Theoretical analysis of the adaptive contractile behaviour of a single cardiomyocyte cultured on elastic substrates with varying stiffness

An idealized human cardiomyocyte finite element model for studying the interaction between the cross-bridge state and cell mechanical response. ANNUAL INTERNATIONAL CONFERENCE OF THE IEEE ENGINEERING IN MEDICINE AND BIOLOGY SOCIETY. IEEE ENGINEERING IN MEDICINE AND BIOLOGY SOCIETY. ANNUAL INTERNATIONAL CONFERENCE 2023;2023:1-5. [PMID: 38082753 DOI: 10.1109/embc40787.2023.10341055] [Citation(s) in RCA: 0] [Impact Index Per Article: 0]

The mechanical state of cardiomyocyte is directly related to the structure and function of internal sarcomeres. In the field of computational cardiac mechanics, attempts to establish models of human cardiomyocyte with a detailed representation of sarcomere cross-bridge (XB) are rare. In this study, we established a computational model for a cardiomyocyte with idealized geometry while containing a representative sarcomere composed of thick filament, thin filament, titin filament, and Z-disc. The formation of XB with passive tension in the model was simulated with the finite element (FE) method, and stochastic FE analyses were further carried out in conjunction with six sigma analysis to explore the interaction between the S1 power stroke and the twitch mechanics of cardiomyocyte. The proposed modeling method may help us better understand the working state of cardiomyocyte, and offer a potential means for exploring the cell-level mechanisms of cardiac diseases.

A cell-based framework for modeling cardiac mechanics

Cardiomyocytes are the functional building blocks of the heart-yet most models developed to simulate cardiac mechanics do not represent the individual cells and their surrounding matrix. Instead, they work on a homogenized tissue level, assuming that cellular and subcellular structures and processes scale uniformly. Here we present a mathematical and numerical framework for exploring tissue-level cardiac mechanics on a microscale given an explicit three-dimensional geometrical representation of cells embedded in a matrix. We defined a mathematical model over such a geometry and parametrized our model using publicly available data from tissue stretching and shearing experiments. We then used the model to explore mechanical differences between the extracellular and the intracellular space. Through sensitivity analysis, we found the stiffness in the extracellular matrix to be most important for the intracellular stress values under contraction. Strain and stress values were observed to follow a normal-tangential pattern concentrated along the membrane, with substantial spatial variations both under contraction and stretching. We also examined how it scales to larger size simulations, considering multicellular domains. Our work extends existing continuum models, providing a new geometrical-based framework for exploring complex cell-cell and cell-matrix interactions.

Arrhythmogenic Current Generation by Myofilament-Triggered Ca2+ Release and Sarcomere Heterogeneity

Heterogeneous mechanical dyskinesis has been implicated in many arrhythmogenic phenotypes. Strain-dependent perturbations to cardiomyocyte electrophysiology may contribute to this arrhythmogenesis through processes referred to as mechanoelectric feedback. Although the role of stretch-activated ion currents has been investigated using computational models, experimental studies suggest that mechanical strain may also promote arrhythmia by facilitating calcium wave propagation. To investigate whether strain-dependent changes in calcium affinity to the myofilament may promote arrhythmogenic intracellular calcium waves, we modified a mathematical model of rabbit excitation-contraction coupling coupled to a model of myofilament activation and force development. In a one-dimensional compartmental analysis, we bidirectionally coupled 50 sarcomere models in series to model calcium diffusion and stress transfer between adjacent sarcomeres. These considerations enabled the model to capture 1) the effects of mechanical feedback on calcium homeostasis at the sarcomeric level and 2) the combined effects of mechanical and calcium heterogeneities at the cellular level. The results suggest that in conditions of calcium overload, the vulnerable window of stretch-release to trigger suprathreshold delayed afterdepolarizations can be affected by heterogeneity in sarcomere length. Furthermore, stretch and sarcomere heterogeneity may modulate the susceptibility threshold for delayed afterdepolarizations and the aftercontraction wave propagation velocity.

Dynamic Model for Characterizing Contractile Behaviors and Mechanical Properties of a Cardiomyocyte

Studies on the contractile dynamics of heart cells have attracted broad attention for the development of both heart disease therapies and cardiomyocyte-actuated micro-robotics. In this study, a linear dynamic model of a single cardiomyocyte cell was proposed at the subcellular scale to characterize the contractile behaviors of heart cells, with system parameters representing the mechanical properties of the subcellular components of living cardiomyocytes. The system parameters of the dynamic model were identified with the cellular beating pattern measured by a scanning ion conductance microscope. The experiments were implemented with cardiomyocytes in one control group and two experimental groups with the drugs cytochalasin-D or nocodazole, to identify the system parameters of the model based on scanning ion conductance microscope measurements, measurement of the cellular Young's modulus with atomic force microscopy indentation, measurement of cellular contraction forces using the micro-pillar technique, and immunofluorescence staining and imaging of the cytoskeleton. The proposed mathematical model was both indirectly and qualitatively verified by the variation in cytoskeleton, beating amplitude, and contractility of cardiomyocytes among the control and the experimental groups, as well as directly and quantitatively validated by the simulation and the significant consistency of 90.5% in the comparison between the ratios of the Young's modulus and the equivalent comprehensive cellular elasticities of cells in the experimental groups to those in the control group. Apart from mechanical properties (mass, elasticity, and viscosity) of subcellular structures, other properties of cardiomyocytes have also been studied, such as the properties of the relative action potential pattern and cellular beating frequency. This work has potential implications for research on cytobiology, drug screening, mechanisms of the heart, and cardiomyocyte-based bio-syncretic robotics.

A two dimensional electromechanical model of a cardiomyocyte to assess intra-cellular regional mechanical heterogeneities

Experimental studies on isolated cardiomyocytes from different animal species and human hearts have demonstrated that there are regional differences in the Ca2+ release, Ca2+ decay and sarcomere deformation. Local deformation heterogeneities can occur due to a combination of factors: regional/local differences in Ca2+ release and/or re-uptake, intra-cellular material properties, sarcomere proteins and distribution of the intracellular organelles. To investigate the possible causes of these heterogeneities, we developed a two-dimensional finite-element electromechanical model of a cardiomyocyte that takes into account the experimentally measured local deformation and cytosolic [Ca2+] to locally define the different variables of the constitutive equations describing the electro/mechanical behaviour of the cell. Then, the model was individualised to three different rat cardiac cells. The local [Ca2+] transients were used to define the [Ca2+]-dependent activation functions. The cell-specific local Young's moduli were estimated by solving an inverse problem, minimizing the error between the measured and simulated local deformations along the longitudinal axis of the cell. We found that heterogeneities in the deformation during contraction were determined mainly by the local elasticity rather than the local amount of Ca2+, while in the relaxation phase deformation was mainly influenced by Ca2+ re-uptake. Our electromechanical model was able to successfully estimate the local elasticity along the longitudinal direction in three different cells. In conclusion, our proposed model seems to be a good approximation to assess the heterogeneous intracellular mechanical properties to help in the understanding of the underlying mechanisms of cardiomyocyte dysfunction.

Probing mechanoregulation of neuronal differentiation by plasma lithography patterned elastomeric substrates

Cells sense and interpret mechanical cues, including cell-cell and cell-substrate interactions, in the microenvironment to collectively regulate various physiological functions. Understanding the influences of these mechanical factors on cell behavior is critical for fundamental cell biology and for the development of novel strategies in regenerative medicine. Here, we demonstrate plasma lithography patterning on elastomeric substrates for elucidating the influences of mechanical cues on neuronal differentiation and neuritogenesis. The neuroblastoma cells form neuronal spheres on plasma-treated regions, which geometrically confine the cells over two weeks. The elastic modulus of the elastomer is controlled simultaneously by the crosslinker concentration. The cell-substrate mechanical interactions are also investigated by controlling the size of neuronal spheres with different cell seeding densities. These physical cues are shown to modulate with the formation of focal adhesions, neurite outgrowth, and the morphology of neuroblastoma. By systematic adjustment of these cues, along with computational biomechanical analysis, we demonstrate the interrelated mechanoregulatory effects of substrate elasticity and cell size. Taken together, our results reveal that the neuronal differentiation and neuritogenesis of neuroblastoma cells are collectively regulated via the cell-substrate mechanical interactions.

Microdomain heterogeneity in 3D affects the mechanics of neonatal cardiac myocyte contraction

Cardiac muscle cells are known to adapt to their physical surroundings, optimizing intracellular organization and contractile function for a given culture environment. A previously developed in vitro model system has shown that the inclusion of discrete microscale domains (or microrods) in three dimensions (3D) can alter long-term growth responses of neonatal ventricular myocytes. The aim of this work was to understand how cellular contact with such a domain affects various mechanical changes involved in cardiac muscle cell remodeling. Myocytes were maintained in 3D gels over 5 days in the presence or absence of 100-μm-long microrods, and the effect of this local heterogeneity on cell behavior was analyzed via several imaging techniques. Microrod abutment resulted in approximately twofold increases in the maximum displacement of spontaneously beating myocytes, as based on confocal microscopy scans of the gel xy-plane or the myocyte long axis. In addition, microrods caused significant increases in the proportion of aligned myofibrils (≤20° deviation from long axis) in fixed myocytes. Microrod-related differences in axial contraction could be abrogated by long-term interruption of certain signals of the RhoA-/Rho-associated kinase (ROCK) or protein kinase C (PKC) pathway. Furthermore, microrod-induced increases in myocyte size and protein content were prevented by ROCK inhibition. In all, the data suggest that microdomain heterogeneity in 3D appears to promote the development of axially aligned contractile machinery in muscle cells, an observation that may have relevance to a number of cardiac tissue engineering interventions.

Cardiac myocytes' dynamic contractile behavior differs depending on heart segment

Cardiac myocytes originating from different parts of the heart exhibit varying morphology and ultrastructure. However, the difference in their dynamic behavior is unclear. We examined the contraction of cardiac myocytes originating from the apex, ventricle, and atrium, and found that their dynamic behavior, such as amplitude and frequency of contraction, differs depending on the heart segment of origin. Using video microscopy and high-precision image correlation, we found that: (1) apex myocytes exhibited the highest contraction rate (∼17 beats/min); (2) ventricular myocytes exhibited the highest contraction amplitude (∼5.2 micron); and (3) as myocyte contraction synchronized, their frequency did not change significantly, but the amplitude of contraction increased in apex and ventricular myocytes. In addition, as myocyte cultures mature they formed contractile filaments, further emphasizing the difference in myocyte dynamics is persistent. These results suggest that the dynamic behavior (in addition to static properties) of myocytes is dependent on their segment of origin.

Hydrogel crosslinking density regulates temporal contractility of human embryonic stem cell-derived cardiomyocytes in 3D cultures

Systematically tunable in vitro platforms are invaluable in gaining insight to stem cell-microenvironment interactions in three-dimensional cultures. Utilizing recombinant protein technology, we independently tune hydrogel properties to systematically isolate the effects of matrix crosslinking density on cardiomyocyte differentiation, maturation, and function. We show that contracting human embryonic stem cell-derived cardiomyocytes (hESC-CMs) remain viable within four engineered elastin-like hydrogels of varying crosslinking densities with elastic moduli ranging from 0.45 to 2.4 kPa. Cardiomyocyte phenotype and function was maintained within hESC embryoid bodies for up to 2 weeks. Interestingly, increased crosslinking density was shown to transiently suspend spontaneous contractility. While encapsulated cells began spontaneous contractions at day 1 in hydrogels of the lowest crosslinking density, onset of contraction was increasingly delayed at higher crosslinking densities up to 6 days. However, once spontaneous contraction was restored, the rate of contraction was similar within all materials (71 ± 8 beats/min). Additionally, all groups successfully responded to electrical pacing at both 1 and 2 Hz. This study demonstrates that encapsulated hESC-CMs respond to 3D matrix crosslinking density within elastin-like hydrogels and stresses the importance of investigating temporal cellular responses in 3D cultures.

A finite element study of micropipette aspiration of single cells: effect of compressibility

Micropipette aspiration (MA) technique has been widely used to measure the viscoelastic properties of different cell types. Cells experience nonlinear large deformations during the aspiration procedure. Neo-Hookean viscohyperelastic (NHVH) incompressible and compressible models were used to simulate the creep behavior of cells in MA, particularly accounting for the effect of compressibility, bulk relaxation, and hardening phenomena under large strain. In order to find optimal material parameters, the models were fitted to the experimental data available for mesenchymal stem cells. Finally, through Neo-Hookean porohyperelastic (NHPH) material model for the cell, the influence of fluid flow on the aspiration length of the cell was studied. Based on the results, we suggest that the compressibility and bulk relaxation/fluid flow play a significant role in the deformation behavior of single cells and should be taken into account in the analysis of the mechanics of cells.

Influence of substrate rigidity on primary nucleation of cell adhesion: a thermal fluctuation model

Experimental investigations have demonstrated that cells can actively sense and respond to physical aspects of their environments, such as substrate stiffness of biomaterials, via integrin receptors with the help of stochastic thermal undulations of cell membranes. This paper develops a physical model for the mechanism of integrin-dependent cell-substrate adhesion nucleation in order to investigate the influence of substrate stiffness on primary adhesion formation. In this model, a series of so-called energy potential wells are established to quantitatively describe force-driven conformational changes of integrins on elastic substrates with different rigidities. A concept of nucleation domain is proposed to characterize the necessary condition of integrin-mediated cell-substrate primary adhesion formation. In the framework of classical statistical mechanics, the competitive relationship is investigated between the local thermal undulations of plasma membranes and the conformational conversions of substrate-binding integrins. The quantitative dependence of integrin-mediated adhesion nucleation on substrate rigidities is systematically explored, which shows a reasonable agreement with existing experimental results.

Micromechanical regulation in cardiac myocytes and fibroblasts: implications for tissue remodeling

Cells of the myocardium are at home in one of the most mechanically dynamic environments in the body. At the cellular level, pulsatile stimuli of chamber filling and emptying are experienced as cyclic strains (relative deformation) and stresses (force per unit area). The intrinsic characteristics of tension-generating myocytes and fibroblasts thus have a continuous mechanical interplay with their extrinsic surroundings. This review explores the ways that the micromechanics at the scale of single cardiac myocytes and fibroblasts have been measured, modeled, and recapitulated in vitro in the context of adaptation. Both types of cardiac cells respond to externally applied strain, and many of the intracellular mechanosensing pathways have been identified with the careful manipulation of experimental variables. In addition to strain, the extent of loading in myocytes and fibroblasts is also regulated by cues from the microenvironment such as substrate surface chemistry, stiffness, and topography. Combinations of these structural cues in three dimensions are needed to mimic the micromechanical complexity derived from the extracellular matrix of the developing, healthy, or pathophysiologic heart. An understanding of cardiac cell micromechanics can therefore inform the design and composition of tissue engineering scaffolds or stem cell niches for future applications in regenerative medicine.

Substrate stiffness regulates apoptosis and the mRNA expression of extracellular matrix regulatory genes in the rat annular cells

Cells are subjected to static tension of different magnitudes when cultured on substrates with different stiffnesses. It has long been recognized that mechanical stress is an important modulator of the intervertebral disc degeneration. Here we studied the influence of substrate stiffness on cell morphology, apoptosis and extracellular matrix (ECM) metabolism of the rat annulus fibrosus (AF) cells which are known to be mechanosensitive cells. Polyacrylamide gel substrates with three different stiffnesses were prepared by varying the concentration of acrylamide and bisacrylamide, and the elastic modulus of the different gel substrates were measured with atomic force microscopy (AFM). First-passage rat annular cells were cultured on soft, intermediate, rigid substrates or plastics for 24 or 48 h. The percentages of apoptotic cells were detected by flow cytometry and caspase-3 activity, and morphologic changes were visualized by Hoechst 33258 staining and F-actin staining. In addition, the expression of ECM genes (Col1α1, Col2α1, aggrecan, MMP-3, MMP-13 and ADAMTS-5) were analyzed by RT-PCR. The three different substrates had elastic moduli varying between 1±0.23 kPa (soft, 5% gel with 0.06% bis), 32±2.89 kPa (intermediate, 10% gel with 0.13% bis) and 63±3.45 kPa (rigid, 10% gel with 0.26% bis) with a thickness about 60-70 μm. Most of the rat AF cells appeared small and rounded, and lost most of their stress fibers when cultured on soft substrate. There was a significant increase in the percentage of apoptotic cells in the rat AF cells cultured on soft and intermediate substrates relative to those on plastic surface, with a parallel decrease in the area of cell spreading and nucleus. The AF cells grown on intermediate or rigid substrate had reduced expression of Col1α1, Col2α1 and aggrecan and enhanced expression of MMP-3, MMP-13, and ADAMTS-5 at 24h or 48 h, respectively, relative to those cultured on plastic surface. Conversely, we observed an up-regulation of Col2α1 and aggrecan and no change in the gene expression of MMP-3, MMP-13, and ADAMTS-5 in AF cells on soft substrates. Rat AF cells are sensitive to substrate stiffness which can regulate the morphology, growth, apoptosis and ECM metabolism of rat AF cells, thus indicating the importance of substrate choice for cell transplantation and regeneration for the treatment of disc degeneration using tissue-engineering technique.

An integrated formulation of anisotropic force-calcium relations driving spatio-temporal contractions of cardiac myocytes

Isolated cardiac myocytes exhibit spontaneous patterns of rhythmic contraction, driven by intracellular calcium waves. In order to study the coupling between spatio-temporal calcium dynamics and cell contraction in large deformation regimes, a new strain-energy function, describing the influence of sarcomere length on the calcium-dependent generation of active intracellular stresses, is proposed. This strain-energy function includes anisotropic passive and active contributions that were first validated separately from experimental stress-strain curves and stress-sarcomere length curves, respectively. An extended validation of this formulation was then conducted by considering this strain-energy function as the core of an integrated mechano-chemical three-dimensional model of cardiac myocyte contraction, where autocatalytic intracellular calcium dynamics were described by a representative two-variable model able to generate realistic intracellular calcium waves similar to those observed experimentally. Finite-element simulations of the three-dimensional cell model, conducted for different intracellular locations of triggering calcium sparks, explained very satisfactorily, both qualitatively and quantitatively, the contraction patterns of cardiac myocytes observed by time-lapse videomicroscopy. This integrative approach of the mechano-chemical couplings driving cardiac myocyte contraction provides a comprehensive framework for analysing active stress regulation and associated mechano-transduction processes that contribute to the efficiency of cardiac cell contractility in both physiological and pathological contexts.