The Kauffman model describes a particularly simple class of random Boolean networks. Despite the simplicity of the model, it exhibits complex behavior and has been suggested as a model for real world network problems. We introduce a novel approach to analyzing attractors in random Boolean networks, and applying it to Kauffman networks we prove that the average number of attractors grows faster than any power law with system size.

Circadian clocks are biological timekeepers that allow living cells to time their activity in anticipation of predictable daily changes in light and other environmental factors. The complexity of the circadian clock in higher plants makes it difficult to understand the role of individual genes or molecular interactions, and mathematical modelling has been useful in guiding clock research in model organisms such as Arabidopsis thaliana. We present a model of the circadian clock in Arabidopsis, based on a large corpus of published time course data. It appears from experimental evidence in the literature that most interactions in the clock are repressive. Hence, we remove all transcriptional activation found in previous models of this system, and instead extend the system by including two new components, the morning-expressed activator RVE8 and the nightly repressor/activator NOX. Our modelling results demonstrate that the clock does not need a large number of activators in order to reproduce the observed gene expression patterns. For example, the sequential expression of the PRR genes does not require the genes to be connected as a series of activators. In the presented model, transcriptional activation is exclusively the task of RVE8. Predictions of how strongly RVE8 affects its targets are found to agree with earlier interpretations of the experimental data, but generally we find that the many negative feedbacks in the system should discourage intuitive interpretations of mutant phenotypes. The dynamics of the clock are difficult to predict without mathematical modelling, and the clock is better viewed as a tangled web than as a series of loops. Like most living organisms, plants are dependent on sunlight, and evolution has endowed them with an internal clock by which they can predict sunrise and sunset. The clock consists of many genes that control each other in a complex network, leading to daily oscillations in protein levels. The interactions between genes can be positive or negative, causing target genes to be turned on or off. By constructing mathematical models that incorporate our knowledge of this network, we can interpret experimental data by comparing with results from the models. Any discrepancy between experimental data and model predictions will highlight where we are lacking in understanding. We compiled more than 800 sets of measured data from published articles about the clock in the model organism thale cress (Arabidopsis thaliana). Using these data, we constructed a mathematical model which compares favourably with previous models for simulating the clock. We used our model to investigate the role of positive interactions between genes, whether they are necessary for the function of the clock and if they can be identified in the model.

Filamentous fungi play a key role as decomposers in Earth’s nutrient cycles. In soils, substrates are heterogeneously distributed in microenvironments. Hence, individual hyphae of a mycelium may experience very different environmental conditions simultaneously. In the current work, we investigated how fungi cope with local environmental variations at single-cell level. We developed a method based on infrared spectroscopy that allows the direct, in-situ chemical imaging of the decomposition activity of individual hyphal tips. Colonies of the ectomycorrhizal Basidiomycete Paxillus involutus were grown on liquid media, while parts of colonies were allowed to colonize lignin patches. Oxidative decomposition of lignin by individual hyphae growing under different conditions was followed for a period of seven days. We identified two sub-populations of hyphal tips: one with low decomposition activity and one with much higher activity. Active cells secreted more extracellular polymeric substances and oxidized lignin more strongly. The ratio of active to inactive hyphae strongly depended on the environmental conditions in lignin patches, but was further mediated by the decomposition activity of entire mycelia. Phenotypic heterogeneity occurring between genetically identical hyphal tips may be an important strategy for filamentous fungi to cope with heterogeneous and constantly changing soil environments.

Background: Signal transduction pathways convey information from the outside of the cell to transcription factors, which in turn regulate gene expression. Our objective is to analyze tumor gene expression data from microarrays in the context of such pathways. Results: We use pathways compiled from the TRANSPATH/TRANSFAC databases and the literature, and three publicly available cancer microarray data sets. Variation in pathway activity, across the samples, is gauged by the degree of correlation between downstream targets of a pathway. Two correlation scores are applied; one considers all pairs of downstream targets, and the other considers only pairs without common transcription factors. Several pathways are found to be differentially active in the data sets using these scores. Moreover, we devise a score for pathway activity in individual samples, based on the average expression value of the downstream targets. Statistical significance is assigned to the scores using permutation of genes as null model. Hence, for individual samples, the status of a pathway is given as a sign, + or -, and a p-value. This approach defines a projection of high-dimensional gene expression data onto low-dimensional pathway activity scores. For each dataset and many pathways we find a much larger number of significant samples than expected by chance. Finally, we find that several sample-wise pathway activities are significantly associated with clinical classifications of the samples. Conclusion: This study shows that it is feasible to infer signal transduction pathway activity, in individual samples, from gene expression data. Furthermore, these pathway activities are biologically relevant in the three cancer data sets.

The circadian clock measures time across a 24 h period, increasing fitness by phasing biological processes to the most appropriate time of day. The interlocking feedback loop mechanism of the clock is conserved across species; however, the number of loops varies. Mathematical and computational analyses have suggested that loop complexity affects the overall flexibility of the oscillator, including its responses to entrainment signals. We used a discriminating experimental assay, at the transition between different photoperiods, in order to test this proposal in a minimal circadian network (in Ostreococcus tauri) and a more complex network (in Arabidopsis thaliana). Transcriptional and translational reporters in O. tauri primarily tracked dawn or dusk, whereas in A. thaliana, a wider range of responses were observed, consistent with its more flexible clock. Model analysis supported the requirement for this diversity of responses among the components of the more complex network. However, these and earlier data showed that the O. tauri network retains surprising flexibility, despite its simple circuit. We found that models constructed from experimental data can show flexibility either from multiple loops and/or from multiple light inputs. Our results suggest that O. tauri has adopted the latter strategy, possibly as a consequence of genomic reduction.

Modern vibrational spectroscopy techniques enable the rapid collection of thousands of spectra in a single hyperspectral image, allowing researchers to study spatially heterogeneous samples at micrometer resolution. A number of algorithms have been developed to correct for effects such as atmospheric absorption, light scattering by cellular structures and varying baseline levels. After preprocessing, spectra are commonly decomposed and clustered to reveal informative patterns and subtle spectral changes. Several of these steps are slow, labor-intensive and require programming skills to make use of published algorithms and code. We here present a free and platform-independent graphical toolbox that allows rapid preprocessing of large sets of spectroscopic images, including atmospheric correction and a new algorithm for resonant Mie scattering with improved speed. The software also includes modules for decomposition into constituent spectra using the popular Multivariate Curve Resolution–Alternating Least Squares (MCR-ALS) algorithm, augmented by region-of-interest selection, as well as clustering and cluster annotation.