Our group's research is focused at the intersection of mechanics and biology. We are interested in elucidating the underlying molecular mechanisms that give rise to the complex mechanical properties of cells, extracellular matrices, and tissues . Conversely, we are investigating how complex mechanical cues influence important biological processes such as cell division, differentiation, or cancer progression. Our approaches involve using force measurement instrumentation, such as atomic force microscopy, to exert and measure forces on materials and cells at the nanoscale, and the development of material systems for 3D cell culture that allow precise and independent manipulation of mechanical properties.
Member, Bio-X (2013 - Present)
Assistant Professor, Department of Mechanical Engineering (2013 - Present)
Honors & Awards
CAREER Award, National Science Foundation (2019)
Rising Star award, Biomedical Engineering Society, Cell and Molecular Bioengineering group (2019)
MERIT award, National Cancer Institute (2018)
Hellman Faculty Scholar, Hellman Fellows Fund (2015)
National Academy of Engineering Frontiers in Engineering Symposium, National Academy of Engineering (2015)
Young Faculty Award, DARPA (2014 - 2016)
National Research Service Award, National Institutes of Health (2010 - 2013)
National Science Foundation Graduate Fellow, National Science Foundation (2006 - 2009)
Graduate Research Award, Biomedical Engineering Society (2006)
National Defense Science and Engineering Graduate Fellow, American Society for Engineering Education (2003 - 2006)
Engineering Science Departmental Citation, University of California, Berkeley (2002)
Engineering Science Departmental Citation, University of California, Berkeley (2001)
Postdoctoral Fellow, Harvard University, Biomaterials (2013)
Ph.D., University of California, Berkeley and San Francisco, Bioengineering (2009)
B.S., University of California, Berkeley, Engineering Physics (2003)
- Introduction to Biomechanics and Mechanobiology
ME 283 (Spr)
- Mechanics of Materials
ME 80 (Win)
- Mechanotransduction in Cells and Tissues
BIOE 283, BIOPHYS 244, ME 244 (Aut)
Independent Studies (12)
- Directed Investigation
BIOE 392 (Aut, Win, Spr, Sum)
- Directed Reading in Biophysics
BIOPHYS 399 (Win, Spr, Sum)
- Engineering Problems
ME 391 (Aut, Win, Spr, Sum)
- Engineering Problems and Experimental Investigation
ME 191 (Aut, Win, Spr)
- Experimental Investigation of Engineering Problems
ME 392 (Aut, Win, Spr, Sum)
- Graduate Research
BIOPHYS 300 (Win, Spr)
- Honors Research
ME 191H (Aut, Win, Spr)
- Ph.D. Research Rotation
ME 398 (Aut, Win, Spr)
- Ph.D. Teaching Experience
ME 491 (Aut, Win, Spr)
- Practical Training
ME 299A (Aut, Win, Spr, Sum)
- Practical Training
ME 299B (Win, Spr)
- Undergraduate Research
MED 199 (Win, Spr, Sum)
- Directed Investigation
Prior Year Courses
- Mechanics of Materials
ME 80 (Win)
- Mechanotransduction in Cells and Tissues
BIOE 283, BIOPHYS 244, ME 244 (Aut)
- Biomechanical Research Symposium
ME 389 (Aut)
- Introduction to Biomechanics and Mechanobiology
ME 283 (Spr)
- Mechanics of Materials
ME 80 (Win)
- Mechanotransduction in Cells and Tissues
BIOE 283, BIOPHYS 244, ME 244 (Aut)
- Mechanics of Materials
Doctoral Dissertation Reader (AC)
Lucas Blauch, Joy Franco, Bauer LeSavage, Chris Lindsay, Aliyeh Mousavi, Alice Stanton
Doctoral Dissertation Advisor (AC)
Omokolade Adebowale, Julie Chang, Frank Charbonier, Vivek Gupta, Dhiraj Indana, Wing-Sum Law, Hong-pyo Lee
Master's Program Advisor
Zonghe Chua, Joy Franco, Vivek Gupta, Jessica Hsueh, Emma Luengo, Oscar Molina, Matthew Park, Radhika Pramod Patil
Doctoral Dissertation Co-Advisor (AC)
Laurel Kroo, Yung-Hao Lin
Matrix stiffness induces a tumorigenic phenotype in mammary epithelium through changes in chromatin accessibility.
Nature biomedical engineering
In breast cancer, the increased stiffness of the extracellular matrix is a key driver of malignancy. Yet little is known about the epigenomic changes that underlie the tumorigenic impact of extracellular matrix mechanics. Here, we show in a three-dimensional culture model of breast cancer that stiff extracellular matrix induces a tumorigenic phenotype through changes in chromatin state. We found that increased stiffness yielded cells with more wrinkled nuclei and with increased lamina-associated chromatin, that cells cultured in stiff matrices displayed more accessible chromatin sites, which exhibited footprints of Sp1 binding, and that this transcription factor acts along with the histone deacetylases 3 and 8 to regulate the induction of stiffness-mediated tumorigenicity. Just as cell culture on soft environments or in them rather than on tissue-culture plastic better recapitulates the acinar morphology observed in mammary epithelium in vivo, mammary epithelial cells cultured on soft microenvironments or in them also more closely replicate the in vivo chromatin state. Our results emphasize the importance of culture conditions for epigenomic studies, and reveal that chromatin state is a critical mediator of mechanotransduction.
View details for DOI 10.1038/s41551-019-0420-5
View details for PubMedID 31285581
- YAP-independent mechanotransduction drives breast cancer progression NATURE COMMUNICATIONS 2019; 10
Volume expansion and TRPV4 activation regulate stem cell fate in three-dimensional microenvironments.
2019; 10 (1): 529
For mesenchymal stem cells (MSCs) cultured in three dimensional matrices, matrix remodeling is associated with enhanced osteogenic differentiation. However, the mechanism linking matrix remodeling in 3D to osteogenesis of MSCs remains unclear. Here, we find that MSCs in viscoelastic hydrogels exhibit volume expansion during cell spreading, and greater volume expansion is associated with enhanced osteogenesis. Restriction of expansion by either hydrogels with slow stress relaxation or increased osmotic pressure diminishes osteogenesis, independent of cell morphology. Conversely, induced expansion by hypoosmotic pressure accelerates osteogenesis. Volume expansion is mediated by activation of TRPV4 ion channels, and reciprocal feedback between TRPV4 activation and volume expansion controls nuclear localization of RUNX2, but not YAP, to promote osteogenesis. This work demonstrates the role of cell volume in regulating cell fate in 3D culture, and identifies TRPV4 as a molecular sensor of matrix viscoelasticity that regulates osteogenic differentiation.
View details for PubMedID 30705265
Cell cycle progression in confining microenvironments is regulated by a growth-responsive TRPV4-PI3K/Akt-p27Kip1 signaling axis.
2019; 5 (8): eaaw6171
In tissues, cells reside in confining microenvironments, which may mechanically restrict the ability of a cell to double in size as it prepares to divide. How confinement affects cell cycle progression remains unclear. We show that cells progressed through the cell cycle and proliferated when cultured in hydrogels exhibiting fast stress relaxation but were mostly arrested in the G0/G1 phase of the cell cycle when cultured in hydrogels that exhibit slow stress relaxation. In fast-relaxing gels, activity of stretch-activated channels (SACs), including TRPV4, promotes activation of the phosphatidylinositol 3-kinase (PI3K)/Akt pathway, which in turn drives cytoplasmic localization of the cell cycle inhibitor p27Kip1, thereby allowing S phase entry and proliferation. Cell growth during G1 activated the TRPV4-PI3K/Akt-p27Kip1 signaling axis, but growth is inhibited in the confining slow-relaxing hydrogels. Thus, in confining microenvironments, cells sense when growth is sufficient for division to proceed through a growth-responsive signaling axis mediated by SACs.
View details for DOI 10.1126/sciadv.aaw6171
View details for PubMedID 31457089
View details for PubMedCentralID PMC6685709
Matrix mechanical plasticity regulates cancer cell migration through confining microenvironments.
2018; 9 (1): 4144
Studies of cancer cell migration have found two modes: one that is protease-independent, requiring micron-sized pores or channels for cells to squeeze through, and one that is protease-dependent, relevant for confining nanoporous matrices such as basement membranes (BMs). However, many extracellular matrices exhibit viscoelasticity and mechanical plasticity, irreversibly deforming in response to force, so that pore size may be malleable. Here we report the impact of matrix plasticity on migration. We develop nanoporous and BM ligand-presenting interpenetrating network (IPN) hydrogels in which plasticity could be modulated independent of stiffness. Strikingly, cells in high plasticity IPNs carry out protease-independent migration through the IPNs. Mechanistically, cells in high plasticity IPNs extend invadopodia protrusions to mechanically and plastically open up micron-sized channels and then migrate through them. These findings uncover a new mode of protease-independent migration, in which cells can migrate through confining matrix if it exhibits sufficient mechanical plasticity.
View details for PubMedID 30297715
- Mitotic cells generate protrusive extracellular forces to divide in three-dimensional microenvironments NATURE PHYSICS 2018; 14 (6): 621-+
Mechanical confinement regulates cartilage matrix formation by chondrocytes.
2017; 16 (12): 1243–51
Cartilage tissue equivalents formed from hydrogels containing chondrocytes could provide a solution for replacing damaged cartilage. Previous approaches have often utilized elastic hydrogels. However, elastic stresses may restrict cartilage matrix formation and alter the chondrocyte phenotype. Here we investigated the use of viscoelastic hydrogels, in which stresses are relaxed over time and which exhibit creep, for three-dimensional (3D) culture of chondrocytes. We found that faster relaxation promoted a striking increase in the volume of interconnected cartilage matrix formed by chondrocytes. In slower relaxing gels, restriction of cell volume expansion by elastic stresses led to increased secretion of IL-1β, which in turn drove strong up-regulation of genes associated with cartilage degradation and cell death. As no cell-adhesion ligands are presented by the hydrogels, these results reveal cell sensing of cell volume confinement as an adhesion-independent mechanism of mechanotransduction in 3D culture, and highlight stress relaxation as a key design parameter for cartilage tissue engineering.
View details for PubMedID 28967913
Strain-enhanced stress relaxation impacts nonlinear elasticity in collagen gels
PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA
2016; 113 (20): 5492-5497
The extracellular matrix (ECM) is a complex assembly of structural proteins that provides physical support and biochemical signaling to cells in tissues. The mechanical properties of the ECM have been found to play a key role in regulating cell behaviors such as differentiation and malignancy. Gels formed from ECM protein biopolymers such as collagen or fibrin are commonly used for 3D cell culture models of tissue. One of the most striking features of these gels is that they exhibit nonlinear elasticity, undergoing strain stiffening. However, these gels are also viscoelastic and exhibit stress relaxation, with the resistance of the gel to a deformation relaxing over time. Recent studies have suggested that cells sense and respond to both nonlinear elasticity and viscoelasticity of ECM, yet little is known about the connection between nonlinear elasticity and viscoelasticity. Here, we report that, as strain is increased, not only do biopolymer gels stiffen but they also exhibit faster stress relaxation, reducing the timescale over which elastic energy is dissipated. This effect is not universal to all biological gels and is mediated through weak cross-links. Mechanistically, computational modeling and atomic force microscopy (AFM) indicate that strain-enhanced stress relaxation of collagen gels arises from force-dependent unbinding of weak bonds between collagen fibers. The broader effect of strain-enhanced stress relaxation is to rapidly diminish strain stiffening over time. These results reveal the interplay between nonlinear elasticity and viscoelasticity in collagen gels, and highlight the complexity of the ECM mechanics that are likely sensed through cellular mechanotransduction.
View details for DOI 10.1073/pnas.1523906113
View details for Web of Science ID 000375977600024
View details for PubMedID 27140623
View details for PubMedCentralID PMC4878492
Hydrogels with tunable stress relaxation regulate stem cell fate and activity
2016; 15 (3): 326-?
Natural extracellular matrices (ECMs) are viscoelastic and exhibit stress relaxation. However, hydrogels used as synthetic ECMs for three-dimensional (3D) culture are typically elastic. Here, we report a materials approach to tune the rate of stress relaxation of hydrogels for 3D culture, independently of the hydrogel's initial elastic modulus, degradation, and cell-adhesion-ligand density. We find that cell spreading, proliferation, and osteogenic differentiation of mesenchymal stem cells (MSCs) are all enhanced in cells cultured in gels with faster relaxation. Strikingly, MSCs form a mineralized, collagen-1-rich matrix similar to bone in rapidly relaxing hydrogels with an initial elastic modulus of 17 kPa. We also show that the effects of stress relaxation are mediated by adhesion-ligand binding, actomyosin contractility and mechanical clustering of adhesion ligands. Our findings highlight stress relaxation as a key characteristic of cell-ECM interactions and as an important design parameter of biomaterials for cell culture.
View details for DOI 10.1038/NMAT4489
View details for PubMedID 26618884
Substrate stress relaxation regulates cell spreading.
2015; 6: 6364-?
Studies of cellular mechanotransduction have converged upon the idea that cells sense extracellular matrix (ECM) elasticity by gauging resistance to the traction forces they exert on the ECM. However, these studies typically utilize purely elastic materials as substrates, whereas physiological ECMs are viscoelastic, and exhibit stress relaxation, so that cellular traction forces exerted by cells remodel the ECM. Here we investigate the influence of ECM stress relaxation on cell behaviour through computational modelling and cellular experiments. Surprisingly, both our computational model and experiments find that spreading for cells cultured on soft substrates that exhibit stress relaxation is greater than cells spreading on elastic substrates of the same modulus, but similar to that of cells spreading on stiffer elastic substrates. These findings challenge the current view of how cells sense and respond to the ECM.
View details for DOI 10.1038/ncomms7365
View details for PubMedID 25695512
- Extracellular matrix stiffness and composition jointly regulate the induction of malignant phenotypes in mammary epithelium NATURE MATERIALS 2014; 13 (10): 970-978
Reversible stress softening of actin networks
2007; 445 (7125): 295-298
The mechanical properties of cells play an essential role in numerous physiological processes. Organized networks of semiflexible actin filaments determine cell stiffness and transmit force during mechanotransduction, cytokinesis, cell motility and other cellular shape changes. Although numerous actin-binding proteins have been identified that organize networks, the mechanical properties of actin networks with physiological architectures and concentrations have been difficult to measure quantitatively. Studies of mechanical properties in vitro have found that crosslinked networks of actin filaments formed in solution exhibit stress stiffening arising from the entropic elasticity of individual filaments or crosslinkers resisting extension. Here we report reversible stress-softening behaviour in actin networks reconstituted in vitro that suggests a critical role for filaments resisting compression. Using a modified atomic force microscope to probe dendritic actin networks (like those formed in the lamellipodia of motile cells), we observe stress stiffening followed by a regime of reversible stress softening at higher loads. This softening behaviour can be explained by elastic buckling of individual filaments under compression that avoids catastrophic fracture of the network. The observation of both stress stiffening and softening suggests a complex interplay between entropic and enthalpic elasticity in determining the mechanical properties of actin networks.
View details for DOI 10.1038/nature05459
View details for Web of Science ID 000243504700040
View details for PubMedID 17230186
Multi-scale cellular engineering: From molecules to organ-on-a-chip.
2020; 4 (1): 010906
Recent technological advances in cellular and molecular engineering have provided new insights into biology and enabled the design, manufacturing, and manipulation of complex living systems. Here, we summarize the state of advances at the molecular, cellular, and multi-cellular levels using experimental and computational tools. The areas of focus include intrinsically disordered proteins, synthetic proteins, spatiotemporally dynamic extracellular matrices, organ-on-a-chip approaches, and computational modeling, which all have tremendous potential for advancing fundamental and translational science. Perspectives on the current limitations and future directions are also described, with the goal of stimulating interest to overcome these hurdles using multi-disciplinary approaches.
View details for DOI 10.1063/1.5129788
View details for PubMedID 32161833
View details for PubMedCentralID PMC7054123
Identification of cell context-dependent YAP-associated proteins reveals beta1 and beta4 integrin mediate YAP translocation independently of cell spreading.
2019; 9 (1): 17188
Yes-associated protein (YAP) is a transcriptional regulator and mechanotransducer, relaying extracellular matrix (ECM) stiffness into proliferative gene expression in 2D culture. Previous studies show that YAP activation is dependent on F-actin stress fiber mediated nuclear pore opening, however the protein mediators of YAP translocation remain unclear. Here, we show that YAP co-localizes with F-actin during activating conditions, such as sparse plating and culturing on stiff 2D substrates. To identify proteins mediating YAP translocation, we performed co-immunoprecipitation followed by mass spectrometry (co-IP/MS) for proteins that differentially associated with YAP under activating conditions. Interestingly, YAP preferentially associates with beta1 integrin under activating conditions, and beta4 integrin under inactivating conditions. In activating conditions, CRISPR/Cas9 knockout (KO) of beta1 integrin (DeltaITGB1) resulted in decreased cell area, which correlated with decreased YAP nuclear localization. DeltaITGB1 did not significantly affect the slope of the correlation between YAP nuclear localization with area, but did decrease overall nuclear YAP independently of cell spreading. In contrast, beta4 integrin KO (DeltaITGB4) cells showed no change in cell area and similarly decreased nuclear YAP. These results reveal proteins that differentially associate with YAP during activation, which may aid in regulating YAP nuclear translocation.
View details for DOI 10.1038/s41598-019-53659-4
View details for PubMedID 31748579
Beyond proteases: Basement membrane mechanics and cancer invasion.
The Journal of cell biology
In epithelial cancers, cells must invade through basement membranes (BMs) to metastasize. The BM, a thin layer of extracellular matrix underlying epithelial and endothelial tissues, is primarily composed of laminin and collagen IV and serves as a structural barrier to cancer cell invasion, intravasation, and extravasation. BM invasion has been thought to require protease degradation since cells, which are typically on the order of 10 m in size, are too large to squeeze through the nanometer-scale pores of the BM. However, recent studies point toward a more complex picture, with physical forces generated by cancer cells facilitating protease-independent BM invasion. Moreover, collective cell interactions, proliferation, cancer-associated fibroblasts, myoepithelial cells, and immune cells are all implicated in regulating BM invasion through physical forces. A comprehensive understanding of BM structure and mechanics and diverse modes of BM invasion may yield new strategies for blocking cancer progression and metastasis.
View details for DOI 10.1083/jcb.201903066
View details for PubMedID 31315943
The evolution of spindles and their mechanical implications for cancer metastasis.
Cell cycle (Georgetown, Tex.)
The mitotic spindle has long been known to play a crucial role in mitosis, orchestrating the segregation of chromosomes into two daughter cells during mitosis with high fidelity. Intracellular forces generated by the mitotic spindle are increasingly well understood, and recent work has revealed that the efficiency and the accuracy of mitosis is ensured by the scaling of mitotic spindle size with cell size. However, the role of the spindle in cancer progression has largely been ignored. Two recent studies point toward the role of mitotic spindle evolution in cancer progression through extracellular force generation. Cancer cells with lengthened spindles exhibit highly increased metastatic potential. Further, interpolar spindle elongation drives protrusive extracellular force generation along the mitotic axis to allow mitotic elongation, a morphological change that is required for cell division. Together, these findings open a new research area studying the role of the mitotic spindle evolution in cancer metastasis.
View details for DOI 10.1080/15384101.2019.1632137
View details for PubMedID 31234701
- Varying PEG density to control stress relaxation in alginate-PEG hydrogels for 3D cell culture studies BIOMATERIALS 2019; 200: 15–24
Varying PEG density to control stress relaxation in alginate-PEG hydrogels for 3D cell culture studies.
2019; 200: 15–24
Hydrogels are commonly used as artificial extracellular matrices for 3D cell culture and for tissue engineering. Viscoelastic hydrogels with tunable stress relaxation have recently been developed, and stress relaxation in the hydrogels has been found to play a key role in regulating cell behaviors such as differentiation, spreading, and proliferation. Here we report a simple but precise materials approach to tuning stress relaxation of alginate hydrogels with polyethylene glycol (PEG) covalently grafted onto the alginate. Hydrogel relaxation was modulated independent of the initial elastic modulus by varying molecular weight and concentration of PEG along with calcium crosslinking of the alginate. Increased concentration and molecular weight of the PEG resulted in faster stress relaxation, a higher loss modulus, and increased creep. Interestingly, we found that stress relaxation of the hydrogels is determined by the total mass amount of PEG in the hydrogel, and not the molecular weight or concentration of PEG chains alone. We then evaluated the utility of these hydrogels for 3D cell culture. Faster relaxation in RGD-coupled alginate-PEG hydrogels led to increased spreading and proliferation of fibroblasts, and enhanced osteogenic differentiation of mesenchymal stem cells (MSCs). Thus, this work establishes a new materials approach to tuning stress relaxation in alginate hydrogels for 3D cell culture.
View details for PubMedID 30743050
YAP-independent mechanotransduction drives breast cancer progression.
2019; 10 (1): 1848
Increased tissue stiffness is a driver of breast cancer progression. The transcriptional regulator YAP is considered a universal mechanotransducer, based largely on 2D culture studies. However, the role of YAP during in vivo breast cancer remains unclear. Here, we find that mechanotransduction occurs independently of YAP in breast cancer patient samples and mechanically tunable 3D cultures. Mechanistically, the lack of YAP activity in 3D culture and in vivo is associated with the absence of stress fibers and an order of magnitude decrease in nuclear cross-sectional area relative to 2D culture. This work highlights the context-dependent role of YAP in mechanotransduction, and establishes that YAP does not mediate mechanotransduction in breast cancer.
View details for PubMedID 31015465
Covalent cross-linking of basement membrane-like matrices physically restricts invasive protrusions in breast cancer cells.
Matrix biology : journal of the International Society for Matrix Biology
The basement membrane (BM) provides a physical barrier to invasion in epithelial tumors, and alterations in the molecular makeup and structural integrity of the BM have been implicated in cancer progression. Invadopodia are the invasive protrusions that enable cancer cells to breach the nanoporous basement membrane, through matrix degradation and generation of force. However, the impact of covalent cross-linking on invadopodia extension into the BM remains unclear. Here, we examine the impact of covalent cross-linking of extracellular matrix on invasive protrusions using biomaterials that present ligands relevant to the basement membrane and provide a nanoporous, confining microenvironment. We find that increased covalent cross-linking of reconstituted basement membrane (rBM) matrix diminishes matrix mechanical plasticity, or the ability of the matrix to permanently retain deformation due to force. Covalently cross-linked rBM matrices, and rBM-alginate interpenetrating networks (IPNs) with covalent cross-links and low plasticity, restrict cell spreading and protrusivity. The reduced spreading and reduced protrusivity in response to low mechanical plasticity occurred independent of proteases. Mechanistically, our computational model reveals that the reduction in mechanical plasticity due to covalent cross-linking is sufficient to mechanically prevent cell protrusions from extending, independent of the impact of covalent cross-linking or matrix mechanical plasticity on cell signaling pathways. These findings highlight the biophysical role of covalent cross-linking in regulating basement membrane plasticity, as well as cancer cell invasion of this confining tissue layer.
View details for DOI 10.1016/j.matbio.2019.05.006
View details for PubMedID 31163245
- p300 and STAT3 drive YAP-independent mechanotransduction during breast cancer invasion AMER ASSOC CANCER RESEARCH. 2018
Dynamic Hyaluronan Hydrogels with Temporally Modulated High Injectability and Stability Using a Biocompatible Catalyst.
Advanced materials (Deerfield Beach, Fla.)
2018; 30 (22): e1705215
Injectable and biocompatible hydrogels have become increasingly important for cell transplantation to provide mechanical protection of cells during injection and a stable scaffold for cell adhesion post-injection. Injectable hydrogels need to be easily pushed through a syringe needle and quickly recover to a gel state, thus generally requiring noncovalent or dynamic cross-linking. However, a dilemma exists in the design of dynamic hydrogels: hydrogels with fast exchange of cross-links are easier to eject using less force, but lack long-term stability; in contrast, slow exchange of cross-links improves stability, but compromises injectability and thus the ability to protect cells under flow. A new concept to resolve this dilemma using a biocompatible catalyst to modulate the dynamic properties of hydrogels at different time points of application to have both high injectability and high stability is presented. Hyaluronic acid based hydrogels are formed through dynamic covalent hydrazone cross-linking in the presence of a biocompatible benzimidazole-based catalyst. The catalyst accelerates the formation and exchange of hydrazone bonds, enhancing injectability, but rapidly diffuses away from the hydrogel after injection to retard the exchange and improve the long-term stability for cell culture.
View details for PubMedID 29682801
Matching material and cellular timescales maximizes cell spreading on viscoelastic substrates
PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA
2018; 115 (12): E2686–E2695
Recent evidence has shown that, in addition to rigidity, the viscous response of the extracellular matrix (ECM) significantly affects the behavior and function of cells. However, the mechanism behind such mechanosensitivity toward viscoelasticity remains unclear. In this study, we systematically examined the dynamics of motor clutches (i.e., focal adhesions) formed between the cell and a viscoelastic substrate using analytical methods and direct Monte Carlo simulation. Interestingly, we observe that, for low ECM rigidity, maximum cell spreading is achieved at an optimal level of viscosity in which the substrate relaxation time falls between the timescale for clutch binding and its characteristic binding lifetime. That is, viscosity serves to stiffen soft substrates on a timescale faster than the clutch off-rate, which enhances cell-ECM adhesion and cell spreading. On the other hand, for substrates that are stiff, our model predicts that viscosity will not influence cell spreading, since the bound clutches are saturated by the elevated stiffness. The model was tested and validated using experimental measurements on three different material systems and explained the different observed effects of viscosity on each substrate. By capturing the mechanism by which substrate viscoelasticity affects cell spreading across a wide range of material parameters, our analytical model provides a useful tool for designing biomaterials that optimize cellular adhesion and mechanosensing.
View details for PubMedID 29507238
- Regulation of Breast Cancer Progression by Extracellular Matrix Mechanics: Insights from 3D Culture Models ACS BIOMATERIALS SCIENCE & ENGINEERING 2018; 4 (2): 302–13
Mechanisms of Plastic Deformation in Collagen Networks Induced by Cellular Forces
2018; 114 (2): 450–61
Contractile cells can reorganize fibrous extracellular matrices and form dense tracts of fibers between neighboring cells. These tracts guide the development of tubular tissue structures and provide paths for the invasion of cancer cells. Here, we studied the mechanisms of the mechanical plasticity of collagen tracts formed by contractile premalignant acinar cells and fibroblasts. Using fluorescence microscopy and second harmonic generation, we quantified the collagen densification, fiber alignment, and strains that remain within the tracts after cellular forces are abolished. We explained these observations using a theoretical fiber network model that accounts for the stretch-dependent formation of weak cross-links between nearby fibers. We tested the predictions of our model using shear rheology experiments. Both our model and rheological experiments demonstrated that increasing collagen concentration leads to substantial increases in plasticity. We also considered the effect of permanent elongation of fibers on network plasticity and derived a phase diagram that classifies the dominant mechanisms of plasticity based on the rate and magnitude of deformation and the mechanical properties of individual fibers. Plasticity is caused by the formation of new cross-links if moderate strains are applied at small rates or due to permanent fiber elongation if large strains are applied over short periods. Finally, we developed a coarse-grained model for plastic deformation of collagen networks that can be employed to simulate multicellular interactions in processes such as morphogenesis, cancer invasion, and fibrosis.
View details for PubMedID 29401442
View details for PubMedCentralID PMC5984980
Stress Relaxing Hyaluronic Acid-Collagen Hydrogels Promote Cell Spreading, Fiber Remodeling, and Focal Adhesion Formation in 3D Cell Culture
2018; 154: 213-222
View details for DOI 10.1016/j.biomaterials.2017.11.004
Viscoelastic hydrogels for 3D cell culture.
In tissues, many cells are surrounded by and interact with a three-dimensional soft extracellular matrix (ECM). Both the physical and biochemical properties of the ECM play a major role in regulating cell behaviours. To better understand the impact of ECM properties on cell behaviours, natural and synthetic hydrogels have been developed for use as synthetic ECMs for 3D cell culture. It has long been known that ECM and tissues are viscoelastic, or display a time-dependent response to deformation or mechanical loading, exhibiting stress relaxation and creep. However, only recently have there been efforts made to understand the role of the time-dependent aspects of the ECM mechanics on regulating cell behaviours using hydrogels for 3D culture. Here we review the characterization and molecular basis of hydrogel viscoelasticity and plasticity, and describe newly developed approaches to tuning viscoelasticity in hydrogels for 2D and 3D culture. Then we highlight several recent studies finding a potent impact of hydrogel stress relaxation or creep on cell behaviours such as cell spreading, proliferation, and differentiation of mesenchymal stem cells. The role of time-dependent mechanics on cell biology remains largely unclear, and ripe for further exploration. Further elucidation of this topic may substantially advance our understanding of cell-matrix interactions during development, homeostasis, wound healing, and disease, and guide the design of biomaterials for regenerative medicine.
View details for DOI 10.1039/c7bm00261k
View details for PubMedID 28584885
Stress relaxing hyaluronic acid-collagen hydrogels promote cell spreading, fiber remodeling, and focal adhesion formation in 3D cell culture.
2017; 154: 213–22
The physical and architectural cues of the extracellular matrix (ECM) play a critical role in regulating important cellular functions such as spreading, migration, proliferation, and differentiation. Natural ECM is a complex viscoelastic scaffold composed of various distinct components that are often organized into a fibrillar microstructure. Hydrogels are frequently used as synthetic ECMs for 3D cell culture, but are typically elastic, due to covalent crosslinking, and non-fibrillar. Recent work has revealed the importance of stress relaxation in viscoelastic hydrogels in regulating biological processes such as spreading and differentiation, but these studies all utilize synthetic ECM hydrogels that are non-fibrillar. Key mechanotransduction events, such as focal adhesion formation, have only been observed in fibrillar networks in 3D culture to date. Here we present an interpenetrating network (IPN) hydrogel system based on HA crosslinked with dynamic covalent bonds and collagen I that captures the viscoelasticity and fibrillarity of ECM in tissues. The IPN hydrogels exhibit two distinct processes in stress relaxation, one from collagen and the other from HA crosslinking dynamics. Stress relaxation in the IPN hydrogels can be tuned by modulating HA crosslinker affinity, molecular weight of the HA, or HA concentration. Faster relaxation in the IPN hydrogels promotes cell spreading, fiber remodeling, and focal adhesion (FA) formation - behaviors often inhibited in other hydrogel-based materials in 3D culture. This study presents a new, broadly adaptable materials platform for mimicking key ECM features of viscoelasticity and fibrillarity in hydrogels for 3D cell culture and sheds light on how these mechanical and structural cues regulate cell behavior.
View details for PubMedID 29132046
3D Cell Culture in Interpenetrating Networks of Alginate and rBM Matrix.
Methods in molecular biology (Clifton, N.J.)
2017; 1612: 29–37
Altered tissue mechanical properties have been implicated in many key physiological and pathological processes. Hydrogel-based materials systems, made with native extracellular matrix (ECM) proteins, nonnative biopolymers, or synthetic polymers are often used to study these processes in vitro in 3D cell culture experiments. However, each of these materials systems present major limitations when used in mechanobiological studies. While native ECM-based hydrogels may enable good recapitulation of physiological behavior, the mechanics of these hydrogels are often manipulated by increasing or decreasing the protein concentration. This manipulation changes cell adhesion ligand density, thereby altering cell signaling. Alternatively, synthetic polymer-based hydrogels and nonnative biopolymer-based hydrogels can be mechanically tuned and engineered to present cell adhesion peptide motifs, but still may not fully promote physiologically relevant behavior. Here, we combine the advantages of native ECM proteins and nonnative biopolymers in interpenetrating network (IPN) hydrogels consisting of rBM matrix, which contains ligands native to epithelial basement membrane, and alginate, an inert biopolymer derived from seaweed. The following protocol details the generation of IPNs for mechanical testing or for 3D cell culture. This biomaterial system offers the ability to tune the stiffness of the 3D microenvironment without altering cell adhesion ligand concentration or pore size.
View details for PubMedID 28634933
Maintenance of neural progenitor cell stemness in 3D hydrogels requires matrix remodelling.
2017; 16 (12): 1233–42
Neural progenitor cell (NPC) culture within three-dimensional (3D) hydrogels is an attractive strategy for expanding a therapeutically relevant number of stem cells. However, relatively little is known about how 3D material properties such as stiffness and degradability affect the maintenance of NPC stemness in the absence of differentiation factors. Over a physiologically relevant range of stiffness from ∼0.5 to 50 kPa, stemness maintenance did not correlate with initial hydrogel stiffness. In contrast, hydrogel degradation was both correlated with, and necessary for, maintenance of NPC stemness. This requirement for degradation was independent of cytoskeletal tension generation and presentation of engineered adhesive ligands, instead relying on matrix remodelling to facilitate cadherin-mediated cell-cell contact and promote β-catenin signalling. In two additional hydrogel systems, permitting NPC-mediated matrix remodelling proved to be a generalizable strategy for stemness maintenance in 3D. Our findings have identified matrix remodelling, in the absence of cytoskeletal tension generation, as a previously unknown strategy to maintain stemness in 3D.
View details for PubMedID 29115291
Evaluation of a bioengineered construct for tissue engineering applications.
Journal of biomedical materials research. Part B, Applied biomaterials
Effective biomaterial options for tissue repair and regeneration are limited. Current biologic meshes are derived from different tissue sources and are generally sold as decellularized tissues. This work evaluated two collagen based bioengineered constructs and a commercial product in a model of abdominal full thickness defect repair. To prepare the bioengineered construct, collagen type 1 from porcine skin was isolated using an acid solubilization method. After purification, the collagen was formed into collagen sheets that were physically bonded to form a mechanically robust construct that was subsequently laser micropatterned with pores as a means to promote tissue integration (collagen only construct). A second engineered construct consisted of the aforementioned collagen construct embedded in an RGD-functionalized alginate gel that serves as a bioactive interface (collagen-alginate construct). The commercial product is a biologic mesh derived from bovine pericardium (Veritas® ). We observed enhanced vascularization in the midportion of the engineered collagen-alginate construct 2 weeks after implantation. Overall, the performance of the bioengineered constructs was similar to that of the commercial product with comparable integration strength at 8 weeks. Bioengineered constructs derived from monomeric collagen demonstrate promise for a variety of load bearing applications in tissue engineering. © 2017 Wiley Periodicals, Inc. J Biomed Mater Res Part B: Appl Biomater, 2017.
View details for DOI 10.1002/jbm.b.34042
View details for PubMedID 29130596
Viscoplasticity Enables Mechanical Remodeling of Matrix by Cells
2016; 111 (10): 2296-2308
Living tissues consist largely of cells and extracellular matrices (ECMs). The mechanical properties of ECM have been found to play a key role in regulating cell behaviors such as migration, proliferation, and differentiation. Although most studies to date have focused on elucidating the impact of matrix elasticity on cell behaviors, recent studies have revealed an impact of matrix viscoelasticity on cell behaviors and reported plastic remodeling of ECM by cells. In this study, we rigorously characterized the plasticity in materials commonly used for cell culture. This characterization of plasticity revealed time-dependent plasticity, or viscoplasticity, in collagen gels, reconstituted basement membrane matrix, agarose gels, alginate gels, and fibrin gels, but not in polyacrylamide gels. Viscoplasticity was associated with gels that contained weak bonds, and covalent cross-linking diminished viscoplasticity in collagen and alginate gels. Interestingly, the degree of plasticity was found to be nonlinear, or dependent on the magnitude of stress or strain, in collagen gels, but not in the other viscoplastic materials. Viscoplastic models were employed to describe plasticity in the viscoplastic materials. Relevance of matrix viscoplasticity to cell-matrix interactions was established through a quantitative assessment of plastic remodeling of collagen gels by cells. Plastic remodeling of collagen gels was found to be dependent on cellular force, mediated through integrin-based adhesions, and occurred even with inhibition of proteolytic degradation of the matrix. Together, these results reveal that matrix viscoplasticity facilitates plastic remodeling of matrix by cellular forces.
View details for DOI 10.1016/j.bpj.2016.10.002
View details for Web of Science ID 000388545600020
View details for PubMedID 27851951
- CD44 alternative splicing in gastric cancer cells is regulated by culture dimensionality and matrix stiffness BIOMATERIALS 2016; 98: 152-162
Matrix elasticity of void-forming hydrogels controls transplanted-stem-cell-mediated bone formation
2015; 14 (12): 1269-1277
The effectiveness of stem cell therapies has been hampered by cell death and limited control over fate. These problems can be partially circumvented by using macroporous biomaterials that improve the survival of transplanted stem cells and provide molecular cues to direct cell phenotype. Stem cell behaviour can also be controlled in vitro by manipulating the elasticity of both porous and non-porous materials, yet translation to therapeutic processes in vivo remains elusive. Here, by developing injectable, void-forming hydrogels that decouple pore formation from elasticity, we show that mesenchymal stem cell (MSC) osteogenesis in vitro, and cell deployment in vitro and in vivo, can be controlled by modifying, respectively, the hydrogel's elastic modulus or its chemistry. When the hydrogels were used to transplant MSCs, the hydrogel's elasticity regulated bone regeneration, with optimal bone formation at 60 kPa. Our findings show that biophysical cues can be harnessed to direct therapeutic stem cell behaviours in situ.
View details for DOI 10.1038/NMAT4407
View details for Web of Science ID 000365839000025
View details for PubMedID 26366848
View details for PubMedCentralID PMC4654683
Engineered composite fascia for stem cell therapy in tissue repair applications.
2015; 26: 1-12
A critical challenge in tissue regeneration is to develop constructs that effectively integrate with the host tissue. Here, we describe a composite, laser micromachined, collagen-alginate construct containing human mesenchymal stem cells (hMSCs) for tissue repair applications. Collagen type I was fashioned into laminated collagen sheets to form a mechanically robust fascia that was subsequently laser micropatterned with pores of defined dimension and spatial distribution as a means to modulate mechanical behavior and promote tissue integration. Significantly, laser micromachined patterned constructs displayed both substantially greater compliance and suture retention strength than non-patterned constructs. hMSCs were loaded in an RGD-functionalized alginate gel modified to degrade in vivo. Over a 7day observation period in vitro, high cell viability was observed with constant levels of VEGF, PDGF-β and MCP-1 protein expression. In a full thickness abdominal wall defect model, the composite construct prevented hernia recurrence in Wistar rats over an 8-week period with de novo tissue and vascular network formation and the absence of adhesions to underlying abdominal viscera. As compared to acellular constructs, constructs containing hMSCs displayed greater integration strength (cell seeded: 0.92±0.19N/mm vs. acellular: 0.59±0.25N/mm, p=0.01), increased vascularization (cell seeded: 2.7-2.1/hpf vs. acellular: 1.7-2.1/hpf, p<0.03), and increased infiltration of macrophages (cell seeded: 2021-3630μm(2)/hpf vs. acellular: 1570-2530μm(2)/hpf, p<0.05). A decrease in the ratio of M1 macrophages to total macrophages was also observed in hMSC-populated samples. Laser micromachined collagen-alginate composites containing hMSCs can be used to bridge soft tissue defects with the capacity for enhanced tissue repair and integration.Effective restoration of large soft tissue defects caused by trauma or treatment complications represents a critical challenge in the clinic. In this study, a novel composite construct was engineered and evaluated for stem cell delivery and tissue repair. Laser micromachining was used to fabricate patterned, microporous constructs designed with pores of defined size and distribution as a means to tune mechanical responses, accommodate and protect incorporated cells, and enhance tissue integration. The construct was embedded within an engineered alginate gel containing hMSCs. Upon repair of a full thickness abdominal wall defect in a rat model, the composite construct modulated host innate immunity towards a reparative phenotypic response, promoted neovascularization and associated matrix production, and increased the strength of tissue integration.
View details for DOI 10.1016/j.actbio.2015.08.012
View details for PubMedID 26283165
View details for PubMedCentralID PMC4584209
- Biological materials and molecular biomimetics - filling up the empty soft materials space for tissue engineering applications JOURNAL OF MATERIALS CHEMISTRY B 2015; 3 (1): 13-24
- Substrate stress relaxation regulates cell spreading. Nature communications 2015; 6: 6365-?
- Oxidized alginate hydrogels for bone morphogenetic protein-2 delivery in long bone defects ACTA BIOMATERIALIA 2014; 10 (10): 4390-4399
Influence of the stiffness of three-dimensional alginate/collagen-I interpenetrating networks on fibroblast biology.
2014; 35 (32): 8927-8936
Wound dressing biomaterials are increasingly being designed to incorporate bioactive molecules to promote healing, but the impact of matrix mechanical properties on the biology of resident cells orchestrating skin repair and regeneration remains to be fully understood. This study investigated whether tuning the stiffness of a model wound dressing biomaterial could control the behavior of dermal fibroblasts. Fully interpenetrating networks (IPNs) of collagen-I and alginate were fabricated to enable gel stiffness to be tuned independently of gel architecture, polymer concentration or adhesion ligand density. Three-dimensional cultures of dermal fibroblasts encapsulated within matrices of different stiffness were shown to promote dramatically different cell morphologies, and enhanced stiffness resulted in upregulation of key-mediators of inflammation such as IL-10 and COX-2. These findings suggest that simply modulating the matrix mechanical properties of a given wound dressing biomaterial deposited at the wound site could regulate the progression of wound healing.
View details for DOI 10.1016/j.biomaterials.2014.06.047
View details for PubMedID 25047628
Highly stretchable and tough hydrogels
2012; 489 (7414): 133-136
Hydrogels are used as scaffolds for tissue engineering, vehicles for drug delivery, actuators for optics and fluidics, and model extracellular matrices for biological studies. The scope of hydrogel applications, however, is often severely limited by their mechanical behaviour. Most hydrogels do not exhibit high stretchability; for example, an alginate hydrogel ruptures when stretched to about 1.2 times its original length. Some synthetic elastic hydrogels have achieved stretches in the range 10-20, but these values are markedly reduced in samples containing notches. Most hydrogels are brittle, with fracture energies of about 10 J m(-2) (ref. 8), as compared with ∼1,000 J m(-2) for cartilage and ∼10,000 J m(-2) for natural rubbers. Intense efforts are devoted to synthesizing hydrogels with improved mechanical properties; certain synthetic gels have reached fracture energies of 100-1,000 J m(-2) (refs 11, 14, 17). Here we report the synthesis of hydrogels from polymers forming ionically and covalently crosslinked networks. Although such gels contain ∼90% water, they can be stretched beyond 20 times their initial length, and have fracture energies of ∼9,000 J m(-2). Even for samples containing notches, a stretch of 17 is demonstrated. We attribute the gels' toughness to the synergy of two mechanisms: crack bridging by the network of covalent crosslinks, and hysteresis by unzipping the network of ionic crosslinks. Furthermore, the network of covalent crosslinks preserves the memory of the initial state, so that much of the large deformation is removed on unloading. The unzipped ionic crosslinks cause internal damage, which heals by re-zipping. These gels may serve as model systems to explore mechanisms of deformation and energy dissipation, and expand the scope of hydrogel applications.
View details for DOI 10.1038/nature11409
View details for Web of Science ID 000308347000049
View details for PubMedID 22955625
- STEM-CELL DIFFERENTIATION Anchoring cell-fate cues NATURE MATERIALS 2012; 11 (7): 568-569
Actin filament curvature biases branching direction
PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA
2012; 109 (8): 2913-2918
Mechanical cues affect many important biological processes in metazoan cells, such as migration, proliferation, and differentiation. Such cues are thought to be detected by specialized mechanosensing molecules linked to the cytoskeleton, an intracellular network of protein filaments that provide mechanical rigidity to the cell and drive cellular shape change. The most abundant such filament, actin, forms branched networks nucleated by the actin-related protein (Arp) 2/3 complex that support or induce membrane protrusions and display adaptive behavior in response to compressive forces. Here we show that filamentous actin serves in a mechanosensitive capacity itself, by biasing the location of actin branch nucleation in response to filament bending. Using an in vitro assay to measure branching from curved sections of immobilized actin filaments, we observed preferential branch formation by the Arp2/3 complex on the convex face of the curved filament. To explain this behavior, we propose a fluctuation gating model in which filament binding or branch nucleation by Arp2/3 occur only when a sufficiently large, transient, local curvature fluctuation causes a favorable conformational change in the filament, and we show with Monte Carlo simulations that this model can quantitatively account for our experimental data. We also show how the branching bias can reinforce actin networks in response to compressive forces. These results demonstrate how filament curvature can alter the interaction of cytoskeletal filaments with regulatory proteins, suggesting that direct mechanotransduction by actin may serve as a general mechanism for organizing the cytoskeleton in response to force.
View details for DOI 10.1073/pnas.1114292109
View details for Web of Science ID 000300495100052
View details for PubMedID 22308368
Mechanics and contraction dynamics of single platelets and implications for clot stiffening
2011; 10 (1): 61-66
Platelets interact with fibrin polymers to form blood clots at sites of vascular injury. Bulk studies have shown clots to be active materials, with platelet contraction driving the retraction and stiffening of clots. However, neither the dynamics of single-platelet contraction nor the strength and elasticity of individual platelets, both of which are important for understanding clot material properties, have been directly measured. Here we use atomic force microscopy to measure the mechanics and dynamics of single platelets. We find that platelets contract nearly instantaneously when activated by contact with fibrinogen and complete contraction within 15 min. Individual platelets can generate an average maximum contractile force of 29 nN and form adhesions stronger than 70 nN. Our measurements show that when exposed to stiffer microenvironments, platelets generated higher stall forces, which indicates that platelets may be able to contract heterogeneous clots more uniformly. The high elasticity of individual platelets, measured to be 10 kPa after contraction, combined with their high contractile forces, indicates that clots may be stiffened through direct reinforcement by platelets as well as by strain stiffening of fibrin under tension due to platelet contraction. These results show how the mechanosensitivity and mechanics of single cells can be used to dynamically alter the material properties of physiologic systems.
View details for DOI 10.1038/NMAT2903
View details for Web of Science ID 000285339100022
View details for PubMedID 21131961
- Portrusive forces generated by dendritic actin networks during cell crawling Actin-Based Motility El Sevier. 2010: 359–379
Combined atomic force microscopy and side-view optical imaging for mechanical studies of cells
2009; 6 (5): 383-U92
The mechanical rigidity of cells and adhesion forces between cells are important in various biological processes, including cell differentiation, proliferation and tissue organization. Atomic force microscopy has emerged as a powerful tool to quantify the mechanical properties of individual cells and adhesion forces between cells. Here we demonstrate an instrument that combines atomic force microscopy with a side-view fluorescent imaging path that enables direct imaging of cellular deformation and cytoskeletal rearrangements along the axis of loading. With this instrument, we directly observed cell shape under mechanical load, correlated changes in shape with force-induced ruptures and imaged formation of membrane tethers during cell-cell adhesion measurements. Additionally, we observed cytoskeletal reorganization and stress-fiber formation while measuring the contractile force of an individual cell. This instrument can be a useful tool for understanding the role of mechanics in biological processes.
View details for DOI 10.1038/NMETH.1320
View details for Web of Science ID 000265661600020
View details for PubMedID 19363493
View details for PubMedCentralID PMC2810651
Differential force microscope for long time-scale biophysical measurements
REVIEW OF SCIENTIFIC INSTRUMENTS
2007; 78 (4)
Force microscopy techniques including optical trapping, magnetic tweezers, and atomic force microscopy (AFM) have facilitated quantification of forces and distances on the molecular scale. However, sensitivity and stability limitations have prevented the application of these techniques to biophysical systems that generate large forces over long times, such as actin filament networks. Growth of actin networks drives cellular shape change and generates nano-Newtons of force over time scales of minutes to hours, and consequently network growth properties have been difficult to study. Here, we present an AFM-based differential force microscope with integrated epifluorescence imaging in which two adjacent cantilevers on the same rigid support are used to provide increased measurement stability. We demonstrate 14 nm displacement control over measurement times of 3 hours and apply the instrument to quantify actin network growth in vitro under controlled loads. By measuring both network length and total network fluorescence simultaneously, we show that the average cross-sectional density of the growing network remains constant under static loads. The differential force microscope presented here provides a sensitive method for quantifying force and displacement with long time-scale stability that is useful for measurements of slow biophysical processes in whole cells or in reconstituted molecular systems in vitro.
View details for DOI 10.1063/1.2727478
View details for Web of Science ID 000246073500032
View details for PubMedID 17477674
View details for PubMedCentralID PMC3236676
Loading history determines the velocity of actin-network growth
NATURE CELL BIOLOGY
2005; 7 (12): 1219-1223
Directional polymerization of actin filaments in branched networks is one of the most powerful force-generating systems in eukaryotic cells. Growth of densely cross-linked actin networks drives cell crawling, intracellular transport of vesicles and organelles, and movement of intracellular pathogens such as Listeria monocytogenes. Using a modified atomic force microscope (AFM), we obtained force-velocity (Fv) measurements of growing actin networks in vitro until network elongation ceased at the stall force. We found that the growth velocity of a branched actin network against increasing forces is load-independent over a wide range of forces before a convex decline to stall. Surprisingly, when force was decreased on a growing network, the velocity increased to a value greater than the previous velocity, such that two or more stable growth velocities can exist at a single load. These results demonstrate that a single Fv relationship does not capture the complete behaviour of this system, unlike other molecular motors in cells, because the growth velocity depends on loading history rather than solely on the instantaneous load.
View details for DOI 10.1038/ncb1336
View details for Web of Science ID 000233748900015
View details for PubMedID 16299496