Session V28: Rheology of Biopolymer Solutions

Massively-parallel fluorescence correlation spectroscopy using a spinning disk confocal microscope

We describe an extension of fluorescence correlation spectroscopy (FCS) using a spinning disk confocal microscope. This approach can spatially map diffusion coefficients or flow velocities at up to $\sim $10$^{5}$ independent locations simultaneously. Complex media---e.g., a tumor, cell nucleus, or extracellular matrix---are spatially-heterogeneous, making this spatially-resolved technique an ideal tool to understand hindered diffusion. There have been a number of recent extensions to FCS based on laser scanning microscopy. Spinning disk confocal microscopy, however, can be much faster at high resolution---potentially up to 1000 Hz at full resolution for the fastest available cameras---and without temporal delays between pixels. We show how to correct for a pixel size effect not encountered with standard or scanning FCS, and we introduce a method to correct for photobleaching. Finally, we apply this technique to microspheres diffusing in Type I collagen, which show non-trivial spatially varying diffusion caused by hydrodynamic and steric interactions with the collagen matrix.   

Diffractive Imaging of Single Biomolecules

The resolution of Electron Microscopy (EM) images is limited by instrumentation lens aberration. Moreover, many biomolecules and supramolecular complexes are too soft and too large to be crystallized, and crystalline diffraction provides only aggregate structural properties. Coherent nanobeam electron diffraction in principle allows for diffraction-limited resolution analysis of single biomolecules. Image recovery can be achieved using oversampling and iterative phase retrieval to solve the phase problem. We will discuss the use of coherent electron diffraction and its potential to improve TEM image resolution of biomolecular systems. Preliminary diffraction data obtained from cryogenically prepared biomolecules will be presented.   

Mechanical Properties of Actin Networks near the Polymerization Transition

Here we present studies of the mechanical properties of actin networks close to the polymerization transition. In the presence of divalent ions, the critical concentration (CC) for polymerization of actin decreases by two orders of magnitude. By studying concentrated actin samples (3 mg/mL) with and without added ions, we compare the behavior near and far above the CC for a sample with very similar concentrations of filamentous actin. To study the response to large forces we use holographic laser tweezers to pull microspheres through an actin network. We found that in samples far above the CC the microspheres strongly resist pulling, and have a well-defined relaxation time. Near the CC, the microspheres are easily pulled through the actin networks, and the relaxation is far more variable, which indicates that the actin filaments may be more dynamic and breakable.   

Rheological Investigation of Protein Interactions in Synovial Fluid

Hyaluronic acid and the plasma proteins, albumin and $\gamma $-globulins, are the most abundant macromolecules in synovial fluid, the fluid that lubricates our freely moving (synovial) joints. In previous studies, bovine synovial fluid, a synovial fluid model and albumin in phosphate buffered saline (PBS) were observed to be rheopectic---viscosity increases over time under constant shear. Rheopexy is indicative of structure building in solution. To further investigate the contribution of albumin to the observed rheopexy, rheological experiments were conducted on bovine serum albumin (BSA) in PBS at concentrations comparable to those found in the synovial joints. Our data suggests that the plasma proteins aggregate together under these low shear conditions further entangling the hyaluronic acid chains, which results in an increase in the apparent viscosity of the synovial fluid over time. The nature of the proposed aggregation was probed by varying the salt concentration and pH in order to partially denature the protein and interrupt any hydrogen bonding. Additionally, similar rheological experiments were carried out using methylated albumin in order to observe the role of the disulfide bridges in the protein aggregation.   

Influence of Anti-inflammatory Drugs on the Rheological Properties of Synovial Fluid and Its Components

The polyelectrolyte hyaluronic acid (HA, hyaluronan), its interactions with anti-inflammatory drugs and other biopolymers, and its role in synovial fluid are being studied. We are investigating the rheological properties of sodium hyaluronate (NaHA) solutions and an experimental model of synovial fluid (comprised of NaHA, and the plasma proteins albumin and $\gamma $-globulins). Steady shear measurements on bovine synovial fluid, the synovial fluid model, and plasma protein solutions indicate that the fluids are rheopectic (stress increases with time under steady shear). In addition, the influence of anti-inflammatory agents on these solutions is being explored. Initial results indicate that D-penicillamine and hydroxychloroquine (HCQ) affect the rheology of the synovial fluid model and its components. While HCQ has no effect on the viscosity of NaHA solutions, it inhibits/suppresses the observed rheopexy of the synovial fluid model and plasma protein solutions. In contrast, D-penicillamine has a complex, time dependent effect on the viscosity of NaHA solutions,---reducing the zero shear rate viscosity of a 3 mg/mL NaHA (in phosphate buffered saline) by \textit{ca}. 40{\%} after 44 days. The potential implications of these results will be discussed.   

Micromechanics of the pericellular matrix

In recent years, much attention has been directed towards the properties and activities of the cell surface. In particular, the coupling of the membrane to the underlying protein polymer network called the actin cortex plays an important role in many events. The other side of the cell surface is less studied, although it too has a bound polymer network comprised of gigantic cross-linked polysaccharides (sugars). Called the pericellular matrix (PCM), it is associated with many cells including fibroblasts, chondrocytes, endothelial and smooth muscle cells. Its thickness can vary from 10's of nanometers to 10 microns and it is associated with adhesion dependent events like migration and mitosis. Biologists often hypothesize that its viscoelastic properties are responsible for the modulation of cell adhesion activities. To investigate this proposal, we measure the PCM's viscoelasticity using microrheology and probe the sharpness of its edge and its mesh size. The elastic modulus of the PCM under different condition is determined, and we characterize the long, elastic cables that can be pulled from the PCM. These results are compared with an externally reconstituted model PCM on the cell surface.   

Microrheology of active actin networks

To provide insight into the viscoelastic response of non-equilibrium, entangled semi-flexible polymeric networks, we study the model system of F-actin networks in the presence of active fragments of skeletal myosin. To characterize the microrheological response of this system, polystyrene microspheres of 1$\mu $m in diameter are suspended into the three-dimensional, entangled F-actin network and diffusing wave spectroscopy is used to measure the mean-squared displacement of the particles on timescales from 100ns to 10ms. Particle motion is a result of both random thermal forces and the dissipation of actin filament fluctuations caused by the interactions of the suspended motor proteins with the network. Upon addition of myosin, we observe an increase in the MSD of the tracer particles and a shift in the scaling--dependence with respect to lag time from $t^{3/4 }$to $t^{x}$, where 3/4 $<$ x $<$ 1. This shift indicates that the random, parallel ``tugs'' on the filaments by the motor proteins cause the filaments to develop an apparent decreased persistence length at length scales longer than the crossover length. Finally, we demonstrate that the addition of the cross-linking protein, $\alpha $-actinin, suppresses this ``active'' scaling behavior, while maintaining elevated probe particle diffusivity relative to the control.   

Filamin cross-linkers as rheology regulators in biopolymer networks

We report on the nonlinear mechanical properties of a statistically homogeneous, isotropic semiflexible network cross-linked by polymers containing numerous small unfolding domains. This model captures the main mechanical features of F-actin networks cross-linked by filamin proteins, which contain twenty-four such Ig-domains that may unfold under applied strain. We show that under sufficiently high strain the network spontaneously organizes itself so that an appreciable fraction of the filamin cross-linkers are at the threshold of domain unfolding. We discuss via a simple model the cause of this network organization. We also discuss how observation of this critical state validates a mechanism proposed by Crocker {\em et al.} to explain the weak power law dependence of the measured strain modulus as observed in intracellular microrheology experiments.   

Microrheology of Microtubules ``Networks''

Microtubules are the largest of the three protein biopolymers comprising the cytoskeleton, the other two being intermediate filaments and filamentous actin. While the mechanical properties of actin networks have been studied extensively, less is known about the mechanical properties of microtubules at high concentrations in the cytosol. Microtubules are involved in many of the cell functions, such as cell division and cargo transport within the cell. We use passive microrheology, extracting a viscoelastic modulus of the network based on the thermal motion of micron sized beads, to measure the elasticity of microtubules under various conditions in vitro. Our results show that the bead motion varies from highly confined to free, indicating the heterogeneous, structure of the network. We study the mechanical properties and the spatial heterogeneity and structure of these microtubule ``networks'' as a function of tubulin monomer concentration, ratio of microtubule associated protein to tubulin monomer concentration, and DMSO or nucleating factor concentration.   

Anisotropic dynamic response of stiff biopolymers

We have analyzed the dynamic response of stiff polymers under different force protocols, such as the sudden onset/release of a longitudinal or transverse point forces. In these non-equilibrium situations, an ordinary small gradient expansion fails to describe the Brownian motion of stiff polymers in the limit of short times due to the neglect of tension dynamics. We present an improved (multiple scale) perturbation theory unravelling the underlying nonlinear phenomenon that renders the short time dynamics quite complex. The polymer’s response exhibits asymptotic power law behaviour with distinct dynamic exponents that depend on the experimental scenario and the time regime.   

Biopolymers in Aqueous Medium: Solvent Forces Explored through Atomistic Dynamics Simulations and Continuum Modeling of Solvent Effects

Molecular interactions in solution are modulated by the bulk liquid and by the solvent-induced forces (SIF) originating in the structure of the liquid surrounding the solutes. Because of the difficulty in representing these effects, purely empirical solvation models are commonly used in simulations. Here, a semi-empirical continuum model is presented based on the theory of polar/polarizable liquids, which allows for a derivation of the electrostatic component of the potential. The effects of SIF are still introduced empirically to reproduce interaction energies in amino acids dimers (AAD). The limitations of the model are discussed based on its performance to reproduce structural, dynamic, and thermodynamic properties of peptides and proteins. To reduce the level of empiricism, the molecular origins of the SIF are investigated through dynamics simulations in explicit solvent. The solvent forces on AAD in pure water and NaCl solutions are studied. The reorganization of water and ions due to dimer dissociation is analyzed based on spatial density profiles. The solvent forms a network of high-density peaks consistent with extensive H-bonded water clusters. Long-range structural order develops in the space separating the monomers and contributes to the intermolecular SIF. The ions disrupt this network leading to either a stabilization or destabilization of the dimers. The relevance of these results to quantify SIF in complex solutes en route to a parameter-free continuum model is discussed.   

Random energy model for heteropolymer sequence design: the role of solvation

We study the role of surface of the globule and the role of interactions with the solvent for the process of sequence design for heteropolymers. We follow the method developed in recent work (P.Geissler et al, Phys. Rev. E, \textbf{70}, 021802, 2004) in which solvation of random sequence heteropolymer was addressed using properly generalized random energy model (REM). By comparing the freezing transition in random and designed sequence heteropolymers, we discuss the effects of design. We discuss phase diagram of the system in the traditional variables of actual temperature versus design temperature. Based on our results we are able to show under which conditions solvation effects improve the quality of sequence design. Finally we discuss sequence space entropy and study how many sequences are available for design at a certain design condition.   

Recovery and Stiffening -Transition of Hydrogels Formed Via Peptide Self-Assembly

In this work we present the local nano- and overall network structure, and resultant viscoelastic properties, of hydrogels that are formed via $\beta $-hairpin peptide self-assembly that is triggered either by increasing the solution pH, temperature or ionic strength. These physiological stimuli induce the random-coil to $\beta $ -sheet intramolecular folding event that, in turn, causes intermoleculer self-assembly. The peptide molecules are locally amphiphilic with two linear strands flanking a central tetrapeptide turn sequence. SANS and TEM studies reveal that the peptide molecules self-assemble into semiflexible, fibrillar structures with monodisperse width that is dictated by the strand length of the molecule. Rheological measurements demonstrate that the hydrogels behave as soft-solid materials with tunable rigidity. Hydrogels recover their initial viscoelastic properties after cessation of high magnitude of strain due to the physically crosslinked network structure and strong inter-fibrillar interactions. These interactions can be turned off by either condensing anions or covalently attaching PEG chains on the lysine-decorated fibrillar surfaces. In addition, stiffening transitions are observed when the hydrogels are cooled due to the hydrogen bonding capability of boric acid/borate ion with lysine residues.   

Nanoscale structure and dynamics of colloid-semiflexible polymer solutions

Interactions and structure in colloid-polymer solutions control the phase behavior, viscoelasticity, stability, and vitrification, which play significant roles in many industrial applications. Filled semiflexible networks demonstrate distinctive rheological properties due to their large persistence length. They are important in many biological and surfactant systems, and display additional complexity because of the alignment and isotropic-nematic transition. In this work, we report diffusing wave spectroscopy studies of the dynamics of colloidal particles suspended in F-actin solutions in time scales 10$^{-6}<$t$<$10$^{-2}$s, and in the concentration of 14.7$\mu $M. Monodisperse polystyrene spheres are coated using bovin serum albumin to reduce filament adsorption. By adjusting the actin filament length with the capping protein gelsolin, we observe the entanglement transition from dilute to semi-dilute regimes. Our data shows quantitative agreement with the theory of semiflexible polymer solutions in the dilute limit$^{[1]}$. However, we find discrepancies in the entangled limit which may indicate the difference between local and bulk properties. Using a shell model for the local viscoelastic response$^{[2]}$, we find that the response is consistent with a depletion-like structure surrounding the embedded colloidal particles$^{[3]}$. [1]Shankar et al., \textit{J. Rheol}. 46, 1111 (2002) [2]A. Levine and T. Lubensky, \textit{Phys. Rev. E} 63, 041510 (2001) [3]Y. L. Chen and K. S. Schweizer, \textit{J. Phys. Chem. B} 108, 6687 (2004)   

Relaxation Behavior of Acrylic Triblock Copolymer Gels

When dissolved in alcohol, poly(methyl methacrylate)-poly(n-butyl actylate)-poly(methyl methacrylate) triblock copolymers form physical gels by the aggregation of the PMMA blocks into sperhical domains. Shear rheometry was used to study the relaxation behavior of gels formed in 2-ethylhexanol with different block lengths and polymer concentrations. Master curves were used to determine relaxation times at different temperatures. The relaxation time given by zero shear viscosity divided by the plateau modulus were in good agreement with the low frequency limit for a system with a single relaxation time. By increasing the PMMA block length from 9k to 25k or increasing polymer concentration from 5 to 30 vol. percent, the relaxation time increases by five orders of magnitude at a given temperature. The effect of block length and concentration on the aggregation number of the PMMA domains was determined by small angle X-ray scattering. Relaxation behavior is of practical importance because these gels are used for thermoreversible gelcasting of ceramics.