to a decrease of the electronic energy of the combined system that is significantly larger than the thermal energy and thus promotes interchain aggregation. We consider the competition of this attractive interaction with the screened electrostatic repulsion and thereby propose a phase diagram for such polymers in solution; depending on the charge density and persistence length of the chains, the polymers may be unbound, bound in loose, braidlike structures, or tightly bound in a parallel configuration.

Direct observation of counterion organization in F-actin polyelectrolyte bundles

Attractions between like-charged polyelectrolytes have been observed in a variety of systems (W.M. Gelbart, R.F. Bruinsma, P.A. Pincus, V.A. Parsegian, Phys. Today 53, September issue, 38 (2000)). Recent biological examples include DNA, filamentous viruses, and F-actin. Theoretical investigations on idealized systems indicate that counterion correlations play a central role, but no experiments that specifically probe such correlations have been performed. Using synchrotron X-ray diffraction, we have directly observed the organization of multivalent ions on cytoskeletal filamentous actin (a well-defined biological polyelectrolyte) and found an unanticipated symmetry-breaking collective counterion mechanism for generating attractions. Surprisingly, the counterions do not form a lattice that simply follows actin's helical symmetry; rather, the counterions organize into "frozen" ripples parallel to the actin filaments and form structures reminiscent of charge density waves. Moreover, these 1D counterion charge density waves form a coupled mode with twist deformations of the oppositely charged actin filaments. This counterion organization is not sensitive to thermal fluctuations in temperature range accessible to protein-based polyelectrolyte systems. Moreover, the counterion density waves are "pinned" to the spatial periodicity of charges on the actin filament even if the global filament charge density is varied, indicating the importance of charge periodicity on the polyelectrolyte substrate.

Dielectric control of counterion-induced single-chain folding transition of DNA

In the presence of condensing agents, single chains of giant double-stranded DNA undergo a first-order phase transition between an elongated coil state and a folded compact state. To connect this like-charged attraction phenomenon to counterion condensation, we performed a series of single-chain experiments on aqueous solutions of DNA, where we varied the extent of counterion condensation by varying the relative dielectric constant epsilon(r) from 80 to 170. Single-chain observations of changes in the conformation of giant DNA were performed by transmission electron microscopy and fluorescence microscopy, with tetravalent spermine (SPM(4+)) as a condensing agent. At a fixed dielectric constant, single DNA chains fold into a compact state upon the addition of spermine, whereas at a constant spermine concentration single DNA chains unfold with an increase in epsilon(r). In both cases, the transition is largely discrete at the level of single chains. We found that the critical concentration of spermine necessary to induce the single-chain folding transition increases exponentially as the dielectric constant increases, corresponding to 87-88% of the DNA charge neutralized at the onset of the transition. We also observed that the toroidal morphology of compact DNA partially unfolds when epsilon(r) is increased.

Crawling toward a unified model of cell mobility: spatial and temporal regulation of actin dynamics

Crawling cells of various morphologies displace themselves in their biological environments by a similar overall mechanism of protrusion through actin assembly at the front coordinated with retraction at the rear. Different cell types organize very distinct protruding structures, yet they do so through conserved biochemical mechanisms to regulate actin polymerization dynamics and vary the mechanical properties of these structures. The moving cell must spatially and temporally regulate the biochemical interactions of its protein components to exert control over higher-order dynamic structures created by these proteins and global cellular responses four or more orders of magnitude larger in scale and longer in time than the individual protein-protein interactions that comprise them. To fulfill its biological role, a cell globally responds with high sensitivity to a local perturbation or signal and coordinates its many intracellular actin-based functional structures with the physical environment it experiences to produce directed movement. This review attempts to codify some unifying principles for cell motility that span organizational scales from single protein polymer filaments to whole crawling cells.

Onset of DNA aggregation in presence of monovalent and multivalent counterions

We address theoretically aggregation of DNA segments by multivalent polyamines such as spermine and spermidine. In experiments, the aggregation occurs above a certain threshold concentration of multivalent ions. We demonstrate that the dependence of this threshold on the concentration of DNA has a simple form. When the DNA concentration c(DNA) is smaller than the monovalent salt concentration, the threshold multivalent ion concentration depends linearly on c(DNA), having the form alphac(DNA) + beta. The coefficients alpha and beta are related to the density profile of multivalent counterions around isolated DNA chains, at the onset of their aggregation. This analysis agrees extremely well with recent detailed measurements on DNA aggregation in the presence of spermine. From the fit to the experimental data, the number of condensed multivalent counterions per DNA chain can be deduced. A few other conclusions can then be reached: 1), the number of condensed spermine ions at the onset of aggregation decreases with the addition of monovalent salt; 2), the Poisson-Boltzmann theory overestimates the number of condensed multivalent ions at high monovalent salt concentrations; and 3), our analysis of the data indicates that the DNA charge is not overcompensated by spermine at the onset of aggregation.

Lamellar phase of stacked two-dimensional rafts of actin filaments

We examined liquid crystalline phases of the cytoskeletal polyelectrolyte filamentous (F-)actin in the presence of multivalent counterions. As a function of increasing ion concentration, the F-actin rods in either an isotropic or a nematic phase will transform into a new and unexpected lamellar phase of cross-linked rafts (L(XR) phase), before condensing into a bundled phase of parallel, close-packed rods. This behavior is generic for alkali earth divalent ions Mg2+, Ca2+, Sr2+, and Ba2+, and the structural transitions are achieved without any architecture-specific actin-binding linker proteins.

Polymorphism of cross-linked actin networks in giant vesicles

Actin networks cross-linked by natural linkers alpha-actinin and filamin are generated in giant vesicles by polymerization through ionophore-mediated influx of Mg2+. alpha-actinin induces the formation of randomly linked networks at 25 degrees C which transform at <15 degrees C into spiderweblike gels or ringlike bundles depending on the vesicle size. Muscle filamin forms ringlike structures under all experimental conditions which can supercoil by subsequent Mg2+ addition. The polymorphism is rationalized in terms of recent models of bivalent ion coupled semiflexible polyelectrolytes and by considering the topology of the linkers.