Ultrashort pulses from x-ray free-electron laser (XFEL) sources promise to assist in obtaining the structures of membrane proteins at high resolution. We have reconstructed the electron density distribution of a two-dimensional (2D) aquaporin crystal from simulated XFEL data using ptychography, a diffractive imaging technique based on multiple exposures. Increasing the number of exposures compensates for Poisson noise, indicating that the achievable resolution is limited by the reproducibility of the crystals. This technique should therefore be applicable at all future ultrashort-pulsed hard x-ray sources.