Mathematical modeling of plant cell fate transitions controlled by hormonal signals.

Coordination of fate transition and cell division is crucial to maintain the plant architecture and to achieve efficient production of plant organs. In this paper, we analysed the stem cell dynamics at the shoot apical meristem (SAM) that is one of the plant stem cells locations. We designed a mathematical model to elucidate the impact of hormonal signaling on the fate transition rates between different zones corresponding to slowly dividing stem cells and fast dividing transit amplifying cells. The model is based on a simplified two-dimensional disc geometry of the SAM and accounts for a continuous displacement towards the periphery of cells produced in the central zone. Coupling growth and hormonal signaling results in a nonlinear system of reaction-diffusion equations on a growing domain with the growth rate depending on the model components. The model is tested by simulating perturbations in the level of key transcription factors that maintain SAM homeostasis. The model provides new insights on how the transcription factor HECATE is integrated in the regulatory network that governs stem cell differentiation.

Electrodiffusion models of neurons and extracellular space using the Poisson-Nernst-Planck equations--numerical simulation of the intra- and extracellular potential for an axon model.

In neurophysiology, extracellular signals-as measured by local field potentials (LFP) or electroencephalography-are of great significance. Their exact biophysical basis is, however, still not fully understood. We present a three-dimensional model exploiting the cylinder symmetry of a single axon in extracellular fluid based on the Poisson-Nernst-Planck equations of electrodiffusion. The propagation of an action potential along the axonal membrane is investigated by means of numerical simulations. Special attention is paid to the Debye layer, the region with strong concentration gradients close to the membrane, which is explicitly resolved by the computational mesh. We focus on the evolution of the extracellular electric potential. A characteristic up-down-up LFP waveform in the far-field is found. Close to the membrane, the potential shows a more intricate shape. A comparison with the widely used line source approximation reveals similarities and demonstrates the strong influence of membrane currents. However, the electrodiffusion model shows another signal component stemming directly from the intracellular electric field, called the action potential echo. Depending on the neuronal configuration, this might have a significant effect on the LFP. In these situations, electrodiffusion models should be used for quantitative comparisons with experimental data.

Fast extraction of neuron morphologies from large-scale SBFSEM image stacks.

Neuron morphology is frequently used to classify cell-types in the mammalian cortex. Apart from the shape of the soma and the axonal projections, morphological classification is largely defined by the dendrites of a neuron and their subcellular compartments, referred to as dendritic spines. The dimensions of a neuron's dendritic compartment, including its spines, is also a major determinant of the passive and active electrical excitability of dendrites. Furthermore, the dimensions of dendritic branches and spines change during postnatal development and, possibly, following some types of neuronal activity patterns, changes depending on the activity of a neuron. Due to their small size, accurate quantitation of spine number and structure is difficult to achieve (Larkman, J Comp Neurol 306:332, 1991). Here we follow an analysis approach using high-resolution EM techniques. Serial block-face scanning electron microscopy (SBFSEM) enables automated imaging of large specimen volumes at high resolution. The large data sets generated by this technique make manual reconstruction of neuronal structure laborious. Here we present NeuroStruct, a reconstruction environment developed for fast and automated analysis of large SBFSEM data sets containing individual stained neurons using optimized algorithms for CPU and GPU hardware. NeuroStruct is based on 3D operators and integrates image information from image stacks of individual neurons filled with biocytin and stained with osmium tetroxide. The focus of the presented work is the reconstruction of dendritic branches with detailed representation of spines. NeuroStruct delivers both a 3D surface model of the reconstructed structures and a 1D geometrical model corresponding to the skeleton of the reconstructed structures. Both representations are a prerequisite for analysis of morphological characteristics and simulation signalling within a neuron that capture the influence of spines.

Modelling in vitro growth of dense root networks.

Hairy roots are plants genetically transformed by Agrobacterium rhizogenes, which do not produce shoots and are composed mainly by roots. Hairy roots of Ophiorrhiza mungos Linn. are currently gaining interest of pharmacologists, since a secondary product of their metabolism, camptothecin, is used in chemotherapy. To optimize the production of valuable secondary metabolites it is necessary to understand the metabolism and growth of these roots systems. In this work, a mathematical model for description of apical growth of a dense root network (e.g. hairy roots) is derived. A continuous approach is used to define densities of root tips and root volume. Equations are posed to describe the evolution of these and are coupled to the distribution of nutrient concentration in the medium and inside the network. Following the principles of irreversible thermodynamics, growth velocity is defined as the sum over three different driving forces: nutrient concentration gradients, space gradients and root tip diffusion. A finite volume scheme was used for the simulation and parameters were chosen to fit experimental data from O. mungos Linn. hairy roots. Internal nutrient concentration determines short-term growth. Long-term behavior is limited by the total nutrient amount in the medium. Therefore, mass yield could be increased by guaranteeing a constant supply of nutrients. Increasing the initial mass of inoculation did not result in higher mass yields, since nutrient consumption due to metabolism also rose. Four different growth strategies are compared and their properties discussed. This allowed to understand which strategy might be the best to increase mass production optimally. The model is able to describe very well the temporal evolution of mass increase and nutrient uptake. Our results provide further understanding of growth and density distribution of hairy root network and therefore it is a sound base for future applications to describe, e.g., secondary metabolite production.

A prospective randomized controlled trial of injection of dexamethasone versus triamcinolone for idiopathic trigger finger.

PURPOSE: This study was designed to test the null hypothesis that there is no difference in resolution of triggering 3 months after injection with either a soluble (dexamethasone) or insoluble (triamcinolone) corticosteroid for idiopathic trigger finger. METHODS: Eighty-four patients were enrolled in a prospective randomized controlled trial comparing dexamethasone and triamcinolone injection for idiopathic trigger finger. Sixty-seven patients completed the 6-week follow-up (35 triamcinolone arm, 32 dexamethasone arm), and 72 patients completed the 3-month follow-up (41 triamcinolone arm, 31 dexamethasone arm). Outcome measures included the Disabilities of the Arm, Shoulder, and Hand (DASH) questionnaire, trigger finger grading according to Quinnell, and satisfaction on a visual analog scale. To preserve autonomy, patients were permitted additional injections and operative treatment at any time. Twenty-five patients requested a second injection (10 triamcinolone arm, 15 dexamethasone arm), and 21 elected operative treatment (10 triamcinolone arm, 11 dexamethasone arm) during the study period. The analysis was according to intention to treat principles. RESULTS: Six weeks after injection, absence of triggering was documented in 22 of 35 patients in the triamcinolone cohort and in 12 of 32 patients in the dexamethasone cohort. The rates 3 months after injection were 27 of 41 in the triamcinolone cohort and 22 of 31 in the dexamethasone cohort. The triamcinolone cohort had significantly better satisfaction and Quinnell grades than did the dexamethasone cohort at the 6-week follow-up but not at the 3-month follow-up. There were no significant differences between Disabilities of the Arm, Shoulder, and Hand scores at the 6-week follow-up and the 3-month follow-up. After the close of the study, there were 8 recurrences among patients with documented absence of triggering in the triamcinolone cohort and 1 in the dexamethasone cohort. CONCLUSIONS: Although there were no differences 3 months after injection, our data suggest that triamcinolone may have a more rapid but ultimately less durable effect on idiopathic trigger finger than does dexamethasone.