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Background: Traction Force Microscopy (TFM) is a widespread technique to estimate the tractions that cells exert on the surrounding substrate. To recover the tractions, it is necessary to solve an inverse problem, which is ill-posed and needs regularization to make the solution stable. The typical regularization scheme is given by the minimization of a cost functional, which is divided in two terms: the error present in the data or data fidelity term; and the regularization or penalty term. The classical approach is to use zero-order Tikhonov or L2-regularization, which uses the L2-norm for both terms in the cost function. Recently, some studies have demonstrated an improved performance using L1-regularization (L1-norm in the penalty term) related to an increase in the spatial resolution and sensitivity of the recovered traction field. In this manuscript, we present a comparison between the previous two regularization schemes (relying in the L2-norm for the data fidelity term) and the full L1-regularization (using the L1-norm for both terms in the cost function) for synthetic and real data. Results: Our results reveal that L1-regularizations give an improved spatial resolution (more important for full L1-regularization) and a reduction in the background noise with respect to the classical zero-order Tikhonov regularization. In addition, we present an approximation, which makes feasible the recovery of cellular tractions over whole cells on typical full-size microscope images when working in the spatial domain. Conclusions: The proposed full L1-regularization improves the sensitivity to recover small stress footprints. Moreover, the proposed method has been validated to work on full-field microscopy images of real cells, what certainly demonstrates it is a promising tool for biological applications. [ABSTRACT FROM AUTHOR]

Background: High-density oligonucleotide microarray is an appropriate technology for genomic analysis, and is particulary useful in the generation of transcriptional maps, ChIP-on-chip studies and re-sequencing of the genome.Transcriptome analysis of tiling microarray data facilitates the discovery of novel transcripts and the assessment of differential expression in diverse experimental conditions. Although new technologies such as next-generation sequencing have appeared, microarrays might still be useful for the study of small genomes or for the analysis of genomic regions with custom microarrays due to their lower price and good accuracy in expression quantification. Results: Here, we propose a novel wavelet-based method, named ZCL (zero-crossing lines), for the combined denoising and segmentation of tiling signals. The denoising is performed with the classical SUREshrink method and the detection of transcriptionally active regions is based on the computation of the Continuous Wavelet Transform (CWT). In particular, the detection of the transitions is implemented as the thresholding of the zero-crossing lines. The algorithm described has been applied to the public Saccharomyces cerevisiae dataset and it has been compared with two well-known algorithms: pseudo-median sliding window (PMSW) and the structural change model (SCM). As a proof-of-principle, we applied the ZCL algorithm to the analysis of the custom tiling microarray hybridization results of a S. aureus mutant deficient in the sigma B transcription factor. The challenge was to identify those transcripts whose expression decreases in the absence of sigma B. Conclusions: The proposed method archives the best performance in terms of positive predictive value (PPV) while its sensitivity is similar to the other algorithms used for the comparison. The computation time needed to process the transcriptional signals is low as compared with model-based methods and in the same range to those based on the use of filters. Automatic parameter selection has been incorporated and moreover, it can be easily adapted to a parallel implementation. We can conclude that the proposed method is well suited for the analysis of tiling signals, in which transcriptional activity is often hidden in the noise. Finally, the quantification and differential expression analysis of S. aureus dataset have demonstrated the valuable utility of this novel device to the biological analysis of the S. aureus transcriptome. [ABSTRACT FROM AUTHOR]

Background: Traction Force Microscopy (TFM) is a widespread technique to estimate the tractions that cells exert on the surrounding substrate. To recover the tractions, it is necessary to solve an inverse problem, which is ill-posed and needs regularization to make the solution stable. The typical regularization scheme is given by the minimization of a cost functional, which is divided in two terms: the error present in the data or data fidelity term; and the regularization or penalty term. The classical approach is to use zero-order Tikhonov or L 2 -regularization, which uses the L 2 -norm for both terms in the cost function. Recently, some studies have demonstrated an improved performance using L 1 -regularization (L 1 -norm in the penalty term) related to an increase in the spatial resolution and sensitivity of the recovered traction field. In this manuscript, we present a comparison between the previous two regularization schemes (relying in the L 2 -norm for the data fidelity term) and the full L 1 -regularization (using the L 1 -norm for both terms in the cost function) for synthetic and real data., Results: Our results reveal that L 1 -regularizations give an improved spatial resolution (more important for full L 1 -regularization) and a reduction in the background noise with respect to the classical zero-order Tikhonov regularization. In addition, we present an approximation, which makes feasible the recovery of cellular tractions over whole cells on typical full-size microscope images when working in the spatial domain., Conclusions: The proposed full L 1 -regularization improves the sensitivity to recover small stress footprints. Moreover, the proposed method has been validated to work on full-field microscopy images of real cells, what certainly demonstrates it is a promising tool for biological applications.