Virtual blebbistatin: A robust and rapid software approach to motion artifact removal in optical mapping of cardiomyocytes

Fluorescent reporters of cardiac electrophysiology provide valuable information on heart cell and tissue function. However, motion artifacts caused by cardiac muscle contraction interfere with accurate measurement of fluorescence signals. Although drugs such as blebbistatin can be applied to stop cardiac tissue from contracting by uncoupling calcium-contraction, their usage prevents the study of excitation-contraction coupling and, as we show, impacts cellular structure. We therefore developed a robust method to remove motion computationally from images of contracting cardiac muscle and to map fluorescent reporters of cardiac electrophysiological activity onto images of undeformed tissue. When validated on cardiomyocytes derived from human induced pluripotent stem cells (iPSCs), in both monolayers and engineered tissues, the method enabled efficient and robust reduction of motion artifact. As with pharmacologic approaches using blebbistatin for motion removal, our algorithm improved the accuracy of optical mapping, as demonstrated by spatial maps of calcium transient decay. However, unlike pharmacologic motion removal, our computational approach allowed direct analysis of calcium-contraction coupling. Results revealed calcium-contraction coupling to be more uniform across cells within engineered tissues than across cells in monolayer culture. The algorithm shows promise as a robust and accurate tool for optical mapping studies of excitation-contraction coupling in heart tissue.

A review on qualifications and cost effectiveness of induced pluripotent stem cells (IPSCs)-induced cardiomyocytes in drug screening tests

Human induced pluripotent stem cells (hIPSCs) have initiated a higher degree of successes in disease modelling, preclinical evaluation of drug therapy and pharmaco-toxicological testing. Since the discovery of iPSCs in 2006, many advanced techniques have been introduced to differentiate iPSCs to cardiomyocytes, which have been progressively improved. The disease models from iPSC-induced cardiomyocytes (iPSC-CM) have been successfully helping to study a variety of cardiac diseases such as long QT syndrome, drug-induced long QT, different cardiomyopathies related to mutations in mitochondria or desmosomal proteins and other rare genetic diseases. IPSC-CMs have also been used to screen the role of chemicals in cardiovascular drug discovery and individualisation of drug dosages. In this review, the quality of current procedures for characterisation and maturation of iPSC-CM lines will be discussed. Also, we will focus on time efficiency and cost of standard differentiation methods after reprogramming.

The Balance between Actomyosin Contractility and Microtubule Polymerization Regulates Hierarchical Protrusions That Govern Efficient Fibroblast-Collagen Interactions

Fibroblasts undergo a critical transformation from an initially inactive state to a morphologically different and contractile state after several hours of being embedded within a physiologically relevant three-dimensional (3D) fibrous collagen-based extracellular matrix (ECM). However, little is known about the critical mechanisms by which fibroblasts adapt themselves and their microenvironment in the earliest stage of cell-matrix interaction. Here, we identified the mechanisms by which fibroblasts interact with their 3D collagen fibrous matrices in the early stages of cell-matrix interaction and showed that fibroblasts use energetically efficient hierarchical micro/nano-scaled protrusions in these stages as the primary means for the transformation and adaptation. We found that actomyosin contractility in these protrusions in the early stages of cell-matrix interaction restricts the growth of microtubules by applying compressive forces on them. Our results show that actomyosin contractility and microtubules work in concert in the early stages of cell-matrix interaction to adapt fibroblasts and their microenvironment to one another. These early stage interactions result in responses to disruption of the microtubule network and/or actomyosin contractility that are opposite to well-known responses to late-stage disruption and reveal insight into the ways that cells adapt themselves and their ECM recursively.

Fluorescence Correlation Spectroscopy and Photon Counting Histograms in Finite, Bounded Domains

Analysis of fluctuations arising as fluorescent particles pass through a focused laser beam has enabled quantitative characterization of a broad range of molecular kinetic processes. Two key mathematical frameworks that have enabled these quantifications are fluorescence correlation spectroscopy (FCS) and photon counting histogram (PCH) analysis. Although these frameworks are effective and accurate when the focused laser beam is well approximated by an infinite Gaussian beam with a waist that is small compared to the size of the region over which the fluorescent particles can diffuse, they cannot be applied to situations in which this region is bounded at the nanoscale. We therefore derived general forms of the FCS and PCH frameworks for bounded systems. The finite-domain form of FCS differs from the classical form in its boundary and initial conditions and requires development of a new Fourier space solution for fitting data. Our finite-domain FCS predicts simulated data accurately and reduces to a previous model for the special case when the system is much larger than the Gaussian beam and can be considered to be infinite. We also derived the PCH form for the bounded systems. Our approach enables estimation of the concentration of diffusing fluorophores within a finite domain for the first time, to our knowledge. The method opens the possibility of quantification of kinetics in several systems for which this has never been possible.

A model for positive feedback control of the transformation of fibroblasts to myofibroblasts

The phenotypic conversion of normal fibroblasts to myofibroblasts is central to normal wound healing and to pathological fibrosis that can occur in the heart and many other tissues. The transformation occurs in two stages. The first stage is driven mainly by mechanical changes such as increased stiffness of the heart due to hypertension and cellular contractility. The second stage requires both increasing stiffness and biochemical factors such as the growth factor, TGFβ. As more and more cells convert from weakly contractile fibroblasts to strongly contractile myofibroblasts, the stiffness of the ventricular muscle increases. We propose a simple model for the establishment of non-equilibrium steady states with different compositions of fibroblasts and myofibroblasts. Under some conditions a positive feedback loop resulting from the increasing stiffness caused by increasing numbers of myofibroblasts can produce a bifurcation between steady states with low and high myofibroblast content. We illustrate the large mechanical differences between normal fibroblasts and myofibroblasts with measurements in engineered tissue constructs.

Atomic force microscopy of phase separation on ruptured, giant unilamellar vesicles, and a mechanical pathway for the co-existence of lipid gel phases

Giant unilamellar vesicles (GUVs) and supported lipid bilayers (SLBs) are synthetic model systems widely used in biophysical studies of lipid membranes. Although SLBs are advantageous for biophysical analysis, phase separation behaviors of lipid species in these two model systems can differ due to the lipid-substrate interactions that are present only for SLBs. In the present study, we report that in binary systems, certain phase domains on GUVs retain their original shapes and patterns after the GUVs rupture on glass surfaces. This enabled atomic force microscopy (AFM) experiments on phase domains, a procedure difficult to perform and interpret when applied to GUVs. Unusual phase behavior was evident in binary GUVs containing DLPC and either DPPC or DSPC. These DLPC/DSPC and DLPC/DPPC GUVs both presented the thermodynamic anomaly of having two co-existing gel phases. One phase (a bright phase) included a relatively high concentration of DiI-C20 but excluded Bodipy-HPC, and the other (dark phase) excluded both probes. The bright phases are of interest because they seem to stabilize dark phases against coalescence. Results suggested that the gel phases labeled by DiIC20 in the DLPC/DSPC membrane, which surround the dark gel phase, is an extra layer of membrane, indicating a highly curved structure that might stabilize the interior dark domains, thereby enabling the co-existence of two different gel phases. Results show the utility of AFM on collapsed GUVs, and suggest a possible mechanism for stabilization of lipid domains.

Energy dissipation in quasi-linear viscoelastic tissues, cells, and extracellular matrix

Characterizing how a tissue's constituents give rise to its viscoelasticity is important for uncovering how hidden timescales underlie multiscale biomechanics. These constituents are viscoelastic in nature, and their mechanics must typically be assessed from the uniaxial behavior of a tissue. Confounding the challenge is that tissue viscoelasticity is typically associated with nonlinear elastic responses. Here, we experimentally assessed how fibroblasts and extracellular matrix (ECM) within engineered tissue constructs give rise to the nonlinear viscoelastic responses of a tissue. We applied a constant strain rate, "triangular-wave" loading and interpreted responses using the Fung quasi-linear viscoelastic (QLV) material model. Although the Fung QLV model has several well-known weaknesses, it was well suited to the behaviors of the tissue constructs, cells, and ECM tested. Cells showed relatively high damping over certain loading frequency ranges. Analysis revealed that, even in cases where the Fung QLV model provided an excellent fit to data, the the time constant derived from the model was not in general a material parameter. Results have implications for design of protocols for the mechanical characterization of biological materials, and for the mechanobiology of cells within viscoelastic tissues.

Investigation of Nanoscopic Phase Separations in Lipid Membranes Using Inverse FCS

Measurement of the sizes of nanoscopic particles is a difficult challenge, especially in two-dimensional systems such as cell membranes. We have extended inverse fluorescence correlation spectroscopy (iFCS) to endow it with unique advantages for measuring particle size from the nano- to the microscale. We have augmented iFCS with an analysis of moments of fluorescence fluctuations and used it to measure stages of phase separation in model lipid bilayer membranes. We observed two different pathways for the growth of phase domains. In one, nanoscopic gel domains appeared first and then gradually grew to micrometer size. In the other, the domains reached micrometer size quickly, and their number gradually increased. These measurements demonstrate the value of iFCS measurements through their ability, to our knowledge, to provide new information about the mechanism of lipid phase separation and potentially about the physical basis of naturally occurring nanodomains such as lipid rafts.

Discrete quasi-linear viscoelastic damping analysis of connective tissues, and the biomechanics of stretching

The time- and frequency-dependent properties of connective tissue define their physiological function, but are notoriously difficult to characterize. Well-established tools such as linear viscoelasticity and the Fung quasi-linear viscoelastic (QLV) model impose forms on responses that can mask true tissue behavior. Here, we applied a more general discrete quasi-linear viscoelastic (DQLV) model to identify the static and dynamic time- and frequency-dependent behavior of rabbit medial collateral ligaments. Unlike the Fung QLV approach, the DQLV approach revealed that energy dissipation is elevated at a loading period of ∼10s. The fitting algorithm was applied to the entire loading history on each specimen, enabling accurate estimation of the material's viscoelastic relaxation spectrum from data gathered from transient rather than only steady states. The application of the DQLV method to cyclically loading regimens has broad applicability for the characterization of biological tissues, and the results suggest a mechanistic basis for the stretching regimens most favored by athletic trainers.

Fibroblasts Slow Conduction Velocity in a Reconstituted Tissue Model of Fibrotic Cardiomyopathy

Myocardial function deteriorates over the course of fibrotic cardiomyopathy, due to electrophysiological and mechanical effects of myofibroblasts that are not completely understood. Although a range of experimental model systems and associated theoretical treatments exist at the levels of isolated cardiomyocytes and planar co-cultures of myofibroblasts and cardiomyocytes, interactions between these cell types at the tissue level are less clear. We studied these interactions through an engineered heart tissue (EHT) model of fibrotic myocardium and a mathematical model of the effects of cellular composition on EHT impulse conduction velocity. The EHT model allowed for modulation of cardiomyocyte and myofibroblast volume fractions, and observation of cell behavior in a three-dimensional environment that is more similar to native heart tissue than is planar cell culture. The cardiomyocyte and myofibroblast volume fractions determined the retardation of impulse conduction (spread of the action potential) in EHTs as measured by changes of the fluorescence of the Ca²⁺ probe, Fluo-2. Interpretation through our model showed retardation far in excess of predictions by homogenization theory, with conduction ceasing far below the fibroblast volume fraction associated with steric percolation. Results point to an important multiscale structural role of myofibroblasts in attenuating impulse conduction in fibrotic cardiomyopathy.

A discrete spectral analysis for determining quasi-linear viscoelastic properties of biological materials

The viscoelastic behaviour of a biological material is central to its functioning and is an indicator of its health. The Fung quasi-linear viscoelastic (QLV) model, a standard tool for characterizing biological materials, provides excellent fits to most stress-relaxation data by imposing a simple form upon a material's temporal relaxation spectrum. However, model identification is challenging because the Fung QLV model's 'box'-shaped relaxation spectrum, predominant in biomechanics applications, can provide an excellent fit even when it is not a reasonable representation of a material's relaxation spectrum. Here, we present a robust and simple discrete approach for identifying a material's temporal relaxation spectrum from stress-relaxation data in an unbiased way. Our 'discrete QLV' (DQLV) approach identifies ranges of time constants over which the Fung QLV model's typical box spectrum provides an accurate representation of a particular material's temporal relaxation spectrum, and is effective at providing a fit to this model. The DQLV spectrum also reveals when other forms or discrete time constants are more suitable than a box spectrum. After validating the approach against idealized and noisy data, we applied the methods to analyse medial collateral ligament stress-relaxation data and identify the strengths and weaknesses of an optimal Fung QLV fit.

An approach to quantifying 3D responses of cells to extreme strain

The tissues of hollow organs can routinely stretch up to 2.5 times their length. Although significant pathology can arise if relatively large stretches are sustained, the responses of cells are not known at these levels of sustained strain. A key challenge is presenting cells with a realistic and well-defined three-dimensional (3D) culture environment that can sustain such strains. Here, we describe an in vitro system called microscale, magnetically-actuated synthetic tissues (micro-MASTs) to quantify these responses for cells within a 3D hydrogel matrix. Cellular strain-threshold and saturation behaviors were observed in hydrogel matrix, including strain-dependent proliferation, spreading, polarization, and differentiation, and matrix adhesion retained at strains sufficient for apoptosis. More broadly, the system shows promise for defining and controlling the effects of mechanical environment upon a broad range of cells.

Tissue constructs: platforms for basic research and drug discovery

The functions, form and mechanical properties of cells are inextricably linked to their extracellular environment. Cells from solid tissues change fundamentally when, isolated from this environment, they are cultured on rigid two-dimensional substrata. These changes limit the significance of mechanical measurements on cells in two-dimensional culture and motivate the development of constructs with cells embedded in three-dimensional matrices that mimic the natural tissue. While measurements of cell mechanics are difficult in natural tissues, they have proven effective in engineered tissue constructs, especially constructs that emphasize specific cell types and their functions, e.g. engineered heart tissues. Tissue constructs developed as models of disease also have been useful as platforms for drug discovery. Underlying the use of tissue constructs as platforms for basic research and drug discovery is integration of multiscale biomaterials measurement and computational modelling to dissect the distinguishable mechanical responses separately of cells and extracellular matrix from measurements on tissue constructs and to quantify the effects of drug treatment on these responses. These methods and their application are the main subjects of this review.

Efficient and optimized identification of generalized Maxwell viscoelastic relaxation spectra

Viscoelastic relaxation spectra are essential for predicting and interpreting the mechanical responses of materials and structures. For biological tissues, these spectra must usually be estimated from viscoelastic relaxation tests. Interpreting viscoelastic relaxation tests is challenging because the inverse problem is expensive computationally. We present here an efficient algorithm that enables rapid identification of viscoelastic relaxation spectra. The algorithm was tested against trial data to characterize its robustness and identify its limitations and strengths. The algorithm was then applied to identify the viscoelastic response of reconstituted collagen, revealing an extensive distribution of viscoelastic time constants.

Diffusion of human replication protein A along single-stranded DNA

Replication protein A (RPA) is a eukaryotic single-stranded DNA (ssDNA) binding protein that plays critical roles in most aspects of genome maintenance, including replication, recombination and repair. RPA binds ssDNA with high affinity, destabilizes DNA secondary structure and facilitates binding of other proteins to ssDNA. However, RPA must be removed from or redistributed along ssDNA during these processes. To probe the dynamics of RPA-DNA interactions, we combined ensemble and single-molecule fluorescence approaches to examine human RPA (hRPA) diffusion along ssDNA and find that an hRPA heterotrimer can diffuse rapidly along ssDNA. Diffusion of hRPA is functional in that it provides the mechanism by which hRPA can transiently disrupt DNA hairpins by diffusing in from ssDNA regions adjacent to the DNA hairpin. hRPA diffusion was also monitored by the fluctuations in fluorescence intensity of a Cy3 fluorophore attached to the end of ssDNA. Using a novel method to calibrate the Cy3 fluorescence intensity as a function of hRPA position on the ssDNA, we estimate a one-dimensional diffusion coefficient of hRPA on ssDNA of D1~5000nt(2) s(-1) at 37°C. Diffusion of hRPA while bound to ssDNA enables it to be readily repositioned to allow other proteins access to ssDNA.

The role of mechanics in actin stress fiber kinetics

The dynamic responses of actin stress fibers within a cell's cytoskeleton are central to the development and maintenance of healthy tissues and organs. Disturbances to these underlie a broad range of pathologies. Because of the importance of these responses, extensive experiments have been conducted in vitro to characterize actin cytoskeleton dynamics of cells cultured upon two-dimensional substrata, and the first experiments have been conducted for cells within three-dimensional tissue models. Three mathematical models exist for predicting the dynamic behaviors observed. Surprisingly, despite differing viewpoints on how actin stress fibers are stabilized or destabilized, all of these models are predictive of a broad range of available experimental data. Coarsely, the models of Kaunas and co-workers adopt a strategy whereby mechanical stretch can hasten the depolymerization actin stress fibers that turn over constantly, while the models of Desphande and co-workers adopt a strategy whereby mechanical stress is required to activate the formation of stress fibers and subsequently stabilize them. In three-dimensional culture, elements of both approaches appear necessary to predict observed phenomena, as embodied by the model of Lee et al. After providing a critical review of existing models, we propose lines of experimentation that might be able to test the different principles underlying their kinetic laws.

Confidence intervals for concentration and brightness from fluorescence fluctuation measurements

The theory of photon count histogram (PCH) analysis describes the distribution of fluorescence fluctuation amplitudes due to populations of fluorophores diffusing through a focused laser beam and provides a rigorous framework through which the brightnesses and concentrations of the fluorophores can be determined. In practice, however, the brightnesses and concentrations of only a few components can be identified. Brightnesses and concentrations are determined by a nonlinear least-squares fit of a theoretical model to the experimental PCH derived from a record of fluorescence intensity fluctuations. The χ(2) hypersurface in the neighborhood of the optimum parameter set can have varying degrees of curvature, due to the intrinsic curvature of the model, the specific parameter values of the system under study, and the relative noise in the data. Because of this varying curvature, parameters estimated from the least-squares analysis have varying degrees of uncertainty associated with them. There are several methods for assigning confidence intervals to the parameters, but these methods have different efficacies for PCH data. Here, we evaluate several approaches to confidence interval estimation for PCH data, including asymptotic standard error, likelihood joint-confidence region, likelihood confidence intervals, skew-corrected and accelerated bootstrap (BCa), and Monte Carlo residual resampling methods. We study these with a model two-dimensional membrane system for simplicity, but the principles are applicable as well to fluorophores diffusing in three-dimensional solution. Using simulated fluorescence fluctuation data, we find the BCa method to be particularly well-suited for estimating confidence intervals in PCH analysis, and several other methods to be less so. Using the BCa method and additional simulated fluctuation data, we find that confidence intervals can be reduced dramatically for a specific non-Gaussian beam profile.

Physically-induced cytoskeleton remodeling of cells in three-dimensional culture

Characterizing how cells in three-dimensional (3D) environments or natural tissues respond to biophysical stimuli is a longstanding challenge in biology and tissue engineering. We demonstrate a strategy to monitor morphological and mechanical responses of contractile fibroblasts in a 3D environment. Cells responded to stretch through specific, cell-wide mechanisms involving staged retraction and reinforcement. Retraction responses occurred for all orientations of stress fibers and cellular protrusions relative to the stretch direction, while reinforcement responses, including extension of cellular processes and stress fiber formation, occurred predominantly in the stretch direction. A previously unreported role of F-actin clumps was observed, with clumps possibly acting as F-actin reservoirs for retraction and reinforcement responses during stretch. Responses were consistent with a model of cellular sensitivity to local physical cues. These findings suggest mechanisms for global actin cytoskeleton remodeling in non-muscle cells and provide insight into cellular responses important in pathologies such as fibrosis and hypertension.

Fluorescence correlation spectroscopy: past, present, future

In recent years fluorescence correlation spectroscopy (FCS) has become a routine method for determining diffusion coefficients, chemical rate constants, molecular concentrations, fluorescence brightness, triplet state lifetimes, and other molecular parameters. FCS measures the spatial and temporal correlation of individual molecules with themselves and so provides a bridge between classical ensemble and contemporary single-molecule measurements. It also provides information on concentration and molecular number fluctuations for nonlinear reaction systems that complement single-molecule measurements. Typically implemented on a fluorescence microscope, FCS samples femtoliter volumes and so is especially useful for characterizing small dynamic systems such as biological cells. In addition to its practical utility, however, FCS provides a window on mesoscopic systems in which fluctuations from steady states not only provide the basis for the measurement but also can have important consequences for the behavior and evolution of the system. For example, a new and potentially interesting field for FCS studies could be the study of nonequilibrium steady states, especially in living cells.

Short communication: vascular smooth muscle cell stiffness as a mechanism for increased aortic stiffness with aging

RATIONALE

Increased aortic stiffness, an important feature of many vascular diseases, eg, aging, hypertension, atherosclerosis, and aortic aneurysms, is assumed because of changes in extracellular matrix (ECM).

OBJECTIVE

We tested the hypothesis that the mechanisms also involve intrinsic stiffening of vascular smooth muscle cells (VSMCs).

METHODS AND RESULTS

Stiffness was measured in vitro both by atomic force microscopy (AFM) and in a reconstituted tissue model, using VSMCs from aorta of young versus old male monkeys (Macaca fascicularis) (n=7/group), where aortic stiffness increases by 200% in vivo. The apparent elastic modulus was increased (P<0.05) in old (41.7+/-0.5 kPa) versus young (12.8+/-0.3 kPa) VSMCs but not after disassembly of the actin cytoskeleton with cytochalasin D. Stiffness of the VSMCs in the reconstituted tissue model was also higher (P<0.05) in old (23.3+/-3.0 kPa) than in young (13.7+/-2.4 kPa).

CONCLUSIONS

These data support the novel concept, not appreciated previously, that increased vascular stiffness with aging is attributable not only to changes in ECM but also to intrinsic changes in VSMCs.

Phase separation in biological membranes: integration of theory and experiment

Lipid bilayer model membranes that contain a single lipid species can undergo transitions between ordered and disordered phases, and membranes that contain a mixture of lipid species can undergo phase separations. Studies of these transformations are of interest for what they can tell us about the interaction energies of lipid molecules of different species and conformations. Nanoscopic phases (<200 nm) can provide a model for membrane rafts, specialized membrane domains enriched in cholesterol and sphingomyelin, which are believed to have essential biological functions in cell membranes. Crucial questions are whether lipid nanodomains can exist in stable equilibrium in membranes and what is the distribution of their sizes and lifetimes in membranes of different composition. Theoretical methods have supplied much information on these questions, but better experimental methods are needed to detect and characterize nanodomains under normal membrane conditions. This review summarizes linkages between theoretical and experimental studies of phase separation in lipid bilayer model membranes.

Whole cell mechanics of contractile fibroblasts: relations between effective cellular and extracellular matrix moduli

While much is known about the subcellular structures responsible for the mechanical functioning of a contractile fibroblast, debate exists about how these components combine to endow a cell with its form and mechanical function. We present an analysis of mechanical characterization experiments performed on bio-artificial tissue constructs, which we believe serve as a more realistic testing environment than two-dimensional cell culture. These model tissues capture many features of real tissues with the advantage that they can be engineered to model different physiological and pathological characteristics. We study here a model tissue consisting of reconstituted type I collagen and varying concentrations of activated contractile fibroblasts that is relevant to modelling different stages of wound healing. We applied this system to assess how cell and extracellular matrix (ECM) mechanics vary with cell concentration. Short-term and long-term moduli of the ECM were estimated through analytical and numerical analysis of two-phase elastic solids containing cell-shaped voids. The relative properties of cells were then deduced from the results of numerical analyses of two-phase elastic solids containing mechanically isotropic cells of varying modulus. With increasing cell concentration, the short-term and long-term tangent moduli of the reconstituted collagen ECM increased sharply from a baseline value, while those of the cells decreased monotonically.

Stretch-activated force shedding, force recovery, and cytoskeletal remodeling in contractile fibroblasts

The stress fiber network within contractile fibroblasts structurally reinforces and provides tension, or "tone", to tissues such as those found in healing wounds. Stress fibers have previously been observed to polymerize in response to mechanical forces. We observed that, when stretched sufficiently, contractile fibroblasts diminished the mechanical tractions they exert on their environment through depolymerization of actin filaments then restored tissue tension and rebuilt actin stress fibers through staged Ca(++)-dependent processes. These staged Ca(++)-modulated contractions consisted of a rapid phase that ended less than a minute after stretching, a plateau of inactivity, and a final gradual phase that required several minutes to complete. Active contractile forces during recovery scaled with the degree of rebuilding of the actin cytoskeleton. This complementary action demonstrates a programmed regulatory mechanism that protects cells from excessive stretch through choreographed active mechanical and biochemical healing responses.

Oligomerization of the EGF receptor investigated by live cell fluorescence intensity distribution analysis

Recent evidence suggests that the EGF receptor oligomerizes or clusters in cells even in the absence of agonist ligand. To assess the status of EGF receptors in live cells, an EGF receptor fused to eGFP was stably expressed in CHO cells and studied using fluorescence correlation spectroscopy and fluorescent brightness analysis. By modifying FIDA for use in a two-dimensional system with quantal brightnesses, a method was developed to quantify the degree of clustering of the receptors on the cell surface. The analysis demonstrates that under physiological conditions, the EGF receptor exists in a complex equilibrium involving single molecules and clusters of two or more receptors. Acute depletion of cellular cholesterol enhanced EGF receptor clustering whereas cholesterol loading decreased receptor clustering, indicating that receptor aggregation is sensitive to the lipid composition of the membrane.

A simplified approach to quasi-linear viscoelastic modeling

The fitting of quasi-linear viscoelastic (QLV) constitutive models to material data often involves somewhat cumbersome numerical convolution. A new approach to treating quasi-linearity in 1-D is described and applied to characterize the behavior of reconstituted collagen. This approach is based on a new principle for including nonlinearity and requires considerably less computation than other comparable models for both model calibration and response prediction, especially for smoothly applied stretching. Additionally, the approach allows relaxation to adapt with the strain history. The modeling approach is demonstrated through tests on pure reconstituted collagen. Sequences of "ramp-and-hold" stretching tests were applied to rectangular collagen specimens. The relaxation force data from the "hold" was used to calibrate a new "adaptive QLV model" and several models from literature, and the force data from the "ramp" was used to check the accuracy of model predictions. Additionally, the ability of the models to predict the force response on a reloading of the specimen was assessed. The "adaptive QLV model" based on this new approach predicts collagen behavior comparably to or better than existing models, with much less computation.

Cellular and matrix mechanics of bioartificial tissues during continuous cyclic stretch

Bioartificial tissues are useful model systems for studying cell and extra-cellular matrix mechanics. These tissues provide a 3D environment for cells and allow tissue components to be easily modified and quantified. In this study, we fabricated bioartificial tissue rings from a 1 ml solution containing one million cardiac fibroblasts and 1 mg collagen. After 8 days, rings compacted to <1% of original volume and cell number increased 2.4 fold. We initiated continuous cyclic stretching of the rings after 2, 4, or 8 days of incubation, while monitoring the tissue forces. Peak tissue force during each cycle decreased rapidly after initiating stretch, followed by further slow decline. We added 2 μM Cytochalasin-D to some rings prior to initiation of stretch to determine the force contributed by the matrix. Cell force was estimated by subtracting matrix force from tissue force. After 12 h, matrix force-strain curves were highly nonlinear. Cell force-strain curves were linear during loading and showed hysteresis indicating viscoelastic behavior. Cell stiffness increased with stretching frequency from 0.001–0.25 Hz. Cell stiffness decreased with stretch amplitude (5–25%) at 0.1 Hz. The trends in cell stiffness do not fit simple viscoelastic models previously proposed, and suggest possible strain-amplitude related changes during cyclic stretch.

Cellular and matrix contributions to tissue construct stiffness increase with cellular concentration

The mechanics of bio-artificial tissue constructs result from active and passive contributions of cells and extracellular matrix (ECM). We delineated these for a fibroblast-populated matrix (FPM) consisting of chick embryo fibroblast cells in a type I collagen ECM through mechanical testing, mechanical modeling, and selective biochemical elimination of tissue components. From a series of relaxation tests, we found that contributions to overall tissue mechanics from both cells and ECM increase exponentially with the cell concentration. The force responses in these relaxation tests exhibited a logarithmic decay over the 3600 second test duration. The amplitudes of these responses were nearly linear with the amplitude of the applied stretch. The active component of cellular forces rose dramatically for FPMs containing higher cell concentrations.

Reconstitution of the Frank-Starling mechanism in engineered heart tissues

According to the Frank-Starling mechanism, as the heart is stretched, it increases its contraction force. Reconstitution of the Frank-Starling mechanism is an important milestone for producing functional heart tissue constructs. Spontaneously contracting engineered heart tissues (EHTs) were reconstituted by growing dissociated chicken embryo cardiomyocytes in collagen matrices. Twitch and baseline tensions were recorded at precisely controlled levels of tissue strain. The EHTs showed a steep increase in twitch tension from 0.47 +/- 0.02 to 0.91 +/- 0.02 mN/mm2 as they were stretched at a constant rate (2.67% per min) from 86% to 100% of the length at which maximum twitch force was exerted. In response to a sudden stretch (3.3%), the twitch tension increased gradually (approximately 60 s) in a Gd3+-sensitive manner, suggesting the presence of stretch-activated Ca2+ channels. A large difference in baseline tension between lengthening (loading) and shortening (unloading) was also recorded. Disruption of nonsarcomeric actin filaments by cytochalasin D and latrunculin B decreased this difference. A simple mechanical model interprets these results in terms of mechanical connections between myocytes and nonmuscle cells. The experimental results strongly suggest that regulation of twitch tension in EHTs is similar to that of natural myocardium.

Myosin-based contraction is not necessary for cardiac c-looping in the chick embryo

During the initial phase of cardiac looping, known as c-looping, the heart bends and twists into a c-shaped tube with the convex outer curvature normally directed toward the right side of the embryo. Despite intensive study for more than 80 years, the biophysical mechanisms that drive and regulate looping remain poorly understood, although some investigators have speculated that differential cytoskeletal contraction supplies the driving force for c-looping. The purpose of this investigation was to test this hypothesis. To inhibit contraction, embryonic chick hearts at stages 10-12 (10-16 somites, 33-48 h) were exposed to the myosin inhibitors 2,3-butanedione monoxime (BDM), ML-7, Y-27632, and blebbistatin. Experiments were conducted in both whole embryo culture and, to focus on bending alone, isolated heart culture. Measurements of heart stiffness and phosphorylation of the myosin regulatory light chains showed that BDM, Y-27632, and blebbistatin significantly reduced myocardial contractility, while ML-7 had a lesser effect. None of these drugs significantly affected looping during the studied stages. These results suggest that active contraction is not required for normal c-looping of the embryonic chick heart between stages 10 and 12.

Role of actin polymerization in bending of the early heart tube

During cardiac c-looping, the heart transforms from a straight tube into a c-shaped tube, presenting the first evidence of left-right asymmetry in the embryo. C-looping consists of two primary deformation components: ventral bending and dextral rotation. This study examines the role of actin polymerization in bending of the heart tube. Exposure of stage 9-11 chick embryos to low concentrations of the actin polymerization inhibitors cytochalasin D (5 nM-2.0 microM) and latrunculin A (LA; 25 nM-2.0 microM) suppressed looping in a stage- and concentration-dependent manner in both whole embryos and isolated hearts. Local exposure of either the dorsal or ventral sides of isolated hearts to LA also inhibited looping, but less than global exposure, indicating that both sides contribute to the bending mechanism. Taken together, these data suggest that ongoing actin polymerization is required for the bending component of cardiac c-looping, and we speculate that polymerization-driven myocardial cell shape changes cause this deformation.

On the application of strain factors for approximation of the contribution of anisotropic cells to the mechanics of a tissue construct

Bio-artificial tissue constructs consisting of fibroblast cells embedded in a collagenous matrix are valuable in vitro systems in which to study cellular mechanics. Deriving cellular mechanics from the results of experimentation on tissue constructs requires a mathematical relationship that delineates amongst the contributions of the constituents of a tissue construct. A scaling between the average strain in a uniformly stretched tissue and the axial strain in isotropic cells was used in earlier work to study relations between cell mechanics and the overall mechanics of a tissue construct. That work showed that a scaling factor called a "strain factor" provided an accurate representation of the average axial strain in isotropic cells. The present study analyzes such relationships for anisotropic cells. We incorporate Eshelby's (1957; Proceedings of the Royal Society of London A 241, 376; 1959; Proceedings of the Royal Society of London A 252, 561) exact solution for the strain field in isolated ellipsoidal inclusions into the Zahalak (Biophysical journal 79, 2369) constitutive model for tissue constructs. Results showed that, for the case of prolate cells, the strain along the major cell axis is mostly influenced by the remote strain projected along that axis; off-axis cell mechanics plays only a small role in most tissues. The strain factor approximation is shown to be accurate for anisotropic cells to within a few percent for the vast majority of tissues. The results presented in this paper provide an explicit measure of the effects of cellular anisotropy, and a mechanism for calculating the contributions of these effects to overall tissue mechanics when these effects are important.

Wave motion in relaxation-testing of nonlinear elastic media

Relaxation testing is a fundamental tool for mechanical characterization of viscoelastic materials. Inertial effects are usually neglected when analysing these tests. However, relaxation tests involve sudden stretching of specimens, which causes propagation of waves whose effects may be significant. We study wave motion in a nonlinear elastic model specimen and derive expressions for the conditions under which loading may be considered to be quasi-static. Additionally, we derive expressions for wave properties such as wave speed and the time needed to reach a steady-state wave pattern. These expressions can be used to deduce nonlinear elastic material properties from dynamic experiments.

The kinetics of conformational fluctuations in an unfolded protein measured by fluorescence methods

The simplest dynamic model for an unfolded protein is a statistical coil that continually undergoes substantial conformational fluctuations. A growing number of studies indicate that the unfolded protein is not a simple random coil but rather forms transient structures. We have directly measured the rate of conformational fluctuations of unfolded intestinal fatty acid binding protein (131 aa, 15 kDa) by using fluorescence self-quenching in combination with fluorescence correlation spectroscopy. The conformational fluctuations in this state have an apparent relaxation time, tauR, of 1.6 microsec in 3 M guanidine-HCl at pH 7 and 20 degrees C. The value of tauR increases with increasing solution viscosity, suggesting a diffusive process. In the molten globule state at pH 2, tauR is 2.5 microsec, increasing further with the formation of salt-induced secondary structure. These measurements, which should be widely applicable to other systems, can provide important information about the still incompletely understood conformational properties of unfolded proteins and the mechanism of protein folding.

Thin bio-artificial tissues in plane stress: the relationship between cell and tissue strain, and an improved constitutive model

Constitutive models are needed to relate the active and passive mechanical properties of cells to the overall mechanical response of bio-artificial tissues. The Zahalak model attempts to explicitly describe this link for a class of bio-artificial tissues. A fundamental assumption made by Zahalak is that cells stretch in perfect registry with a tissue. We show this assumption to be valid only for special cases, and we correct the Zahalak model accordingly. We focus on short-term and very long-term behavior, and therefore consider tissue constituents that are linear in their loading response (although not necessarily linear in unloading). In such cases, the average strain in a cell is related to the macroscopic tissue strain by a scalar we call the "strain factor". We incorporate a model predicting the strain factor into the Zahalak model, and then reinterpret experiments reported by Zahalak and co-workers to determine the in situ stiffness of cells in a tissue construct. We find that, without the modification in this article, the Zahalak model can underpredict cell stiffness by an order of magnitude.

The relationship between cell and tissue strain in three-dimensional bio-artificial tissues

Continuum constitutive laws are needed to ensure that bio-artificial tissue constructs replicate the mechanical response of the tissues they replace, and to understand how the constituents of these constructs contribute to their overall mechanical response. One model designed to achieve both of these aims is the Zahalak model, which was modified by Marquez and co-workers to incorporate inhomogeneous strain fields within very thin tissues. When applied to reinterpret previous measurements, the modified Zahalak model predicted higher values of the continuum stiffness of fibroblasts than earlier estimates. In this work, we further modify the Zahalak model to account for inhomogeneous strain fields in constructs whose cell orientations have a significant out-of-plane component. When applied to reinterpret results from the literature, the new model shows that estimates of continuum cell stiffness might need to be revised upward. As in this article's companion, we updated the average cell strain by defining a correction factor ("strain factor"), based upon the elastic response. Three different cell orientation distributions were studied. We derived an approximate scaling model for the strain factor, and validated it against exact and self-consistent (mean-field) solutions from the literature for dilute cell concentrations, and Monte Carlo simulations involving three-dimensional finite element analyses for high cell concentrations.

Cell orientation influences the biaxial mechanical properties of fibroblast populated collagen vessels

Bioartificial tissues, composed of cells in a collagen matrix, can be fabricated with preferred cell orientations to mimic the histologic arrangement of biologic tissues. The influence of preferred cell orientations on the biaxial mechanical behavior of bioartificial tissues is unknown. Characterizing the biaxial mechanical behavior is necessary for better predicting the in vivo behavior of bioartificial tissues. Fibroblast populated collagen vessels (FPCVs) were fabricated with two different cell orientations by controlling the mechanical constraints during incubation. The cell orientation was verified by confocal microscopy and the collagen fiber organization was examined by confocal reflection and scanning electron microscopy (SEM). Pressure-diameter, force-length tests were performed to determine the influence of cell orientation on the biaxial mechanical behavior. FPCVs were more extensible in the direction perpendicular to the preferred cell orientation, than in the direction parallel to the cell orientation. Biaxial tests were also performed in the presence of Cytochalasin D (Cyto D) to minimize the mechanical contribution of the cells. After Cyto D treatment, the FPCVs remained more extensible in the direction perpendicular to the cell orientation, even though a preferred collagen fiber orientation was not observed in the microscopy images.

Measuring unfolding of proteins in the presence of denaturant using fluorescence correlation spectroscopy

IFABP is a small (15 kDa) protein consisting mostly of antiparallel beta-strands that surround a large cavity into which ligands bind. We have previously used FCS to show that the native protein, labeled with fluorescein, exhibits dynamic fluctuation with a relaxation time of 35 micros. Here we report the use of FCS to study the unfolding of the protein induced by guanidine hydrochloride. Although the application of this technique to measure diffusion coefficients and molecular dynamics is straightforward, the FCS results need to be corrected for both viscosity and refractive index changes as the guanidine hydrochloride concentration increases. We present here a detailed study of the effects of viscosity and refractive index of guanidine hydrochloride solutions to calibrate FCS data. After correction, the increase in the diffusion time of IFABP corresponds well with the unfolding transition monitored by far ultraviolet circular dichroism. We also show that the magnitude of the 35 micros phase, reflecting the conformational fluctuation in the native state, decreases sharply as the concentration of denaturant increases and the protein unfolds. Although FCS experiments indicate that the unfolded state at pH 2 is rather compact and native-like, the radius in the presence of guanidine hydrochloride falls well within the range expected for a random coil.