Multispectral imaging is an established method to extend the number of colours usable in fluorescence imaging beyond the typical limit of three or four. However, standard approaches are poorly suited to live-cell imaging owing to the need to separate light into many spectral channels, and unmixing algorithms struggle with low signal-to-noise ratio data. Here we introduce an approach for multispectral imaging in live cells that comprises an iterative spectral unmixing algorithm and eight-channel camera-based image-acquisition hardware. This enables the accurate unmixing of low signal-to-noise ratio datasets captured at video rates, while maintaining diffraction-limited spatial resolution. We use this approach on a commercial spinning-disk confocal microscope and a home-built oblique-plane light-sheet microscope to image one to seven spectrally distinct fluorophore species simultaneously, using both fluorescent protein fusions and small-molecule dyes. We further develop protein-binding proteins (minibinders), labelled with organic fluorophores, and use these in combination with our multispectral imaging approach to study the endosomal trafficking of cell-surface receptors at endogenous levels.

A new horizontally explicit/vertically implicit (HEVI) time splitting scheme for atmospheric modelling is introduced, for which the horizontal divergence terms are applied within the implicit vertical substep. The new HEVI scheme is implemented in conjunction with a mixed mimetic spectral element spatial discretisation and semi-implicit vertical time stepping scheme that both preserve the skew-symmetric structure of the non-canonical Hamiltonian form of the equations of motion. Within this context the new HEVI scheme allows for the exact balance of all energetic exchanges in space and time. However since the choice of horizontal fluxes for which this balance is satisfied is not consistent with the horizontal velocity at the end of the time level the scheme still admits a temporal energy conservation error. Linearised eigenvalue analysis shows that similar to a fully implicit method, the new HEVI scheme is neutrally stable for all buoyancy modes, and unlike a second order trapezoidal HEVI scheme is stable for all acoustic modes below a certain horizontal CFL number. The scheme is validated against standard test cases for both planetary and non-hydrostatic regimes. For the planetary scale baroclinic instability test case, the new formulation exhibits a secondary oscillation in the potential to kinetic energy power exchanges, with a temporal frequency approximately four times that exhibited by a horizontally third order, vertically second order trapezoidal scheme. For the non-hydrostatic test case, the vertical upwinding of the potential temperature diagnostic equation is shown to reduce spurious oscillations without altering the energetics of the solution, since this upwinding is performed in an energetically consistent manner. For this test case, which is configured on an affine geometry, the exact balance of energy exchanges allows the model to run stably without any form of dissipation.