Mathematical modeling of gonadotropin-releasing hormone signaling.

Gonadotropin-releasing hormone (GnRH) acts via G-protein coupled receptors on pituitary gonadotropes to control reproduction. These are Gq-coupled receptors that mediate acute effects of GnRH on the exocytotic secretion of luteinizing hormone (LH) and follicle-stimulating hormone (FSH), as well as the chronic regulation of their synthesis. GnRH is secreted in short pulses and GnRH effects on its target cells are dependent upon the dynamics of these pulses. Here we overview GnRH receptors and their signaling network, placing emphasis on pulsatile signaling, and how mechanistic mathematical models and an information theoretic approach have helped further this field.

Calcium/Calmodulin-dependent protein kinase is negatively and positively regulated by calcium, providing a mechanism for decoding calcium responses during symbiosis signaling.

The establishment of symbiotic associations in plants requires calcium oscillations that must be decoded to invoke downstream developmental programs. In animal systems, comparable calcium oscillations are decoded by calmodulin (CaM)-dependent protein kinases, but symbiotic signaling involves a calcium/CaM-dependent protein kinase (CCaMK) that is unique to plants. CCaMK differs from the animal CaM kinases by its dual ability to bind free calcium, via calcium binding EF-hand domains on the protein, or to bind calcium complexed with CaM, via a CaM binding domain. In this study, we dissect this dual regulation of CCaMK by calcium. We find that calcium binding to the EF-hand domains promotes autophosphorylation, which negatively regulates CCaMK by stabilizing the inactive state of the protein. By contrast, calcium-dependent CaM binding overrides the effects of autophosphorylation and activates the protein. The differential calcium binding affinities of the EF-hand domains compared with those of CaM suggest that CCaMK is maintained in the inactive state at basal calcium concentrations and is activated via CaM binding during calcium oscillations. This work provides a model for decoding calcium oscillations that uses differential calcium binding affinities to create a robust molecular switch that is responsive to calcium concentrations associated with both the basal state and with oscillations.

The influence of light on microtubule dynamics and alignment in the Arabidopsis hypocotyl.

Light and dark have antagonistic effects on shoot elongation, but little is known about how these effects are translated into changes of shape. Here we provide genetic evidence that the light/gibberellin-signaling pathway affects the properties of microtubules required to reorient growth. To follow microtubule dynamics for hours without triggering photomorphogenic inhibition of growth, we used Arabidopsis thaliana light mutants in the gibberellic acid/DELLA pathway. Particle velocimetry was used to map the mass movement of microtubule plus ends, providing new insight into the way that microtubules switch between orthogonal axes upon the onset of growth. Longitudinal microtubules are known to signal growth cessation, but we observed that cells also self-organize a strikingly bipolarized longitudinal array before bursts of growth. This gives way to a radial microtubule star that, far from being a random array, seems to be a key transitional step to the transverse array, forecasting the faster elongation that follows. Computational modeling provides mechanistic insight into these transitions. In the faster-growing mutants, the microtubules were found to have faster polymerization rates and to undergo faster reorientations. This suggests a mechanism in which the light-signaling pathway modifies the dynamics of microtubules and their ability to switch between orthogonal axes.