Spatial and temporal traction response in human airway smooth muscle cells

Tractions that cells exert on theirsubstrates are essential in cell spreading, migration, and contraction.These tractions can be determined by plating the cells on a flexiblegel and measuring the deformation of the gel by using fluorescent beadsembedded just below the surface of the gel. In this article we describe the image correlation method (ICM) optimized for determining the displacement field of the gel under a contracting cell. For the calculation of the traction field from the displacement field we usethe recently developed method of Fourier transform traction cytometry(FTTC). The ICM and FTTC methods are applied to human airway smoothmuscle cells during stimulation with the contractile agonist histamineor the relaxing agonist isoproterenol. The overall intensity of thecell contraction (the median traction magnitude, the energy transferredfrom the cell to the gel, and the net contractile moment) increasedafter activation with histamine, and decreased after treatment withisoproterenol. Cells exhibited regional differences in the time courseof traction during the treatment. Both temporal evolution and magnitudeof traction increase induced by histamine varied markedly amongdifferent cell protrusions, whereas the nuclear region showed thesmallest response. These results suggest that intracellular mediatorsof cell adhesion and contraction respond to contractile stimuli withdifferent rates and intensities in different regions of the cell.

     

Traction fields, moments, and strain energy that cells exert on their surroundings

Adherent cells exert tractions on theirsurroundings. These tractions can be measured by observing thedisplacements of beads embedded on a flexible gel substrate on whichthe cells are cultured. This paper presents an exact solution to theproblem of computing the traction field from the observed displacementfield. The solution rests on recasting the relationship betweendisplacements and tractions into Fourier space, where the recovery ofthe traction field is especially simple. We present two subcases of thesolution, depending on whether or not tractions outside the observedcell boundaries are set to be zero. The implementation iscomputationally efficient. We also give the solution for the tractionfield in a representative human airway smooth muscle cell contracted by treatment with histamine. Finally, we give explicit formulas for reducing the traction and displacement fields to contraction moments, the orientation of the principal axes of traction, and the strain energy imparted by the cell to the substrate.

     

High resolution traction force microscopy based on experimental and computational advances

Cell adhesion and migration crucially depend on the transmission of actomyosin-generated forces through sites of focal adhesion to the extracellular matrix. Here we report experimental and computational advances in improving the resolution and reliability of traction force microscopy. First, we introduce the use of two differently colored nanobeads as fiducial markers in polyacrylamide gels and explain how the displacement field can be computationally extracted from the fluorescence data. Second, we present different improvements regarding standard methods for force reconstruction from the displacement field, which are the boundary element method, Fourier-transform traction cytometry, and traction reconstruction with point forces. Using extensive data simulation, we show that the spatial resolution of the boundary element method can be improved considerably by splitting the elastic field into near, intermediate, and far field. Fourier-transform traction cytometry requires considerably less computer time, but can achieve a comparable resolution only when combined with Wiener filtering or appropriate regularization schemes. Both methods tend to underestimate forces, especially at small adhesion sites. Traction reconstruction with point forces does not suffer from this limitation, but is only applicable with stationary and well-developed adhesion sites. Third, we combine these advances and for the first time reconstruct fibroblast traction with a spatial resolution of ∼1 μm.     

A Bayesian adaptive basis algorithm for single particle reconstruction

Traditional single particle reconstruction methods use either the Fourier or the delta function basis to represent the particle density map. This paper proposes a more flexible algorithm that adaptively chooses the basis based on the data. Because the basis adapts to the data, the reconstruction resolution and signal-to-noise ratio (SNR) is improved compared to a reconstruction with a fixed basis. Moreover, the algorithm automatically masks the particle, thereby separating it from the background. This eliminates the need for ad hoc filtering or masking in the refinement loop. The algorithm is formulated in a Bayesian maximum-a-posteriori framework and uses an efficient optimization algorithm for the maximization. Evaluations using simulated and actual cryogenic electron microscopy data show resolution and SNR improvements as well as the effective masking of particle from background.     

Improved processing of the steady-state evoked potential

Two related procedures for estimating the parameters of steady-state evoked potentials (SSEPs) are introduced. The first procedure involves an initial stage of digital bandpass filtering followed by a Discrete Fourier Transform analysis. In the second method, a high resolution method based on parametric modelling is applied to the filtered data. The digital pre-filter consists of a non-phase shifting Chebychev bandpass filter. The parametric modelling method considers the evoked-response-plus-noise distribution to consist of a set of exponentially damped sinusoids. The frequency, amplitude, phase and damping factors of these components are estimated by calculating the mean of the forward and backward prediction filters and linear regression.We compared the signal-to-noise ratio (SNR) of the new procedures to the conventional Discrete Fourier Transform method for Monte Carlo simulations utilizing known sinusoids buried in white noise, known sinusoids buried in human EEG noise and for a sample of visual evoked potential data. Both of the new methods produce substantially more accurate and less variable estimates of test sinusoid amplitude. For VEP recording, the EEG background noise level is reduced by 5–6 dB over that obtained with the DFT. The new methods also provide approximately 5 dB better SNR than the DFT for detection of sinusoids based on the Rayleigh statistic. The parametric modelling approach is particularly suited for the analysis of very short data records including cycle-by-cycle analysis of the SSEP.     

Separation of propulsive and adhesive traction stresses in locomoting keratocytes

Strong, actomyosin-dependent, pinching tractions in steadily locomoting (gliding) fish keratocytes revealed by traction imaging present a paradox, since only forces perpendicular to the direction of locomotion are apparent, leaving the actual propulsive forces unresolved. When keratocytes become transiently "stuck" by their trailing edge and adopt a fibroblast-like morphology, the tractions opposing locomotion are concentrated into the tail, leaving the active pinching and propulsive tractions clearly visible under the cell body. Stuck keratocytes can develop approximately 1 mdyn (10,000 pN) total propulsive thrust, originating in the wings of the cell. The leading lamella develops no detectable propulsive traction, even when the cell pulls on its transient tail anchorage. The separation of propulsive and adhesive tractions in the stuck phenotype leads to a mechanically consistent hypothesis that resolves the traction paradox for gliding keratocytes: the propulsive tractions driving locomotion are normally canceled by adhesive tractions resisting locomotion, leaving only the pinching tractions as a resultant. The resolution of the traction pattern into its components specifies conditions to be met for models of cytoskeletal force production, such as the dynamic network contraction model (Svitkina, T.M., A.B. Verkhovsky, K.M. McQuade, and G.G. Borisy. 1997. J. Cell Biol. 139:397-415). The traction pattern associated with cells undergoing sharp turns differs markedly from the normal pinching traction pattern, and can be accounted for by postulating an asymmetry in contractile activity of the opposed lateral wings of the cell.     

Wavelets filtering for classification of very noisy electron microscopic single particles images- application on structure determination of VP5-VP19C recombinant

Background

Images of frozen hydrated [vitrified] virus particles were taken close-to-focus in an electron microscope containing structural signals at high spatial frequencies. These images had very low contrast due to the high levels of noise present in the image. The low contrast made particle selection, classification and orientation determination very difficult. The final purpose of the classification is to improve the signal-to-noise ratio of the particle representing the class, which is usually the average. In this paper, the proposed method is based on wavelet filtering and multi-resolution processing for the classification and reconstruction of this very noisy data. A multivariate statistical analysis (MSA) is used for this classification.

Results

The MSA classification method is noise dependant. A set of 2600 projections from a 3D map of a herpes simplex virus -to which noise was added- was classified by MSA. The classification shows the power of wavelet filtering in enhancing the quality of class averages (used in 3D reconstruction) compared to Fourier band pass filtering. A 3D reconstruction of a recombinant virus (VP5-VP19C) is presented as an application of multi-resolution processing for classification and reconstruction.

Conclusion

The wavelet filtering and multi-resolution processing method proposed in this paper offers a new way for processing very noisy images obtained from electron cryo-microscopes. The multi-resolution and filtering improves the speed and accuracy of classification, which is vital for the 3D reconstruction of biological objects. The VP5-VP19C recombinant virus reconstruction presented here is an example, which demonstrates the power of this method. Without this processing, it is not possible to get the correct 3D map of this virus.

     

Determining substrate displacement and cell traction fields--a new approach

This paper presents a new approach for the traction force microscopy (TFM) method which determines traction forces exerted by adherent cells on a thin, elastic polyacrylamide gel embedded with fluorescent microbeads. In this enhanced TFM method, a pattern recognition technique is first applied to match the pair of microbead embedded images before and after deformation, which subsequently provides the displacement field of the elastic substrate. Once the displacement field is obtained, the 3-D finite element method (FEM) is used to compute cell traction forces. The new TFM has been applied to determine traction forces of human tendon fibroblasts. Compared to existing TFM methods, the present method has the following advantages: (1) its displacement field obtained is associated with microbead movements; (2) it considers the finite thickness of the thin polyacrylamide gel and is therefore free from the infinite half-space approximation adopted by existing TFM methods; and (3) its computation procedure for determining cell traction forces is fast.     

Modelling Temporal Stability of EPI Time Series Using Magnitude Images Acquired with Multi-Channel Receiver Coils

In 2001, Krueger and Glover introduced a model describing the temporal SNR (tSNR) of an EPI time series as a function of image SNR (SNR₀). This model has been used to study physiological noise in fMRI, to optimize fMRI acquisition parameters, and to estimate maximum attainable tSNR for a given set of MR image acquisition and processing parameters. In its current form, this noise model requires the accurate estimation of image SNR. For multi-channel receiver coils, this is not straightforward because it requires export and reconstruction of large amounts of k-space raw data and detailed, custom-made image reconstruction methods. Here we present a simple extension to the model that allows characterization of the temporal noise properties of EPI time series acquired with multi-channel receiver coils, and reconstructed with standard root-sum-of-squares combination, without the need for raw data or custom-made image reconstruction. The proposed extended model includes an additional parameter κ which reflects the impact of noise correlations between receiver channels on the data and scales an apparent image SNR (SNR′₀) measured directly from root-sum-of-squares reconstructed magnitude images so that κ = SNR′₀/SNR₀ (under the condition of SNR₀>50 and number of channels ≤32). Using Monte Carlo simulations we show that the extended model parameters can be estimated with high accuracy. The estimation of the parameter κ was validated using an independent measure of the actual SNR₀ for non-accelerated phantom data acquired at 3T with a 32-channel receiver coil. We also demonstrate that compared to the original model the extended model results in an improved fit to human task-free non-accelerated fMRI data acquired at 7T with a 24-channel receiver coil. In particular, the extended model improves the prediction of low to medium tSNR values and so can play an important role in the optimization of high-resolution fMRI experiments at lower SNR levels.     

Maximum-Entropy Three-Dimensional Reconstruction with Deconvolution of the Contrast Transfer Function: A Test Application with Adenovirus

We have developed an objective, quantitative, and general algorithm to improve the fidelity of three-dimensional reconstructions made from electron micrographs while at the same time filtering much of the noise present in the recorded data. The new technique is called constrained maximum entropy tomography (COMET). The essence of the method is that it will produce the most featureless reconstruction that fits the projection data within their observational accuracy. In particular, the COMET procedure will minimise the detrimental effects of errors in the measured data and deconvolute the effects of the contrast transfer function. An objective test has been performed using COMET on a conventional image reconstruction obtained from cryo-electron micrographs of adenovirus. The density for hexon, the major coat protein of the virus, which is known to high resolution from X-ray crystallography, provided a known high-resolution control. The COMET reconstruction is in considerably better agreement with the crystallographic electron density than the original reconstruction, throughout the entire resolution range.     

Improved throughput traction microscopy reveals pivotal role for matrix stiffness in fibroblast contractility and TGF-β responsiveness

Lung fibroblast functions such as matrix remodeling and activation of latent transforming growth factor-β1 (TGF-β1) are associated with expression of the myofibroblast phenotype and are directly linked to fibroblast capacity to generate force and deform the extracellular matrix. However, the study of fibroblast force-generating capacities through methods such as traction force microscopy is hindered by low throughput and time-consuming procedures. In this study, we improved at the detail level methods for higher-throughput traction measurements on polyacrylamide hydrogels using gel-surface-bound fluorescent beads to permit autofocusing and automated displacement mapping, and transduction of fibroblasts with a fluorescent label to streamline cell boundary identification. Together these advances substantially improve the throughput of traction microscopy and allow us to efficiently compute the forces exerted by lung fibroblasts on substrates spanning the stiffness range present in normal and fibrotic lung tissue. Our results reveal that lung fibroblasts dramatically alter the forces they transmit to the extracellular matrix as its stiffness changes, with very low forces generated on matrices as compliant as normal lung tissue. Moreover, exogenous TGF-β1 selectively accentuates tractions on stiff matrices, mimicking fibrotic lung, but not on physiological stiffness matrices, despite equivalent changes in Smad2/3 activation. Taken together, these results demonstrate a pivotal role for matrix mechanical properties in regulating baseline and TGF-β1-stimulated contraction of lung fibroblasts and suggest that stiff fibrotic lung tissue may promote myofibroblast activation through contractility-driven events, whereas normal lung tissue compliance may protect against such feedback amplification of fibroblast activation.     

High Resolution,Large Deformation 3D Traction Force Microscopy

Traction Force Microscopy (TFM) is a powerful approach for quantifying cell-material interactions that over the last two decades has contributed significantly to our understanding of cellular mechanosensing and mechanotransduction. In addition, recent advances in three-dimensional (3D) imaging and traction force analysis (3D TFM) have highlighted the significance of the third dimension in influencing various cellular processes. Yet irrespective of dimensionality, almost all TFM approaches have relied on a linear elastic theory framework to calculate cell surface tractions. Here we present a new high resolution 3D TFM algorithm which utilizes a large deformation formulation to quantify cellular displacement fields with unprecedented resolution. The results feature some of the first experimental evidence that cells are indeed capable of exerting large material deformations, which require the formulation of a new theoretical TFM framework to accurately calculate the traction forces. Based on our previous 3D TFM technique, we reformulate our approach to accurately account for large material deformation and quantitatively contrast and compare both linear and large deformation frameworks as a function of the applied cell deformation. Particular attention is paid in estimating the accuracy penalty associated with utilizing a traditional linear elastic approach in the presence of large deformation gradients.     

Micropatterning tractional forces in living cells

Here we describe a method for quantifying traction in cells that are physically constrained within micron-sized adhesive islands of defined shape and size on the surface of flexible polyacrylamide gels that contain fluorescent microbeads (0.2-microm diameter). Smooth muscle cells were plated onto square (50 x 50 microm) or circular (25- or 50-microm diameter) adhesive islands that were created on the surface of the gels by applying a collagen coating through microengineered holes in an elastomeric membrane that was later removed. Adherent cells spread to take on the size and shape of the islands and cell tractions were quantitated by mapping displacement fields of the fluorescent microbeads within the gel. Cells on round islands did not exhibit any preferential direction of force application, but they exerted their strongest traction at sites where they formed protrusions. When cells were confined to squares, traction was highest in the corners both in the absence and presence of the contractile agonist, histamine, and cell protrusions were also observed in these regions. Quantitation of the mean traction exerted by cells cultured on the different islands revealed that cell tension increased as cell spreading was promoted. These results provide a mechanical basis for past studies that demonstrated a similar correlation between spreading and growth within various anchorage-dependent cells. This new approach for analyzing the spatial distribution of mechanical forces beneath individual cells that are experimentally constrained to defined sizes and shapes may provide additional insight into the biophysical basis of cell regulation.     

Weak-Periodic Stochastic Resonance in a Parallel Array of Static Nonlinearities

This paper studies the output-input signal-to-noise ratio (SNR) gain of an uncoupled parallel array of static, yet arbitrary, nonlinear elements for transmitting a weak periodic signal in additive white noise. In the small-signal limit, an explicit expression for the SNR gain is derived. It serves to prove that the SNR gain is always a monotonically increasing function of the array size for any given nonlinearity and noisy environment. It also determines the SNR gain maximized by the locally optimal nonlinearity as the upper bound of the SNR gain achieved by an array of static nonlinear elements. With locally optimal nonlinearity, it is demonstrated that stochastic resonance cannot occur, i.e. adding internal noise into the array never improves the SNR gain. However, in an array of suboptimal but easily implemented threshold nonlinearities, we show the feasibility of situations where stochastic resonance occurs, and also the possibility of the SNR gain exceeding unity for a wide range of input noise distributions.     

Contractile forces in tumor cell migration

Cancer is a deadly disease primarily because of the ability of tumor cells to spread from the primary tumor, to invade into the connective tissue, and to form metastases at distant sites. In contrast to cell migration on a planar surface where large cell tractions and contractile forces are not essential, tractions and forces are thought to be crucial for overcoming the resistance and steric hindrance of a dense three-dimensional connective tissue matrix. In this review, we describe recently developed biophysical tools, including 2-D and 3-D traction microscopy to measure contractile forces of cells. We discuss evidence indicating that tumor cell invasiveness is associated with increased contractile force generation.     

Modelling Biological Gel Contraction by Cells: Mechanocellular Formulation and Cell Traction Force Quantification

Traction forces developed by most cell types play a significant role in the spatial organisation of biological tissues. However, due to the complexity of cell-extracellular matrix interactions, these forces are quantitatively difficult to estimate without explicitly considering cell properties and extracellular mechanical matrix responses. Recent experimental devices elaborated for measuring cell traction on extracellular matrix use cell deposits on a piece of gel placed between one fixed and one moving holder. We formulate here a mathematical model describing the dynamic behaviour of the cell-gel medium in such devices. This model is based on a mechanical force balance quantification of the gel visco-elastic response to the traction forces exerted by the diffusing cells. Thus, we theoretically analyzed and simulated the displacement of the free moving boundary of the system under various conditions for cells and gel concentrations. This modelis then used as the theoretical basis of an experimental device where endothelial cells are seeded on a rectangular biogel of fibrin cast between two floating holders, one fixed and the other linked to a force sensor. From a comparison of displacement of the gel moving boundary simulated by the model and the experimental data recorded from the moving holder displacement, the magnitude of the traction forces exerted by the endothelial cell on the fibrin gel was estimated for different experimental situations. Different analytical expressions for the cell traction term are proposed and the corresponding force quantifications are compared to the traction force measurements reported for various kind of cells with the use of similar or different experimental devices. This revised version was published online in June 2006 with corrections to the Cover Date.     

Signal/noise analysis of FRET-based sensors

Molecular sensors based on intramolecular Förster resonance energy transfer (FRET) have become versatile tools to monitor regulatory molecules in living tissue. However, their use is often compromised by low signal strength and excessive noise. We analyzed signal/noise (SNR) aspects of spectral FRET analysis methods, with the following conclusions: The most commonly used method (measurement of the emission ratio after a single short wavelength excitation) is optimal in terms of signal/noise, if only relative changes of this uncalibrated ratio are of interest. In the case that quantitative data on FRET efficiencies are required, these can be calculated from the emission ratio and some calibration parameters, but at reduced SNR. Lux-FRET, a recently described method for spectral analysis of FRET data, allows one to do so in three different ways, each based on a ratio of two out of three measured fluorescence signals (the donor and acceptor signal during a short-wavelength excitation and the acceptor signal during long wavelength excitation). Lux-FRET also allows for calculation of the total abundance of donor and acceptor fluorophores. The SNR for all these quantities is lower than that of the plain emission ratio due to unfavorable error propagation. However, if ligand concentration is calculated either from lux-FRET values or else, after its calibration, from the emission ratio, SNR for both analysis modes is very similar. Likewise, SNR values are similar, if the noise of these quantities is related to the expected dynamic range. We demonstrate these relationships based on data from an Epac-based cAMP sensor and discuss how the SNR changes with the FRET efficiency and the number of photons collected.     

The effect of high pass filtering and non-linear normalization on the EMG–force relationship during sub-maximal finger exertions

Muscle force estimates are important for full understanding of the musculoskeletal system and EMG is a modeling method used to estimate muscle force. The purpose of this investigation was to examine the effect of high pass filtering and non-linear normalization on the EMG–force relationship of sub-maximal finger exertions. Sub-maximal isometric ramp exertions were performed under three conditions (i) extension with restraint at the mid-proximal phalanx, (ii) flexion at the proximal phalanx and (iii) flexion at the distal phalanx. Thirty high pass filter designs were compared to a standardized processing procedure and an exponential fit equation was used for non-linear normalization. High pass filtering significantly reduced the %RMS error and increased the peak cross correlation between EMG and force in the distal flexion condition and in the other two conditions there was a trend towards improving force predictions with high pass filtering. The degree of linearity differed between the three contraction conditions and high pass filtering improved the linearity in all conditions. Non-linear normalization had greater impact on the EMG–force relationship than high pass filtering. The difference in optimal processing parameters suggests that high pass filtering and linearity are dependent on contraction mode as well as the muscle analyzed.     

MR Image Reconstruction Using Block Matching and Adaptive Kernel Methods

An approach to Magnetic Resonance (MR) image reconstruction from undersampled data is proposed. Undersampling artifacts are removed using an iterative thresholding algorithm applied to nonlinearly transformed image block arrays. Each block array is transformed using kernel principal component analysis where the contribution of each image block to the transform depends in a nonlinear fashion on the distance to other image blocks. Elimination of undersampling artifacts is achieved by conventional principal component analysis in the nonlinear transform domain, projection onto the main components and back-mapping into the image domain. Iterative image reconstruction is performed by interleaving the proposed undersampling artifact removal step and gradient updates enforcing consistency with acquired k-space data. The algorithm is evaluated using retrospectively undersampled MR cardiac cine data and compared to k-t SPARSE-SENSE, block matching with spatial Fourier filtering and k-t ℓ₁-SPIRiT reconstruction. Evaluation of image quality and root-mean-squared-error (RMSE) reveal improved image reconstruction for up to 8-fold undersampled data with the proposed approach relative to k-t SPARSE-SENSE, block matching with spatial Fourier filtering and k-t ℓ₁-SPIRiT. In conclusion, block matching and kernel methods can be used for effective removal of undersampling artifacts in MR image reconstruction and outperform methods using standard compressed sensing and ℓ₁-regularized parallel imaging methods.     

Spectral analysis of flow cytometric data: design of a special-purpose low-pass digital filter

Spectral decomposition of flow cytometric datafiles of arbitrary dimension reveal information of both the signal and the noise components that constitute the histograms. This spectral information is used to construct a low-pass digital filter, which removes the high-frequency noise from the actual data. It is shown that this procedure guarantees non-trivial smoothing of the flow cytometric data in accordance with the local experimental situation. As a consequence optimal reconstruction of the signal is possible, which facilitates unambiguous interpretation of the data files and mathematical estimation of the statistical parameters.