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Section: New Results

Off-grid fitting method

Participants : Alexandre Hoffmann, Sergei Grudinin.

Figure 25.

We developed a novel Fast Fourier Transform (FFT)-based exhaustive search method extended to off-grid translational and rotational degrees of freedom [5]. The method combines the advantages of the FFT-based exhaustive search, which samples all the conformations of a system under study on a grid, with a local optimization technique that guarantees to find the nearest optimal off-grid conformation. The method is demonstrated on a fitting problem and can be readily applied to a docking problem.

The algorithm first samples a scoring function on a six-dimensional grid of size $N^6$ using the FFT. This operation has the asymptotic complexity of $O(N^{6}logN)$. Then, the method performs the off-grid search using a local quadratic approximation of the cost function and the trust region optimization algorithm. The computation of the quadratic approximation is also accelerated by FFT at the same additional asymptotic cost of $O(N^{6}logN)$. We demonstrate our method on fitting atomic protein models into several simulated and experimental maps from cryo-electron microscopy. The method is available at https://team.inria.fr/nano-d/software/offgridfit.