External Mechanical Constraints Research Articles

Continuum theory for confluent cell monolayers: Interplay between cell growth, division, and intercalation

Mechanical forces generated by dynamic cellular activities play a crucial role in the morphogenesis and growth of biological tissues. While the influence of mechanics is clear, many questions arise regarding the way by which mechanical forces communicate with biological processes at the level of a confluent cell population. Some answers may be found in the development of mathematical models that are capable of describing the emerging behavior of a large population of active agents based on individualistic rules (single-cell response). In this perspective, the present work presents a continuum-scale model that can capture, in an average sense, the active mechanics and evolution of a confluent tissue with or without external mechanical constraints. For this, we conceptualize a confluent cell population (in a monolayer) as a deformable dynamic network, where a single cell can modify the topology of its neighborhood by swapping neighbors or dividing. With this description, we use concepts from statistical mechanics and the transient network theory to derive an equivalent active visco-elastic continuum model, which can recapitulate some of the salient features of the underlying network at the macroscale. Without loss of generality, the cell network is here assumed to follow well-known rules used in vertex model simulations, which are: (a) cell elasticity based on its bulk and cortical elasticity, (b) cell intercalation (or T1 transition), and (c) cell proliferation (expansion and division). We show, through examples and illustrations, that the model is able to characterize complex cross-talk between mechanical forces and biological processes, which are likely to drive the emergent growth and deformation of cell aggregates.

Hierarchical and synergistic organization of control variables during the multi-digit grasp of a free and an externally fixed object.

In the referent control theory, grip force emerges by designating the referent aperture (Ra) as a threshold position inside the object. This study quantified Ra and investigated whether the synergistic control of digit referent coordinate (RC) and apparent stiffness (k) depend on the external mechanical constraints on the hand-held object. Subjects held a motorized handle capable of adjusting the grip width and performed static multi-digit prehension tasks in which the handle was free and externally fixed in different conditions. The RC and k of individual digits were reconstructed from the changes in digit normal forces and the positions as the grip width was modulated. RCs of the thumb and virtual finger were used to calculate the width and midpoint of Ra, and synergy indices quantifying the task-specific covariation in the space of the digit normal forces and {RC, k} variables were computed. We found that the k and width of the Ra were larger when holding a free handle than the fixed handle. The higher stiffness in the free condition could be a strategy to ensure grip stability. The midpoint of Ra was skewed toward the virtual finger, reflecting different magnitudes of k for the two digits. Further, the normal forces and control variables {RC, k} displayed synergistic covariation for stabilization of the total grasping force. Finally, the synergies were weaker when the handle was externally fixed, demonstrating the dependence of synergies on external constraints. These results add to the current literature by demonstrating that grasp control involves modulation of digit apparent stiffness in addition to the referent coordinate and by identifying the synergistic organization of the control variables during static grasp.

External Mechanical Cues Reveal a Katanin-Independent Mechanism behind Auxin-Mediated Tissue Bending in Plants.

Tissue folding is a central building block of plant and animal morphogenesis. In dicotyledonous plants, hypocotyl folds to form hooks after seedling germination that protects their aerial stem cell niche during emergence from soil. Auxin response factors and auxin transport are reported to play a key role in this process. Here, we show that the microtubule-severing enzyme katanin contributes to hook formation. However, by exposing hypocotyls to external mechanical cues mimicking the natural soil environment, we reveal that auxin response factors ARF7/ARF19, auxin influx carriers, and katanin are dispensable for apical hook formation, indicating that these factors primarily play the role of catalyzers of tissue bending in the absence of external mechanical cues. Instead, our results reveal the key roles of the non-canonical TMK-mediated auxin pathway, PIN efflux carriers, and cellulose microfibrils as components of the core pathway behind hook formation in the presence or absence of external mechanical cues.

Tailoring the separation properties of flexible metal-organic frameworks using mechanical pressure

Metal-organic frameworks are widely considered for the separation of chemical mixtures due to their adjustable physical and chemical properties. However, while much effort is currently devoted to developing new adsorbents for a given separation, an ideal scenario would involve a single adsorbent for multiple separations. Porous materials exhibiting framework flexibility offer unique opportunities to tune these properties since the pore size and shape can be controlled by the application of external stimuli. Here, we establish a proof-of-concept for the molecular sieving separation of species with similar sizes (CO2/N2 and CO2/CH4), via precise mechanical control of the pore size aperture in a flexible metal-organic framework. Besides its infinite selectivity for the considered gas mixtures, this material shows excellent regeneration capability when releasing the external mechanical constraint. This strategy, combining an external stimulus applied to a structurally compliant adsorbent, offers a promising avenue for addressing some of the most challenging gas separations.

Particle dynamics predicts shear rheology of soft particle glasses

Soft particle glasses are amorphous materials made of soft and deformable particles that are jammed above close-packing. They behave like weak solids at rest, but they yield and flow under external mechanical constraints. Although soft particle glasses are widely used in applications, little is known about how the particle softness and microscopic dynamics determine the macroscopic rheology. Here, we use three-dimensional particle dynamic simulations to analyze the dynamical properties of soft particle glasses at different scales. We demonstrate how the dynamics is determined by the persistence time and the magnitude of the fluctuating elastic forces that develop at contact in the flow. The shear-induced diffusion coefficient, the local structural relaxation times, the shear stress, and the normal stress differences are interconnected through simple relationships that allow the prediction of the macroscopic rheology from the microscopic dynamics.

Assessment of swelling and constituent redistribution in uranium-zirconium fuel using phenomena identification and ranking tables (PIRT)

Metallic alloy U-Zr nuclear fuels remain a candidate for future US fast reactors. However, with more than 30 years of investigation into the system, U-Zr fuel remains unqualified and lacks predictive modeling capabilities. Phenomenon identification and ranking tables (PIRT) were developed for U-Zr fuels to prioritize the study of microstructural phenomena related to fuel performance and to aid predictive models. Two areas of emphasis, fuel swelling and constituent redistribution, were identified with PIRT and were evaluated in detail. The analysis identified influencing parameters that should be considered during future studies including: external mechanical constraint, temperature, composition, crystallographic texture, temperature gradient, fabrication constraints, fission density, fission rate, initial porosity, and pre-irradiation grain size. The PIRT results support the need for a comprehensive study that focus on the decoupling of fission rate, irradiation temperature, and alloy composition to independently investigate the microstructural evolution in the multiple phases typical of advanced reactor conditions.

Correlation between wire feed speed and external mechanical constraint for enhanced process stability in underwater wet flux-cored arc welding

It is a great challenge to improve the process stability in conventional underwater wet welding due to the formation of unstable bubble. In this study, mechanical constraint method was employed to interfere the bubble generated by underwater wet welding, and the new method was named as mechanical constraint assisted underwater wet welding. The aim of the study was to quantify the combined effect of wire feed speed and condition of mechanical constraint on the process stability in mechanical constraint assisted underwater wet welding. Experimental results demonstrated that the introduction of mechanical constraint not only suppressed the bubble without floating but also stabilized the arc burning process. The degree of influence of mechanical constraint, which changed with wire feed speed, played an important role during the mechanical constraint assisted underwater wet welding process. For all wire feed speeds, the fluctuations of welding electrical signal were decreased through introduction of mechanical constraint. The difference in the proportion of arc extinction process between underwater wet welding and mechanical constraint assisted underwater wet welding became less with increasing wire feed speed. At wire feed speed lower than 7.5 m/min, the improvement of process stability was very significant by mechanical constraint. However, the further improvement produced limited effect when the wire feed speed was greater than 7.5 m/min. The observation results showed that a better weld appearance was afforded at a large wire feed speed, corresponding to a lower variation coefficient.

Three-Dimensional Culture in a Methylcellulose-Based Hydrogel to Study the Impact of Stiffness on Megakaryocyte Differentiation.

The differentiation and maturation of megakaryocytes (MKs) occurs in a 3D environment where the cells must constantly adapt to the external physical and mechanical constraints during their development and migration to sinusoid vessels. In this chapter, we present a method for culture of mouse MKs from bone marrow hematopoietic progenitor cells in a methylcellulose 3D medium with a stiffness mimicking that of bone marrow. In addition, we describe how the MKs can be recovered to allow for analysis of their differentiation and maturation state by transmission electron microscopy, immunofluorescence or flow cytometry techniques and to evaluate their ability to form proplatelets. This approach allows (1) generation of MKs with a morphology that more closely resembles the MKs that differentiate in vivo, (2) recovery of megakaryocyte phenotypes sometimes observed in vivo but not found in classical liquid cultures, and (3) study of mechanotransduction pathways induced by the stiffness of the medium.

Mechanotransduction at the Nuclear Envelope

LINC complexes are transmembrane protein assemblies that physically connect the nucleo- and cytoskeletons through the nuclear envelope. Dysfunctions of LINC complexes are associated with pathologies such as cancer and muscular dystrophies. The mechanical roles of LINC complex proteins in these contexts are poorly understood. To address this issue, we have developed genetically encoded FRET biosensors that measure molecular tension in LINC complex proteins.We have evidenced that LINC complex proteins are under tension generated by the cytoskeleton and sensitive to various external and internal mechanical constraints in fibroblastic and epithelial cells. In addition, we have shown that some of the same constraints result in the localization at the nuclear envelope of alpha-catenin, an actin- binding protein required for intercellular adhesion that can also act as a transcription regulator. These results are consistent with a mechanotransduction activity of LINC complex proteins, the targets of which we currently investigate.

Zygomatic bone shape in intentional cranial deformations: a model for the study of the interactions between skull growth and facial morphology.

Intentional cranial deformations (ICD) were obtained by exerting external mechanical constraints on the skull vault during the first years of life to permanently modify head shape. The repercussions of ICD on the face are not well described in the midfacial region. Here we assessed the shape of the zygomatic bone in different types of ICDs. We considered 14 non-deformed skulls, 19 skulls with antero-posterior deformation, nine skulls with circumferential deformation and seven skulls with Toulouse deformation. The shape of the zygomatic bone was assessed using a statistical shape model after mesh registration. Euclidian distances between mean models and Mahalanobis distances after canonical variate analysis were computed. Classification accuracy was computed using a cross-validation approach. Different ICDs cause specific zygomatic shape modifications corresponding to different degrees of retrusion but the shape of the zygomatic bone alone is not a sufficient parameter for classifying populations into ICD groups defined by deformation types. We illustrate the fact that external mechanical constraints on the skull vault influence midfacial growth. ICDs are a model for the study of the influence of epigenetic factors on craniofacial growth and can help to understand the facial effects of congenital skull malformations such as single or multi-suture synostoses, or of external orthopedic devices such as helmets used to correct deformational plagiocephaly.

Engineering 3D Cellularized Collagen Gels for Vascular Tissue Regeneration

Synthetic materials are known to initiate clinical complications such as inflammation, stenosis, and infections when implanted as vascular substitutes. Collagen has been extensively used for a wide range of biomedical applications and is considered a valid alternative to synthetic materials due to its inherent biocompatibility (i.e., low antigenicity, inflammation, and cytotoxic responses). However, the limited mechanical properties and the related low hand-ability of collagen gels have hampered their use as scaffold materials for vascular tissue engineering. Therefore, the rationale behind this work was first to engineer cellularized collagen gels into a tubular-shaped geometry and second to enhance smooth muscle cells driven reorganization of collagen matrix to obtain tissues stiff enough to be handled. The strategy described here is based on the direct assembling of collagen and smooth muscle cells (construct) in a 3D cylindrical geometry with the use of a molding technique. This process requires a maturation period, during which the constructs are cultured in a bioreactor under static conditions (without applied external dynamic mechanical constraints) for 1 or 2 weeks. The “static bioreactor” provides a monitored and controlled sterile environment (pH, temperature, gas exchange, nutrient supply and waste removal) to the constructs. During culture period, thickness measurements were performed to evaluate the cells-driven remodeling of the collagen matrix, and glucose consumption and lactate production rates were measured to monitor the cells metabolic activity. Finally, mechanical and viscoelastic properties were assessed for the resulting tubular constructs. To this end, specific protocols and a focused know-how (manipulation, gripping, working in hydrated environment, and so on) were developed to characterize the engineered tissues.

Engineering 3D Cellularized Collagen Gels for Vascular Tissue Regeneration.

Synthetic materials are known to initiate clinical complications such as inflammation, stenosis, and infections when implanted as vascular substitutes. Collagen has been extensively used for a wide range of biomedical applications and is considered a valid alternative to synthetic materials due to its inherent biocompatibility (i.e., low antigenicity, inflammation, and cytotoxic responses). However, the limited mechanical properties and the related low hand-ability of collagen gels have hampered their use as scaffold materials for vascular tissue engineering. Therefore, the rationale behind this work was first to engineer cellularized collagen gels into a tubular-shaped geometry and second to enhance smooth muscle cells driven reorganization of collagen matrix to obtain tissues stiff enough to be handled.The strategy described here is based on the direct assembling of collagen and smooth muscle cells (construct) in a 3D cylindrical geometry with the use of a molding technique. This process requires a maturation period, during which the constructs are cultured in a bioreactor under static conditions (without applied external dynamic mechanical constraints) for 1 or 2 weeks. The “static bioreactor” provides a monitored and controlled sterile environment (pH, temperature, gas exchange, nutrient supply and waste removal) to the constructs. During culture period, thickness measurements were performed to evaluate the cells-driven remodeling of the collagen matrix, and glucose consumption and lactate production rates were measured to monitor the cells metabolic activity. Finally, mechanical and viscoelastic properties were assessed for the resulting tubular constructs. To this end, specific protocols and a focused know-how (manipulation, gripping, working in hydrated environment, and so on) were developed to characterize the engineered tissues.

Photomechanical bending mechanics of polydomain azobenzene liquid crystal polymer network films

Glassy, polydomain azobenzene liquid crystal polymer networks (azo-LCNs) have been synthesized, characterized, and modeled to understand composition dependence on large amplitude, bidirectional bending, and twisting deformation upon irradiation with linearly polarized blue-green (440–514 nm) light. These materials exhibit interesting properties for adaptive structure applications in which the shape of the photoresponsive material can be rapidly reconfigured with light. The basis for the photomechanical output observed in these materials is absorption of actinic light by azobenzene, which upon photoisomerization dictates an internal stress within the local polymer network. The photoinduced evolution of the underlying liquid crystal microstructure is manifested as macroscopic deformation of the glassy polymer film. Accordingly, this work examines the polarization-controlled bidirectional bending of highly concentrated azo-LCN materials and correlates the macroscopic output (observed as bending) to measured blocked stresses upon irradiation with blue-green light of varying polarization. The resulting photomechanical output is highly dependent on the concentration of crosslinked azobenzene mesogens employed in the formulation. Experiments that quantify photomechanical bending and photogenerated stress are compared to a large deformation photomechanical shell model to quantify the effect of polarized light interactions with the material during static and dynamic polarized light induced deformation. The model comparisons illustrate differences in internal photostrain and deformation rates as a function of composition and external mechanical constraints.

Nanoscale phase boundaries: a new twist to novel functionalities

In functional materials, nanoscale phase boundaries exhibit exotic phenomena that are notably absent in their parent phases. Over the past two decades, much of the research into complex oxides (such as cuprate superconductors, CMR manganites and relaxor ferroelectrics) has demonstrated the key role that nanoscale inhomogeneities play in controlling the electronic and/or ionic structure of these materials. One of the key characteristics in such systems is the strong susceptibility to external perturbations, such as magnetic, electric and mechanical fields. A direct consequence of the accommodation of a large number of cationic substitutions in complex oxides is the emergence of a number of physical phenomena from essentially the same crystal framework. Recently, multiferroic behavior, which is characterized by the co-existence and potential coupling of multiple ferroic order parameters, has captured considerable worldwide research interest. The perovskite, BiFeO(3), exhibits robust ferroelectricity coupled with antiferromagnetism at room temperature. A rather unique feature of this material system is its ability to "morph" its ground state when an external mechanical constraint is imposed on it. A particularly striking example is observed when a large (~4 to 5%) compressive strain is imposed on a thin film through the epitaxial constraint from the underlying substrate. Under these conditions, the ground state rhombohedral phase transforms into a tetragonal-like (or a derivative thereof) phase with a rather large unit cell (c/a ratio of ~1.26). When the epitaxial constraint is partially relaxed by increasing the film thickness, this tetragonal-like phase evolves into a "mixed-phase" state, consisting of a nanoscale admixture of the rhombohedral-like phase embedded in the tetragonal-like phase. Such a system gives us a new pathway to explore a variety of mechanical, magnetic and transport phenomena in constrained dimensions. This article reviews our progress to date in this direction and also captures some possible areas of future research. We use the electromechanical response and the magnetic properties as examples to illustrate that its novel functionalities are intrinsically due to the phase boundaries and not the constituent phases. The possible origin of the giant piezoelectric response and enhanced magnetic moment across the boundaries is proposed based on the flexoelectric and flexomagnetic effects.

Some analytical formulas for the equilibrium states of a swollen hydrogel shell

A polymer network can imbibe water, forming an aggregate called hydrogel, and undergo a large and inhomogeneous deformation with external mechanical constraint. Due to the large deformation, nonlinearity plays a crucial role, which also causes the mathematical difficulty for obtaining analytical solutions. Based on an existing model for the equilibrium states of a swollen hydrogel with a core-shell structure, this paper seeks analytical (or semi-analytical) solutions to deformation by perturbation methods for three cases, i.e. free-swelling, nearly free-swelling and general inhomogeneous swelling. Particularly for the general inhomogeneous swelling, we introduce an extended method of matched asymptotics to construct the semi-analytical solution of the governing nonlinear second-order variable-coefficient differential equation. The semi-analytical solution captures the boundary layer behavior of the deformation. Also, analytical formulas for the radial and hoop stretches and stresses are obtained at the two boundary surfaces of the shell, making the influence of the parameters explicit. An interesting finding is that the deformation is characterized by a single material parameter (called the hydrogel deformation constant, which is one-fifth power of the ratio of the shear modulus due to mixing to the shear modulus due to stretching), although the free-energy function for the hydrogel contains two material parameters. Comparisons with numerical solutions are also made and good agreements are found.

Interaction of n-Octyl β,d-Glucopyranoside with Giant Magnetic-Fluid-Loaded Phosphatidylcholine Vesicles: Direct Visualization of Membrane Curvature Fluctuations As a Function of Surfactant Partitioning between Water and Lipid Bilayer

The present study deals with the morphological modifications of giant dioleoyl phosphatidylcholine vesicles (DOPC GUVs) induced by the nonionic surfactant n-octyl β,D-glucopyranoside at sublytic levels, i.e., in the first steps of the vesicle-to-micelle transition process, when surfactant inserts into the vesicle bilayer without disruption. Experimental conditions were perfected to exactly control the surfactant bilayer composition of the vesicles, in line with former work focused on the mechanical properties of the membrane of magnetic-fluid-loaded DOPC GUVs submitted to a magnetic field. The purpose here was to systematically examine, in the absence of any external mechanical constraint, the dynamics of giant vesicle shape and membrane deformations as a function of surfactant partitioning between the aqueous phase and the lipid membrane, beforehand established by turbidity measurements from small unilamellar vesicles.

Control of a Speech Robot via an Optimum Neural-Network-Based Internal Model With Constraints

An optimum internal model with constraints is proposed and discussed for the control of a speech robot, which is based on the human-like behavior. The main idea of the study is that the robot movements are carried out in such a way that the length of the path traveled in the internal space, under external acoustical and mechanical constraints, is minimized. This optimum strategy defines the designed internal model, which is responsible for the robot task planning. First, an exact analytical way to deal with the problem is proposed. Next, by using some empirical findings, an approximate solution for the designed internal model is developed. Finally, the implementation of this solution, which is applied to the control of a speech robot, yields interesting results in the field of task-planning strategies, task anticipation (namely, speech coarticulation), and the influence of force on the accuracy of executed tasks.

The Effect of Apelin on Single Isolated Cardiac Myocytes from Wild-Type and Apelin / APJ KO Mice

Apelin, an endogenously produced peptide discovered in 1998, is regarded as one of the most potent substances to increase net contractile output in isolated heart and whole animals, apparently in a load-dependent manner. Unlike other inotropic agents, apelin has not been shown to cause cardiac hypertrophy. However, little is known about its cellular effects, with only two papers on isolated cardiomyocytes, neither of which imposed external mechanical constraints. This study assesses dynamic parameters of cardiomyocytes from wild type (WT), apelin-receptor knockout (AJP-KO) and apelin knockout (Ap-KO) mice. In addition to steady-state parameters such as fractional shortening, we measured time to peak contraction (TTP), and maximum velocities of contraction and relaxation.Apelin administration to unloaded cells did not change fractional shortening, but significantly (p<0.05) decreased TTP both in WT (93.1%±2%, n=90) and Ap-KO cardiomyocytes (83.1%±5%, n=14). The specificity of apelin effects was verified in AJP-KO myocytes, where no significant change in TTP was seen (98.2%±2%, n=69).After application of mechanical pre-loads, using the two-carbonfibre technique, TTP reduction was enhanced in Ap-KO myocytes (64.6%±5%, n=11). To characterise apelin effects on developed tension, the ratio between the slopes of end-systolic and end-diastolic tension-length relations was obtained. This is a non-dimensional parameter, termed Frank-Starling-Gain (FSG), that is independent of cell cross-section and allows inter-individual comparisons. Under control conditions, FSG was 1.36±0.05 (n=10). After application of 10nM apelin this rose to 1.96±0.23 (n=6, p<0.05), indicating improved net contractile output. Interestingly, this was caused largely by a slope reduction of the end-diastolic tension-length relation. This could explain the combination of increased net force output with lack of hypertrophy induction, and suggests that apelin more appropriately be described as a positive lusitropic agent, rather than an inotropic one.

Inhomogeneous and anisotropic equilibrium state of a swollen hydrogel containing a hard core

A polymer network can imbibe water from environment and swell to an equilibrium state. If the equilibrium is reached when the network is subject to external mechanical constraint, the deformation of the network is typically anisotropic and the concentration of water inhomogeneous. Such an equilibrium state in a network constrained by a hard core is modeled here with a nonlinear differential equation. The presence of the hard core markedly reduces the concentration of water near the interface and causes high stresses.

Elasticity of Solids with a Large Concentration of Point Defects

AbstractThe elastic behavior of solids with a large concentration of interacting point defects has been analyzed. The analysis predicts that, in such solids, mechanical stress may be partially relieved by a shift in the association/dissociation equilibrium of the point defects. Association/dissociation of the point defects in response to an external stress will proceed until the decrease in elastic energy is balanced by the increased chemical energy of the defect distribution. The resulting change in the linear dimensions may be called “chemical strain”, in analogy to the previously studied “chemical stress”. A solid in which chemical strain may develop in response to external stress should exhibit two distinct Young's moduli: relaxed, on a time scale which allows the defects to reach equilibrium; and unrelaxed, on a time scale which is too short for the defect equilibrium to be established. Our analysis suggests that materials exhibiting the chemical‐strain effect are capable of reversible adaptation to external mechanical constraints. Measurements on a self‐supported film of Ce0.8Gd0.2O1.9 strongly support the theoretical predictions.