We developed an advanced computational framework to accelerate the study of the impact of post-translational modifications on protein structures and interactions (PTM-Psi) using asynchronous, loosely coupled workflows on the Azure Quantum Elements Cloud platform. We seamlessly integrate emerging cloud computing assets that further expand the scope and capability of PTM-Psi Python package by refactoring it into a cloud-compatible library. We employed a "workflow of workflows" approach, wherein a parent workflow spawns one or more child workflows, managing them, and acting on their results. This approach enabled us to optimize resource allocation according to each workflow's needs and allowed us to use the cloud heterogeneous architecture for the computational investigation of a combinatorial explosion of thiol protein PTMs on an exemplary protein megacomplex critical to the Calvin-Benson cycle of light-dependent sugar production in cyanobacteria. With PTM-Psi on the cloud, we transformed the pipeline for the thiol PTM analysis to achieve high throughput by leveraging the strengths of the cloud service. PTM-Psi on the cloud reduces operational complexity and lowers entry barriers to data interpretation with structural modeling for a redox proteomics mass spectrometry specialist.