2D-dwell-time analysis with simulations of ion-channel gating using high-performance computing.

Single-channel patch-clamp recordings allow observing the action of a single protein complex in real time and hence the deduction of the underlying conformational changes in the ion-channel protein. Commonly, recordings are modeled using hidden Markov chains, connecting open and closed states in the experimental data with protein conformations. The rates between states denote transition probabilities that could be modified by membrane voltage or ligand binding. Modeling algorithms have to deal with limited recording bandwidth and a very noisy background. It was previously shown that the fit of two-dimensional (2D)-dwell-time histograms with simulations is very robust in that regard. Errors introduced by the low-pass filter or noise cancel out to a certain degree when comparing experimental and simulated data. In addition, the topology of models (that is, the chain of open and closed states) could be inferred from 2D-histograms. However, the 2D-fit was never applied to its full potential. A major reason may be the extremely time-consuming and often unreliable fitting process, due to the stochastic variability in the simulations. We have now solved these issues by introducing a message-passing interface (MPI) allowing massive parallel computing on a high-performance computing (HPC) cluster and obtaining ensemble solutions. With ensembles, we have demonstrated how important ranked solutions are for difficult tasks related to a noisy background, fast gating events beyond the corner frequency of the low-pass filter, and topology estimation of the underlying Markov model. Finally, we have shown that, by combining the objective function of the 2D-fit with the deviation of the current amplitude distributions, automatic determination of the current level of the conducting state is possible, even with an apparent current reduction due to low-pass filtering. Making use of an HPC cluster, the power of 2D-dwell-time analysis can be used to its fullest with minor input of the experimenter.

Multiway p-spectral graph cuts on Grassmann manifolds.

Nonlinear reformulations of the spectral clustering method have gained a lot of recent attention due to their increased numerical benefits and their solid mathematical background. We present a novel direct multiway spectral clustering algorithm in the p-norm, for p ∈ ( 1 , 2 ] . The problem of computing multiple eigenvectors of the graph p-Laplacian, a nonlinear generalization of the standard graph Laplacian, is recasted as an unconstrained minimization problem on a Grassmann manifold. The value of p is reduced in a pseudocontinuous manner, promoting sparser solution vectors that correspond to optimal graph cuts as p approaches one. Monitoring the monotonic decrease of the balanced graph cuts guarantees that we obtain the best available solution from the p-levels considered. We demonstrate the effectiveness and accuracy of our algorithm in various artificial test-cases. Our numerical examples and comparative results with various state-of-the-art clustering methods indicate that the proposed method obtains high quality clusters both in terms of balanced graph cut metrics and in terms of the accuracy of the labelling assignment. Furthermore, we conduct studies for the classification of facial images and handwritten characters to demonstrate the applicability in real-world datasets.