scholarly journals Recovery of Tractions Exerted by Single Cells in Three-Dimensional Nonlinear Matrices

2020 ◽  
Vol 142 (8) ◽  
Author(s):  
Dawei Song ◽  
Li Dong ◽  
Mukund Gupta ◽  
Linqing Li ◽  
Ottmar Klaas ◽  
...  
Keyword(s):  
Cancer Metastasis ◽  
Single Cells ◽  
Three Dimensional ◽  
Traction Force ◽  
Simulated Data ◽  
Nonlinear Effects ◽  
Stem Cell Differentiation ◽  
Large Strains ◽  
The Matrix ◽  
Minimization Procedure

Abstract Cell-generated tractions play an important role in various physiological and pathological processes such as stem-cell differentiation, cell migration, wound healing, and cancer metastasis. Traction force microscopy (TFM) is a technique for quantifying cellular tractions during cell–matrix interactions. Most applications of this technique have heretofore assumed that the matrix surrounding the cells is linear elastic and undergoes infinitesimal strains, but recent experiments have shown that the traction-induced strains can be large (e.g., more than 50%). In this paper, we propose a novel three-dimensional (3D) TFM approach that consistently accounts for both the geometric nonlinearity introduced by large strains in the matrix, and the material nonlinearity due to strain-stiffening of the matrix. In particular, we pose the TFM problem as a nonlinear inverse hyperelasticity problem in the stressed configuration of the matrix, with the objective of determining the cellular tractions that are consistent with the measured displacement field in the matrix. We formulate the inverse problem as a constrained minimization problem and develop an efficient adjoint-based minimization procedure to solve it. We first validate our approach using simulated data, and quantify its sensitivity to noise. We then employ the new approach to recover tractions exerted by NIH 3T3 cells fully encapsulated in hydrogel matrices of varying stiffness. We find that neglecting nonlinear effects can induce significant errors in traction reconstructions. We also find that cellular tractions roughly increase with gel stiffness, while the strain energy appears to saturate.

scholarly journals Collective forces of tumor spheroids in three-dimensional biopolymer networks

eLife ◽  
2020 ◽  
Vol 9 ◽  
Author(s):  
Christoph Mark ◽  
Thomas J Grundy ◽  
Pamela L Strissel ◽  
David Böhringer ◽  
Nadine Grummel ◽  
...  
Keyword(s):  
Single Cells ◽  
Three Dimensional ◽  
Traction Force ◽  
Tumor Spheroids ◽  
Scale Invariant ◽  
Tissue Samples ◽  
Force Microscopy ◽  
Surrounding Matrix ◽  
Highly Nonlinear ◽  
Contractile Forces

We describe a method for quantifying the contractile forces that tumor spheroids collectively exert on highly nonlinear three-dimensional collagen networks. While three-dimensional traction force microscopy for single cells in a nonlinear matrix is computationally complex due to the variable cell shape, here we exploit the spherical symmetry of tumor spheroids to derive a scale-invariant relationship between spheroid contractility and the surrounding matrix deformations. This relationship allows us to directly translate the magnitude of matrix deformations to the total contractility of arbitrarily sized spheroids. We show that our method is accurate up to strains of 50% and remains valid even for irregularly shaped tissue samples when considering only the deformations in the far field. Finally, we demonstrate that collective forces of tumor spheroids reflect the contractility of individual cells for up to 1 hr after seeding, while collective forces on longer timescales are guided by mechanical feedback from the extracellular matrix.

scholarly journals Loss of vimentin intermediate filaments decreases peri-nuclear stiffness and enhances cell motility through confined spaces

2018 ◽  
Author(s):  
Alison E. Patteson ◽  
Katarzyna Pogoda ◽  
Fitzroy J. Byfield ◽  
Elisabeth E. Charrier ◽  
Peter A. Galie ◽  
...  
Keyword(s):  
Cell Motility ◽  
Cancer Metastasis ◽  
Structural Integrity ◽  
Three Dimensional ◽  
Large Strains ◽  
Mechanical Resistance ◽  
Intermediate Filament Protein ◽  
Migratory Cells ◽  
Filament Protein ◽  
Extracellular Matrix Receptors

The migration of cells through tight constricting spaces or along fibrous tracks in tissues is important for biological processes, such as embryogenesis, wound healing, and cancer metastasis, and depends on the mechanical properties of the cytoskeleton. Migratory cells often express and upregulate the intermediate filament protein vimentin. The viscoelasticity of vimentin networks in shear deformation has been documented, but its role in motility is largely unexplored. Here, we studied the effects of vimentin on cell motility and stiffness using mouse embryo fibroblasts derived from wild-type and vimentin-null mice. We find that loss of vimentin increases motility through small pores and along thin capillaries. Atomic force microscopy measurements reveal that the presence of vimentin enhances the perinuclear stiffness of the cell, to an extent that depends on surface ligand presentation and therefore signaling from extracellular matrix receptors. Together, our results indicate that vimentin hinders three-dimensional motility by providing mechanical resistance against large strains and may thereby protect the structural integrity of cells.

scholarly journals Sensing Traction Force on Matrix Induces Cell-Cell Distant Mechanical Communications for Self-assembly

2019 ◽  
Author(s):  
Mingxing Ouyang ◽  
Zhili Qian ◽  
Bing Bu ◽  
Yang Jin ◽  
Jiajia Wang ◽  
...  
Keyword(s):  
Long Range ◽  
Self Assembly ◽  
Cancer Metastasis ◽  
Traction Force ◽  
Airway Smooth Muscle Cells ◽  
Type I ◽  
Force Transmission ◽  
Biomechanical Force ◽  
The Matrix ◽  
Cell Cell

AbstractThe long-range biomechanical force propagating across large scale may reserve the capability to trigger coordinative responses within cell population such as during angiogenesis, epithelial tubulogenesis, and cancer metastasis. How cells communicate in a distant manner within the group for self-assembly remains largely unknown. Here we found that airway smooth muscle cells (ASMCs) rapidly self-assembled into well-constructed network on 3D Matrigel containing type I collagen (COL), which relied on long-range biomechanical force across the matrix to direct cell-cell distant interactions. Similar results happened by HUVEC cells to mimic angiogenesis. Interestingly, single ASMCs initiated multiple extended protrusions precisely pointing to neighboring cells in distance, depending on traction force sensing. Separate ASMCs sensed each other to move directionally on both non-fibrous Matrigel and more efficiently when containing fibrous COL, but lost mutual sensing on fixed gel or coated glass due to no long-range force transmission. Beads tracking assay demonstrated distant transmission of traction force, and finite element method modeling confirmed the consistency between maximum strain distribution on matrix and cell directional movements in experiments. Furthermore, ASMCs recruited COL from the hydrogel to build fibrous network to mechanically stabilize cell network. Our results revealed for the first time that cells can sense traction force transmitted through the matrix to initiate cell-cell distant mechanical communications, resulting in cell directional migration and coordinative self-assembly with active matrix remodeling. As an interesting phenomenon, cells sound able to ‘make phone call’ via long-range biomechanics, which implicates physiological importance such as for tissue pattern formation.

A Sampled Randomization Test for Examining Single Cells of Behavioural Transition Matrices

Behaviour ◽  
1979 ◽  
Vol 69 (3-4) ◽  
pp. 217-227 ◽  
Author(s):  
Catherine Rechten ◽  
Russell D. Fernald
Keyword(s):  
Single Cells ◽  
Simulated Data ◽  
Randomization Test ◽  
Transition Matrices ◽  
Standard Procedures ◽  
The Matrix ◽  
Expected Values ◽  
Decisive Advantage

AbstractA Sampled Randomization test for analysing individual cells of behavioural transition matrices is described. The test is compared with two standard procedures by running all three on simulated data. The Randomization test proves roughly as efficient as the X2 test applied to a collapsed matrix; both are more powerful than a test proposed by SLATER & OLLASON (1972). The decisive advantage of the Randomization test lies in its ability to assess the interrelatedness of cell results within a matrix: expected values can be adjusted to show how any mechanism assumed to explain one cell result would affect the rest of the matrix.

scholarly journals Non-muscle myosin IIB is critical for nuclear translocation during 3D invasion

2015 ◽  
Vol 210 (4) ◽  
pp. 583-594 ◽  
Author(s):  
Dustin G. Thomas ◽  
Aishwarya Yenepalli ◽  
Celine Marie Denais ◽  
Andrew Rape ◽  
Jordan R. Beach ◽  
...  
Keyword(s):  
Cell Migration ◽  
Cancer Metastasis ◽  
Nuclear Translocation ◽  
Three Dimensional ◽  
Traction Force ◽  
Embryonic Cell ◽  
Migration And Invasion ◽  
Force Microscopy ◽  
Gland Carcinoma ◽  
Muscle Myosin

Non-muscle myosin II (NMII) is reported to play multiple roles during cell migration and invasion. However, the exact biophysical roles of different NMII isoforms during these processes remain poorly understood. We analyzed the contributions of NMIIA and NMIIB in three-dimensional (3D) migration and in generating the forces required for efficient invasion by mammary gland carcinoma cells. Using traction force microscopy and microfluidic invasion devices, we demonstrated that NMIIA is critical for generating force during active protrusion, and NMIIB plays a major role in applying force on the nucleus to facilitate nuclear translocation through tight spaces. We further demonstrate that the nuclear membrane protein nesprin-2 is a possible linker coupling NMIIB-based force generation to nuclear translocation. Together, these data reveal a central biophysical role for NMIIB in nuclear translocation during 3D invasive migration, a result with relevance not only to cancer metastasis but for 3D migration in other settings such as embryonic cell migration and wound healing.

scholarly journals Collective forces of tumor spheroids in three-dimensional biopolymer networks

2019 ◽  
Author(s):  
Christoph Mark ◽  
Thomas J. Grundy ◽  
David Böhringer ◽  
Julian Steinwachs ◽  
Geraldine M. O’Neill ◽  
...  
Keyword(s):  
Single Cells ◽  
Three Dimensional ◽  
Traction Force ◽  
Tumor Spheroids ◽  
Scale Invariant ◽  
Force Microscopy ◽  
Surrounding Matrix ◽  
Highly Nonlinear ◽  
Nonlinear Matrix ◽  
Contractile Forces

ABSTRACTWe describe a method for quantifying the contractile forces that tumor spheroids collectively exert on highly nonlinear three-dimensional collagen networks. While three-dimensional traction force microscopy for single cells in a nonlinear matrix is computationally complex due to the variable cell shape, here we exploit the spherical symmetry of tumor spheroids to derive a scale-invariant relationship between spheroid contractility and the surrounding matrix deformations. This relationship allows us to directly translate the magnitude of matrix deformations to the total contractility of arbitrarily sized spheroids. We show that collective forces of tumor spheroids reflect the contractility of individual cells for up to 1h after seeding, while collective forces on longer time-scales are guided by mechanical feedback from the extracellular matrix.

Transition alpha structure in beta-isomorphous Nb-Hf alloys

1987 ◽  
Vol 45 ◽  
pp. 232-233
Author(s):  
R.W. Carpenter ◽  
Changhai Li ◽  
David J. Smith
Keyword(s):  
Solid Solution ◽  
Solution Phase ◽  
Miscibility Gap ◽  
Large Strains ◽  
Solid Solution Phase ◽  
Two Phase ◽  
Diffuse Intensity ◽  
Metastable Form ◽  
The Matrix ◽  
Equilibrium Morphology

Binary Nb-Hf alloys exhibit a wide bcc solid solution phase field at temperatures above the Hfα→ß transition (2023K) and a two phase bcc+hcp field at lower temperatures. The β solvus exhibits a small slope above about 1500K, suggesting the possible existence of a miscibility gap. An earlier investigation showed that two morphological forms of precipitate occur during the bcc→hcp transformation. The equilibrium morphology is rod-type with axes along <113> bcc. The crystallographic habit of the rod precipitate follows the Burgers relations: {110}||{0001}, <112> || <1010>. The earlier metastable form, transition α, occurs as thin discs with {100} habit. The {100} discs induce large strains in the matrix. Selected area diffraction examination of regions ∼2 microns in diameter containing many disc precipitates showed that, a diffuse intensity distribution whose symmetry resembled the distribution of equilibrium α Bragg spots was associated with the disc precipitate.

Designing TIMP (tissue inhibitor of metalloproteinases) variants that are selective metalloproteinase inhibitors

2003 ◽  
Vol 70 ◽  
pp. 201-212 ◽  
Author(s):  
Hideaki Nagase ◽  
Keith Brew
Keyword(s):  
Three Dimensional ◽  
Therapeutic Interventions ◽  
Tissue Inhibitors Of Metalloproteinases ◽  
Structural Basis ◽  
Structural Elements ◽  
Ridge Structure ◽  
Extracellular Matrix Components ◽  
Metalloproteinase Inhibitors ◽  
The Matrix ◽  
A Disintegrin And Metalloproteinase

The tissue inhibitors of metalloproteinases (TIMPs) are endogenous inhibitors of the matrix metalloproteinases (MMPs), enzymes that play central roles in the degradation of extracellular matrix components. The balance between MMPs and TIMPs is important in the maintenance of tissues, and its disruption affects tissue homoeostasis. Four related TIMPs (TIMP-1 to TIMP-4) can each form a complex with MMPs in a 1:1 stoichiometry with high affinity, but their inhibitory activities towards different MMPs are not particularly selective. The three-dimensional structures of TIMP-MMP complexes reveal that TIMPs have an extended ridge structure that slots into the active site of MMPs. Mutation of three separate residues in the ridge, at positions 2, 4 and 68 in the amino acid sequence of the N-terminal inhibitory domain of TIMP-1 (N-TIMP-1), separately and in combination has produced N-TIMP-1 variants with higher binding affinity and specificity for individual MMPs. TIMP-3 is unique in that it inhibits not only MMPs, but also several ADAM (a disintegrin and metalloproteinase) and ADAMTS (ADAM with thrombospondin motifs) metalloproteinases. Inhibition of the latter groups of metalloproteinases, as exemplified with ADAMTS-4 (aggrecanase 1), requires additional structural elements in TIMP-3 that have not yet been identified. Knowledge of the structural basis of the inhibitory action of TIMPs will facilitate the design of selective TIMP variants for investigating the biological roles of specific MMPs and for developing therapeutic interventions for MMP-associated diseases.

3D simulation of emulsion flow using the boundary element method on the heterogeneous computational systems

2012 ◽  
Vol 9 (1) ◽  
pp. 142-146
Author(s):  
O.A. Solnyshkina
Keyword(s):  
Boundary Element Method ◽  
Boundary Element ◽  
Three Dimensional ◽  
Reynolds Numbers ◽  
Problem Size ◽  
Low Reynolds Numbers ◽  
Infinite Domains ◽  
The Matrix ◽  
Computational Systems ◽  
Element Method

In this work the 3D dynamics of two immiscible liquids in unbounded domain at low Reynolds numbers is considered. The numerical method is based on the boundary element method, which is very efficient for simulation of the three-dimensional problems in infinite domains. To accelerate calculations and increase the problem size, a heterogeneous approach to parallelization of the computations on the central (CPU) and graphics (GPU) processors is applied. To accelerate the iterative solver (GMRES) and overcome the limitations associated with the size of the memory of the computation system, the software component of the matrix-vector product

scholarly journals Macroporous chitosan/methoxypoly(ethylene glycol) based cryosponges with unique morphology for tissue engineering applications

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Pradeep Kumar ◽  
Viness Pillay ◽  
Yahya E. Choonara
Keyword(s):  
Tissue Engineering ◽  
Polymer Network ◽  
Three Dimensional ◽  
Hysteresis Loops ◽  
Interpenetrating Polymer Network ◽  
Morphological Data ◽  
Porous Scaffolds ◽  
Morphological Variations ◽  
Molecular Stability ◽  
The Matrix

AbstractThree-dimensional porous scaffolds are widely employed in tissue engineering and regenerative medicine for their ability to carry bioactives and cells; and for their platform properties to allow for bridging-the-gap within an injured tissue. This study describes the effect of various methoxypolyethylene glycol (mPEG) derivatives (mPEG (-OCH3 functionality), mPEG-aldehyde (mPEG-CHO) and mPEG-acetic acid (mPEG-COOH)) on the morphology and physical properties of chemically crosslinked, semi-interpenetrating polymer network (IPN), chitosan (CHT)/mPEG blend cryosponges. Physicochemical and molecular characterization revealed that the –CHO and –COOH functional groups in mPEG derivatives interacted with the –NH2 functionality of the chitosan chain. The distinguishing feature of the cryosponges was their unique morphological features such as fringe thread-, pebble-, curved quartz crystal-, crystal flower-; and canyon-like structures. The morphological data was well corroborated by the image processing data and physisorption curves corresponding to Type II isotherm with open hysteresis loops. Functionalization of mPEG had no evident influence on the macro-mechanical properties of the cryosponges but increased the matrix strength as determined by the rheomechanical analyses. The cryosponges were able to deliver bioactives (dexamethasone and curcumin) over 10 days, showed varied matrix degradation profiles, and supported neuronal cells on the matrix surface. In addition, in silico simulations confirmed the compatibility and molecular stability of the CHT/mPEG blend compositions. In conclusion, the study confirmed that significant morphological variations may be induced by minimal functionalization and crosslinking of biomaterials.

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