Can Zipf's law be adapted to normalize microarrays?

Background  

Normalization is the process of removing non-biological sources of variation between array experiments. Recent investigations of data in gene expression databases for varying organisms and tissues have shown that the majority of expressed genes exhibit a power-law distribution with an exponent close to -1 (i.e. obey Zipf's law). Based on the observation that our single channel and two channel microarray data sets also followed a power-law distribution, we were motivated to develop a normalization method based on this law, and examine how it compares with existing published techniques. A computationally simple and intuitively appealing technique based on this observation is presented.     

Cellular determinants affecting the rate of cytokine in cultures of human hematopoietic cells

The present study was undertaken to define parameters that may limit the cytokine-mediated expansion of primitive hematopoietic cells in stirred suspension cultures of normal human marrow cells. In a first series of experiments, parallel measurements of the rate and extent of progenitor expansion and cytokine depletion from the medium were made for such cultures in which the cells were exposed to different cytokine concentrations. Supplementation of the medium with 2 ng/mL of interleukin-3 (IL-3), IL-6 and IL-11 plus 10 ng/mL of Flt-3 ligand (FL) and Steel factor (SF) allowed a 45-fold expansion of directly clonogenic cell (CFC) numbers within 2 weeks along with a 2.5-fold expansion of their precursors, detectable as longterm culture-initiating cells (LTC-IC). The addition of 5-fold higher levels of these cytokines enhanced the 2 week output of both CFC and LTC-IC numbers (to 66-fold and 9-fold above input respectively). However, this was also associated with an increase in the individual average rates of depletion of immunoreactive IL-3, SF and FL. As a result, even biweekly addition of fresh medium supplemented with the highest concentrations of cytokines tested failed to prevent a continuing decline in their levels relative to the input medium levels. A similar dependence of the IL-3 depletion rate on its extracellular concentration was demonstrable in suspension cultures of Mo7e cells, an IL-3-dependent human leukemic cell line.Additional experiments with various highly purified marrow cell fractions showed that the rate of cytokine depletion varied according to the type of responding cell as well as the specific cytokine. CD34(+)CD38(-) cells exhibited the greatest average cell-specific cytokine depletion rates (35-fold higher than unseparated bone marrow cells). These findings establish new principles that will be important for the optimization of hematopoietic cell bioreactors. In addition, they suggest that cytokine depletion may provide a novel feedback control mechanism in vivo which would contribute to the control of primitive hematopoietic cell proliferation and differentiation. (c) 1997 John Wiley & Sons, Inc. Biotechnol Bioeng 54: 58-66, 1997.