Session QK: Biofluids: Cellular III

Stochastic Intravasation Model for Cancer Metastasis

We develop a two-part model that simulates circulating tumor cells (CTCs) entering and then traveling through the human vasculatory system. The first part of our model explores a three-dimensional cluster of CTCs attached to a blood vessel wall in a linear shear flow. The surface of the cells is represented by a 2D Gaussian probability distribution function, and it is discretized with regularized Stokeslets at each grid point. As the system of cells grows stochastically over time, one or more of the cells can detach from the system when the shear forces on the surface exceed a maximum threshold value. In the second part of our model, the newly free-floating CTCs are treated as a dynamical system of multiple, interacting point particles. These particles are represented by singular Stokeslets that are serially introduced into the flow, and the trajectory of each is calculated. The influence of the blood vessel wall is included using the method of images for Stokeslets for a plane boundary. Additional regularized Stokeslets without images are included to represent ambient white blood cells in the bloodstream.   

Dynamics of a microsphere in an anisotropic gel: a frontier in intracellular microrheology

Particle tracking microrheology determines the properties of a viscoelastic medium from the measured resistance of a moving, immersed microsphere. A crucial assumption in this method is that the medium is isotropic and the sphere experiences Stokes drag. However, the intracellular domain usually presents a pronounced directional structure and anisotropic rheological properties. Current lack of understanding of the dynamics of the probe in this complex environment challenges the application of microrheology to live cells. To overcome this difficulty, we study the drag force experienced by a microsphere in an anisotropic viscoelastic network (the cytoskeleton) permeated by a background liquid (the cytosol). In the limit of strong frictional coupling between the network and the liquid, the flow around the sphere is modeled with a generalized Stokes equation using several viscosity parameters. We solve this equation analytically to provide new closed-form microrheology formulae that relate the resistance measured experimentally to the anisotropic properties of the network. For high levels of anisotropy, such as those encountered in live cells, previous methods that assume Stokes Drag with different effective viscosities along different directions become ill-posed due to the incompressibility of the background liquid.   

Probing the directional structure and intracellular microrheology of the eukaryotic cytoplasm

The rheological properties of the cytoplasm of animal cells play an important role in cell functions such as migration, mechanotransduction, etc. The magnitude of these properties is important because it sets the level of intracellular deformation in response to stress. The directionality of these properties is equally important because it allows the cell to modulate the stress-strain relation differently along different directions. We aim to elucidate the relation between the structural organization of the cytoplasm and the directionality of its rheological properties by 1) measuring the local orientation of fluorescently labeled intracellular filaments and 2) determining the local directions of the maximum and minimum intracellular viscosity. Directional intracellular viscosities are measured by tracking the random motion of endogenous particles in 2D and applying novel microrheology formulae obtained by studying the motion of a microsphere in a transversely isotropic fluid. Our results indicate that the local viscosity is lowest along the direction parallel to the filaments and that the viscosity in the perpendicular direction is approximately 5 times larger. Under these conditions previous microrhelogy methods that assumed Stokes drag for the particles have errors in excess of 500{\%}.   

Do choanoflagellate cells cooperate hydrodynamically to increase feeding fluxes?

\textit{Salpingoeca rosetta} is a choanoflagellate, a protozoan that creates water flow with a single flagellum and captures bacterial prey on a collar of microvilli around its flagellum. In response to certain environmental cues \textit{S. rosetta} switches between unicellular and colonial forms. Analysis of this transition may provide clues about the evolutionary and physical forces that guided the first emergence of multicellular life. Our experiments and numerical models show how colonial living changes the feeding currents generated by cells within the colony. Our models also reveal the hidden potential for conflict among the cells in a colony by allowing direct calculation of the iniquitous division of cooperative benefits and costs between cells.   

Cellular flow in a small blood vessel

In the tubes and vessels with diameters $D < 8\mu$m red blood cells organize into single-file trains. Simulations are used to investigate flow in a model blood vessel slightly larger than this, $D = 11.3\mu$m, for which the cells deviate from this single-file arrangement, deforming continuously and significantly. The effective viscosity of the flow is found to become shear-rate insensitive at higher shear rates ($U/D > 50$s$^{-1}$) and to match experimental data. At lower shear rates (down to $U/D = 3.7$s$^{-1}$), the effective viscosity increases by over 50 percent. The cell-free layer that forms along the vessel walls thickens with increasing shear rate and is the key factor governing the overall flow resistance. Cells near the vessel wall are on average inclined relative to the wall, as might be expected for a lubrication mechanism leading to its formation. Metrics are developed to quantify the kinematics in terms of the well-known tank-treading and tumbling behaviors often observed for isolated cells. These rates are found to scale with the velocity difference across the cell-rich core and are thus significantly slower than the overall shear rate in the flow.   

Cell Transport in Microchannel

Cell transport through microscale channels occurs in many biomedical applications such as cell separation by magnetic/electromagnetic forces and cell injection in flow cytometry. Few studies have been performed to understand the motion of the cells as they travel through a microfluidic channel. The objective of this project is to model the velocity of the cells passing through a microfluidic channel under the action of both pressure driven and electrically driven flow fields. Two candidate models of cell transport will be considered. First, the cell transport will be modeled by considering it carried by Poiseuille or electroosmotic flow electrophoretically near walls. Second, the dilute cell population will be treated as a solute, and a general mass transport model will be developed. For realistic values of the channel dimensions and the cell diameter, the presence of the walls is expected to be a leading order effect. The relative magnitude of the various forces that can act on a cell moving in a microfluidic channel are also discussed. The differences between and the validity of the two models will be studied based on the values of the governing parameters. The results will be compared with experiments involving several lines of cancer cells.   

Sticks in honey - Motor-connected Microtubules at low Reynolds number

It is known that suspensions of microtubules (MTs) and molecular motors spontaneously form ordered asters and vortices. We consider the motion of MTs' assemblages connected by molecular motors at low Reynolds number. The MTs are modeled as rigid sticks and their hydrodynamic interaction with the medium is determined using slender body approximation. The motors are modeled as moving points which provide kinematic constrains for the sticks' motion. The hydrodynamic alignment of a pair of MTs for two possible motor connections is considered: a single head motor connection, in which the motor moves on one of the sticks and carries the other one, and a dual head motor connection whereas the motor advances on both sticks. We further address the formation of an aster from the vortex of inter-connected MTs. The forces the motors need to exert on the MTs in the course of closing the vortex and their dependence on the number of MTs are computed.   

Time course of pH change in plant epidermis using microscopic pH imaging system

We established a microscopic pH imaging system to track the time course of pH change in plant epidermis \textit{in vivo}. In the previous research, we have found out that anthocyanin containing cells have higher pH. However, it was not clear whether the anthocyanin increased the pH or anthocyanin was synthesized result from the higher pH. Therefore, we further investigated the relationship between anthocyanin and pH change. To track the time course of pH change in plant epidermis, we established a system using luminescent imaging technique. We used HPTS (8-Hydroxypyrene-1,3,6-Trisulfonate) as pH indicator and applied excitation ratio imaging method. Luminescent image was converted to a pH distribution by obtained \textit{in vitro} calibration using known pH solution. Cellular level observation was enabled by merging microscopic color picture of the same region to the pH change image. The established system was applied to epidermal cells of red-tip leaf lettuce, \textit{Lactuca Sativa L.} and the time course was tracked in the growth process. We would discuss about the relationship between anthocyanin and pH change in plant epidermis.