Home Physical Sciences Physical cues of biomaterials guide stem cell fate of differentiation: The effect of elasticity of cell culture biomaterials
Article Open Access

Physical cues of biomaterials guide stem cell fate of differentiation: The effect of elasticity of cell culture biomaterials

  • Vincent Irawan , Akon Higuchi and Toshiyuki Ikoma EMAIL logo
Published/Copyright: December 31, 2018
Download Article (PDF)
Open Physics
From the journal Open Physics Volume 16 Issue 1

Abstract

It is widely accepted that stem cells directly sense the elasticity of two-dimensional (2-D) substrates and differentiate into a distinct cell type dependent on the substrate elasticity (direct-sensing differentiation: soft and hard substrates promote differentiation into soft and hard tissue lineage, respectively). Biologically, native extracellular matrices (ECMs) are constantly remodeled through out the life of individuals, which inadvertently introduce changes of mechanical properties. Therefore, direct-sensing differentiation might not fully take into account the responses of stem cells in the actual ECMs microenvironment. Recent investigations in three-dimensional (3-D) cell culture environment suggested the inconsistency of direct-sensing differentiation. Stem cells specifically differentiate not only by sensing the elasticity of materials but also by considering the cellular traction exerted to reorganize the matrices and the matrices deformation. This paper aims to expand further how the cells incorporate the elasticity cues and traction-mediated deformation in final differentiation fates of stem cells. To achieve the aim, we introduced an empirical model based on the investigations in 3-D cell culture environment. The empirical model would serve as a useful framework for future studies intended to investigate the relationship of traction-mediated deformation and commitment of stem cells for variety of tissue lineage in 2-D or 3-D cell culture environment.

Keywords: mechanosensing, stem cell differentiation; traction-mediated deformation; 2-D cell culture; 3-D cell culture
PACS: 87.17.Rt; 87.19.rd; 87.15.la

1 Introduction

Stem cells are the potential agent to treat the degenerative disease or heavy tissue injury, owing to the capability of self-renewal [1, 2, 3] and the capacity to differentiate into functionally mature cells [4, 5, 6]. Several types of stem cell, such as embryonic stem cells (ESCs) and induced-pluripotent stem cells (iPSCs), are pluripotent, and are able to differentiate into any cell types derived from three germ layers: ectoderm (nerves and epidermal tissue), mesoderm (bone, muscle, cartilage), and endoderm (functional organ) [7, 8, 9, 10]. Other types of stem cell, such as mesenchymal stem cells (MSCs) and hematopoietic stem cells (HSCs), are more limited in the differentiation capacity with limited life span, in which MSCs are only able to differentiate into cells of mesodermal origin (fat, bone, muscle, cartilage) [11, 12, 13, 14, 15]. Regardless of the differentiation capacity, it is clear that stem cells are useful in medical applications, and an ideal culture system should be established to effectively expand the stem cell number and guide the differentiation of stem cells.

In the past decade, researchers have focused on improving the efficiency of stem cell differentiation by tuning the physical properties of biomaterials (elasticity [16, 17], surface topography [18, 19], architecture [20, 21]) in culturing. The biological cues (growth factors, hormones, peptides) conventionally used to differentiate the stem cells have been widely investigated [22, 23, 24, 25], thus it is difficult to discover novel biological cues to increase efficiency of stem cell differentiation [10].

Elasticity, as one of the physical cues, was recently shown to be able to selectively induce the differentiation of stem cells into the specific lineage [8, 26, 27]. MSCs were specifically differentiated into neuron, muscle, and bone cells when MSCs were cultured on two-dimensional (2-D) substrates with elastic modulus (E) approaching the elasticity of native tissues (brain (E~0.1-1 kPa), muscle (E~ 8-17 kPa), and bones (E~40 kPa)). Such idea of elasticity-driven commitment of stem cells was replicated for other types of stem cell, such as ESCs [8, 28], or non-bone marrowderived MSCs [29, 30]. In these studies [8, 26], the substrates made of synthetic polymers (e.g., poly(acrylamide) (PA), poly(ϵ-caprolactone)) were used, which show pure elasticity.However, the cells in native tissue environment reside in extracellular matrices (ECMs) which are nonelastic and constantly remodeled (resorbed and rebuilt) [31, 32]. Therefore, the cell responses observed on 2-D elastic materials may not reflect the true mechanism on how the cells detect the physical cues of cell culture substrates in actual setting.

Unlike 2-D substrates, elasticity of three-dimensional (3-D) matrices indirectly regulates the stem cell differentiation by allowing or preventing the cellular traction-mediated deformation of matrices [31, 33, 34]. Khetan et al. demonstrated thatif the hydrogels were stable enough to prevent mechanical reorganization of matrices by stem cells, then the stem cells consistently adopted differentiation fate into adipocytes (fat tissue) in all range of hydrogel elasticity (~4-95 kPa) [33]. Introduction of degradable bonds in the hydrogels allowed cells to exert traction to the matrices, and subsequently stem cell fate shifted to osteogenic differentiation (bone tissue) [33]. Despite the apparent difference on how the elasticity of the cell culture matrices would influence stem cell fate in 2-D and 3-D environments, cellular contractility remains the main driving force for differentiation of stem cell fate [26, 33, 35].

In this review, we aim to expand further how the cells incorporate the elasticity cues and traction-mediated deformation in final differentiation decisions. Initially, key papers establishing on how the stem cells directly perceived the elasticity of 2-D environment were reviewed. Next, we discussed the interplay of elasticity and dynamic physical properties of cell culture materials in influencing the differentiation of stem cell fate in 3-D cell culture environment. In the same section, the empirical model to explain how the traction-mediated deformation would regulate the lineage specification of stem cells was proposed. We concluded how the model can be stretched to the basic research in 2-D cell culture setting and the limitation of the empirical model.

2 The specific induction of stem cell fates by elasticity cues in 2-D environment

Elasticity of 2-D substrates or 3-D matrices refers to the resistance of materials to elastic deformation, as represented by elastic modulus or Young’s modulus (E, Pa = N/m2) [33, 35, 36]. Elasticity is the inherent property of materials and used interchangeably with ‘stiffness’ or ‘rigidity’. The term ‘stiffness’ in cell biology is rarely assigned to the other definition of stiffness (N/m) which refer to the resistance of component to deformation. Elasticity is also defined by the viscoelasticity parameter (e.g., storage or loss modulus) [37, 38]. Moreover, it is general practice to indicate materials with high and low elastic modulus as ‘stiff’ and ‘soft’, respectively. The elasticity of 2-Dsubstrates or 3-Dmatrices can be measured by atomic force microscopy (AFM) (elastic modulus) [27], compression test (elastic modulus) [39], tensile test (elastic modulus) [8], or rheometer (viscoelastic modulus) [37, 38].

The influence of elasticity cues was initially focused on the motility and contractility of cells, such as cell locomotion [40], morphology [41], or spreading area [42], and not for the differentiation of stem cells. From these studies [40, 41, 42], it was found that the elastic modulus of substrates could regulate the intracellular formation of stress fiber (F-actin), which in turn lead to the modulation of cellular traction mode and magnitude. The strong correlation between cellular traction and substrate elasticity lead to the idea of ‘mechanosensing’, that is, cells were able to sense the elasticity of the surrounding environment by means of generating contractile force (Figure 1(A)) [36, 40].

Figure 1 (A) Schematic illustration of mechanosensing by cells. (B) MSCs cultured on PAAm hydrogel of different stiffness (0.1-1 kPa, 8-17 kPa, 25-40 kPa) undergo differentiation correspondingly to neurogenic (nerve), myogenic (muscle), osteogenic (bone). (C) Magnitude of cellular traction exerted by MSCs at soft and stiff substrate. Cells gradually increase the traction when cell culture substrate is stiffened (soft-to-stiff ) (D) Deformation of matrices as given by the displacement of fluorescent particles embedded in PA substrates of different stiffness (4 kPa and 30 kPa) by MSCs. Parts of figure are adapted with permission from [27] (A), (D), [26] (B), [42] (C)
Figure 1

(A) Schematic illustration of mechanosensing by cells. (B) MSCs cultured on PAAm hydrogel of different stiffness (0.1-1 kPa, 8-17 kPa, 25-40 kPa) undergo differentiation correspondingly to neurogenic (nerve), myogenic (muscle), osteogenic (bone). (C) Magnitude of cellular traction exerted by MSCs at soft and stiff substrate. Cells gradually increase the traction when cell culture substrate is stiffened (soft-to-stiff ) (D) Deformation of matrices as given by the displacement of fluorescent particles embedded in PA substrates of different stiffness (4 kPa and 30 kPa) by MSCs. Parts of figure are adapted with permission from [27] (A), (D), [26] (B), [42] (C)

The results of mechanosensing were communicated back-and-forth to the intracellular signaling pathway (focal adhesion kinase- (FAK), paxillin-, vinculin-dependent pathway) yielding the dynamic cellular responses (e.g., low traction at soft substrate, migration to stiff substrate) [9, 40]. The transduction of mechanical signals into intracellular signal and subsequently into cellular responses is termed as “mechanotransduction”. Inhibition of cellular contractility by addition of blebbistatin (non-muscle II myosin inhibitor) [36, 42] or Y-27632 (Rho-kinase (ROCK) inhibitor) [40] strongly hindered cellular migration or focal adhesion formation, emphasizing the important role of cellular contractility in mechanotransduction.

By the similar hypothesis, elasticity of cell culture substrates was shown to selectively induce differentiation of stem cells in contractility-dependent manner (direct-sensing differentiation) [26]. Engleret al. demonstrated that collagen-coated PA hydrogels with elasticity mimicking stiffness of brain (E~0.1-1 kPa), muscle (E~ 8-17 kPa), or bones (E~40 kPa) were able to selectively induce the differentiation of MSCs in the corresponding pathway; soft hydrogels at 0.1 and 1 kPa induced neurogenic differentiation, etc. (Figure 1(B)). Addition of blebbistatin blocked the elasticity-induced differentiation of MSCs, implying the important role of cellular contractility in the elasticitydriven fate specification of MSCs [26]. However, despite the strong correlation of elasticity and MSCs differentiation, the exact molecular mechanisms of mechanosensing and mechanotransduction are still elusive [43].

MSCs exert lower traction at soft substrates and higher traction at stiff substrates (Figure 1(C)) [36, 42, 44] and MSCs seemed to compensate the magnitude of these exerted traction by adjusting the internal stresses (prestress) and membrane stiffness (cortical stiffness) [26]. Based on these results, calculation of substrate deformation was conducted and it was suggested that larger deformation occurred on matrices for soft substrates [27], while smaller deformation of matrices occurred for stiff substrates [26]. Follow-up experiments found that deformation of substrates by MSCs was maximized and minimized on soft and stiff substrates, respectively (Figure 1(D)) [27].

Despite the significant influence of substrate elasticity on initial commitment fate of MSCs, elasticity is unable to alter the fate of committed MSCs. Guvendirenet al. cultured MSCs on the soft substrates of methacrylated hyaluronic acid (MeHA) in the mixture of osteogenic and adipogenic mediums for 14 days [42]. As expected, the majority of MSCs, cultured on soft gels, differentiated into fat cells (adipogenic pathway). However,when the soft hydrogelswere stiffened at 1 day, majority of MSCs differentiated into bone cells (osteogenic) and only small fraction differentiated into fat cells (adipogenic). The trend continued to increase when hydrogels were stiffened at 3 and 7 days later. These data suggested that, before the substrates stiffened, MSCs perceived the low elasticity cues of substrates and correspondingly differentiated in the adipogenic pathway. However, as the substrate was stiffened, undifferentiated MSCs no longer ‘feel’ the soft substrates, instead MSCs sensed the high elastic substrates. As the results, MSCs committed to osteogenic pathway. The facts that adipogenic cells were still remained after the gels stiffened indicated that committed MSCs (adipogenic cells) would be insensitive for changes of elasticity. Another study employing iPSCs also confirmed the similar findings, that is, differentiation of iPSCs into myocardium was more sensitive to elasticity cues, while partially committed iPSCs were insensitive to elasticity cues [28].

2.1 The modulation of optimum substrate elasticity by the types of ECM molecules

Contrasting to Engler’s finding, optimum elasticity to maximize the differentiation of stem cells seemed to be not only strictly dependent on the elasticity of the native tissues, but also on the types of ECM proteins used to coat the substrates [37, 39, 45]. Rowland et al. initially showed that the optimum elasticity to maximize the gene expression of MyoD1 (myogenic marker) and Runx2 (osteogenic marker) for MSCs was dependent on the types of ECMs used to coat the PA substrate [39]. Collagen I-coated PA showed the highest gene expression of MyoD1 and Runx2 for MSCs cultured on the hydrogels at 80 kPa of elasticity. In contrast, collagen IV-coated and fibronectin-coated PA showed the highest gene expression of MyoD1 and Runx2 for MSCs on the hydrogels at 25 kPa of elasticity. Theses observation suggested the possible interplay between elasticity and the types of ECMs in optimizing the specific differentiation of stem cells.

To conclude that the particular substrates are more osteogenic or myogenic than others, one need to demonstrate the upregulation of several transcription factors relevant with the differentiation pathway. Therefore, from the study of Rowland et al., it was not possible to conclude that collagen I-coated PA (80 kPa) was more osteogenic than fibronectin-coated PA (80 kPa), since they investigated only one particular transcription factor (MyoD1 or Runx2) for each differentiation pathway. To overcome this limitation, Hirata et al. investigated the expression of three different transcription factors-associated with cardiomyocte differentiation (heart muscle) of iPSCs cultured on PA substrates varying stiffness (9, 20, 180 kPa) and types of ECMs (collagen I, gelatin, and fibronectin) [45]. The elasticity of heart muscle tissue was found to be ~13 kPa [47]. The analyzed transcription factors were GATA-binding protein 4 (GATA4), T-box transcription factor 5 (Tbx5), andmyocyte-specific enhancer factor 2C (MEF2C). The elasticity of collagen I-coated PA had no effects on the cardiogenic differentiation, as evidenced by the unchanged expression of GATA4 and Tbx5. In contrast, gelatin and fibronectincoated PA showed the relationship of elasticity and ECM proteins on the cardiogenic differentiation; the expression of GATA4, Tbx5, and MEF2C was maximized on PA with 20 kPa and minimized on PA with 9 kPa and 180 kPa. Taken together, these findings implied that elasticity of substrates would not be an overriding factor in specifying commitment of stem cells, since optimal elasticity would be dependent on the types of ECMs used.

Expansion of hematopoietic stem cells (HSCs) was previously shown to be influenced by the elasticity of substrates [12]. Choi et al. employed collagen I-coated PA and found that expansion of HSCs was maximized on the soft PA with 0.0442 kPa of elastic modulus, but not on stiff PA with 3.48 kPa and stiffer glass-coated with collagen I [48]. Contrary to these findings, Kumar et al. demonstrated that the substrates with the elasticity ranging from 12.2 kPa to 30.4 kPa (storage modulus) of poly(vinyl alcohol-co-vinyl acetate-co-itaconic acid gels were required to maximize the expansion of hematopoietic stem and progenitor cells (HSPCs) on fibronectin or its oligopeptide (CS1, EILDVPST) coated substrates [37].

Several hypotheses have been raised to explain why different combinations of substrates and ECMs show different optimum elasticity to specifically differentiate stem cells. In one hypothesis, some ECM molecules have been known to bind different sites of integrin, resulting in possible different activations of mechanotransduction pathways [39]. In the other hypothesis, cells are argued to consider the mechanical feedback from ECMs, instead of directly sensing the elasticity of substrates (Figure 2(B)) [10, 37]. Each ECM molecule possesses a different mechanical property (e.g., elasticity, molecule weight and length), meanwhile the modification of hydrogel elasticity is associated with the changes of pore size [46] or ECM anchoring density on the substrates [13]. Therefore, different combinations of ECM molecules and hydrogels with different elasticities yield the varying optimum values to activate stem cells [13]. The variations of optimum elasticity and ECMs molecule to support the stem cell differentiation and expansion are summarized in Table 1.

Figure 2 Schematic illustration of alternative mechanosensing mechanism. Instead of directly interacting with substrate, cells consider the mechanical feedback of ECMs molecules (collagen). Soft and stiff gel show different mesh size, thus different anchoring point of ECMs. As a result, cell sense loose mechanical feedback of collagen at soft gel and intense mechanical feedback at stiff gel. Sulfo-SANPAH is the chemical linker of collagen and poly(acrylamide) substrate (PAAm). Parts of figure are adapted with permission from [46]
Figure 2

Schematic illustration of alternative mechanosensing mechanism. Instead of directly interacting with substrate, cells consider the mechanical feedback of ECMs molecules (collagen). Soft and stiff gel show different mesh size, thus different anchoring point of ECMs. As a result, cell sense loose mechanical feedback of collagen at soft gel and intense mechanical feedback at stiff gel. Sulfo-SANPAH is the chemical linker of collagen and poly(acrylamide) substrate (PAAm). Parts of figure are adapted with permission from [46]

Table 1

Variation of optimum elasticity-type of ECM to support specific differentiation or expansion of stem cells

Type of Lineage CommitmentElasticity of Original TissueType of ECMsOptimum Substrate Elasticity
1. Myogenic~8-17 kPa (muscleCollagen I-coated PA11 kPa (Elastic modulus) [26]
(muscle tissue)tissue) [26]80 kPa (Elastic modulus) [39]
Fibrinogen-coated PA25 kPa (Elastic modulus) [39]
2. Osteogenic~40 kPa (bone osteoid)Collagen I- coated PA40 kPa (Elastic modulus) [26]
(bone tissue)[26]80 kPa (Elastic modulus) [39]
Fibrinogen-coated PA25 kPa (Elastic modulus) [39]
3. Cardiomyogenic~13 kPa (normal heartCollagen I- coatedNo effect of elasticity [45]
(heart muscle)muscle tissue) [47]Fibrinogen-coated PA20 kPa (Elastic modulus) [45]
4. HSCs expansion~150 Pa (bone marrowGelatin-coated PA Collagen I-coated PA20 kPa (Elastic modulus) [45] 0.0442 kPa (Elastic modulus) [48]
(bone marrow)niche) [37]Fibrinogen-coated PA~12-30 kPa (Storage modulus) [37]

2.2 The interplay of soluble factors and substrate elasticity for stem cell differentiation

Stem cells are conventionally induced by adding soluble factors (growth factors, small ECMs and chemical molecules) [49, 50]; however, elasticity of cell culture substrates is capable to mimic the inductive effects of such soluble factors. In the initial study of Engler et al., MSCs cultured on PA with different elasticities were induced to different types of lineage cells without the addition of differentiation-inducing factors [26]. Other investigators described that annulus fibrosis-derived stem cells would be differentiated into chondrogenic or osteogenic pathway, simply by adjusting the elastic modulus of substrates, such as poly(ether carbonate urethane)urea with the elasticity ranging from 2.5 MPa to 13.4MPa [17].

Holst et al. showed that elasticity of thin films of tropoelastin with a cell binding sequence of VGVAPG on oxidized polystyrene was able to selectively expand the fraction of Lin− Sca-1+ c-Kit+(LSK)-expressing HSCs [15]. The selective expansion effect was absence on the tropoelastin-uncoated dishes, but it was achieved by subjecting LSK-expressing HSCs on the uncoated dishes with cocktail of cytokines (interleukine-3 (IL-3) and IL-6, and stem cell factor). Addition of blebbistatin in culture medium abrogated the effect of tropoelastin on LSK-expressing HSCs cells, indicating the correlation of selective expansion effect to the cellular mechanotransduction.

The inductive effects of soluble factors and elasticity cues are synergism. Jiang et al. reported higher expression of osteogenic markers for MSCs cultured on stiff gels than that for MSCs on soft gels [51]. Addition of alendronate (promoter of osteogenic differentiation) further enhanced the expression of osteogenic markers by MSCs on the stiff gels [51]. The synergistic effect of elasticity and soluble factors implies that elasticity and soluble factors would affect the cell differentiation through different mechanisms [12]. It is summarized that the elasticity of the cell culture substrates only guides the lineage specification at early stage of differentiation, and inductive media are still necessary to mature the differentiation of MSCs [10, 42].

3 Do the current studies of elasticity-driven commitment of stem cells reflect the true responses of stem cells in the actual ECMs microenvironment?

The most of studies of elasticity-driven fate commitment of stem cells are mainly conducted on 2-D cell culture substrates with different Young’s modulus or storage modulus, based on the static experimental setting [8, 26, 37]. These researches are invaluable in revealing the fundamental insights on how cells response to the physical cues (e.g., cells exert low traction and high deformation on soft hydrogels and high traction and low deformation on stiff hydrogels [40]), suggesting that stem cells would adapt its behavior and fate corresponding to the elasticity of substrates [26]. However, the 2-D culture systemlack the dimensional and mechanical complexity of native 3-D ECMs environment, which exhibits viscoelasticity (stress-relaxing properties): that is, ECMs undergo continuous deformation under a constant stress (Figure 3) [31]. Moreover, native ECMs are constantly remodeled throughout the life of individuals, which introduce the changes of mechanical properties inadvertently [31, 32, 52]. Thus, simple responses of stem cells to the stiffness of 2D substrates (tendency of stem cells to efficiently differentiate into specific tissue lineage when stem cells were cultured on the biomaterials with similar elasticity to the tissue) might not fully reflect the responses of stem cells in the actual ECMs microenvironment.

Figure 3 (A) Schematic illustration of cells cultured on 2-D substrate and cells in actual ECMs environment. So far, responses of stem cells to elasticity when cultured in biologically relevant system are unknown. (B) Viscoelastic measurement of various living tissues. Covalently crosslinked hydrogel is poly(acrylamide). Parts of figure are adapted with permission from [31] (B)
Figure 3

(A) Schematic illustration of cells cultured on 2-D substrate and cells in actual ECMs environment. So far, responses of stem cells to elasticity when cultured in biologically relevant system are unknown. (B) Viscoelastic measurement of various living tissues. Covalently crosslinked hydrogel is poly(acrylamide). Parts of figure are adapted with permission from [31] (B)

In this section, we discuss the interplay of elasticity and dynamic physical properties of cell culture materials in influencing the differentiation fates of stem cells. An empirical model to simplify the lineage specification of stem cells in dynamic cell culture environment is discussed and proposed. To the best of our knowledge, the responses of stem cells to the dynamic properties of cell culture materials are largely conducted in the 3-D cell culture environment. Therefore, the studies conducted in 3-D cell culture setting aremainly discussed.

3.1 Lineage specification of stem cell cultured in the material exhibiting dynamic physical properties

In the 3-D cell culture setting, adipogenic and osteogenic commitments of stem cells are commonly used to elucidate the effect of elasticity matrices on the lineage specification of stem cells [31, 33, 34]. From the biological point of view, soft and hard tissues originated from fat (adipogenic) and bone (osteogenic)provide contrasting results on how elasticity of substrates would influence the commitment tendency of stem cells. Adipogenic and osteogenic pathways are previously shown to be highly sensitive to the changes of elasticity of cell culture materials [42]. Therefore, it is possible to identify non-elasticity factors that affect the elasticity-driven lineage specification of stem cells by keeping constant elasticity of matrices. From the technical point of view, the ratios of adipogenic to osteogenic differentiations are easily quantified by employing Oil Red O staining and alkaline phosphatase (ALP) staining [34].

Khetan et al. showed that if the stem cells are unable to exert traction to deform matrices, elasticity is not an overriding factor in determining lineage specification of stem cells [33]. They initially employed chemically-crosslinked hydrogels (restricted hydrogels) with stable bonds strong enough to prevent cells from reorganizing the matrices mechanically. As a result, MSCs cultured on this hydrogel with various elasticities (4-95 kPa) consistently adopted the adipogenic fate of differentiation (Figure 4(A)). Introducing degradable bonds to the structure of hydrogels (permissive hydrogels) allowed the stem cells to exert cellular traction on the matrices, which subsequently shifted the fate of stem cell differentiation into osteogenic pathway (Figure 4(B)). It is speculated that stem cells would attempt to modify the local microenvironment by degrading their surroundings and resulting in a deformable microenvironment. These observations suggest that traction-mediated deformation is necessary to promote the osteogenic differentiation, whereas the absence of such deformation is required for adipogenic differentiation of the stem cells.

Figure 4 Degradation-mediated traction in chemically-crosslinked hydrogel. (A) Osteogenic and adipogenic differentiation of MSCs in chemically-crosslinked hydrogel of different stiffness in the mixed media. (B) Average drift-corrected bead displacement within 15 μm of cell surface as given by traction force microscopy. –UV is the degradable chemically-crosslinked hydrogel and D0UV is the non-degradable chemically crosslinked hydrogel. Parts of figure are adapted with permission from [33] (A),(B)
Figure 4

Degradation-mediated traction in chemically-crosslinked hydrogel. (A) Osteogenic and adipogenic differentiation of MSCs in chemically-crosslinked hydrogel of different stiffness in the mixed media. (B) Average drift-corrected bead displacement within 15 μm of cell surface as given by traction force microscopy. –UV is the degradable chemically-crosslinked hydrogel and D0UV is the non-degradable chemically crosslinked hydrogel. Parts of figure are adapted with permission from [33] (A),(B)

Correlation of the degree of traction-mediated deformation and the commitment fate of stem cells was investigated by Huebsch et al. [34]. MSCs were cultured in the alginate hydrogels crosslinked physically with different elasticity at 2.5, 5, 12, 20, or 110 kPa (Figure 5(A) [34]; the hydrogels were mobile enough to allow cells to sense the matrices mechanically. It is thus possible to correlate the extent of matrix reorganization to the fates of stem cell differentiation. Adipogenic differentiation of MSCs predominated in soft microenvironments of the hydrogels at 2.5-5 kPa, whereas osteogenic differentiation occurred mainly in the intermediate hydrogels at 12-20 kPa. Interestingly, osteogenic differentiation of MSCs in the stiffest hydrogel at 110 kPa was apparently downregulated compared with that in the hydrogel at 20kPa, as evidenced by lower ALP staining. Further investigation revealed that traction-mediated deformation in the hydrogel at 20 kPa became maximum compared to those in the softest and stiffest hydrogels (Figure 5(B)). It would be explained by the fact that any cells could not assemble cytoskeleton-adhesion complexes in the extremely soft hydrogels and exert sufficient traction to deform extremely stiff hydrogels [44]. Taken together, these results are consistent with the study by Khetan et al.; the correlation of osteogenic/adipogenic differentiation of MSCs withthe degree of traction-mediated deformations.

Figure 5 Elasticity-driven lineage of stem cells in 3-D matrix. (A) Osteogenic and adipogenic differentiations of MSCs in the hydrogel of different elasticity (2.5-110 kPa) in the presence of osteogenic-and adipogenic-inducing medium. (B) Measurement of ligand adhesion (RGD) displacement in hydrogels of different stiffness by fluorescence energy transfer (FRET). DFRET is the degree of energy transfer. (*p< 0.01 compared with other conditions, Holm-Bonferroni test). Error bars represented standard deviation for clustering measurements (n = 3). (C) Quantification of adipogenic and osteogenic differentiations of MSCs when cultured on the hydrogel of constant elastic modulus (9 and 17 kPa), yet different viscoelasticity (expressed by relaxation time: 2300 – 60 s). Parts of figure are adapted with permission from [34] (A),(B), and [31] (C)
Figure 5

Elasticity-driven lineage of stem cells in 3-D matrix. (A) Osteogenic and adipogenic differentiations of MSCs in the hydrogel of different elasticity (2.5-110 kPa) in the presence of osteogenic-and adipogenic-inducing medium. (B) Measurement of ligand adhesion (RGD) displacement in hydrogels of different stiffness by fluorescence energy transfer (FRET). DFRET is the degree of energy transfer. (*p< 0.01 compared with other conditions, Holm-Bonferroni test). Error bars represented standard deviation for clustering measurements (n = 3). (C) Quantification of adipogenic and osteogenic differentiations of MSCs when cultured on the hydrogel of constant elastic modulus (9 and 17 kPa), yet different viscoelasticity (expressed by relaxation time: 2300 – 60 s). Parts of figure are adapted with permission from [34] (A),(B), and [31] (C)

Viscoelastic materials sometimes show non-elastic deformation under a constant stress, which is an ideal system to investigate the correlation of traction-mediated deformation and lineage specification of stem cells. Chaudhuri et al. investigated the hydrogel system with different viscoelasticity but a constant initial Young’s modulus at 9 and 17 kPa [31]. The viscoelasticity of hydrogels is expressed by relaxation time (τ1/2); briefly, the hydrogels with the faster τ1/2 shows quick remodeling under a constant value of stress and slow remodelling for hydrogels with slower τ1/2. If elasticity of materials solely governs the differentiation of stem cells, faster (lower) relaxation time would be a factor for downregulation (upregulation) of the osteogenic (adipogenic) differentiation of the cells. Interestingly, the experimental data showed the opposite results. Osteogenic (adipogenic) differentiation was upregulated (downregulated) in hydrogels with faster τ1/2 (slower τ1/2) (Figure 5(C)). It is suggested that the viscoelastic materials cause traction-mediated deformation, which in turn enhances (inhibits) the osteogenic (adipogenic) differentiation of MSCs.

Other studies also confirmed the importance of traction-mediated deformation in determining lineage specification of stem cells. Toda et al. described that osteogenic differentiation of MSCs was promoted in the decrease of elasticity (storage modulus) of hydrogels during the culture period [38]. Das et al. investigated the promotion of adipogenic differentiation of MSCs in the stress-stiffening hydrogels with lower critical stress (the threshold stress value to initiate the stiffening of hydrogels); however, the hydrogels with higher critical stress upregulated the osteogenic differentiation of MSCs [53]. These results do not conform with the idea that the stem cell differentiations of stiff/ soft tissue lineage only occur at stiff/soft substrates. These observations can be only explained by taking into account the correlation of traction-mediated deformation and stem cell differentiation.

In summary, when the stem cells are allowed to exert traction to deform the matrices significantly, the cells commit to differentiate into the osteogenic fate (hard tissue). Meanwhile, when the stem cells are unable to deform the matrices significantly, the cells adopt the differentiation into adipogenic lineage (soft tissue).

3.2 Empirical model of traction-mediated deformation to explain the lineage specification of stem cells

An empirical model to explain how the traction-mediated deformation regulates the lineage specification of stem cells is proposed (Figure 6) based on four major assumptions:

Figure 6 Model of traction-mediated deformation to explain the lineage specification of stem cells in dynamic microenvironment. Cellular traction and matrix stability are the function of elastic modulus. Traction gradually increases with E up to the EX where the traction is saturated and incapable to increase further with elasticity. Stability gradually increases with elasticity and keep increasing even after the elasticity is beyond EX. Net product is represented by rectangular with different fillers. Net products in soft, intermediate, and stiff regions of hydrogels are represented by dotted, lined, open rectangular, respectively
Figure 6

Model of traction-mediated deformation to explain the lineage specification of stem cells in dynamic microenvironment. Cellular traction and matrix stability are the function of elastic modulus. Traction gradually increases with E up to the EX where the traction is saturated and incapable to increase further with elasticity. Stability gradually increases with elasticity and keep increasing even after the elasticity is beyond EX. Net product is represented by rectangular with different fillers. Net products in soft, intermediate, and stiff regions of hydrogels are represented by dotted, lined, open rectangular, respectively

  1. Cells exert “traction” with the magnitude corresponding to elastic modulus (E) of materials. At the stiff materials with E ∝ EX, cells are unable to increase the magnitude of “traction” [40, 54]. Thus, the cellular traction is saturated beyond the point at EX. The traction force is generally measured by a traction force microscopy, and subsequently expressed in the dimension, pN/μm2, of force/surface area (normalized against the focal adhesion size) [55].

  2. The tentative term ‘stability’ should be introduced; it is defined as the compliancy of materials to deform under a stress applied. The magnitude is proportional to E value. Pure elastic materials exhibit time-independent deformation [56], therefore “stability” is unchanged with time (t); stability(elastic) ≈ f(E). On the other hand, deformation in viscoelastic materials is time-dependent, therefore “stability” of viscoelastic materials gradually decreases over a period of time; stability(viscoelastic) ≈ f(E,t) [56]. Low “stability” implies significant deformation under a stress applied and vice versa for high “stability”. When the materials are deformable by cells, it is followed that the gradient of “traction” is larger than the “stability” at any points before EX. “Stability” possesses same dimensional unit with elasticity that is force/surface area.

  3. The “net product” is defined as subtraction of “stability” from “traction”, of which physical interpretation is net cellular traction; it might also corresponds to the net matrix deformation. Due to the restriction of physical interpretation, the lowest value of “net product” is zero. The “net product” shows biphasic relationship with elasticity; it gradually increases from low elasticity, maximizes near EX, and steadily decreases afterwards. Traction and stability lines meet at hypothetical point Ed, and consequently the net product is zero.

  4. Lineage specification of stem cells depends on the “net product”. The relationship of “net product” and differentiation fate is depicted in (Figure 7). Adipogenic differentiation of stem cells was maximized at small values of “net product” and gradually decreased as net product became larger. On the other hand, osteogenic differentiation of stem cells was minimized at small value of “net product” and gradually increased and maximized near the point EX. Beyond the point EX, the cellular traction was saturated, while the stability continues to increase. As a result, the value of net product gradually decreases, concurrently with the downregulation of osteogenic differentiation. However, beyond the EX point, the changes of net product do not correlates with adipogenic differentiation as shown in previous experimental results [34].

Figure 7 Relationship of net product (y-axis)and the extent of lineage specification of stem cells (x-axis). Osteogenic differentiation is optimized when the magnitude of net product is maximized. On the other hand, adipogenic differentiation is optimized when the magnitude of net product is minimized
Figure 7

Relationship of net product (y-axis)and the extent of lineage specification of stem cells (x-axis). Osteogenic differentiation is optimized when the magnitude of net product is maximized. On the other hand, adipogenic differentiation is optimized when the magnitude of net product is minimized

The proposed empirical modelcan explain the prevalent results of direct-sensing differentiation of stem cells. Pure elastic materials exhibit time-independent deformation and no plastic deformation occurs under higher magnitude of stress [57, 58]. Therefore, the “stability” line strictly depends on the elasticity. As a result, “net product” and commitment of stem cells simply depends on the elasticity of substrates. As previously described, direct-sensing differentiation is insufficient to explain the lineage specification of stem cells cultured in mechanically dynamic materials [31, 33]. In the viscoelastic materials, plastic deformation of materials continuously occurs at a constant stress after enough time of stress application, thus stability value at a given elastic modulus should be shifted down.

Based on the data by Huebsch et al. [34], the net product is low for MSCs cultured in the hydrogels at 2.5 or 5 kPa (soft region). The net product is maximized for MSCs cultured at 12 or 20 kPa hydrogel (intermediate region), and gradually decreased for that cultured at 110 kPa (stiff region). In the similar manner, adipogenic and osteogenic differentiations are maximized at the lowest and highest net products in the soft and intermediate regions (Figure 7). It is interesting to note that the decrease of net product in the stiff only affects the osteogenic differentiation but not the adipogenic differentiation, suggesting the involvement of other types of mechanosensing mechanism on the excessively stiff substrate (beyond Ex point).

We further expand the model to apply the results investigated by Chaudhuri et al. [31] and Khetan et al. [33] in Figure 8. Although the elastic modulus of the hydrogels was kept constant at 9 kPa and 17 kPa, each hydrogel exhibited different relaxation times at 60 - 2600 seconds [31]. The hydrogels with faster relaxation time were quickly deformed compared to those with slower relaxation time, therefore the soft hydrogels decreased stability. On the other hand, cells exerted the constant traction value. As a result, net product (osteogenic differentiation) was maximized for the hydrogels with faster relaxation time.

Figure 8 Model of traction-dependent differentiation used to explain the studies by (A) Chaudhuri et al. [31], (B) Khetan et al. [33]. There are two types of stability lines: (1) full-line indicates stability of matrix capable to be mechanically reorganized (e.g., physically-crosslinked hydrogel). (2) dot-line indicates stability of matrix incapable to be mechanically reorganized (e.g., chemically-crosslinked hydrogel). Vertical dot-line connecting traction and stability indicates net product with the length correspond to the magnitude of net product. Full-arrow indicates shift of stability of materials with different viscoelastic properties. Dot-arrow indicates shift of stability when local degradation occurs at the matrices incapable to be mechanically reorganized
Figure 8

Model of traction-dependent differentiation used to explain the studies by (A) Chaudhuri et al. [31], (B) Khetan et al. [33]. There are two types of stability lines: (1) full-line indicates stability of matrix capable to be mechanically reorganized (e.g., physically-crosslinked hydrogel). (2) dot-line indicates stability of matrix incapable to be mechanically reorganized (e.g., chemically-crosslinked hydrogel). Vertical dot-line connecting traction and stability indicates net product with the length correspond to the magnitude of net product. Full-arrow indicates shift of stability of materials with different viscoelastic properties. Dot-arrow indicates shift of stability when local degradation occurs at the matrices incapable to be mechanically reorganized

The chemically-crosslinked hydrogels used by Khetan et al. were stable enough to prevent matrix reorganization by cellular traction. Therefore, the stability magnitude is significantly greater than traction at all values of elasticity, resulting in the depreciation of net product at any ranges of elasticity of hydrogels (commitment to adipogenic lineage of differentiation). In the hydrogels with degradable bonds, the stem cells were capable of locally degrading the matrix, and the stability therefore would shift to the lower magnitude. As a result, the stem cells are able to exert traction todeform the matrices and differentiate in osteogenic pathway.

Two important points were summarized based on the empirical model proposed; 1) the net product determines the lineage differentiation of stem cells and 2) the time-dependent deformation of viscoelastic material changes the stability value, which in turn alters the net product (cell commitment) for a given initial elastic modulus.

3.3 Lineage specification of stem cells on 2-D substrates and 3-D materials based on the empirical model

As previously mentioned in section II, investigations of mechanotransduction of stem cells on 2-D substrates have been conducted by defining elasticity as the elastic and viscoelastic parameters [8, 27, 37, 38]. Based on our model, it is clear that viscoelasticity may influence the final fates of stem cell differentiations. Cameron et al. cultured MSCs on the substrate exhibiting similar storage modulus but different loss modulus [59]; the cell surface area on the substrate was increased with large loss modulus. Chaudhuri et al. further demonstrated that variation in storage modulus may alter the commitment fates of stem cells [31]. Failure in taking into account the viscoelasticity of material may explain the discrepancies observed in the elasticity-driven mechanotransduction literatures [27, 37, 46, 60, 61].

The influences of degradability of substrates to the mechanotransduction of stem cells were rarely investigated. Peng et al. cultured MSCs on the 2-D poly(ethyleneglycol) (PEG) substrates with different degradation rates [52] and the substrates with the highest degradation rate had the highest loss of elastic modulus (softening of substrate). Interestingly, the highly degraded substrates promoted the osteogenic differentiation of MSCs, which would be contradicted the conventional direct-sensing differentiation. Based on our model, MSCs cultured on PEG substrates with elastic modulus in the range of ~500 - 1,000 kPa saturated the cellular traction. The degradation of material would reduce the elastic modulus, resulting in the decrease of both traction and stability. As a result, the net product would be maximized and osteogenic differentiation was promoted.

It is worth to mention that the empirical model developed here was intended to augment the direct-sensing differentiation model widely used in 2-D cell culture study. In other words, both of these models are based on the cellular contractility as the main agent of mechanosensing. Several investigators have raised the possibilities of different mechanisms of mechanosensing in 2-D and 3-D environments [62]. If such case was true, then the empirical model might not be fully applicable to explain the stem cell differentiation in mechanically dynamic 2-D environment.

4 Conclusions and future outlooks

Elasticity of materials for culturing cells is commonly characterized by the elastic modulus or viscoelastic modulus. Adult cells have been known to adjust their motility (cell locomotion) or contractility (e.g., membrane stiffness, exerted traction) in response to elasticity of substrates. The responses of adult cells to substrate elasticity were speculated to be mediated by the mechanotransduction process. Not only adult cells but also stem cells were shown to be responsive to the elasticity. Stem cells efficiently differentiate into the particular tissue lineage of the cells when the cells are cultured on the materials of which elasticity mimic the stiffness of targeted tissue.

Sensitivity of stem cells to elastic cues depends on the differentiation stages of the cells, with the early differentiated stem cells being more sensitive to elasticity cues than the late differentiated stem cells. The optimum value to induce the specific differentiation of the cells depends on the type of ECMs used to connect materials and cells. Several explanations have been raised why different types of ECMs alter the optimum elasticity for the differentiation of stem cells into specific lineages of the cells. ECMs bind different receptor (integrin) of the cells, and thus activate the different mechanism of mechanotransduction. Some investigators proposed that the stem cells did not directly sense the elasticity of substrates, but instead interacted with the ECMs [10]. Future investigations are necessary to elucidate the factors underlying the variation of optimum elasticity.

Direct-sensing differentiation is insufficient to explain the fate commitment of stem cells cultured on materials with dynamic physical properties. It is found that stem cells exert cellular traction to deform the matrices and differentiate into hard or soft tissue lineage of the cells by considering the traction-mediated deformation. Viscoelastic materials accommodate the traction-mediated deformation. Therefore, highly viscoelastic materials would promote or inhibit the osteogenic (hard tissue) oradipogenic (soft tissue) differentiation of stem cells.

In this paper, the empirical model based on the traction-mediated deformation is proposed. There are three important components in this model: (1) traction, (2) stability, (3) net product. Differentiation of stem cells is largely determined by magnitude of net product. By changing the elasticity of materials, it is possible to shift the traction and stability points. For the pure elastic materials, it is not possible to shift the traction and stability points independently, resulting in the common responses observed for direct-sensing differentiation. However, the viscoelastic or degradable materials allow the shift of stability points independent of cellular traction, resulting in inconsistence of direct-sensing differentiation. Range of substrate elasticity seems to alter the responses of stem cells to changes of net products. It is necessary to further investigate the physiologically relevant elastic modulus of materials. Lastly, the empirical model of tractionmediated deformation can be applied as a framework to design future studies to investigate the differentiation of stem cells into various lineages in mechanically dynamic 2-D or 3-D cell culture materials.

Acknowledgement

First author acknowledges Petrus Caesario (Tokyo Institute of Technology) for assistance with empirical model.

References

[1] Lanza R., et al. (eds), Essentials of Stem Cell Biology, 2006, El-sevier Academic Press, San Diego.Search in Google Scholar

[2] Chung C., Burdick J.A., Influence of Three-Dimensional Hyaluronic Acid Microenvironments on Mesenchymal Stem Cell Chondrogenesis, Tissue Eng. Part A, 2009, 15, 243-254.10.1089/ten.tea.2008.0067Search in Google Scholar PubMed PubMed Central

[3] Anderson H.J., Sahoo J.K., Ulijn R.V., Dalby MJ., Mesenchymal Stem Cell Fate: Applying Biomaterials for Control of Stem Cell Behavior, Front. Bioeng. Biotechnol., 2016, 4, 1-14.10.3389/fbioe.2016.00038Search in Google Scholar PubMed PubMed Central

[4] Watt F.M., Huck W.T.S., Role of the extracellular matrix in regulating stem cell fate, Nat. Rev. Mol. Cell Biol., 2013, 14, 467-473.10.1038/nrm3620Search in Google Scholar PubMed

[5] Hui T.Y., Cheung K.M.C., Cheung W.L., Chan D., Chan B.P., In vitro chondrogenic differentiation of human mesenchymal stem cells in collagen microspheres: Influence of cell seeding density and collagen concentration, Biomaterials, 2008, 29, 3201-3212.10.1016/j.biomaterials.2008.04.001Search in Google Scholar PubMed

[6] Higuchi A., Kumar S.S., Ling Q., Hsu S., Benelli G., Umezawa A., Progress in Polymer Science Polymeric design of cell culturematerials that guide the differentiation of human pluripotent stem cells, Prog. Polym. Sci, 2017, 65, 83-126.10.1016/j.progpolymsci.2016.09.002Search in Google Scholar

[7] Chowdhury F., et al., Material properties of the cell dictate stress-induced spreading and differentiation in embryonic stemcells, Nat. Mater, 2010, 9, 82-88.10.1038/nmat2563Search in Google Scholar PubMed PubMed Central

[8] Zoldan J., Karagiannis E.D., Lee C.Y., Anderson D.G., Langer R., Levenberg S., The influence of scaffold elasticity on germ layer specification of human embryonic stem cells, Biomaterials, 2011, 32, 9612-9621.10.1016/j.biomaterials.2011.09.012Search in Google Scholar PubMed PubMed Central

[9] Goetzke R., et al., Why the impact of mechanical stimuli on stem cells remains a challenge, Cell. Mol. Life Sci, 2018, 18, 3297-331210.1007/s00018-018-2830-zSearch in Google Scholar PubMed

[10] Higuchi A., Ling Q.D., Chang Y., Hsu S.T., Umezawa A., Physical cues of biomaterials guide stem cell differentiation fate, Chem. Rev, 2013, 113, 3297-3328.10.1021/cr300426xSearch in Google Scholar PubMed

[11] Higuchi A., Ling Q.D., Hsu S.T., Umezawa A., Biomimetic cell culture proteins as extracellular matrices for stem cell differentiation, Chem. Rev, 2012, 112, 4507-4540.10.1021/cr3000169Search in Google Scholar PubMed

[12] Holst J., et al., Substrate elasticity provides mechanical signals for the expansion of hemopoietic stem and progenitor cells, Nat. Biotechnol., 2010, 28, 1123-1128.10.1038/nbt.1687Search in Google Scholar PubMed

[13] McCain M.L., Yuan H., Pasqualini F.S., Campbell P.H., Parker K.K., Matrix elasticity regulates the optimal cardiac myocyte shape for contractility, AJP Hear. Circ. Physiol.,2014, 306, H1525-1539.10.1152/ajpheart.00799.2013Search in Google Scholar PubMed PubMed Central

[14] Goldring M.B., Chondrogenesis, chondrocyte differentiation, and articular cartilage metabolism in health and osteoarthritis, Ther. Adv. Musculoskelet. Dis, 2012, 4, 269-285.10.1177/1759720X12448454Search in Google Scholar PubMed PubMed Central

[15] Ullah I., Subbarao R.B., Rho G.J., Human mesenchymal stem cells - current trends and future prospective, Biosci. Rep., 2015, 35, 1-18.10.1042/BSR20150025Search in Google Scholar PubMed PubMed Central

[16] Huebsch N., et al., Matrix elasticity of void-forming hydrogels controls transplanted-stem-cell-mediated bone formation, Nat. Mater. 2015, 14, 1269-1277.10.1038/nmat4407Search in Google Scholar PubMed PubMed Central

[17] Gilbert P.M., et al., Substrate Elasticity Regulates Skeletal Muscle Stem Cell Self-Renewal in Culture, Science, 2010, 329, 1078-1081.10.1126/science.1191035Search in Google Scholar PubMed PubMed Central

[18] Salick M.R, et al., Micropattern width dependent sarcomere development in human ESC-derived cardiomyocytes, Biomaterials, 2014, 35, 4454-4464.10.1016/j.biomaterials.2014.02.001Search in Google Scholar PubMed PubMed Central

[19] Pan F., et al., Topographic effect on human induced pluripotent stem cells differentiation towards neuronal lineage, Biomaterials, 2013, 34, 8131-8139.10.1016/j.biomaterials.2013.07.025Search in Google Scholar PubMed

[20] Shanmugasundaram S., Chaudhry H., Arinzeh T.L., Microscale Versus Nanoscale Scaffold Architecture for Mesenchymal Stem Cell Chondrogenesis, Tissue Eng. Part A., 2011, 17,831-840.10.1089/ten.tea.2010.0409Search in Google Scholar

[21] Matsiko A., Gleeson J.P., O’Brien F.J., Scaffold Mean Pore Size Influences Mesenchymal Stem Cell Chondrogenic Differentiation and Matrix Deposition, Tissue Eng. Part A., 2015, 21, 486-497.10.1089/ten.tea.2013.0545Search in Google Scholar

[22] Lee G., et al., Isolation and directed differentiation of neural crest stem cells derived from human embryonic stem cells,Nat. Biotechnol., 2007, 25, 1468-1475.10.1038/nbt1365Search in Google Scholar PubMed

[23] Sonntag K-C, et al., Enhanced Yield of Neuroepithelial Precursors and Midbrain-Like Dopaminergic Neurons from Human Embryonic Stem Cells Using the Bone Morphogenic Protein Antagonist Noggin,Stem Cells, 2007, 25, 411-418.10.1634/stemcells.2006-0380Search in Google Scholar PubMed PubMed Central

[24] Zhang S.C., Wernig M., Duncan I.D., Brüstle O., Thomson J.A., In vitro differentiation of transplantable neural precursors from human embryonic stem cells, Nat. Biotechnol., 2001, 19, 1129-1133.10.1038/nbt1201-1129Search in Google Scholar PubMed

[25] Tabar V., et al., Migration and differentiation of neural precursors derived from human embryonic stem cells in the rat brain, Nat. Biotechnol., 2005, 23, 601-606.10.1038/nbt1088Search in Google Scholar PubMed

[26] Engler A.J., Sen S., Sweeney H.L., Discher D.E., Matrix Elasticity Directs Stem Cell Lineage Specification, Cell, 2006, 126, 677-689.10.1016/j.cell.2006.06.044Search in Google Scholar PubMed

[27] Wen J.H., et al., Interplay of matrix stiffness and protein tethering in stem cell differentiation, Nat. Mater., 2014, 13, 979-987.10.1038/nmat4051Search in Google Scholar PubMed PubMed Central

[28] Hazeltine L.B., Badur M.G., Lian X., Das A., Han W., Palecek S.P., Temporal impact of substrate mechanics on differentiation of human embryonic stem cells to cardiomyocytes, Acta Biomater., 2014, 10, 604-612.10.1016/j.actbio.2013.10.033Search in Google Scholar PubMed PubMed Central

[29] Zhu C., Li J., Liu C., Zhou P., Yang H., Li B., Modulation of the gene expression of annulus fibrosus-derived stem cells using poly(ether carbonate urethane)urea scaffolds of tunable elasticity. Acta Biomater. 2016, 29, 228-238.10.1016/j.actbio.2015.09.039Search in Google Scholar PubMed

[30] Saha K., et al., Substrate Modulus Directs Neural Stem Cell Behavior, Biophys. J.,2008, 95, 4426-4438.10.1529/biophysj.108.132217Search in Google Scholar PubMed PubMed Central

[31] Chaudhuri O., et al., Hydrogels with tunable stress relaxation regulate stem cell fate and activity, Nat. Mater., 2016, 15, 326-334.10.1038/nmat4489Search in Google Scholar PubMed PubMed Central

[32] Tranqui L., Tracqui P., Signalisation mecanique et angiogenese. Comptes Rendus de l’Académie des Sciences-Series III-Sciences de la Vie,2000, 323, 31-47.10.1016/S0764-4469(00)00110-4Search in Google Scholar

[33] Khetan S., Guvendiren M., Legant W.R., Cohen D.M., Chen C.S., Burdick J.A., Degradation-mediated cellular traction directs stem cell fate in covalently crosslinked three-dimensional hydrogels, Nat. Mater., 2013, 12, 458-465.10.1038/nmat3586Search in Google Scholar PubMed PubMed Central

[34] Huebsch N., et al., Harnessing traction-mediated manipulation of the cell/matrix interface to control stem-cell fate, Nat. Mater. 2010, 9, 518-526.Search in Google Scholar

[35] Chaudhuri O., et al., Substrate stress relaxation regulates cell spreading, Nat. Commun., 2015, 6, 1-7.10.1038/ncomms7365Search in Google Scholar PubMed PubMed Central

[36] Discher D.E., Janmey P., Wang Y.L., Tissue Cells Feel and Respond to the Stiffness of Their Substrate, Science, 2005, 310, 1139-1143.10.1126/science.1116995Search in Google Scholar PubMed

[37] Kumar S.S., et al., The combined influence of substrate elasticity and surface-grafted molecules on the exvivo expansion of hematopoietic stem and progenitor cells, Biomaterials, 2013, 34, 7632-7644.10.1016/j.biomaterials.2013.07.002Search in Google Scholar PubMed

[38] Toda H., Yamamoto M., Uyama H., Tabata Y., Fabrication of hydrogels with elasticity changed by alkaline phosphatase for stem cell culture, Acta Biomater., 2016, 29, 215-227.10.1016/j.actbio.2015.10.036Search in Google Scholar PubMed

[39] Rowlands A.S., George P.A., Cooper-White J.J., Directing osteogenic and myogenic differentiation of MSCs: interplay of stiffness and adhesive ligand presentation, AJP Cell Physiol., 2008, 295, C1037-1044.10.1152/ajpcell.67.2008Search in Google Scholar PubMed

[40] Plotnikov S.V., Pasapera A.M., Sabass B.,Waterman C.M., Force fluctuations within focal adhesions mediate ECM-rigidity sensing to guide directed cell migration, Cell 2012, 151, 1513-1527.10.1016/j.cell.2012.11.034Search in Google Scholar PubMed PubMed Central

[41] Kuznetsova T.G., Starodubtseva M.N., Yegorenkov N.I., Chizhik S.A., Zhdanov R.I., Atomic force microscopy probing of cell elasticity, Micron., 2007, 38, 824-833.10.1016/j.micron.2007.06.011Search in Google Scholar PubMed

[42] Guvendiren M., Burdick J.A., Stiffening hydrogels to probe short- and long-term cellular responses to dynamic mechanics. Nat. Commun., 2012, 3, 792-799.10.1038/ncomms1792Search in Google Scholar PubMed

[43] Higuchi A., Ling Q,. Chang Y., Hsu S., Umezawa A., Physical Cues of Biomaterials Guide Stem Cell Differentiation Fate, Chem. Rev., 2013, 113, 3297-332810.1021/cr300426xSearch in Google Scholar PubMed

[44] Wang N., et al., Cell prestress. I. Stiffness and prestress are closely associated in adherent contractile cells, Am. J. Physiol. Physiol, 2002, 282, C606-616.10.1152/ajpcell.00269.2001Search in Google Scholar PubMed

[45] Hirata M., Yamaoka T., Effect of stem cell niche elasticity/ECM protein on the self-beating cardiomyocyte differentiation of induced pluripotent stem (iPS) cells at different stages, Acta Biomater., 2017, 65, 44-52.10.1016/j.actbio.2017.10.032Search in Google Scholar PubMed

[46] Trappmann B., et al., Extracellular-matrix tethering regulates stem-cell fate, Nat. Mater., 2012, 11, 642-649.10.1038/nmat3339Search in Google Scholar PubMed

[47] Engler A.J., et al., Embryonic cardiomyocytes beat best on amatrix with heart-like elasticity: scar-like rigidity inhibits beating, J. Cell Sci, 2008, 121, 3794-3802.10.1242/jcs.029678Search in Google Scholar PubMed PubMed Central

[48] Choi J.S., Harley B.A.C., The combined influence of substrate elasticity and ligand density on the viability and biophysical properties of hematopoietic stem and progenitor cells, Biomaterials, 2012, 33, 4460-4468.10.1016/j.biomaterials.2012.03.010Search in Google Scholar PubMed

[49] Park J.S., et al., The effect of matrix stiffness on the differentiation of mesenchymal stem cells in response to TGF-β Biomaterials,2011, 32, 3921-3930.10.1016/j.biomaterials.2011.02.019Search in Google Scholar PubMed PubMed Central

[50] Chen C.W., et al., Type I and II collagen regulation of chondrogenic differentiation by mesenchymal progenitor cells, J. Orthop. Res., 2005, 23, 446-453.10.1016/j.orthres.2004.09.002Search in Google Scholar PubMed

[51] Jiang P., Mao Z., Gao C., Combinational effect ofmatrix elasticity and alendronate density on differentiation of rat mesenchymal stem cells, Acta Biomater., 2015, 19, 76-84.10.1016/j.actbio.2015.03.018Search in Google Scholar PubMed

[52] Peng Y., Liu Q.J., He T., Ye K., Yao X., Ding J., Degradation rate affords a dynamic cue to regulate stem cells beyond varied matrix stiffness, Biomaterials, 2018, 178, 467-480.10.1016/j.biomaterials.2018.04.021Search in Google Scholar PubMed

[53] Das R.K., Gocheva V., Hammink R., Zouani O.F., Rowan A.E., Stress-stiffening-mediated stem-cell commitment switch in soft responsive hydrogels, Nat. Mater., 2016, 15, 318-325.10.1038/nmat4483Search in Google Scholar PubMed

[54] Kong H.J., Polte T.R., Alsberg E., Mooney D.J., FRET measurements of cell-traction forces and nano-scale clustering of adhesion ligands varied by substrate stiffness, Proc. Natl. Acad. Sci., 2005, 102, 4300-4305.10.1073/pnas.0405873102Search in Google Scholar PubMed PubMed Central

[55] Franck C., Maskarinec S.A., Tirrell D.A., Ravichandran G., Three-dimensional traction force microscopy: A new tool for quantifying cell-matrix interactions, PLoS One, 2011, 6, e17833.10.1371/journal.pone.0017833Search in Google Scholar PubMed PubMed Central

[56] Madl C.M., Heilshorn S.C., Blau H.M., Bioengineering strategies to accelerate stem cell therapeutics, Nature, 2018, 557, 335-342.10.1038/s41586-018-0089-zSearch in Google Scholar PubMed PubMed Central

[57] Schwarz U.S., Safran S.A., Elastic Interactions of Cells, Phys Rev Let., 2002, 88, 048102.10.1103/PhysRevLett.88.048102Search in Google Scholar PubMed

[58] Buxboim A., Ivanovska I.L., Discher D.E., Matrix elasticity, cytoskeletal forces and physics of the nucleus : how deeply do cells ‘ feel ’ outside and in?, J. Cell Sci., 2010, 123, 297-308.10.1242/jcs.041186Search in Google Scholar PubMed PubMed Central

[59] Cameron A.R., Frith J.E., Cooper-White J.J., The influence of substrate creep on mesenchymal stem cell behaviour and phenotype, Biomaterials, 2011,32, 5979-5993.10.1016/j.biomaterials.2011.04.003Search in Google Scholar PubMed

[60] Haugh M.G., Heilshorn S.C., Integrating concepts of material mechanics, ligand chemistry, dimensionality and degradation to control differentiation of mesenchymal stem cells, Curr. Opin. Solid State Mater. Sci., 2016, 20, 171-9.10.1016/j.cossms.2016.04.001Search in Google Scholar PubMed PubMed Central

[61] Irawan V., Sung T.C., Higuchi A., Ikoma T., Collagen Scaffolds in Cartilage Tissue Engineering and Relevant Approaches for Future Development, Tissue Eng. Regen. Med., 2018, 1-2510.1007/s13770-018-0135-9Search in Google Scholar PubMed PubMed Central

[62] Lv H., et al., Mechanism of regulation of stem cell differentiation by matrix stiffness, Stem Cell Res. Ther., 2015, 6, 103.10.1186/s13287-015-0083-4Search in Google Scholar PubMed PubMed Central

Received: 2018-08-17
Accepted: 2018-10-29
Published Online: 2018-12-31

© 2018 V. Irawan et al., published by De Gruyter

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Articles in the same Issue

  1. Regular Articles
  2. A modified Fermi-Walker derivative for inextensible flows of binormal spherical image
  3. Algebraic aspects of evolution partial differential equation arising in the study of constant elasticity of variance model from financial mathematics
  4. Three-dimensional atom localization via probe absorption in a cascade four-level atomic system
  5. Determination of the energy transitions and half-lives of Rubidium nuclei
  6. Three phase heat and mass transfer model for unsaturated soil freezing process: Part 1 - model development
  7. Three phase heat and mass transfer model for unsaturated soil freezing process: Part 2 - model validation
  8. Mathematical model for thermal and entropy analysis of thermal solar collectors by using Maxwell nanofluids with slip conditions, thermal radiation and variable thermal conductivity
  9. Constructing analytic solutions on the Tricomi equation
  10. Feynman diagrams and rooted maps
  11. New type of chaos synchronization in discrete-time systems: the F-M synchronization
  12. Unsteady flow of fractional Oldroyd-B fluids through rotating annulus
  13. A note on the uniqueness of 2D elastostatic problems formulated by different types of potential functions
  14. On the conservation laws and solutions of a (2+1) dimensional KdV-mKdV equation of mathematical physics
  15. Computational methods and traveling wave solutions for the fourth-order nonlinear Ablowitz-Kaup-Newell-Segur water wave dynamical equation via two methods and its applications
  16. Siewert solutions of transcendental equations, generalized Lambert functions and physical applications
  17. Numerical solution of mixed convection flow of an MHD Jeffery fluid over an exponentially stretching sheet in the presence of thermal radiation and chemical reaction
  18. A new three-dimensional chaotic flow with one stable equilibrium: dynamical properties and complexity analysis
  19. Dynamics of a dry-rebounding drop: observations, simulations, and modeling
  20. Modeling the initial mechanical response and yielding behavior of gelled crude oil
  21. Lie symmetry analysis and conservation laws for the time fractional simplified modified Kawahara equation
  22. Solitary wave solutions of two KdV-type equations
  23. Applying industrial tomography to control and optimization flow systems
  24. Reconstructing time series into a complex network to assess the evolution dynamics of the correlations among energy prices
  25. An optimal solution for software testing case generation based on particle swarm optimization
  26. Optimal system, nonlinear self-adjointness and conservation laws for generalized shallow water wave equation
  27. Alternative methods for solving nonlinear two-point boundary value problems
  28. Global model simulation of OH production in pulsed-DC atmospheric pressure helium-air plasma jets
  29. Experimental investigation on optical vortex tweezers for microbubble trapping
  30. Joint measurements of optical parameters by irradiance scintillation and angle-of-arrival fluctuations
  31. M-polynomials and topological indices of hex-derived networks
  32. Generalized convergence analysis of the fractional order systems
  33. Porous flow characteristics of solution-gas drive in tight oil reservoirs
  34. Complementary wave solutions for the long-short wave resonance model via the extended trial equation method and the generalized Kudryashov method
  35. A Note on Koide’s Doubly Special Parametrization of Quark Masses
  36. On right-angled spherical Artin monoid of type Dn
  37. Gas flow regimes judgement in nanoporous media by digital core analysis
  38. 4 + n-dimensional water and waves on four and eleven-dimensional manifolds
  39. Stabilization and Analytic Approximate Solutions of an Optimal Control Problem
  40. On the equations of electrodynamics in a flat or curved spacetime and a possible interaction energy
  41. New prediction method for transient productivity of fractured five-spot patterns in low permeability reservoirs at high water cut stages
  42. The collinear equilibrium points in the restricted three body problem with triaxial primaries
  43. Detection of the damage threshold of fused silica components and morphologies of repaired damage sites based on the beam deflection method
  44. On the bivariate spectral quasi-linearization method for solving the two-dimensional Bratu problem
  45. Ion acoustic quasi-soliton in an electron-positron-ion plasma with superthermal electrons and positrons
  46. Analysis of projectile motion in view of conformable derivative
  47. Computing multiple ABC index and multiple GA index of some grid graphs
  48. Terahertz pulse imaging: A novel denoising method by combing the ant colony algorithm with the compressive sensing
  49. Characteristics of microscopic pore-throat structure of tight oil reservoirs in Sichuan Basin measured by rate-controlled mercury injection
  50. An activity window model for social interaction structure on Twitter
  51. Transient thermal regime trough the constitutive matrix applied to asynchronous electrical machine using the cell method
  52. On the zagreb polynomials of benzenoid systems
  53. Integrability analysis of the partial differential equation describing the classical bond-pricing model of mathematical finance
  54. The Greek parameters of a continuous arithmetic Asian option pricing model via Laplace Adomian decomposition method
  55. Quantifying the global solar radiation received in Pietermaritzburg, KwaZulu-Natal to motivate the consumption of solar technologies
  56. Sturm-Liouville difference equations having Bessel and hydrogen atom potential type
  57. Study on the response characteristics of oil wells after deep profile control in low permeability fractured reservoirs
  58. Depiction and analysis of a modified theta shaped double negative metamaterial for satellite application
  59. An attempt to geometrize electromagnetism
  60. Structure of traveling wave solutions for some nonlinear models via modified mathematical method
  61. Thermo-convective instability in a rotating ferromagnetic fluid layer with temperature modulation
  62. Construction of new solitary wave solutions of generalized Zakharov-Kuznetsov-Benjamin-Bona-Mahony and simplified modified form of Camassa-Holm equations
  63. Effect of magnetic field and heat source on Upper-convected-maxwell fluid in a porous channel
  64. Physical cues of biomaterials guide stem cell fate of differentiation: The effect of elasticity of cell culture biomaterials
  65. Shooting method analysis in wire coating withdrawing from a bath of Oldroyd 8-constant fluid with temperature dependent viscosity
  66. Rank correlation between centrality metrics in complex networks: an empirical study
  67. Special Issue: The 18th International Symposium on Electromagnetic Fields in Mechatronics, Electrical and Electronic Engineering
  68. Modeling of electric and heat processes in spot resistance welding of cross-wire steel bars
  69. Dynamic characteristics of triaxial active control magnetic bearing with asymmetric structure
  70. Design optimization of an axial-field eddy-current magnetic coupling based on magneto-thermal analytical model
  71. Thermal constitutive matrix applied to asynchronous electrical machine using the cell method
  72. Temperature distribution around thin electroconductive layers created on composite textile substrates
  73. Model of the multipolar engine with decreased cogging torque by asymmetrical distribution of the magnets
  74. Analysis of spatial thermal field in a magnetic bearing
  75. Use of the mathematical model of the ignition system to analyze the spark discharge, including the destruction of spark plug electrodes
  76. Assessment of short/long term electric field strength measurements for a pilot district
  77. Simulation study and experimental results for detection and classification of the transient capacitor inrush current using discrete wavelet transform and artificial intelligence
  78. Magnetic transmission gear finite element simulation with iron pole hysteresis
  79. Pulsed excitation terahertz tomography – multiparametric approach
  80. Low and high frequency model of three phase transformer by frequency response analysis measurement
  81. Multivariable polynomial fitting of controlled single-phase nonlinear load of input current total harmonic distortion
  82. Optimal design of a for middle-low-speed maglev trains
  83. Eddy current modeling in linear and nonlinear multifilamentary composite materials
  84. The visual attention saliency map for movie retrospection
  85. AC/DC current ratio in a current superimposition variable flux reluctance machine
  86. Influence of material uncertainties on the RLC parameters of wound inductors modeled using the finite element method
  87. Cogging force reduction in linear tubular flux switching permanent-magnet machines
  88. Modeling hysteresis curves of La(FeCoSi)13 compound near the transition point with the GRUCAD model
  89. Electro-magneto-hydrodynamic lubrication
  90. 3-D Electromagnetic field analysis of wireless power transfer system using K computer
  91. Simplified simulation technique of rotating, induction heated, calender rolls for study of temperature field control
  92. Design, fabrication and testing of electroadhesive interdigital electrodes
  93. A method to reduce partial discharges in motor windings fed by PWM inverter
  94. Reluctance network lumped mechanical & thermal models for the modeling and predesign of concentrated flux synchronous machine
  95. Special Issue Applications of Nonlinear Dynamics
  96. Study on dynamic characteristics of silo-stock-foundation interaction system under seismic load
  97. Microblog topic evolution computing based on LDA algorithm
  98. Modeling the creep damage effect on the creep crack growth behavior of rotor steel
  99. Neighborhood condition for all fractional (g, f, n′, m)-critical deleted graphs
  100. Chinese open information extraction based on DBMCSS in the field of national information resources
  101. 10.1515/phys-2018-0079
  102. CPW-fed circularly-polarized antenna array with high front-to-back ratio and low-profile
  103. Intelligent Monitoring Network Construction based on the utilization of the Internet of things (IoT) in the Metallurgical Coking Process
  104. Temperature detection technology of power equipment based on Fiber Bragg Grating
  105. Research on a rotational speed control strategy of the mandrel in a rotary steering system
  106. Dynamic load balancing algorithm for large data flow in distributed complex networks
  107. Super-structured photonic crystal fiber Bragg grating biosensor image model based on sparse matrix
  108. Fractal-based techniques for physiological time series: An updated approach
  109. Analysis of the Imaging Characteristics of the KB and KBA X-ray Microscopes at Non-coaxial Grazing Incidence
  110. Application of modified culture Kalman filter in bearing fault diagnosis
  111. Exact solutions and conservation laws for the modified equal width-Burgers equation
  112. On topological properties of block shift and hierarchical hypercube networks
  113. Elastic properties and plane acoustic velocity of cubic Sr2CaMoO6 and Sr2CaWO6 from first-principles calculations
  114. A note on the transmission feasibility problem in networks
  115. Ontology learning algorithm using weak functions
  116. Diagnosis of the power frequency vacuum arc shape based on 2D-PIV
  117. Parametric simulation analysis and reliability of escalator truss
  118. A new algorithm for real economy benefit evaluation based on big data analysis
  119. Synergy analysis of agricultural economic cycle fluctuation based on ant colony algorithm
  120. Multi-level encryption algorithm for user-related information across social networks
  121. Multi-target tracking algorithm in intelligent transportation based on wireless sensor network
  122. Fast recognition method of moving video images based on BP neural networks
  123. Compressed sensing image restoration algorithm based on improved SURF operator
  124. Design of load optimal control algorithm for smart grid based on demand response in different scenarios
  125. Face recognition method based on GA-BP neural network algorithm
  126. Optimal path selection algorithm for mobile beacons in sensor network under non-dense distribution
  127. Localization and recognition algorithm for fuzzy anomaly data in big data networks
  128. Urban road traffic flow control under incidental congestion as a function of accident duration
  129. Optimization design of reconfiguration algorithm for high voltage power distribution network based on ant colony algorithm
  130. Feasibility simulation of aseismic structure design for long-span bridges
  131. Construction of renewable energy supply chain model based on LCA
  132. The tribological properties study of carbon fabric/ epoxy composites reinforced by nano-TiO2 and MWNTs
  133. A text-Image feature mapping algorithm based on transfer learning
  134. Fast recognition algorithm for static traffic sign information
  135. Topical Issue: Clean Energy: Materials, Processes and Energy Generation
  136. An investigation of the melting process of RT-35 filled circular thermal energy storage system
  137. Numerical analysis on the dynamic response of a plate-and-frame membrane humidifier for PEMFC vehicles under various operating conditions
  138. Energy converting layers for thin-film flexible photovoltaic structures
  139. Effect of convection heat transfer on thermal energy storage unit
https://doi.org/10.1515/phys-2018-0116
Keywords for this article
mechanosensing, stem cell differentiation; traction-mediated deformation; 2-D cell culture; 3-D cell culture
Creative Commons
BY-NC-ND 4.0

Articles in the same Issue

  1. Regular Articles
  2. A modified Fermi-Walker derivative for inextensible flows of binormal spherical image
  3. Algebraic aspects of evolution partial differential equation arising in the study of constant elasticity of variance model from financial mathematics
  4. Three-dimensional atom localization via probe absorption in a cascade four-level atomic system
  5. Determination of the energy transitions and half-lives of Rubidium nuclei
  6. Three phase heat and mass transfer model for unsaturated soil freezing process: Part 1 - model development
  7. Three phase heat and mass transfer model for unsaturated soil freezing process: Part 2 - model validation
  8. Mathematical model for thermal and entropy analysis of thermal solar collectors by using Maxwell nanofluids with slip conditions, thermal radiation and variable thermal conductivity
  9. Constructing analytic solutions on the Tricomi equation
  10. Feynman diagrams and rooted maps
  11. New type of chaos synchronization in discrete-time systems: the F-M synchronization
  12. Unsteady flow of fractional Oldroyd-B fluids through rotating annulus
  13. A note on the uniqueness of 2D elastostatic problems formulated by different types of potential functions
  14. On the conservation laws and solutions of a (2+1) dimensional KdV-mKdV equation of mathematical physics
  15. Computational methods and traveling wave solutions for the fourth-order nonlinear Ablowitz-Kaup-Newell-Segur water wave dynamical equation via two methods and its applications
  16. Siewert solutions of transcendental equations, generalized Lambert functions and physical applications
  17. Numerical solution of mixed convection flow of an MHD Jeffery fluid over an exponentially stretching sheet in the presence of thermal radiation and chemical reaction
  18. A new three-dimensional chaotic flow with one stable equilibrium: dynamical properties and complexity analysis
  19. Dynamics of a dry-rebounding drop: observations, simulations, and modeling
  20. Modeling the initial mechanical response and yielding behavior of gelled crude oil
  21. Lie symmetry analysis and conservation laws for the time fractional simplified modified Kawahara equation
  22. Solitary wave solutions of two KdV-type equations
  23. Applying industrial tomography to control and optimization flow systems
  24. Reconstructing time series into a complex network to assess the evolution dynamics of the correlations among energy prices
  25. An optimal solution for software testing case generation based on particle swarm optimization
  26. Optimal system, nonlinear self-adjointness and conservation laws for generalized shallow water wave equation
  27. Alternative methods for solving nonlinear two-point boundary value problems
  28. Global model simulation of OH production in pulsed-DC atmospheric pressure helium-air plasma jets
  29. Experimental investigation on optical vortex tweezers for microbubble trapping
  30. Joint measurements of optical parameters by irradiance scintillation and angle-of-arrival fluctuations
  31. M-polynomials and topological indices of hex-derived networks
  32. Generalized convergence analysis of the fractional order systems
  33. Porous flow characteristics of solution-gas drive in tight oil reservoirs
  34. Complementary wave solutions for the long-short wave resonance model via the extended trial equation method and the generalized Kudryashov method
  35. A Note on Koide’s Doubly Special Parametrization of Quark Masses
  36. On right-angled spherical Artin monoid of type Dn
  37. Gas flow regimes judgement in nanoporous media by digital core analysis
  38. 4 + n-dimensional water and waves on four and eleven-dimensional manifolds
  39. Stabilization and Analytic Approximate Solutions of an Optimal Control Problem
  40. On the equations of electrodynamics in a flat or curved spacetime and a possible interaction energy
  41. New prediction method for transient productivity of fractured five-spot patterns in low permeability reservoirs at high water cut stages
  42. The collinear equilibrium points in the restricted three body problem with triaxial primaries
  43. Detection of the damage threshold of fused silica components and morphologies of repaired damage sites based on the beam deflection method
  44. On the bivariate spectral quasi-linearization method for solving the two-dimensional Bratu problem
  45. Ion acoustic quasi-soliton in an electron-positron-ion plasma with superthermal electrons and positrons
  46. Analysis of projectile motion in view of conformable derivative
  47. Computing multiple ABC index and multiple GA index of some grid graphs
  48. Terahertz pulse imaging: A novel denoising method by combing the ant colony algorithm with the compressive sensing
  49. Characteristics of microscopic pore-throat structure of tight oil reservoirs in Sichuan Basin measured by rate-controlled mercury injection
  50. An activity window model for social interaction structure on Twitter
  51. Transient thermal regime trough the constitutive matrix applied to asynchronous electrical machine using the cell method
  52. On the zagreb polynomials of benzenoid systems
  53. Integrability analysis of the partial differential equation describing the classical bond-pricing model of mathematical finance
  54. The Greek parameters of a continuous arithmetic Asian option pricing model via Laplace Adomian decomposition method
  55. Quantifying the global solar radiation received in Pietermaritzburg, KwaZulu-Natal to motivate the consumption of solar technologies
  56. Sturm-Liouville difference equations having Bessel and hydrogen atom potential type
  57. Study on the response characteristics of oil wells after deep profile control in low permeability fractured reservoirs
  58. Depiction and analysis of a modified theta shaped double negative metamaterial for satellite application
  59. An attempt to geometrize electromagnetism
  60. Structure of traveling wave solutions for some nonlinear models via modified mathematical method
  61. Thermo-convective instability in a rotating ferromagnetic fluid layer with temperature modulation
  62. Construction of new solitary wave solutions of generalized Zakharov-Kuznetsov-Benjamin-Bona-Mahony and simplified modified form of Camassa-Holm equations
  63. Effect of magnetic field and heat source on Upper-convected-maxwell fluid in a porous channel
  64. Physical cues of biomaterials guide stem cell fate of differentiation: The effect of elasticity of cell culture biomaterials
  65. Shooting method analysis in wire coating withdrawing from a bath of Oldroyd 8-constant fluid with temperature dependent viscosity
  66. Rank correlation between centrality metrics in complex networks: an empirical study
  67. Special Issue: The 18th International Symposium on Electromagnetic Fields in Mechatronics, Electrical and Electronic Engineering
  68. Modeling of electric and heat processes in spot resistance welding of cross-wire steel bars
  69. Dynamic characteristics of triaxial active control magnetic bearing with asymmetric structure
  70. Design optimization of an axial-field eddy-current magnetic coupling based on magneto-thermal analytical model
  71. Thermal constitutive matrix applied to asynchronous electrical machine using the cell method
  72. Temperature distribution around thin electroconductive layers created on composite textile substrates
  73. Model of the multipolar engine with decreased cogging torque by asymmetrical distribution of the magnets
  74. Analysis of spatial thermal field in a magnetic bearing
  75. Use of the mathematical model of the ignition system to analyze the spark discharge, including the destruction of spark plug electrodes
  76. Assessment of short/long term electric field strength measurements for a pilot district
  77. Simulation study and experimental results for detection and classification of the transient capacitor inrush current using discrete wavelet transform and artificial intelligence
  78. Magnetic transmission gear finite element simulation with iron pole hysteresis
  79. Pulsed excitation terahertz tomography – multiparametric approach
  80. Low and high frequency model of three phase transformer by frequency response analysis measurement
  81. Multivariable polynomial fitting of controlled single-phase nonlinear load of input current total harmonic distortion
  82. Optimal design of a for middle-low-speed maglev trains
  83. Eddy current modeling in linear and nonlinear multifilamentary composite materials
  84. The visual attention saliency map for movie retrospection
  85. AC/DC current ratio in a current superimposition variable flux reluctance machine
  86. Influence of material uncertainties on the RLC parameters of wound inductors modeled using the finite element method
  87. Cogging force reduction in linear tubular flux switching permanent-magnet machines
  88. Modeling hysteresis curves of La(FeCoSi)13 compound near the transition point with the GRUCAD model
  89. Electro-magneto-hydrodynamic lubrication
  90. 3-D Electromagnetic field analysis of wireless power transfer system using K computer
  91. Simplified simulation technique of rotating, induction heated, calender rolls for study of temperature field control
  92. Design, fabrication and testing of electroadhesive interdigital electrodes
  93. A method to reduce partial discharges in motor windings fed by PWM inverter
  94. Reluctance network lumped mechanical & thermal models for the modeling and predesign of concentrated flux synchronous machine
  95. Special Issue Applications of Nonlinear Dynamics
  96. Study on dynamic characteristics of silo-stock-foundation interaction system under seismic load
  97. Microblog topic evolution computing based on LDA algorithm
  98. Modeling the creep damage effect on the creep crack growth behavior of rotor steel
  99. Neighborhood condition for all fractional (g, f, n′, m)-critical deleted graphs
  100. Chinese open information extraction based on DBMCSS in the field of national information resources
  101. 10.1515/phys-2018-0079
  102. CPW-fed circularly-polarized antenna array with high front-to-back ratio and low-profile
  103. Intelligent Monitoring Network Construction based on the utilization of the Internet of things (IoT) in the Metallurgical Coking Process
  104. Temperature detection technology of power equipment based on Fiber Bragg Grating
  105. Research on a rotational speed control strategy of the mandrel in a rotary steering system
  106. Dynamic load balancing algorithm for large data flow in distributed complex networks
  107. Super-structured photonic crystal fiber Bragg grating biosensor image model based on sparse matrix
  108. Fractal-based techniques for physiological time series: An updated approach
  109. Analysis of the Imaging Characteristics of the KB and KBA X-ray Microscopes at Non-coaxial Grazing Incidence
  110. Application of modified culture Kalman filter in bearing fault diagnosis
  111. Exact solutions and conservation laws for the modified equal width-Burgers equation
  112. On topological properties of block shift and hierarchical hypercube networks
  113. Elastic properties and plane acoustic velocity of cubic Sr2CaMoO6 and Sr2CaWO6 from first-principles calculations
  114. A note on the transmission feasibility problem in networks
  115. Ontology learning algorithm using weak functions
  116. Diagnosis of the power frequency vacuum arc shape based on 2D-PIV
  117. Parametric simulation analysis and reliability of escalator truss
  118. A new algorithm for real economy benefit evaluation based on big data analysis
  119. Synergy analysis of agricultural economic cycle fluctuation based on ant colony algorithm
  120. Multi-level encryption algorithm for user-related information across social networks
  121. Multi-target tracking algorithm in intelligent transportation based on wireless sensor network
  122. Fast recognition method of moving video images based on BP neural networks
  123. Compressed sensing image restoration algorithm based on improved SURF operator
  124. Design of load optimal control algorithm for smart grid based on demand response in different scenarios
  125. Face recognition method based on GA-BP neural network algorithm
  126. Optimal path selection algorithm for mobile beacons in sensor network under non-dense distribution
  127. Localization and recognition algorithm for fuzzy anomaly data in big data networks
  128. Urban road traffic flow control under incidental congestion as a function of accident duration
  129. Optimization design of reconfiguration algorithm for high voltage power distribution network based on ant colony algorithm
  130. Feasibility simulation of aseismic structure design for long-span bridges
  131. Construction of renewable energy supply chain model based on LCA
  132. The tribological properties study of carbon fabric/ epoxy composites reinforced by nano-TiO2 and MWNTs
  133. A text-Image feature mapping algorithm based on transfer learning
  134. Fast recognition algorithm for static traffic sign information
  135. Topical Issue: Clean Energy: Materials, Processes and Energy Generation
  136. An investigation of the melting process of RT-35 filled circular thermal energy storage system
  137. Numerical analysis on the dynamic response of a plate-and-frame membrane humidifier for PEMFC vehicles under various operating conditions
  138. Energy converting layers for thin-film flexible photovoltaic structures
  139. Effect of convection heat transfer on thermal energy storage unit
Sign up now to receive a 20% welcome discount
Institutional Access
How does access work?
Have an idea on how to improve our website?
Please write us.
© 2026 De Gruyter Brill
Downloaded on 12.2.2026 from https://www.degruyterbrill.com/document/doi/10.1515/phys-2018-0116/html
Scroll to top button