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A new matched alternating direction implicit (ADI) method is proposed in this paper for solving three-dimensional (3D) parabolic interface problems with discontinuous jumps and complex interfaces. This scheme inherits the merits of its ancestor for two-dimensional problems, while possesses several novel features, such as a non-orthogonal local coordinate system for decoupling the jump conditions, two-side estimation of tangential derivatives at an interface point, and a new Douglas–Rachford ADI formulation that minimizes the number of perturbation terms, to attack more challenging 3D problems. In time discretization, this new ADI method is found to be of first order and stable in various experiments. In space discretization, the matched ADI method achieves the second order accuracy based on simple Cartesian grids for various irregularly-shaped surfaces and spatial–temporal dependent jumps. Computationally, the matched ADI method is as efficient as the fastest implicit scheme based on the geometrical multigrid for solving 3D parabolic equations, in the sense that its complexity in each time step scales linearly with respect to the spatial degree of freedom N , i.e., O ( N ) . Furthermore, unlike iterative methods, the ADI method is an exact or non-iterative algebraic solver which guarantees to stop after a certain number of computations for a fixed N . Therefore, the proposed matched ADI method provides a very promising tool for solving 3D parabolic interface problems.

κ-Carrageenase belongs to glycoside hydrolase family 16 and cleaves the β-(1→4) linkages of κ-carrageenan. In this study, genes encoding the full-length (cgkZ), Por secretion tail-truncated (cgkZΔPst) and carbohydrate binding domain-truncated (cgkZΔCBM) κ-carrageenase proteins were expressed in Pichia pastoris. The copy numbers of gene cgkZ, cgkZΔPst and cgkZΔCBM were 7, 7 and 6, respectively. The enzymatic activities of recombinant enzymes cgkZ, cgkZΔPst and cgkZΔCBM reached 4.68, 5.70, and 3.02 U/mL, respectively, after 120 h of shake flask fermentation at 22°C and pH 6 in the presence of 1 % (v/v) methanol. The molecular weights of recombinant cgkZ, cgkZΔPst, and cgkZΔCBM were approximately 65, 45, and 40 kDa; their Km values were 2.07, 1.85, and 1.04 mg/mL; and they exhibited optimal activity at 45–50°C and pH 6–7. All the recombinant enzymes were stimulated by Na+, Mg2+, Ca2+, and dithiothreitol. The end-products of enzymatic hydrolysis were mainly composed of κ-carrageenan tetrasaccharide and hexasaccharide. The removal of the Por secretion tail of κ-carrageenase promoted the transcription of κ-carrageenase gene, enhancing the specific activity of κ-carrageenase without significantly changing its catalytic properties. Although the transcription level of κ-carrageenase gene after the removal of the carbohydrate binding domain was relatively high, the specific activity of the recombinant enzyme significantly decreased. The comprehensive application of the P. pastoris expression system combined with the rational modification of genes may provide a novel approach for the heterologous expression of various marine enzymes with high activities.