Session MK: Biofluids: Cellular II

Rheology of capsule suspension

Rheology of suspension of liquid-filled elastic capsules in linear shear flow is studied by three-dimensional numerical simulations using a front-tracking method. First, we consider dilute suspension capsules of spherical resting shape for which only a steady tank- treading motion is observed. We find a novel result that the capsule suspension exhibits a shear viscosity minimum at moderate values of the viscosity ratio, and high capillary numbers. The shear viscosity minimum exists for capsules with area-dilating membranes, but not for those with nearly-incompressible membranes. Physical mechanisms underlying these results are studied by decomposing the particle stress tensor into a contribution due to the elastic stresses in the capsule membrane, and a contribution due to the viscosity differences between the internal and suspending fluids. It is shown that the elastic contribution is shear-thinning, but the viscous contribution is shear-thickening. We then consider dilute suspension of oblate shape capsules which undergo unsteady motion such as swinging and tumbling. The effect of such unsteady dynamics on time-dependent rheology is addressed. Finally, we consider dense suspension, and observe that the shear viscosity minimum disappears with increasing capsule volume fraction.   

Capsule deformation and orientation in general linear flows

We considered the response of spherical and non-spherical capsules to general flows. (A capsule is an elastic membrane enclosing a fluid, immersed in fluid.) First, we established that nonspherical capsules align with the imposed irrotational linear flow; this means that initial orientation does not affect steady-state capsule deformation, so this steady-state deformation can be determined entirely by the capillary number and the type of flow. The type of flow is characterized by $r$: $r=0$ for axisymmetric flows, and $r=1$ for planar flows; intermediate values of $r$ are combinations of planar and axisymmetric flow. By varying the capillary number and $r$, all irrotational linear Stokes flows can be generated. For the same capillary number, planar flows lead to more deformation than uniaxial or biaxial extensional flows. Deformation varies monotonically with $r$, so one can determine bounds on capsule deformation in general flow by only looking at uniaxial, biaxial, and planar flow. These results are applicable to spheres in all linear flows and to ellipsoids in irrotational linear flow.   

An integrated model of microtubule-based pronuclear motion in the single-celled \emph{C. elegans} embryo

We present an integrated computational model of microtubule-based pronuclear motion in the single-celled \emph{C. elegans} embryo. In this model, centrosomes initiate stochastic microtubule growth and these microtubules interact with motor proteins distributed in the cytoplasm. Consequent pulling forces drag the pronucleus through the cytoplasm, here modeled as an incompressible, Newtonian fluid whose motions are constrained by contact with the cell periphery. The cell periphery also limits microtubule growth. Our computational method is based on an immersed boundary formulation which allows for the simultaneous treatment of fluid flow and the dynamics of structures immersed within. Our simulations show pronuclear migration, and moreover, a geometry-dependent pronuclear centration and rotation very similar to that observed \emph{in vivo}. We study the dynamic interaction of motor proteins embedded in the fluid with microtubule filaments, allowing for relative motion of fluid along MT tracks as has been observed experimentally. We demonstrate numerically that this is sufficient to propel the pronucleus while causing a counterflow of the cytoplasm.   

Monte Carlo Simulations of Absolute Binding Free Energy of Targeted Nanocarriers to Cell Surfaces

We have developed a computational methodology based on Metropolis Monte Carlo and the weighted histogram analysis method (WHAM) to calculate the absolute binding free energy between functionalized nanocarriers (NC) and endothelial cell (EC) surfaces. The calculated binding affinities agree quantitatively with the measurements of specific antibody coated NCs (100 nm in diameter) to intracellular adhesion molecule-1 (ICAM-1) expressing EC surface in \textit{in vitro} experiments. We then systematically explore the effects of experimentally tunable parameters including the antibody surface coverage $\sigma_s$ of NC, glycocalyx, shear flow and NC size. Of particular biological significance, our model predicts a threshold $\sigma_s$ value below which the NC binding affinities reduce drastically and drop below that of single anti-ICAM-1 molecule to ICAM-1; our results reveal that this is due to a change in the multivalency (or number of bonds formed per NC). This trend and threshold value are recovered exactly in the \textit{in vivo} measurements of the endothelium targeting of NCs in the pulmonary vascular in mice.   

Measurement of Cytoplasmic Streaming in Drosophila Melanogaster

During stage 9 of \emph{Drosophila melanogastor} oogenesis flow of the oocyte cytoplasm, driven by kinesin 1 motor protein is observed. This cytoplasmic streaming is analyzed by PIV in both wild type and kinesin light chain mutants, revealing striking statistical differences. Further measurements of the rheology of the oocyte allow for estimations of the mechanical energy needed to generate the observed flows.   

Microrheology Using Optical Tweezers at the Air-Water Interface

Microrheological techniques have been used successfully to determine mechanical properties of materials important in cellular structure.~ Also critical to cellular mechanical functions are biological membranes. Many aspects of biological membranes can be modeled using Langmuir monolayers, which are single layers surfactants at the air-water interface. The macroscopic mechanical properties of Langmuir monolayers have been extensively characterized. In contrast to macroscopic measurements, we report on experimental methods for studying the rheological properties of Langmuir monolayers on the micron scale.~ A water immersion optical tweezers system is used to trap $\sim $1 micron diameter beads in a monolayer. The passive motion of the trapped beads is recorded at high frequency and the complex shear modulus is calculated. ~Preliminary microrheological data of a fatty acid monolayer showing dependence on surface pressure will be presented. Experimental obstacles will also be discussed.   

Protein amyloid formation: Effects of shear, advection and interfaces

The aggregation of proteins into amyloid assemblies, which is associated with diseases such as Alzheimer's, is characterized by the unfolding of a given protein from its native state, the aggregation of some of these denatured species into nuclei, and further elongation into fibrils from these precursors. Previous observations have shown that shearing of the protein solution has a significant effect on the aggregation kinetics, but a clear understanding of the separate effects of shear forces, convective transport of species, and interfaces on the amyloid formation process is yet to be established. In the present work, we consider various shearing flow geometries and boundary conditions (e.g. gas/liquid and solid/liquid interfaces). The kinetics of the process are followed in time by measuring the change of protein in solution, and by microscopic observation of the aggregated species at the interfaces and in the bulk.   

Modelling Protein-induced Membrane Deformation using Monte Carlo and Langevin Dynamics Simulations

In eukaryotic cells, internalization of extracellular cargo via the cellular process of endocytosis is orchestrated by a variety of proteins, many of which are implicated in membrane deformation/bending. We model the energetics of deformations membranes by using the Helfrich Hamiltonian using two different formalisms: (i) Cartesian or Monge Gauge using Langevin dynamics; (ii) Curvilinear coordinate system using Monte Carlo (MC). Monge gauge approach which has been extensively studied is limited to small deformations of the membrane and cannot describe extreme deformations. Curvilinear coordinate approach can handle large deformation limits as well as finite-temperature membrane fluctuations; here we employ an unstructured triangular mesh to compute the local curvature tensor, and we evolve the membrane surface using a MC method. In our application, we compare the two approaches (i and ii above) to study how the spatial assembly of curvature inducing proteins leads to vesicle budding from a planar membrane. We also quantify how the curvature field of the membrane impacts the spatial segregation of proteins.   

Effect of Reynolds number on 2-D protein crystallization at the air/water interface

X-ray diffraction is the primary technique used to obtain a detailed description of a protein on the molecular level and as such, has yielded essential information about protein structures and protein-ligand interactions. However a major drawback of this technique is that the protein must first be crystallized which is often a very difficult and inefficient process. It has been shown previously that the process of two-dimensional protein crystallization on lipid monolayers at the air/water interface can be enhanced by a shearing flow. Here we examine the relationship between Reynolds number and the crystal growth process using the deep-channel surface viscometer geometry, which consists of an annular region bounded by stationary inner and outer cylinders and driven by a constant rotation of the floor. The interfacial velocity measurements are compared to Navier-Stokes computations with the Boussinesq-Scriven surface model.   

Quantification of Electroporation-Mediated Propidium Iodide Delivery into 3T3 Cells

Electroporation is an effective means to deliver exogenous molecules into the cellular cytoplasm, while simultaneously maintaining cell viability and functionality. In this technique, an applied electric field transiently permeabilizes the cellular membrane to enable molecular exchange. The main objective of the current work is to identify the transport mechanisms involved during electroporation, and to quantify the amount of molecules delivered into the cellular cytoplasm. An optical diagnostic system is developed to examine the transport of Propidium Iodide (PI) into 3T3 mouse fibroblast cells. Upon entering the permeabilized cell, PI binds to DNA/RNA within the cytoplasm to emit fluorescence, which is measured to track the dynamic accumulation of the dye within the cell. The results show that the total fluorescence intensity increases with a decreasing buffer electrical conductivity. The data are compared with numerical simulations, which reveals good agreement. The experimental observations and numerical analysis demonstrate that: 1) Electrophoresis plays a dominant role in mediating the transport. 2) An electrokinetic mechanism, field-amplified sample stacking, controls the achievable delivery efficiency. The study in this work is an important step toward the quantification as well as the eventual improvement of this useful technique.