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.

Macrosystems ecology: Understanding ecological patterns and processes at continental scales

Macrosystems ecology is the study of diverse ecological phenomena at the scale of regions to continents and their interactions with phenomena at other scales. This emerging subdiscipline addresses ecological questions and environmental problems at these broad scales. Here, we describe this new field, show how it relates to modern ecological study, and highlight opportunities that stem from taking a macrosystems perspective. We present a hierarchical framework for investigating macrosystems at any level of ecological organization and in relation to broader and finer scales. Building on well-established theory and concepts from other subdisciplines of ecology, we identify feedbacks, linkages among distant regions, and interactions that cross scales of space and time as the most likely sources of unexpected and novel behaviors in macrosystems. We present three examples that highlight the importance of this multiscaled systems perspective for understanding the ecology of regions to continents. © The Ecological Society of America.

Spanning the scales of granular materials through microscopic force imaging.

If you walk on sand, it supports your weight. How do the disordered forces between particles in sand organize, to keep you from sinking? This simple question is surprisingly difficult to answer experimentally: measuring forces in three dimensions, between deeply buried grains, is challenging. Here we describe experiments in which we have succeeded in measuring forces inside a granular packing subject to controlled deformations. We connect the measured micro-scale forces to the macro-scale packing force response with an averaging, mean field calculation. This calculation explains how the combination of packing structure and contact deformations produce the observed nontrivial mechanical response of the packing, revealing a surprising microscopic particle deformation enhancement mechanism.

Spatial and temporal scales of neuronal correlation in visual area V4.

The spiking activity of nearby cortical neurons is correlated on both short and long time scales. Understanding this shared variability in firing patterns is critical for appreciating the representation of sensory stimuli in ensembles of neurons, the coincident influences of neurons on common targets, and the functional implications of microcircuitry. Our knowledge about neuronal correlations, however, derives largely from experiments that used different recording methods, analysis techniques, and cortical regions. Here we studied the structure of neuronal correlation in area V4 of alert macaques using recording and analysis procedures designed to match those used previously in primary visual cortex (V1), the major input to V4. We found that the spatial and temporal properties of correlations in V4 were remarkably similar to those of V1, with two notable differences: correlated variability in V4 was approximately one-third the magnitude of that in V1 and synchrony in V4 was less temporally precise than in V1. In both areas, spontaneous activity (measured during fixation while viewing a blank screen) was approximately twice as correlated as visual-evoked activity. The results provide a foundation for understanding how the structure of neuronal correlation differs among brain regions and stages in cortical processing and suggest that it is likely governed by features of neuronal circuits that are shared across the visual cortex.

Scaling limits of a model for selection at two scales

The dynamics of a population undergoing selection is a central topic in evolutionary biology. This question is particularly intriguing in the case where selective forces act in opposing directions at two population scales. For example, a fast-replicating virus strain outcompetes slower-replicating strains at the within-host scale. However, if the fast-replicating strain causes host morbidity and is less frequently transmitted, it can be outcompeted by slower-replicating strains at the between-host scale. Here we consider a stochastic ball-and-urn process which models this type of phenomenon. We prove the weak convergence of this process under two natural scalings. The first scaling leads to a deterministic nonlinear integro-partial differential equation on the interval $[0,1]$ with dependence on a single parameter, $\lambda$. We show that the fixed points of this differential equation are Beta distributions and that their stability depends on $\lambda$ and the behavior of the initial data around $1$. The second scaling leads to a measure-valued Fleming-Viot process, an infinite dimensional stochastic process that is frequently associated with a population genetics.

Clinician judgment vs formal scales for predicting intracerebral hemorrhage outcomes.

OBJECTIVE: To compare the performance of formal prognostic instruments vs subjective clinical judgment with regards to predicting functional outcome in patients with spontaneous intracerebral hemorrhage (ICH). METHODS: This prospective observational study enrolled 121 ICH patients hospitalized at 5 US tertiary care centers. Within 24 hours of each patient's admission to the hospital, one physician and one nurse on each patient's clinical team were each asked to predict the patient's modified Rankin Scale (mRS) score at 3 months and to indicate whether he or she would recommend comfort measures. The admission ICH score and FUNC score, 2 prognostic scales selected for their common use in neurologic practice, were calculated for each patient. Spearman rank correlation coefficients (r) with respect to patients' actual 3-month mRS for the physician and nursing predictions were compared against the same correlation coefficients for the ICH score and FUNC score. RESULTS: The absolute value of the correlation coefficient for physician predictions with respect to actual outcome (0.75) was higher than that of either the ICH score (0.62, p = 0.057) or the FUNC score (0.56, p = 0.01). The nursing predictions of outcome (r = 0.72) also trended towards an accuracy advantage over the ICH score (p = 0.09) and FUNC score (p = 0.03). In an analysis that excluded patients for whom comfort care was recommended, the 65 available attending physician predictions retained greater accuracy (r = 0.73) than either the ICH score (r = 0.50, p = 0.02) or the FUNC score (r = 0.42, p = 0.004). CONCLUSIONS: Early subjective clinical judgment of physicians correlates more closely with 3-month outcome after ICH than prognostic scales.

Scaling limits of a model for selection at two scales

The dynamics of a population undergoing selection is a central topic in evolutionary biology. This question is particularly intriguing in the case where selective forces act in opposing directions at two population scales. For example, a fast-replicating virus strain outcompetes slower-replicating strains at the within-host scale. However, if the fast-replicating strain causes host morbidity and is less frequently transmitted, it can be outcompeted by slower-replicating strains at the between-host scale. Here we consider a stochastic ball-and-urn process which models this type of phenomenon. We prove the weak convergence of this process under two natural scalings. The first scaling leads to a deterministic nonlinear integro-partial differential equation on the interval $[0,1]$ with dependence on a single parameter, $\lambda$. We show that the fixed points of this differential equation are Beta distributions and that their stability depends on $\lambda$ and the behavior of the initial data around $1$. The second scaling leads to a measure-valued Fleming-Viot process, an infinite dimensional stochastic process that is frequently associated with a population genetics.