In an entirely different approach to understanding patterning, bioinformatics has also been used. From information about genes whose expression patterns and cis-regulatory modules (CRMs) are already known, model parameters are learned. These can include the contribution of each transcription factor to the activation or repression of genes and cooperativity with other transcription factors. Using the parameter values obtained,

the prediction of expression patterns of target genes becomes possible directly from genome sequences without considering concrete gene regulatory networks [29, 30 and 31]. If real biological systems were deterministic, that is, the Silmitasertib molecular weight systems included no variability or noise, each cell would perfectly recognize its own position without any errors, and precise patterning would be achieved BKM120 nmr using the GRNs described above. However, as many studies have reported, noise is unavoidable [32, 33 and 34]; there is embryo-to-embryo variability in

the spatial profiles of morphogens, which is owing to factors such as variability in source intensity and/or gradient steepness [35 and 36] (Figure 3a). Therefore, cells in different embryos could receive different concentrations, even if their relative positions within the embryos were the same. In such a case, a simple threshold-like response is insufficient to realize patterning that is robust against noise; the position of gene expression (ON) regions along a given axis could differ between embryos (Figure 3a). Considering the importance of accurate positioning

for achieving highly reproducible patterning, organisms are likely to have evolved mechanisms that allow accurate positioning even in the presence of noise. Two approaches are possible to improve the accuracy of spatial recognition by cells: one related to the mechanism of gradient interpretation, and the other related to the spatial profile of the morphogen itself (Figure 1a). In this section, we consider patterning without tissue growth or evolution of morphogen gradients over time. Patterning with these events is discussed in ifenprodil the next section. From an engineering viewpoint, gradient interpretation can be regarded as information decoding by analogy to communications between computers (Figure 1b): each cell recognizes its own position based on the received morphogen concentration, which includes noise, and responds appropriately according to position. This is a problem of estimation of position from a noisy input signal. A useful criterion of the goodness of the estimation or positional information decoding is the mean square error between estimated and true positions; in terms of statistics, the maximum likelihood (ML) estimation of position from a noisy input makes the error minimum (more precisely for Gaussian variations).