Detecting separate time scales in genetic expression data.

BACKGROUND: Biological processes occur on a vast range of time scales, and many of them occur concurrently. As a result, system-wide measurements of gene expression have the potential to capture many of these processes simultaneously. The challenge however, is to separate these processes and time scales in the data. In many cases the number of processes and their time scales is unknown. This issue is particularly relevant to developmental biologists, who are interested in processes such as growth, segmentation and differentiation, which can all take place simultaneously, but on different time scales. RESULTS: We introduce a flexible and statistically rigorous method for detecting different time scales in time-series gene expression data, by identifying expression patterns that are temporally shifted between replicate datasets. We apply our approach to a Saccharomyces cerevisiae cell-cycle dataset and an Arabidopsis thaliana root developmental dataset. In both datasets our method successfully detects processes operating on several different time scales. Furthermore we show that many of these time scales can be associated with particular biological functions. CONCLUSIONS: The spatiotemporal modules identified by our method suggest the presence of multiple biological processes, acting at distinct time scales in both the Arabidopsis root and yeast. Using similar large-scale expression datasets, the identification of biological processes acting at multiple time scales in many organisms is now possible.

Comparison of pattern detection methods in microarray time series of the segmentation clock.

While genome-wide gene expression data are generated at an increasing rate, the repertoire of approaches for pattern discovery in these data is still limited. Identifying subtle patterns of interest in large amounts of data (tens of thousands of profiles) associated with a certain level of noise remains a challenge. A microarray time series was recently generated to study the transcriptional program of the mouse segmentation clock, a biological oscillator associated with the periodic formation of the segments of the body axis. A method related to Fourier analysis, the Lomb-Scargle periodogram, was used to detect periodic profiles in the dataset, leading to the identification of a novel set of cyclic genes associated with the segmentation clock. Here, we applied to the same microarray time series dataset four distinct mathematical methods to identify significant patterns in gene expression profiles. These methods are called: Phase consistency, Address reduction, Cyclohedron test and Stable persistence, and are based on different conceptual frameworks that are either hypothesis- or data-driven. Some of the methods, unlike Fourier transforms, are not dependent on the assumption of periodicity of the pattern of interest. Remarkably, these methods identified blindly the expression profiles of known cyclic genes as the most significant patterns in the dataset. Many candidate genes predicted by more than one approach appeared to be true positive cyclic genes and will be of particular interest for future research. In addition, these methods predicted novel candidate cyclic genes that were consistent with previous biological knowledge and experimental validation in mouse embryos. Our results demonstrate the utility of these novel pattern detection strategies, notably for detection of periodic profiles, and suggest that combining several distinct mathematical approaches to analyze microarray datasets is a valuable strategy for identifying genes that exhibit novel, interesting transcriptional patterns.

Spike avalanches exhibit universal dynamics across the sleep-wake cycle.

BACKGROUND: Scale-invariant neuronal avalanches have been observed in cell cultures and slices as well as anesthetized and awake brains, suggesting that the brain operates near criticality, i.e. within a narrow margin between avalanche propagation and extinction. In theory, criticality provides many desirable features for the behaving brain, optimizing computational capabilities, information transmission, sensitivity to sensory stimuli and size of memory repertoires. However, a thorough characterization of neuronal avalanches in freely-behaving (FB) animals is still missing, thus raising doubts about their relevance for brain function. METHODOLOGY/PRINCIPAL FINDINGS: To address this issue, we employed chronically implanted multielectrode arrays (MEA) to record avalanches of action potentials (spikes) from the cerebral cortex and hippocampus of 14 rats, as they spontaneously traversed the wake-sleep cycle, explored novel objects or were subjected to anesthesia (AN). We then modeled spike avalanches to evaluate the impact of sparse MEA sampling on their statistics. We found that the size distribution of spike avalanches are well fit by lognormal distributions in FB animals, and by truncated power laws in the AN group. FB data surrogation markedly decreases the tail of the distribution, i.e. spike shuffling destroys the largest avalanches. The FB data are also characterized by multiple key features compatible with criticality in the temporal domain, such as 1/f spectra and long-term correlations as measured by detrended fluctuation analysis. These signatures are very stable across waking, slow-wave sleep and rapid-eye-movement sleep, but collapse during anesthesia. Likewise, waiting time distributions obey a single scaling function during all natural behavioral states, but not during anesthesia. Results are equivalent for neuronal ensembles recorded from visual and tactile areas of the cerebral cortex, as well as the hippocampus. CONCLUSIONS/SIGNIFICANCE: Altogether, the data provide a comprehensive link between behavior and brain criticality, revealing a unique scale-invariant regime of spike avalanches across all major behaviors.

The role of tectonic uplift, climate, and vegetation in the long-term terrestrial phosphorous cycle

Phosphorus (P) is a crucial element for life and therefore for maintaining ecosystem productivity. Its local availability to the terrestrial biosphere results from the interaction between climate, tectonic uplift, atmospheric transport, and biotic cycling. Here we present a mathematical model that describes the terrestrial P-cycle in a simple but comprehensive way. The resulting dynamical system can be solved analytically for steady-state conditions, allowing us to test the sensitivity of the P-availability to the key parameters and processes. Given constant inputs, we find that humid ecosystems exhibit lower P availability due to higher runoff and losses, and that tectonic uplift is a fundamental constraint. In particular, we find that in humid ecosystems the biotic cycling seem essential to maintain long-term P-availability. The time-dependent P dynamics for the Franz Josef and Hawaii chronosequences show how tectonic uplift is an important constraint on ecosystem productivity, while hydroclimatic conditions control the P-losses and speed towards steady-state. The model also helps describe how, with limited uplift and atmospheric input, as in the case of the Amazon Basin, ecosystems must rely on mechanisms that enhance P-availability and retention. Our novel model has a limited number of parameters and can be easily integrated into global climate models to provide a representation of the response of the terrestrial biosphere to global change. © 2010 Author(s).

Measuring fast gene dynamics in single cells with time-lapse luminescence microscopy.

Time-lapse fluorescence microscopy is an important tool for measuring in vivo gene dynamics in single cells. However, fluorescent proteins are limited by slow chromophore maturation times and the cellular autofluorescence or phototoxicity that arises from light excitation. An alternative is luciferase, an enzyme that emits photons and is active upon folding. The photon flux per luciferase is significantly lower than that for fluorescent proteins. Thus time-lapse luminescence microscopy has been successfully used to track gene dynamics only in larger organisms and for slower processes, for which more total photons can be collected in one exposure. Here we tested green, yellow, and red beetle luciferases and optimized substrate conditions for in vivo luminescence. By combining time-lapse luminescence microscopy with a microfluidic device, we tracked the dynamics of cell cycle genes in single yeast with subminute exposure times over many generations. Our method was faster and in cells with much smaller volumes than previous work. Fluorescence of an optimized reporter (Venus) lagged luminescence by 15-20 min, which is consistent with its known rate of chromophore maturation in yeast. Our work demonstrates that luciferases are better than fluorescent proteins at faithfully tracking the underlying gene expression.

Elucidating the Space-Time Structure of Low Level Warm Season Precipitation Processes in the Southern Appalachian Mountains Using Models and Observations

Light rainfall is the baseline input to the annual water budget in mountainous landscapes through the tropics and at mid-latitudes. In the Southern Appalachians, the contribution from light rainfall ranges from 50-60% during wet years to 80-90% during dry years, with convective activity and tropical cyclone input providing most of the interannual variability. The Southern Appalachians is a region characterized by rich biodiversity that is vulnerable to land use/land cover changes due to its proximity to a rapidly growing population. Persistent near surface moisture and associated microclimates observed in this region has been well documented since the colonization of the area in terms of species health, fire frequency, and overall biodiversity. The overarching objective of this research is to elucidate the microphysics of light rainfall and the dynamics of low level moisture in the inner region of the Southern Appalachians during the warm season, with a focus on orographically mediated processes. The overarching research hypothesis is that physical processes leading to and governing the life cycle of orographic fog, low level clouds, and precipitation, and their interactions, are strongly tied to landform, land cover, and the diurnal cycles of flow patterns, radiative forcing, and surface fluxes at the ridge-valley scale. The following science questions will be addressed specifically: 1) How do orographic clouds and fog affect the hydrometeorological regime from event to annual scale and as a function of terrain characteristics and land cover?; 2) What are the source areas, governing processes, and relevant time-scales of near surface moisture convergence patterns in the region?; and 3) What are the four dimensional microphysical and dynamical characteristics, including variability and controlling factors and processes, of fog and light rainfall? The research was conducted with two major components: 1) ground-based high-quality observations using multi-sensor platforms and 2) interpretive numerical modeling guided by the analysis of the in situ data collection. Findings illuminate a high level of spatial – down to the ridge scale - and temporal – from event to annual scale - heterogeneity in observations, and a significant impact on the hydrological regime as a result of seeder-feeder interactions among fog, low level clouds, and stratiform rainfall that enhance coalescence efficiency and lead to significantly higher rainfall rates at the land surface. Specifically, results show that enhancement of an event up to one order of magnitude in short-term accumulation can occur as a result of concurrent fog presence. Results also show that events are modulated strongly by terrain characteristics including elevation, slope, geometry, and land cover. These factors produce interactions between highly localized flows and gradients of temperature and moisture with larger scale circulations. Resulting observations of DSD and rainfall patterns are stratified by region and altitude and exhibit clear diurnal and seasonal cycles.