A Discontinuous Galerkin Model for Fluorescence Loss in Photobleaching

Dynamic Mode Decomposition of Fluorescence Loss in Photobleaching Microscopy Data for Model-Free Analysis of Protein Transport and Aggregation in Living Cells

The phase separation and aggregation of proteins are hallmarks of many neurodegenerative diseases. These processes can be studied in living cells using fluorescent protein constructs and quantitative live-cell imaging techniques, such as fluorescence recovery after photobleaching (FRAP) or the related fluorescence loss in photobleaching (FLIP). While the acquisition of FLIP images is straightforward on most commercial confocal microscope systems, the analysis and computational modeling of such data is challenging. Here, a novel model-free method is presented, which resolves complex spatiotemporal fluorescence-loss kinetics based on dynamic-mode decomposition (DMD) of FLIP live-cell image sequences. It is shown that the DMD of synthetic and experimental FLIP image series (DMD-FLIP) allows for the unequivocal discrimination of subcellular compartments, such as nuclei, cytoplasm, and protein condensates based on their differing transport and therefore fluorescence loss kinetics. By decomposing fluorescence-loss kinetics into distinct dynamic modes, DMD-FLIP will enable researchers to study protein dynamics at each time scale individually. Furthermore, it is shown that DMD-FLIP is very efficient in denoising confocal time series data. Thus, DMD-FLIP is an easy-to-use method for the model-free detection of barriers to protein diffusion, of phase-separated protein assemblies, and of insoluble protein aggregates. It should, therefore, find wide application in the analysis of protein transport and aggregation, in particular in relation to neurodegenerative diseases and the formation of protein condensates in living cells.

A discontinuous Galerkin model for fluorescence loss in photobleaching of intracellular polyglutamine protein aggregates

Background

Intracellular phase separation and aggregation of proteins with extended poly-glutamine (polyQ) stretches are hallmarks of various age-associated neurodegenerative diseases. Progress in our understanding of such processes heavily relies on quantitative fluorescence imaging of suitably tagged proteins. Fluorescence loss in photobleaching (FLIP) is particularly well-suited to study the dynamics of protein aggregation in cellular models of Chorea Huntington and other polyQ diseases, as FLIP gives access to the full spatio-temporal profile of intensity changes in the cell geometry. In contrast to other methods, also dim aggregates become visible during time evolution of fluorescence loss in cellular compartments. However, methods for computational analysis of FLIP data are sparse, and transport models for estimation of transport and diffusion parameters from experimental FLIP sequences are missing.

Results

In this paper, we present a computational method for analysis of FLIP imaging experiments of intracellular polyglutamine protein aggregates also called inclusion bodies (IBs). By this method, we can determine the diffusion constant and nuclear membrane transport coefficients of polyQ proteins as well as the exchange rates between aggregates and the cytoplasm. Our method is based on a reaction-diffusion multi-compartment model defined on a mesh obtained by segmentation of the cell images from the FLIP sequence. The discontinuous Galerkin (DG) method is used for numerical implementation of our model in FEniCS, which greatly reduces the computing time. The method is applied to representative experimental FLIP sequences, and consistent estimates of all transport parameters are obtained.

Conclusions

By directly estimating the transport parameters from live-cell image sequences using our new computational FLIP approach surprisingly fast exchange dynamics of mutant Huntingtin between cytoplasm and dim IBs could be revealed. This is likely relevant also for other polyQ diseases. Thus, our method allows for quantifying protein dynamics at different stages of the protein aggregation process in cellular models of neurodegeneration.

Electronic supplementary material

The online version of this article (10.1186/s13628-018-0046-0) contains supplementary material, which is available to authorized users.

Discontinuous Galerkin Model of Cellular Electroporation

Electroporation (EP) is a phenomenon involving both nonlinear biophysical processes and complex geometries. When exposed to strong electric fields, the formation of pores within a cell membrane increases the membrane permeability. Discontinuous Galerkin (DG) finite element methods can directly enforce these flux jumps across the thin cell membrane interface. We implement a DG finite element method to model the electric field, pore formation, and transmembrane flux of charged solutes during EP. Our model is readily extensible for parallel computation on high performance clusters and agrees with previous reports.