The protein structure prediction problem has been revolutionised by AlphaFold2, an algorithm that uses neural networks and evolutionary information to predict accurate models from the primary sequence. However, some proteins remain difficult to predict. Moreover, proteins are dynamic entities that exist in complex environments in vivo. Here, we use the noncanonical amino acid Photo-Leucine to obtain information on residue-residue contacts inside cells by crosslinking mass spectrometry. We then introduce AlphaLink, a modified version of the AlphaFold2 algorithm that synergistically incorporates experimental distance restraint information into its network architecture. AlphaLink improves on the performance of AlphaFold2 in predicting challenging targets in both synthetic and real-world scenarios by employing sparse experimental contacts as anchor points. The program can predict individual conformations of proteins based on the distance restraints provided. The noise-tolerant framework presented here for integrating data in protein structure prediction opens a path to accurate characterisation of protein structures from in-cell data.