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Abstract. We develop a multi-element generalized polynomial chaos (ME-gPC) method for arbitrary probability measures and apply it to solve ordinary and partial differential equations with stochastic inputs. Given a stochastic input with an arbitrary probability measure, its random space is decomposed into smaller elements. Subsequently, in each element a new random variable with respect to a conditional probability density function (PDF) is defined, and a set of orthogonal polynomials in terms of this random variable is constructed numerically. Then, the generalized polynomial chaos (gPC) method is implemented element-by-element. Numerical experiments show that the cost for the construction of orthogonal polynomials is negligible compared to the total time cost. Efficiency and convergence of ME-gPC are studied numerically by considering some commonly used random variables. ME-gPC provides an efficient and flexible approach to solving differential equations with random inputs, especially for problems related to long-term integration, large perturbation, and stochastic discontinuities.

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In this paper we present a Multi-Element generalized Polynomial Chaos (MEgPC) method to deal with stochastic inputs with arbitrary probability measures. Based on the decomposition of the random space of the stochastic inputs, we construct numerically a set of orthogonal polynomials with respect to a conditional probability density function (PDF) in each element and subsequently implement generalized Polynomial Chaos (gPC) locally. Numerical examples show that ME-gPC exhibits both p-and h-convergence for arbitrary probability measures.

Ammonia oxidation to nitrite and its subsequent oxidation to nitrate provides energy to the two populations of nitrifying chemoautotrophs in the energy-starved dark ocean, driving a coupling between reduced inorganic nitrogen (N) pools and production of new organic carbon (C) in the dark ocean. However, the relationship between the flux of new C production and the fluxes of N of the two steps of oxidation remains unclear. Here, we show that, despite orders-of-magnitude difference in cell abundances between ammonia oxidizers and nitrite oxidizers, the two populations sustain similar bulk N-oxidation rates throughout the deep waters with similarly high affinities for ammonia and nitrite under increasing substrate limitation, thus maintaining overall homeostasis in the oceanic nitrification pathway. Our observations confirm the theoretical predictions of a redox-informed ecosystem model. Using balances from this model, we suggest that consistently low ammonia and nitrite concentrations are maintained when the two populations have similarly high substrate affinities and their loss rates are proportional to their maximum growth rates. The stoichiometric relations between the fluxes of C and N indicate a threefold to fourfold higher C-fixation efficiency per mole of N oxidized by ammonia oxidizers compared to nitrite oxidizers due to nearly identical apparent energetic requirements for C fixation of the two populations. We estimate that the rate of chemoautotrophic C fixation amounts to ∼1 × 1013to ∼2 × 1013mol of C per year globally through the flux of ∼1 × 1014to ∼2 × 1014mol of N per year of the two steps of oxidation throughout the dark ocean.

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Phytoplankton assimilation and microbial oxidation of ammonium are two critical conversion pathways in the marine nitrogen cycle. The underlying regulatory mechanisms of these two competing processes remain unclear. Here we show that ambient nitrate acts as a key variable to bifurcate ammonium flow through assimilation or oxidation, and the depth of the nitracline represents a robust spatial boundary between ammonium assimilators and oxidizers in the stratified ocean. Profiles of ammonium utilization show that phytoplankton assemblages in nitrate-depleted regimes have higher ammonium affinity than nitrifiers. In nitrate replete conditions, by contrast, phytoplankton reduce their ammonium reliance and thus enhance the success of nitrifiers. This finding helps to explain existing discrepancies in the understanding of light inhibition of surface nitrification in the global ocean, and provides further insights into the spatial linkages between oceanic nitrification and new production.

The plant metallothionein 2 from Cicer arietinum (chickpea; cicMT2) is a typical member of this subfamily and features two cysteine-rich regions containing eight and six cysteine residues, respectively, separated by a linker region 41 amino acids in length. This metallothionein thus differs significantly from the well-studied vertebrate forms. A synthetic gene encoding cicMT2 was designed, cloned into a suitable vector, and the protein was over-expressed in Escherichia coli. For the first time, an in-depth spectroscopic characterization of cicMT2 in the presence of divalent metal ions is performed showing a binding capacity for five Zn(II), Cd(II), or Co(II) ions and the typical features of metal-thiolate clusters. Based on proteolytic digestion experiments, the cluster arrangement formed by the divalent metal ions and the cysteine thiolate groups connects the amino-terminal with the carboxy-terminal cysteine-rich region. The cluster formation process, put into effect with the addition of the fourth metal ion to the apo protein, was investigated using the characteristic shift of absorption bands observed in the UV/Vis spectra upon titration with Co(II). The pH-dependent Zn(II)- and Cd(II)-thiolate cluster stability is one of the highest observed for plant MTs so far, but lower than that usually found in vertebrate metallothioneins. The dependence of the pH stability on the ionic strength of the solution is more pronounced for the Cd(II)- than for the Zn(II)-form of the protein.