A numerical strategy for efficient modeling of the equatorial wave guide

Convection in the tropics is observed to involve a wide-ranging hierarchy of scales from a few kilometers to the planetary scales and also has a profound impact on short-term climate. The mechanisms responsible for this behavior present a major unsolved problem. A promising emerging approach to address these issues is cloud-resolving modeling. Here a family of numerical models is introduced specifically to model the feedback of small-scale deep convection on tropical planetary waves and tropical circulation in a highly efficient manner compatible with the approach through cloud-resolving modeling. Such a procedure is also useful for theoretical purposes. The basic idea in the approach is to use low-order truncation in the meriodonal direction through Gauss–Hermite quadrature projected onto a simple discrete radiation condition. In this fashion, the cloud-resolving modeling of equatorially trapped planetary waves reduces to the solution of a small number of purely zonal two-dimensional wave systems along a few judiciously chosen meriodonal layers that are coupled only by some additional source terms. The approach is analyzed in detail with full mathematical rigor for linearized equatorial primitive equations with source terms.

Quantitative modeling of stochastic systems in molecular biology by using stochastic Petri nets

An integrated understanding of molecular and developmental biology must consider the large number of molecular species involved and the low concentrations of many species in vivo. Quantitative stochastic models of molecular interaction networks can be expressed as stochastic Petri nets (SPNs), a mathematical formalism developed in computer science. Existing software can be used to define molecular interaction networks as SPNs and solve such models for the probability distributions of molecular species. This approach allows biologists to focus on the content of models and their interpretation, rather than their implementation. The standardized format of SPNs also facilitates the replication, extension, and transfer of models between researchers. A simple chemical system is presented to demonstrate the link between stochastic models of molecular interactions and SPNs. The approach is illustrated with examples of models of genetic and biochemical phenomena where the UltraSAN package is used to present results from numerical analysis and the outcome of simulations.

A global budget for fine root biomass, surface area, and nutrient contents

Global biogeochemical models have improved dramatically in the last decade in their representation of the biosphere. Although leaf area data are an important input to such models and are readily available globally, global root distributions for modeling water and nutrient uptake and carbon cycling have not been available. This analysis provides global distributions for fine root biomass, length, and surface area with depth in the soil, and global estimates of nutrient pools in fine roots. Calculated root surface area is almost always greater than leaf area, more than an order of magnitude so in grasslands. The average C:N:P ratio in living fine roots is 450:11:1, and global fine root carbon is more than 5% of all carbon contained in the atmosphere. Assuming conservatively that fine roots turn over once per year, they represent 33% of global annual net primary productivity.

Biochemical evolution III: Polymerization on organophilic silica-rich surfaces, crystal–chemical modeling, formation of first cells, and geological clues

Catalysis at organophilic silica-rich surfaces of zeolites and feldspars might generate replicating biopolymers from simple chemicals supplied by meteorites, volcanic gases, and other geological sources. Crystal–chemical modeling yielded packings for amino acids neatly encapsulated in 10-ring channels of the molecular sieve silicalite-ZSM-5-(mutinaite). Calculation of binding and activation energies for catalytic assembly into polymers is progressing for a chemical composition with one catalytic Al–OH site per 25 neutral Si tetrahedral sites. Internal channel intersections and external terminations provide special stereochemical features suitable for complex organic species. Polymer migration along nano/micrometer channels of ancient weathered feldspars, plus exploitation of phosphorus and various transition metals in entrapped apatite and other microminerals, might have generated complexes of replicating catalytic biomolecules, leading to primitive cellular organisms. The first cell wall might have been an internal mineral surface, from which the cell developed a protective biological cap emerging into a nutrient-rich “soup.” Ultimately, the biological cap might have expanded into a complete cell wall, allowing mobility and colonization of energy-rich challenging environments. Electron microscopy of honeycomb channels inside weathered feldspars of the Shap granite (northwest England) has revealed modern bacteria, perhaps indicative of Archean ones. All known early rocks were metamorphosed too highly during geologic time to permit simple survival of large-pore zeolites, honeycombed feldspar, and encapsulated species. Possible microscopic clues to the proposed mineral adsorbents/catalysts are discussed for planning of systematic study of black cherts from weakly metamorphosed Archaean sediments.

Mutational analysis and molecular modeling of the nonapeptide hormone binding domains of the [Arg8]vasotocin receptor.

To identify determinants that form nonapeptide hormone binding domains of the white sucker Catostomus commersoni [Arg8]vasotocin receptor, chimeric constructs encoding parts of the vasotocin receptor and parts of the isotocin receptor have been analyzed by [(3,5-3H)Tyr2, Arg8]vasotocin binding to membranes of human embryonic kidney cells previously transfected with the different cDNA constructs and by functional expression studies in Xenopus laevis oocytes injected with mutant cRNAs. The results indicate that the N terminus and a region spanning the second extracellular loop and its flanking transmembrane segments, which contains a number of amino acid residues that are conserved throughout the nonapeptide receptor family, contribute to the affinity of the receptor for its ligand. Nonapeptide selectivity, however, is mainly defined by transmembrane region VI and the third extracellular loop. These results are complemented by a molecular model of the vasotocin receptor obtained by aligning its sequence with those of other G-protein coupled receptors as well as that of bacteriorhodopsin. The model indicates that amino acid residues of transmembrane regions II-VII that are located close to the extracellular surface also contribute to the binding of vasotocin.

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.