Computational models that can explain and predict complex sub-cellular, cellular, and tissue-level drug response mechanisms could speed drug discovery and prioritize patient-specific treatments (i.e., precision medicine). Some models are mechanistic with detailed equations describing known (or supposed) physicochemical processes, while some are statistical or machine learning-based approaches, that explain datasets but have no mechanistic or causal guarantees. These two types of modeling are rarely combined, missing the opportunity to explore possibly causal but data-driven new knowledge while explaining what is already known. Here, we explore combining machine learned associations with mechanistic models to develop computational models that could more fully represent cellular behavior. In this proposed MEMMAL (MEchanistic Modeling with MAchine Learning) framework, machine learning/statistical models built using omics datasets provide predictions for new interactions between genes and proteins where there is physicochemical uncertainty. These interactions are used as a basis for new reactions in mechanistic models. As a test case, we focused on incorporating novel IFNγ/PD-L1 related associations into a large-scale mechanistic model for cell proliferation and death to better recapitulate the recently released NIH LINCS Consortium MCF10A dataset and enable description of the cellular response to checkpoint inhibitor immunotherapies. This work is a template for combining big-data-inferred interactions with mechanistic models, which could be more broadly applicable for building multi-scale precision medicine and whole cell models.