Time-dependent migratory behaviors in the long-term studies of fibroblast durotaxis on a hydrogel substrate fabricated with a soft band

Positive and negative durotaxis - mechanisms and emerging concepts

Cell migration is controlled by the coordinated action of cell adhesion, cytoskeletal dynamics, contractility and cell extrinsic cues. Integrins are the main adhesion receptors to ligands of the extracellular matrix (ECM), linking the actin cytoskeleton to the ECM and enabling cells to sense matrix rigidity and mount a directional cell migration response to stiffness gradients. Most models studied show preferred migration of single cells or cell clusters towards increasing rigidity. This is referred to as durotaxis, and since its initial discovery in 2000, technical advances and elegant computational models have provided molecular level details of stiffness sensing in cell migration. However, modeling has long predicted that, depending on cell intrinsic factors, such as the balance of cell adhesion molecules (clutches) and the motor proteins pulling on them, cells might also prefer adhesion to intermediate rigidity. Recently, experimental evidence has supported this notion and demonstrated the ability of cells to migrate towards lower rigidity, in a process called negative durotaxis. In this Review, we discuss the significant conceptual advances that have been made in our appreciation of cell plasticity and context dependency in stiffness-guided directional cell migration.

Unified multiscale theory of cellular mechanical adaptations to substrate stiffness

Rigidity of the extracellular matrix markedly regulates many cellular processes. However, how cells detect and respond to matrix rigidity remains incompletely understood. Here, we propose a unified two-dimensional multiscale framework accounting for the chemomechanical feedback to explore the interrelated cellular mechanosensing, polarization, and migration, which constitute the dynamic cascade in cellular response to matrix stiffness but are often modeled separately in previous theories. By combining integrin dynamics and intracellular force transduction, we show that substrate stiffness can act as a switch to activate or deactivate cell polarization. Our theory quantitatively reproduces rich stiffness-dependent cellular dynamics, including spreading, polarity selection, migration pattern, durotaxis, and even negative durotaxis, reported in a wide spectrum of cell types, and reconciles some inconsistent experimental observations. We find that a specific bipolarized mode can determine the optimal substrate stiffness, which enables the fastest cell migration rather than the largest traction forces that cells apply on the substrate. We identify that such a mechanical adaptation stems from the force balance across the whole cell. These findings could yield universal insights into various stiffness-mediated cellular processes within the context of tissue morphogenesis, wound healing, and cancer invasion.

Automated Cell Mechanical Characterization by On-Chip Sequential Squeezing: From Static to Dynamic

The mechanical properties of cells are harmless biomarkers for cell identification and disease diagnosis. Although many systems have been developed to evaluate the static mechanical properties of cells for biomedical research, their robustness, effectiveness, and cost do not meet clinical requirements or the experiments with a large number of cell samples. In this paper, we propose an approach for on-chip cell mechanical characterization by analyzing the dynamic behavior of cells as they pass through multiple constrictions. The proposed serpentine microfluidic channel consisted of 20 constrictions connected in series and divided into five rows for tracking cell dynamic behavior. Assisted by computer vision, the squeezing time of each cell through five rows of constrictions was automatically collected and filtered to evaluate the cell's mechanical deformability. We observed a decreasing passage time and increasing dynamic deformability of the cells as they passed through the multiple constrictions. The deformability increase rate of the HeLa cells was eight times greater than that of MEF cells. Moreover, the weak correlation between the deformability increase rate and the cell size indicated that cell recognition based on measuring the deformability increase rate could hardly be affected by the cell size variation. These findings showed that the deformability increase rate of the cell under on-chip sequential squeezing as a new index has great potential in cancer cell recognition.

Characterization of immune cell migration using microfabrication

The immune system provides our defense against pathogens and aberrant cells, including tumorigenic and infected cells. Motility is one of the fundamental characteristics that enable immune cells to find invading pathogens, control tissue damage, and eliminate primary developing tumors, even in the absence of external treatments. These processes are termed "immune surveillance." Migration disorders of immune cells are related to autoimmune diseases, chronic inflammation, and tumor evasion. It is therefore essential to characterize immune cell motility in different physiologically and pathologically relevant scenarios to understand the regulatory mechanisms of functionality of immune responses. This review is focused on immune cell migration, to define the underlying mechanisms and the corresponding investigative approaches. We highlight the challenges that immune cells encounter in vivo, and the microfabrication methods to mimic particular aspects of their microenvironment. We discuss the advantages and disadvantages of the proposed tools, and provide information on how to access them. Furthermore, we summarize the directional cues that regulate individual immune cell migration, and discuss the behavior of immune cells in a complex environment composed of multiple directional cues.

Spatiotemporally Controlled Photoresponsive Hydrogels: Design and Predictive Modeling from Processing through Application

Photoresponsive hydrogels (PRHs) are soft materials whose mechanical and chemical properties can be tuned spatially and temporally with relative ease. Both photo-crosslinkable and photodegradable hydrogels find utility in a range of biomedical applications that require tissue-like properties or programmable responses. Progress in engineering with PRHs is facilitated by the development of theoretical tools that enable optimization of their photochemistry, polymer matrices, nanofillers, and architecture. This review brings together models and design principles that enable key applications of PRHs in tissue engineering, drug delivery, and soft robotics, and highlights ongoing challenges in both modeling and application.

Monitoring matrix remodeling in the cellular microenvironment using microrheology for complex cellular systems

Multiple particle tracking (MPT) microrheology was employed for monitoring the development of extracellular matrix (ECM) mechanical properties in the direct microenvironment of living cells. A customized setup enabled us to overcome current limitations: (i) Continuous measurements were enabled using a cell culture chamber, with this, matrix remodeling by fibroblasts in the heterogeneous environment of macroporous scaffolds was monitored continuously. (ii) Employing tracer laden porous scaffolds for seeding human mesenchymal stem cells (hMSCs), we followed conventional differentiation protocols. Thus, we were, for the first time able to study the massive alterations in ECM elasticity during hMSC differentiation. (iii) MPT measurements in 2D cell cultures were enabled using a long distance objective. Exemplarily, local mechanical properties of the ECM in human umbilical vein endothelial cell (HUVEC) cultures, that naturally form 2D layers, were investigated scaffold-free. Using our advanced setup, we measured local, apparent elastic moduli G_0,app in a range between 0.08 and 60 Pa. For fibroblasts grown in collagen-based scaffolds, a continuous decrease of local matrix elasticity resulted during the first 10 hours after seeding. The osteogenic differentiation of hMSC cells cultivated in similar scaffolds, led to an increase of G_0,app by 100 %, whereas after adipogenic differentiation it was reduced by 80 %. The local elasticity of ECM that was newly secreted by HUVECs increased significantly upon addition of protease inhibitor and in high glucose conditions even a twofold increase in G_0,app was observed. The combination of these advanced methods opens up new avenues for a broad range of investigations regarding cell-matrix interactions and the propagation of ECM mechanical properties in complex biological systems. STATEMENT OF SIGNIFICANCE: Cells sense the elasticity of their environment on a micrometer length scale. For studying the local elasticity of extracellular matrix (ECM) in the direct environment of living cells, we employed an advanced multipleparticle tracking microrheology setup. MPT is based on monitoring the Brownian motion oftracer particles, which is restricted by the surrounding network. Network elasticity can thusbe quantified. Overcoming current limitations, we realized continuous investigations of ECM elasticityduring fibroblast growth. Furthermore, MPT measurements of stem cell ECM showed ECMstiffening during osteogenic differentiation and softening during adipogenic differentiation.Finally, we characterized small amounts of delicate ECM newly secreted in scaffold-freecultures of endothelial cells, that naturally form 2D layers.

The Impact of Elastic Deformations of the Extracellular Matrix on Cell Migration

The mechanical properties of the extracellular matrix, in particular its stiffness, are known to impact cell migration. In this paper, we develop a mathematical model of a single cell migrating on an elastic matrix, which accounts for the deformation of the matrix induced by forces exerted by the cell, and investigate how the stiffness impacts the direction and speed of migration. We model a cell in 1D as a nucleus connected to a number of adhesion sites through elastic springs. The cell migrates by randomly updating the position of its adhesion sites. We start by investigating the case where the cell springs are constant, and then go on to assuming that they depend on the matrix stiffness, on matrices of both uniform stiffness as well as those with a stiffness gradient. We find that the assumption that cell springs depend on the substrate stiffness is necessary and sufficient for an efficient durotactic response. We compare simulations to recent experimental observations of human cancer cells exhibiting durotaxis, which show good qualitative agreement.

Hierarchical Development of Motile Polarity in Durotactic Cells Just Crossing an Elasticity Boundary

Cellular durotaxis has been extensively studied in the field of mechanobiology. In principle, asymmetric mechanical field of a stiffness gradient generates motile polarity in a cell, which is a driving factor of durotaxis. However, the actual process by which the motile polarity in durotaxis develops is still unclear. In this study, to clarify the details of the kinetics of the development of durotactic polarity, we investigated the dynamics of both cell-shaping and the microscopic turnover of focal adhesions (FAs) for Venus-paxillin-expressing fibroblasts just crossing an elasticity boundary prepared on microelastically patterned gels. The Fourier mode analysis of cell-shaping based on a persistent random deformation model revealed that motile polarity at a cell-body scale was established within the first few hours after the leading edges of a moving cell passed through the boundary from the soft to the stiff regions. A fluorescence recovery after photobleaching (FRAP) analysis showed that the mobile fractions of paxillin at FAs in the anterior part of the cells exhibited an asymmetric increase within several tens of minutes after cells entered the stiff region. The results demonstrated that motile polarity in durotactic cells is established through the hierarchical step-wise development of different types of asymmetricity in the kinetics of FAs activity and cell-shaping with a several-hour time lag.Key words: Microelasticity patterned gel, durotaxis, cell polarity, focal adhesions, paxillin.

Cellular Durotaxis Revisited: Initial-Position-Dependent Determination of the Threshold Stiffness Gradient to Induce Durotaxis

Directional cell movement from a softer to a stiffer region on a culture substrate with a stiffness gradient, so-called durotaxis, has attracted considerable interest in the field of mechanobiology. Although the strength of a stiffness gradient has been known to influence durotaxis, the precise manipulation of durotactic cells has not been established due to the limited knowledge available on how the threshold stiffness gradient (TG) for durotaxis is determined. In the present study, to clarify the principles for the manipulation of durotaxis, we focused on the absolute stiffness of the soft region and evaluated its effect on the determination of TG required to induce durotaxis. Microelastically patterned gels that differed with respect to both the absolute stiffness of the soft region and the strength of the stiffness gradient were photolithographically prepared using photo-cross-linkable gelatins, and the TG for mesenchymal stem cells (MSCs) was examined systematically for each stiffness value of the soft region. As a result, the TG values for soft regions with stiffnesses of 2.5, 5, and 10 kPa were 0.14, 1.0, and 1.4 kPa/μm, respectively, i.e., TG markedly increased with an increase in the absolute stiffness of the soft region. An analysis of the area and long-axis length for focal adhesions revealed that the adhesivity of MSCs was more stable on a stiffer soft region. These results suggested that the initial location of cells starting durotaxis plays an essential role in determining the TG values and furthermore that the relationship between the position-dependent TG and intrinsic stiffness gradient (IG) of the culture substrate should be carefully reconsidered for inducing durotaxis; IG must be higher than TG (IG ≥ TG). This principle provides a fundamental guide for designing biomaterials to manipulate cellular durotaxis.

Dynamic Contact Guidance of Myoblasts by Feature Size and Reversible Switching of Substrate Topography: Orchestration of Cell Shape, Orientation, and Nematic Ordering of Actin Cytoskeletons

Biological cells in tissues alter their shapes, positions, and orientations in response to dynamic changes in their physical microenvironments. Here, we investigated the dynamic response of myoblast cells by fabricating substrates displaying microwrinkles that can reversibly change their direction within 60 s by axial compression and relaxation. To quantitatively assess the collective order of cells, we introduced the nematic order parameter of cells that takes not only the distribution of cell-wrinkle angles but also the degree of cell elongation into account. On the subcellular level, we also calculated the nematic order parameter of actin cytoskeletons that takes the rearrangement of actin filaments into consideration. The results obtained on substrates with different wrinkle wavelengths implied the presence of a characteristic wavelength beyond which the order parameters of both cells and actin cytoskeletons level off. Immunofluorescence labeling of vinculin showed that the focal adhesions were all concentrated on the peaks of wrinkles when the wavelength is below the characteristic value. On the other hand, we found focal adhesions on both the peaks and the troughs of wrinkles when the wavelength exceeds the characteristic level. The emergence of collective ordering of cytoskeletons and the adaptation of cell shapes and orientations were monitored by live cell imaging after the seeding of cells from suspensions. After the cells had reached the steady state, the orientation of wrinkles was abruptly changed by 90°. The dynamic response of myoblasts to the drastic change in surface topography was monitored, demonstrating the coordination of the shape and orientation of cells and the nematic ordering of actin cytoskeletons. The "dynamic" substrates established in this study can be used as a powerful tool in mechanobiology that helps us understand how cytoskeletons, cells, and cell ensembles respond to dynamic contact guidance cues.

Frustrated differentiation of mesenchymal stem cells

Mesenchymal stem cells (MSCs) are one of the most useful cell resources for clinical application in regenerative medicine. However, standardization and quality assurance of MSCs are still essential problems because the stemness of MSCs depends on such factors as the collection method, individual differences associated with the source, and cell culture history. As such, the establishment of culture techniques which assure the stemness of MSCs is of vital importance. One important factor affecting MSCs during culture is the effect of the mechanobiological memory of cultured MSCs built up by their encounter with particular mechanical properties of the extracellular mechanical milieu. How can we guarantee that MSCs will remain in an undifferentiated state? Procedures capable of eliminating effects related to the history of the mechanical dose for cultured MSCs are required. For this problem, we have tried to establish the design of microelastically patterned cell-culture matrix which can effectively induce mechanical oscillations during the period of nomadic migration of cells among different regions of the matrix. We have previously observed before that the MSCs exposed to such a growth regimen during nomadic culture keep their undifferentiated state-with this maintenance of stemness believed due to lack of a particular regular mechanical dosage that is likely to determine a specific lineage. We have termed this situation as "frustrated differentiation". In this minireview, I introduce the concept of frustrated differentiation of MSCs and show possibility of purposeful regulation of this phenomenon.

Mathematical modelling of cell migration: stiffness dependent jump rates result in durotaxis

Durotaxis, the phenomena where cells migrate up a gradient in substrate stiffness, remains poorly understood. It has been proposed that durotaxis results from the reinforcement of focal adhesions on stiff substrates. In this paper we formulate a mathematical model of single cell migration on elastic substrates with spatially varying stiffness. We develop a stochastic model where the cell moves by updating the position of its adhesion sites at random times, and the rate of updates is determined by the local stiffness of the substrate. We investigate two physiologically motivated mechanisms of stiffness sensing. From the stochastic model of single cell migration we derive a population level description in the form of a partial differential equation for the time evolution of the density of cells. The equation is an advection–diffusion equation, where the advective velocity is proportional to the stiffness gradient. The model shows quantitative agreement with experimental results in which cells tend to cluster when seeded on a matrix with periodically varying stiffness.

Microstructure, local viscoelasticity and cell culture suitability of 3D hybrid HA/collagen scaffolds

As mechanical properties of cell culture substrates matter, methods for mechanical characterization of scaffolds on a relevant length scale are required. We used multiple particle tracking microrheology to close the gap between elasticity determined from bulk measurements and elastic properties sensed by cells. Structure and elasticity of macroporous, three-dimensional cryogel scaffolds from mixtures of hyaluronic acid (HA) and collagen (Coll) were characterized. Both one-component gels formed homogeneous networks, whereas hybrid gels were heterogeneous in terms of elasticity. Most strikingly, local elastic moduli were significantly lower than bulk moduli presumably due to non-equilibrium chain conformations between crosslinks. This was more pronounced in Coll and hybrid gels than in pure HA gels. Local elastic moduli were similar for all gels, irrespective of their different swelling ratio and bulk moduli. Fibroblast cell culture proved the biocompatibility of all investigated compositions. Coll containing gels enabled cell migration, adhesion and proliferation inside the gels.

Effects of dynamic matrix remodelling on en masse migration of fibroblasts on collagen matrices

Fibroblast migration plays a key role during various physiological and pathological processes. Although migration of individual fibroblasts has been well studied, migration in vivo often involves simultaneous locomotion of fibroblasts sited in close proximity, so-called 'en masse migration', during which intensive cell-cell interactions occur. This study aims to understand the effects of matrix mechanical environments on the cell-matrix and cell-cell interactions during en masse migration of fibroblasts on collagen matrices. Specifically, we hypothesized that a group of migrating cells can significantly deform the matrix, whose mechanical microenvironment dramatically changes compared with the undeformed state, and the alteration of the matrix microenvironment reciprocally affects cell migration. This hypothesis was tested by time-resolved measurements of cell and extracellular matrix movement during en masse migration on collagen hydrogels with varying concentrations. The results illustrated that a group of cells generates significant spatio-temporal deformation of the matrix before and during the migration. Cells on soft collagen hydrogels migrate along tortuous paths, but, as the matrix stiffness increases, cell migration patterns become aligned with each other and show coordinated migration paths. As cells migrate, the matrix is locally compressed, resulting in a locally stiffened and dense matrix across the collagen concentration range studied.

Quantifying 3D chemotaxis in microfluidic-based chips with step gradients of collagen hydrogel concentrations

Cell migration is an essential process involved in crucial stages of tissue formation, regeneration or immune function as well as in pathological processes including tumor development or metastasis. During the last few years, the effect of gradients of soluble molecules on cell migration has been widely studied, and complex systems have been used to analyze cell behavior under simultaneous mechano-chemical stimuli. Most of these chemotactic assays have, however, focused on specific substrates in 2D. The aim of the present work is to develop a novel microfluidic-based chip that allows the long-term chemoattractant effect of growth factors (GFs) on 3D cell migration to be studied, while also providing the possibility to analyze the influence of the interface generated between different adjacent hydrogels. Namely, 1.5, 2, 2.5 and 4 mg ml^-1 concentrations of collagen type I were alternatively combined with 5, 10 or 50 ng ml^-1 concentrations of PDGF and VEGF (as a negative control). To achieve this goal, we have designed a new microfluidic device including three adjacent chambers to introduce hydrogels that allow the generation of a collagen concentration step gradient. This versatile and simple platform was tested by using dermal human fibroblasts embedded in 3D collagen matrices. Images taken over a week were processed to quantify the number of cells in each zone. We found, in terms of cell distribution, that the presence of PDGF, especially in small concentrations, was a strong chemoattractant for dermal human fibroblasts across the gels regardless of their collagen concentration and step gradient direction, whereas the effects of VEGF or collagen step gradient concentrations alone were negligible.

Three-Dimensional Confocal Microscopy Indentation Method for Hydrogel Elasticity Measurement

The stiffness of the extracellular matrix (ECM) plays an important role in controlling cell functions. As an alternative to the ECM, hydrogels of tunable elasticity are widely used for in vitro cell mechanobiology studies. Therefore, characterizing the Young's modulus of the hydrogel substrate is crucial. In this paper, we propose a confocal microscopy indentation method for measuring the elasticity of polyacrylamide gel as a model hydrogel. Our new indentation method is based on three-dimensional imaging of the indented gel using confocal microscopy and automated image processing to measure indentation depth from the three-dimensional image stack. We tested and validated our method by indenting polyacrylamide gels of different rigidities with various sphere indentors and by comparing it with the rheometric method. Our measurements show consistent results regardless of the type of the indentors and agree with rheometric measurements. Therefore, the proposed confocal microscopy indentation method can accurately measure the stiffness of hydrogels.