Transport processes are central to the functioning of neuronal networks in the brain. Membrane diffusion and advection of proteins, ions and neurotransmitters essentially form the backbone of neuronal mechanisms – from cellular homeostasis to action potential propagation, to neuron-neuron signal modulation and thus brain functioning. In this talk, we outline a theoretical framework for understanding curvature effects on membrane-bound transport processes. Then we use computational modeling to demonstrate localization of diffusional species and, to a lesser degree, the effects on advection of species. Specific mechanisms modeled are curvature effects and entropic trapping on ionic and protein diffusion at the dendritic spines, axonal boutons, and the axon initial segment (AIS). Further, we extend these studies to model curvature effects on a few related neuronal injury mechanisms. The computational model employs an IGA-based Kirchhoff-Love thin-shell treatment of neuronal membranes. This model is part of a broader mechano-chemo-electrical modeling framework developed in our group for understanding various membrane-bound neuronal processes that are relevant for Traumatic Brain Injury (TBI).