Lensless coherent imaging of proteins and supramolecular assemblies: Efficient phase retrieval by the charge flipping algorithm

Diffractive imaging using the intense and coherent beam of X-ray free-electron lasers opens new perspectives for structural studies of single nanoparticles and biomolecules. Simulations were carried out to generate 3D oversampled diffraction patterns of non-crystalline biological samples, ranging from peptides and proteins to megadalton complex assemblies, and to recover their molecular structure from nanometer to near-atomic resolutions. Using these simulated data, we show here that iterative reconstruction methods based on standard and variant forms of the charge flipping algorithm, can efficiently solve the phase retrieval problem and extract a unique and reliable molecular structure. Contrary to the case of conventional algorithms, where the estimation and the use of a compact support is imposed, our approach does not require any prior information about the molecular assembly, and is amenable to a wide range of biological assemblies. Importantly, the robustness of this ab initio approach is illustrated by the fact that it tolerates experimental noise and incompleteness of the intensity data at the center of the speckle pattern.