Yue Du

Three-Dimensional Characterization of Mechanical Interactions between Endothelial Cells and Extracellular Matrix during Angiogenic Sprouting

We studied the three-dimensional cell-extracellular matrix interactions of endothelial cells that form multicellular structures called sprouts. We analyzed the data collected in-situ from angiogenic sprouting experiments and identified the differentiated interaction behavior exhibited by the tip and stalk cells. Moreover, our analysis of the tip cell lamellipodia revealed the diversity in their interaction behavior under certain conditions (e.g., when the heading of a sprout is switched approximately between the long-axis direction of two different lamellipodia). This study marks the first time that new characteristics of such interactions have been identified with shape changes in the sprouts and the associated rearrangements of collagen fibers. Clear illustrations of such changes are depicted in three-dimensional views.

A Magneto-Microfluidic System for Investigating the Influence of an Externally Induced Force Gradient in a Collagen Type I ECM on HMVEC Sprouting

Advances in mechanobiology have suggested that physiological and pathological angiogenesis may be differentiated based on the ways in which the cells interact with the extracellular matrix (ECM) that exhibits partially different mechanical properties. This warrants investigating the regulation of ECM stiffness on cell behavior using angiogenesis assays. In this article, we report the application of the technique of active manipulation of ECM stiffness to study in vitro angiogenic sprouting of human microvascular endothelial cells (HMVECs) in a microfluidic device. Magnetic beads were embedded in the ECM through bioconjugation (between the streptavidin-coated beads and collagen fibers) in order to create a pretension in the ECM when under the influence of an external magnetic field. The advantage of using this magneto-microfluidic system is that the resulting change in the local deformability of the collagen fibers is only apparent to a cell at the pericellular level near the site of an embedded bead, while the global intrinsic material properties of the ECM remain unchanged. The results demonstrate that this system represents an effective tool for inducing noninvasively an external force on cells through the ECM, and suggest the possibility of creating desired stiffness gradients in the ECM for manipulating cell behavior in vitro.

Characterization of uniaxial stiffness of extracellular matrix embedded with magnetic beads via bio-conjugation and under the influence of an external magnetic field

In this paper, we study the deformation, and experimentally quantify the change in stiffness, of an extracellular matrix (ECM) embedded with magnetic beads that are bio-conjugated with the collagen fibers and under the influence of an external magnetic field. We develop an analytical model of the viscoelastic behavior of this modified ECM, and design and implement a stretch test to quantify (based on statistically meaningful experiment data) the resulting changes in its stiffness induced by the external magnetic field. The analytical results are in close agreement with that obtained from the experiments. We discuss the implication of these results that point to the possibility of creating desired stiffness gradients in an ECM in vitro to influence cell behavior.

An Electromagnetic System for Inducing a Localized Force Gradient in an ECM and Its Influence on HMVEC Sprouting

Mechanical properties of the extracellular matrix (ECM) have been observed to influence the behavior of cells. Investigations on such an influence commonly rely on using soluble cues to alter the global intrinsic ECM properties in order to study the subsequent response of cells. This article presents an electromagnetic system for inducing a localized force gradient in an ECM, and reports the experimentally observed effect of such a force gradient on in vitro angiogenic sprouting of human microvascular endothelial cells (HMVECs). This force gradient is realized through the induction of magnetic forces on the superparamagnetic microparticle–embedded ECM (sECM). Both analytical and statistically meaningful experimental results demonstrate the effectiveness of this approach in influencing the behavior of a targeted HMVEC sprout without affecting that of other sprouts nearby. These results suggest the possibility of selectively controlling the in vitro behavior of cells by the induction of a localized force gradient in the ECM.

Determination of Green’s function for three-dimensional traction force reconstruction based on geometry and boundary conditions of cell culture matrices

Cell migration plays a particular important role in the initiation and progression of many physical processes and pathological conditions such as tumor invasion and metastasis. Three-dimensional traction force microscopy (TFM) of high resolution and high accuracy is being developed in an effort to unveil the underlying mechanical process of cell migration in a vivo-like environment. Linear elasticity-based TFM (LETM) as a mainstream approach relies on the Greens function (that relates traction forces to matrix deformation), of which the inherent boundary conditions and geometry of the matrix could remarkably affect the result as suggested by previous 2D studies. In this study, we investigated this close linkage in 3D environment, via modeling of a cell sensing a close-by fixed boundary of a 3D matrix surrounding it, and comparing the reconstructed traction forces from three different solutions of the Greens function, including a fully matching solution derived using the adapted Mindlins approach. To increase fidelity in the estimate of traction forces for extreme conditions such as a sparse sampling of deformation field or targeting small focal adhesions, we numerically solved the singularity problem of the Greens function in a non-conventional way to avoid exclusion of singular point regions that could contain representative deformation indicators for such extreme conditions. A single case experimental study was conducted for a multi-cellular structure of endothelial cells that just penetrated into the gel at the early stage of angiogenesis. STATEMENT OF SIGNIFICANCE This study focused on the fundamental issue regarding extension of linear elasticity-based TFM to deal with physically realistic matrices (where cells are encapsulated), which concerns determination of the Greens function matching their geometry and boundary conditions. To increase fidelity in the estimate of traction forces for extreme conditions such as a sparse sampling of deformation field or targeting small focal adhesions, we numerically solved the singularity problem of the Greens function to avoid exclusion of singular point regions that could contain representative deformation indicators for such extreme conditions. The proposed approach to adapting the Greens function for the specific 3D cell culture situation was examined in a single case experimental study of endothelial cells in sprouting angiogenesis.

Analysis of Stiffness in Extracellular Matrix Embedded with Bio-Conjugated Magnetic Beads in a Magnetic Field

In this paper we present a new model for determining the local stiffness of an extracellular matrix (ECM) sample embedded with bio-conjugated magnetic beads under the influence of an external magnetic field. In this model, the viscoelastic deformation of such ECM samples is analyzed using the finite element method. We report results from numerical simulations using our model on two typical scenarios for studying the pre-tension in the ECM caused by beads under a magnetic field. The analytical results are in close agreement with that obtained from COMSOL. We also applied our model on an actual ECM sample embedded with bio-conjugated beads and compared our analytical results with that obtained from stretch tests done on that sample. These results are comparable to that from the stretching tests. In this paper, we present a finite-element model for determining the local stiffness of an ECM sample embedded with bio-conjugated beads under the influence of an external magnetic field. Section II discusses the modification of ECM for manipulating the stiffness of ECM. Section III describes our finite-element method for analyzing viscoelastic deformation of ECM gel embedded with bio-conjugated beads, while Section IV discusses the calculation of magnetic force induced on the beads in the magnetic field generated by a permanent magnet. In Section V we apply this finite-element model to simulate the pre-tension generated in ECM by (i) a single bead, and (ii) two columns of aligned beads, and compare the results to that obtained using COMSOL. We also apply our finite-element model to an ECM sample with randomly distributed beads, and compare the analytical results (in terms of the percentage change in ECM stiffness) with experimental results obtained from a stretch test done on an actual ECM sample. Simulations are also conducted to reveal the influence of the size and concentration of beads on the change in ECM stiffness. We discuss possible improvements for this proposed model in Section VI.