The paper proposes a novel research framework for building probabilistic computational neurogenetic models (pCNGM). The pCNGM is a multilevel modeling framework inspired by the multilevel information processes in the brain. The framework comprises a set of several dynamic models, namely low (molecular) level models, a more abstract dynamic model of a protein regulatory network (PRN) and a probabilistic spiking neural network model (pSNN), all linked together. Genes/proteins from the PRN control parameters of the pSNN and the spiking activity of the pSNN provides feedback to the PRN model. The overall spatio-temporal pattern of spiking activity of the pSNN is interpreted as the highest level state of the pCNGM. The paper demonstrates that this framework can be used for modeling both artificial cognitive systems and brain processes. In the former application, the pCNGM utilises parameters that correspond to sensory elements and neuromodulators. In the latter application a pCNGM uses data obtained from relevant genes/proteins to model their dynamic interaction that matches data related to brain development, higher-level brain function or disorder in different scenarios. An exemplar case study on Alzheimer's Disease is presented. Future applications of pCNGM are discussed.