FACS-style detection for real-time cell viscoelastic cytometry.

Cell mechanical properties have been established as a label-free biophysical marker of cell viability and health; however, real-time methods with significant throughput for accurately and non-destructively measuring these properties remain widely unavailable. Without appropriate labels for use with fluorescence activated cell sorters (FACS), easily implemented real-time technology for tracking cell-level mechanical properties remains a current need. Employing modulated optical forces and enabled by a low-dimensional FACS-style detection method introduced here, we present a viscoelasticity cytometer (VC) capable of real-time and continuous measurements. We demonstrate the utility of this approach by tracking the high-frequency cell physical properties of populations of chemically-modified cells at rates of ~ 1 s-1 and explain observations within the context of a simple theoretical model.

A simple microfluidic dispenser for single-microparticle and cell samples.

Non-destructive isolation of single-cells has become an important need for many biology research laboratories; however, there is a lack of easily employed and inexpensive tools. Here, we present a single-particle sample delivery approach fabricated from simple, economical components that may address this need. In this, we employ unique flow and timing strategies to bridge the significant force and length scale differences inherent in transitioning from single particle isolation to delivery. Demonstrating this approach, we use an optical trap to isolate individual microparticles and red blood cells that are dispensed within separate 50 µl droplets off a microfluidic chip for collection into microscope slides or microtiter plates.

Effect of viscoelasticity on the analysis of single-molecule force spectroscopy on live cells.

Single-molecule force spectroscopy is used to probe the kinetics of receptor-ligand bonds by applying mechanical forces to an intermediate media on which the molecules reside. When this intermediate media is a live cell, the viscoelastic properties can affect the calculation of rate constants. We theoretically investigate the effect of media viscoelasticity on the common assumption that the bond force is equal to the instantaneous applied force. Dynamic force spectroscopy is simulated between two cells of varying micromechanical properties adhered by a single bond with a constant kinetic off-rate. We show that cell and microvilli deformation, and hydrodynamic drag contribute to bond forces that can be 28-90% lower than the applied force for loading rates of 10(3)-10(7) pN/s, resulting in longer bond lifetimes. These longer bond lifetimes are not caused by changes in bond kinetics; rather, they are due to the mechanical response of the intermediate media on which the bonds reside. Under the assumption that the instantaneous bond force is equal to the applied force--thereby ignoring viscoelasticity--leads to 14-39% error in the determination of off-rates. We present an approach that incorporates viscoelastic properties in calculating the instantaneous bond force and kinetic dissociation parameter of the intermolecular bond.

A theoretical method to determine unstressed off-rate from multiple bond force spectroscopy.

Using dynamic force spectroscopy to measure the kinetic off-rates of intermolecular bonds currently requires the isolation of single molecules. This requirement arises in part because no tractable analytic method for determining kinetic off-rates from the rupture of a large number of bonds under dynamic forces is currently available. We introduce a novel method for determining the unstressed off-rate from dynamic force spectroscopy experiments involving a large number of bonds. Using both the Bell and Dembo models we show that the unstressed off-rate calculated using the proposed method is in good agreement with the prescribed unstressed off-rate used in Monte-Carlo simulations of multiple bond dynamic force spectroscopy experiments given initial number of bonds (50-500) and loading rate 10(3)-10(6)pN/s.

Cell elongation via intrinsic antipodal stretching forces.

To probe the mechanical properties of cells, we investigate a technique to perform deformability-based cytometry that inherently induces normal antipodal surface forces using a single line-shaped optical trap. We show theoretically that these opposing forces are generated simultaneously over curved microscopic object surfaces with optimal magnitude at low numerical apertures, allowing the directed stretching of elastic cells with a single, weakly focused laser source. Matching these findings with concomitant experimental observations, we elongate red blood cells, effectively stretching them within the narrow confines of a steep, optically induced potential well.

Effect of cell and microvillus mechanics on the transmission of applied loads to single bonds in dynamic force spectroscopy.

Receptor-ligand interactions that mediate cellular adhesion are often subjected to forces that regulate their detachment via modulating off-rates. Although the dynamics of detachment is primarily controlled by the physical chemistry of adhesion molecules, cellular features such as cell deformability and microvillus viscoelasticity have been shown to affect the rolling velocity of leukocytes in vitro through experiments and simulation. In this work, we demonstrate via various micromechanical models of two cells adhered by a single (intramolecular) bond that cell deformability and microvillus viscoelasticity modulate transmission of an applied external load to an intramolecular bond, and thus the dynamics of detachment. Specifically, it is demonstrated that the intermolecular bond force is not equivalent to the instantaneous applied force and that the instantaneous bond force decreases with cellular and microvillus compliance. As cellular compliance increases, not only does the time lag between the applied load and the bond force increase, an initial response time is observed during which cell deformation is observed without transfer of force to the bond. It is further demonstrated that following tether formation the instantaneous intramoleular bond force increases linearly at a rate dependent on microvillus viscosity. Monte Carlo simulations with fixed kinetic parameters predict that both cell and microvillus compliance increase the average rupture time, although the average rupture force based on bond length remains nearly unchanged.

Tip streaming from a drop in the presence of surfactants.

Drop breakup in a linear extensional flow is simulated numerically using a nonlinear model for the surface tension that accounts for maximum packing at the interface. Surface convection sweeps surfactant to the drop poles, where it accumulates and drives the surface tension to near zero. The drop assumes a transient shape with highly pointed tips. From these tips, thin liquid threads are pulled. Subsequently, small, surfactant-rich droplets are emitted from the termini of these threads. The scale of the shed drops depends on the initial surfactant coverage. Dilute initial coverage leads to tip streaming, while high initial coverage leads to the tip dropping breakup mode.

Calculations of intracapillary oxygen tension distributions in muscle.

Characterizing the resistances to O(2) transport from the erythrocyte to the mitochondrion is important to understanding potential transport limitations. A mathematical model is developed to accurately determine the effects of erythrocyte spacing (hematocrit), velocity, and capillary radius on the mass transfer coefficient. Parameters of the hamster cheek pouch retractor muscle are used in the calculations, since significant amounts of experimental physiological data and mathematical modeling are available for this muscle. Capillary hematocrit was found to have a large effect on the PO(2) distribution and the intracapillary mass transfer coefficient per unit capillary area, k(cap), increased by a factor of 3.7 from the lowest (H=0.25) to the highest (H=0.55) capillary hematocrits considered. Erythrocyte velocity had a relatively minor effect, with only a 2.7% increase in the mass transfer coefficient as the velocity was increased from 5 to 25 times the observed velocity in resting muscle. The capillary radius is varied by up to two standard deviations of the experimental measurements, resulting in variations in k(cap) that are <15% at the reference case. The magnitude of these changes increases with hematocrit. An equation to approximate the dependence of the mass transfer coefficient on hematocrit is developed for use in simulations of O(2) transport from a capillary network.

Predictions of capillary oxygen transport in the presence of fluorocarbon additives.

A mathematical model of capillary oxygen transport was formulated to determine the effect of increasing plasma solubility, e.g., by the addition of an intravascular fluorocarbon emulsion. The effect of increased plasma solubility is studied for two distributions of fluorocarbon, when the fluorocarbon droplets are uniformly distributed throughout the plasma and when the fluorocarbon droplets are concentrated in a layer adjacent to the endothelium. The model was applied to working hamster retractor muscle at normal and lowered hematocrit. The intracapillary mass transfer coefficient was found to increase by 18% as the solubility was increased by a factor of 1.7 at a hematocrit of 43%. An additional increase of 6% was predicted when the solubility increase was concentrated in the layer adjacent to the endothelium. At a hematocrit of 25%, the intracapillary mass transfer coefficient increased 14% when the solubility was increased by a factor of 1.7.

Large deformation of red blood cell ghosts in a simple shear flow.

Red blood cells are known to change shape in response to local flow conditions. Deformability affects red blood cell physiological function and the hydrodynamic properties of blood. The immersed boundary method is used to simulate three-dimensional membrane-fluid flow interactions for cells with the same internal and external fluid viscosities. The method has been validated for small deformations of an initially spherical capsule in simple shear flow for both neo-Hookean and the Evans-Skalak membrane models. Initially oblate spheroidal capsules are simulated and it is shown that the red blood cell membrane exhibits asymptotic behavior as the ratio of the dilation modulus to the extensional modulus is increased and a good approximation of local area conservation is obtained. Tank treading behavior is observed and its period calculated.