Elucidating the motion of uniformly charged polymers in nanoscale channels has been a scientifically and technologically fruitful enterprise. It has long been recognized that underlying this motion is a free energy landscape to which both entropy and electrostatics contribute, but this landscape has proven difficult to measure experimentally. Here we use a non-uniformly charged “diblock copolymer”-like neuronal protein, α-synuclein, to probe the energy landscape governing passage through a nanoscale pore. α-Synuclein is a naturally occurring, intrinsically disordered polypeptide associated with Parkinson disease pathology and mitochondrial bioenergetics. The motion of this electrically heterogeneous polymer through an outer mitochondrial membrane passive transport channel, the voltage-dependent anion channel (VDAC), depends on the electrical and membrane association properties of both the charged and uncharged regions of α-synuclein. We introduce complementary models that describe this motion in two limits: first, a simple Markov model accounts for the simultaneous interaction of multiple α-synuclein molecules with VDAC for high membrane surface α-synuclein coverage. Second, the detailed energy landscape of this motion in the dilute limit can be reconstructed from the entropic, electrostatic, and membrane binding components by optimizing a drift-diffusion framework to the experimental data. The models predict the probability of α-synuclein translocation across VDAC pore, with immediate implications for the (patho-)physiological role of α-synuclein in mitochondrial functioning. Finally, we show that the time-dependent effect of α-synuclein on the electrical properties of VDAC reports on the motion of the junction between the charged and uncharged regions of the polymer through the pore.