Mutations representing spreadsheet edit operations are received at a server from client computers of collaborators and also at a collaborator's client computer from other collaborators and the server. Different mutations may conflict, i.e., provide contradictory instructions on how a spreadsheet is to be edited. Techniques for representing sort operations, cut-and-paste operations, and operations to change cell properties as mutations, and operational transform techniques that can be used to resolve conflicts between such mutations, are disclosed herein. Further disclosed herein are techniques for identifying and processing computationally intensive types of mutations in a calculation thread which operates asynchronously with respect to a UI thread at a collaborator's client computer. The processing may include performing an operational transform on results of the calculation thread based on results obtained in the UI thread.