Mean deformation metrics for quantifying 3D cell–matrix interactions without requiring information about matrix material properties

Abstract

Mechanobiology relates cellular processes to mechanical signals, such as determining the effect of variations in matrix stiffness with cell tractions. Cell traction recorded via traction force microscopy (TFM) commonly takes place on materials such as polyacrylamideand polyethylene glycol-based gels. Such experiments remain limited in physiological relevance because cells natively migrate within complex tissue microenvironments that are spatially heterogeneous and hierarchical. Yet, TFM requires determination of the matrix constitutive law (stress-strain relationship), which is not always readily available. In addition, the currently achievable displacement resolution limits the accuracy of TFM for relatively small cells. To overcome these limitations, and increase the physiological relevance of in vitro experimental design, we present a new approach and a set of associated biomechanical signatures that are based purely on measurements of the matrix's displacements without requiring any knowledge of its constitutive laws. We show that our mean deformation metrics (MDM) approach can provide significant biophysical information without the need to explicitly determine cell tractions. In the process of demonstrating the use of our MDM approach, we succeeded in expanding the capability of our displacement measurement technique such that it can now measure the 3D deformations around relatively small cells (∼10 micrometers), such as neutrophils. Furthermore, we also report previously unseen deformation patterns generated by motile neutrophils in 3D collagen gels.traction force microscopy | confocal microscopy | large deformations | neutrophil M echanical cues within the cellular microenvironment regulate numerous fundamental functions including cell adhesion, deformation, and generation of traction (1-6). Analysis of cellular force generation, and its role in regulating homeostasis across a variety of cellular phenotypes and experimental platforms, has received much attention over the last three decades (7-13). Experimental quantification of cellular forces has produced several cell traction measurement techniques, ranging from surface wrinkle detection and flexure of micropillars to traction force microscopy (TFM) (12,(14)(15)(16)(17)(18)(19)(20). In TFM, measured cell-induced displacements are converted into tractions using various mathematical frameworks (14,15,17,18,21,22). Both twoand 3D TFM techniques have steadily increased in sophistication and now feature high-spatial displacement resolution and advanced computational formalisms to connect this displacement information to complex material constitutive laws (17,23,24).To successfully perform TFM, it is critical to know the stressstrain constitutive behavior of the matrix surrounding the cell. Although many TFM substrates feature relatively simple artificial gel constructs, such as polyacrylamide and polyethylene glycol, these constructs are impenetrable by cells and obviate measures obtained while cells are in a 3D setting (as would be the case within a bodily ...

Mechanophenotyping of 3D Multicellular Clusters using Displacement Arrays of Rendered Tractions

“…We designed a new kinematics based approach called displacement array of rendered tractions (DART) metrics for characterizing the cell-induced matrix deformations without relying on constitutive material model for the 3D biomaterial. We previously demonstrated mean deformation metrics (MDM) to compute average values associated with the deformation fields of individual cells 21 . However, we observed in these experiments that multicellular clusters applied spatially heterogeneous deformation fields over large volumes.…”

“…1b). Although visually pronounced, this heterogeneity is often averaged out in conventional TFM or kinematic metrics based on mean deformations around individual cells 14,21 (Fig. S3).…”

“…Early TFM studies measured cell-cell and cell-matrix interactions of multicellular epithelial clusters on planar 2D substrates [8][9][10][11][12][13] . More recently, TFM has been extended to 3D hydrogels, but has primarily focused on individual cells [14][15][16][17][18][19][20][21][22][23][24] . Notably, epithelial cell lines exhibit more isotropic, spatially uniform tractions, while mesenchymal cell lines exhibit highly anisotropic tractions localized at the leading and trailing edge 14-16, 18, 20, 22, 23 .…”

Microfabricated tissues for investigating traction forces involved in cell migration and tissue morphogenesis

“…This presents a challenge for in vivo systems where it may be difficult to characterize the mechanical properties of the ECM owing to its complex composition and because cells continuously remodel the ECM as they migrate. One potential solution was recently proposed whereby mean deformation metrics could be used to quantify cell-matrix interactions without the mechanical details of the matrix [61]. However, this method does not provide any information about cell tractions and cannot describe the effects of matrix stiffness without first knowing the mechanical properties of the matrix [61].…”

“…One potential solution was recently proposed whereby mean deformation metrics could be used to quantify cell-matrix interactions without the mechanical details of the matrix [61]. However, this method does not provide any information about cell tractions and cannot describe the effects of matrix stiffness without first knowing the mechanical properties of the matrix [61]. A second drawback is that the inverse calculations required to obtain traction stresses can be computationally expensive.…”