There are many efficient ways to connect proteins at termini. However, connecting at a loop is difficult because of lower flexibility and variable environment. Here, we have developed DogCatcher, a protein that forms a spontaneous isopeptide bond with DogTag peptide. DogTag/DogCatcher was generated initially by splitting a Streptococcus pneumoniae adhesin. We optimized DogTag/DogCatcher through rational design and evolution, increasing reaction rate by 250-fold and establishing millimolar solubility of DogCatcher. When fused to a protein terminus, DogTag/DogCatcher reacts slower than SpyTag003/Spy-Catcher003. However, inserted in loops of a fluorescent protein or enzyme, DogTag reacts much faster than SpyTag003. Like many membrane proteins, the ion channel TRPC5 has no surface-exposed termini. DogTag in a TRPC5 extracellular loop allowed normal calcium flux and specific covalent labeling on cells in 1 min. DogTag/DogCatcher reacts under diverse conditions, at nanomolar concentrations, and to 98% conversion. Loop-friendly ligation should expand the toolbox for creating protein architectures.

The problem of second-order water wave diffraction of an incident monochromatic wave field by an array of bottom-mounted circular cylinders is solved by a semi-analytical approach. The solution for the second-order potential is obtained by combining eigenfunction expansions with an integral representation. Unlike the indirect approach for second-order forces (Lighthill 1979; Molin 1979), this approach gives complete information about local flow characteristics (pressure, velocities, wave elevation, etc.) thus providing a basis for solving the third-order problem. The results obtained are compared with other published data, and new detailed results, useful for benchmarking purposes, are given. Finally the influences of wave incidence, cylinder radius and cylinder configuration are considered. This leads to the suggestion that there exists a near-trapping phenomenon for the second-order wave in an array of cylinders, at half the wave frequency at which the corresponding linear near-trapped mode occurs.

A complete semi-analytical solution is given for second-order diffraction of monochromatic waves by a truncated vertical circular cylinder in water of uniform finite depth. The methodology presented in detail elsewhere (Eatock Taylor & Huang 1996) is adopted to find a particular solution which exactly satisfies the governing equation, the inhomogeneous free-surface condition and the seabed condition. In order to satisfy the boundary condition on the cylinder bottom, the fluid domain around the cylinder is divided into two regions. First- and second-order velocity potentials are described separately in the two regions and matched on the interface by the pressure and normal-velocity continuity conditions. Based on the formulation, the second-order wave field in the vicinity of the cylinder and the corresponding wave forces and overturning moments on the cylinder are studied in detail. Numerical results for the double frequency forces obtained by using the present semi-analytical approach are compared with those computed with a higher-order boundary element method (Eatock Taylor & Chau 1992). As well as the exact solution, an approximate solution is also given for the second-order potential and the corresponding forces. Numerical results show that the approximate solution possesses excellent accuracy for the total second-order heave force over a wide range of conditions. When kb > 1.2 (where k, b are the incident wavenumber and the draught of the cylinder respectively), the accuracy for total second-order surge force and pitch moment is also satisfactory. These results could lead to the development of very efficient solutions and corresponding algorithms for the analysis of second-order wave diffraction by more complicated structures such as tension leg platforms. Numerical results based on the present solution show that in many cases, both the first- and the second-order-free surface elevation in the vicinity of a truncated cylinder is very close to that of a bottom-seated cylinder. For waves with larger amplitudes, the maximum free-surface elevation around a vertical cylinder predicted with the second-order theory can significantly exceed that given by linear theory. There is also a considerable difference in the location of the maximum elevation predicted by the linear and nonlinear theories.

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