A comparison of approximation techniques for variance-based sensitivity analysis of biochemical reaction systems

<p>Abstract</p> <p>Background</p> <p>Sensitivity analysis is an indispensable tool for the analysis of complex systems. In a recent paper, we have introduced a thermodynamically consistent variance-based sensitivity analysis approach for studying the robustness and fragility properties of biochemical reaction systems under uncertainty in the standard chemical potentials of the activated complexes of the reactions and the standard chemical potentials of the molecular species. In that approach, key sensitivity indices were estimated by Monte Carlo sampling, which is computationally very demanding and impractical for large biochemical reaction systems. Computationally efficient algorithms are needed to make variance-based sensitivity analysis applicable to realistic cellular networks, modeled by biochemical reaction systems that consist of a large number of reactions and molecular species.</p> <p>Results</p> <p>We present four techniques, derivative approximation (DA), polynomial approximation (PA), Gauss-Hermite integration (GHI), and orthonormal Hermite approximation (OHA), for <it>analytically </it>approximating the variance-based sensitivity indices associated with a biochemical reaction system. By using a well-known model of the mitogen-activated protein kinase signaling cascade as a case study, we numerically compare the approximation quality of these techniques against traditional Monte Carlo sampling. Our results indicate that, although DA is computationally the most attractive technique, special care should be exercised when using it for sensitivity analysis, since it may only be accurate at low levels of uncertainty. On the other hand, PA, GHI, and OHA are computationally more demanding than DA but can work well at high levels of uncertainty. GHI results in a slightly better accuracy than PA, but it is more difficult to implement. OHA produces the most accurate approximation results and can be implemented in a straightforward manner. It turns out that the computational cost of the four approximation techniques considered in this paper is orders of magnitude smaller than traditional Monte Carlo estimation. Software, coded in MATLAB^®, which implements all sensitivity analysis techniques discussed in this paper, is available free of charge.</p> <p>Conclusions</p> <p>Estimating variance-based sensitivity indices of a large biochemical reaction system is a computationally challenging task that can only be addressed via approximations. Among the methods presented in this paper, a technique based on orthonormal Hermite polynomials seems to be an acceptable candidate for the job, producing very good approximation results for a wide range of uncertainty levels in a fraction of the time required by traditional Monte Carlo sampling.</p

Breast imaging technology: Application of magnetic resonance imaging to early detection of breast cancer

Since its first introduction approximately 10 years ago, there has been extensive progress in the application of magnetic resonance imaging (MRI) to the detection and diagnosis of breast cancer. Contrast-enhanced MRI has been shown to have value in the diagnostic work-up of women who present with mammogram or clinical abnormalities. In addition, it has been demonstrated that MRI can detect mammogram occult multifocal cancer in patients who present with unifocal disease. Advances in risk stratification and limitations in mammography have stimulated interest in the use of MRI to screen high-risk women for cancer. Several studies of MRI high-risk screening are ongoing. Preliminary results are encouraging

Gap junctions of the medial collateral ligament: structure, distribution, associations and function

Ligaments are composed of two major components: cells and extracellular matrix. The cells express gap junction proteins and are arranged into a series of rows that traverse the tissue, suggesting that all the cells of the tissue are functionally interconnected. The results of our study demonstrate that medial collateral ligament (MCL) cells do not have a uniform fusiform morphology or placement along a row of cells as previously suggested, but rather display a complex placement and form that weaves within the collagen matrix in a manner that is far more extensive and complex than previously appreciated. Within this morphological context, we find that MCL cells in vivo contain functional gap junctions (verified using fluorescence recovery after photobleaching) that are localized to sites of close cell–cell contact, and this pattern imparts or reflects a bipolarity inherent to each cell. When we studied ligament cells in conventional tissue culture we found that this bipolarity is lost, and the placement of gap junctions and their related proteins, as well as general cell morphology, is also altered. Finally, our study demonstrates, for the first time, that in addition to gap junctions, adherens junctions and desmosomes are also expressed by MCL cells both in vivo and in vitro and map to sites of cell–cell contact