Fundamental patterns underlying gene expression profiles: Simplicity from complexity

Analysis of previously published sets of DNA microarray gene expression data by singular value decomposition has uncovered underlying patterns or “characteristic modes” in their temporal profiles. These patterns contribute unequally to the structure of the expression profiles. Moreover, the essential features of a given set of expression profiles are captured using just a small number of characteristic modes. This leads to the striking conclusion that the transcriptional response of a genome is orchestrated in a few fundamental patterns of gene expression change. These patterns are both simple and robust, dominating the alterations in expression of genes throughout the genome. Moreover, the characteristic modes of gene expression change in response to environmental perturbations are similar in such distant organisms as yeast and human cells. This analysis reveals simple regularities in the seemingly complex transcriptional transitions of diverse cells to new states, and these provide insights into the operation of the underlying genetic networks.

Genetic complexity of pathogen perception by plants: The example of Rcr3, a tomato gene required specifically by Cf-2

Genetic analysis of plant–pathogen interactions has demonstrated that resistance to infection is often determined by the interaction of dominant plant resistance (R) genes and dominant pathogen-encoded avirulence (Avr) genes. It was postulated that R genes encode receptors for Avr determinants. A large number of R genes and their cognate Avr genes have now been analyzed at the molecular level. R gene loci are extremely polymorphic, particularly in sequences encoding amino acids of the leucine-rich repeat motif. A major challenge is to determine how Avr perception by R proteins triggers the plant defense response. Mutational analysis has identified several genes required for the function of specific R proteins. Here we report the identification of Rcr3, a tomato gene required specifically for Cf-2-mediated resistance. We propose that Avr products interact with host proteins to promote disease, and that R proteins “guard” these host components and initiate Avr-dependent plant defense responses.

Slip complexity in earthquake fault models.

We summarize studies of earthquake fault models that give rise to slip complexities like those in natural earthquakes. For models of smooth faults between elastically deformable continua, it is critical that the friction laws involve a characteristic distance for slip weakening or evolution of surface state. That results in a finite nucleation size, or coherent slip patch size, h*. Models of smooth faults, using numerical cell size properly small compared to h*, show periodic response or complex and apparently chaotic histories of large events but have not been found to show small event complexity like the self-similar (power law) Gutenberg-Richter frequency-size statistics. This conclusion is supported in the present paper by fully inertial elastodynamic modeling of earthquake sequences. In contrast, some models of locally heterogeneous faults with quasi-independent fault segments, represented approximately by simulations with cell size larger than h* so that the model becomes "inherently discrete," do show small event complexity of the Gutenberg-Richter type. Models based on classical friction laws without a weakening length scale or for which the numerical procedure imposes an abrupt strength drop at the onset of slip have h* = 0 and hence always fall into the inherently discrete class. We suggest that the small-event complexity that some such models show will not survive regularization of the constitutive description, by inclusion of an appropriate length scale leading to a finite h*, and a corresponding reduction of numerical grid size.

Two types of calcium response limited to single spines in cerebellar Purkinje cells.

Of fundamental importance in understanding neuronal function is the unambiguous determination of the smallest unit of neuronal integration. It was recently suggested that a whole dendritic branchlet, including tens of spines, acts as the fundamental unit in terms of dendritic calcium dynamics in Purkinje cells. By contrast, we demonstrate that the smallest such unit is the single spine. The results show, by two-photon excited fluorescence laser scanning microscopy, that individual spines are capable of independent calcium activation. Moreover, two distinct spine populations were distinguished by their opposite response to membrane hyperpolarization. Indeed, in a subpopulation of spines calcium entry can also occur through a pathway other than voltage-gated channels. These findings challenge the assumption of a unique parallel fiber activation mode and prompt a reevaluation of the level of functional complexity ascribed to single neurons.