Translocation of a cone-shaped HIV-1 capsid through the nuclear pore complex

In recent experiments, it has been observed that an intact cone-shaped HIV-1 capsid translocates through the nuclear pore complex (NPC) before capsid disassembly within the host cell nucleus. Capsid translocation through the NPC raises numerous interesting questions. How does the capsid, with size comparable to the NPC diameter, overcome the nuclear protein (nup) created barrier within the pore? Since the HIV-1 capsid has a cone shape with a narrow tip and a broad back, does translocation efficiency and time depend on the end that enters the NPC first? To answer these questions, we develop an analytical model for the transport of a cone-shaped HIV-1 capsid through the NPC, focusing on the energy barrier created by nups within the pore and the capsid-nup interactions that can reduce the barrier. We derive the free energy profile for the capsid as it translocates along the pore and use it to compute the capsid's translocation probability for reaching the trans end of the pore. Our results show that the capsid's translocation through NPC is favored for entry with the narrow end first. We also predict a minimal strength for the capsid-nup interaction below which translocation is arrested and above which the capsid's probability of reaching the nucleus increases, and the translocation process speeds up. Our results are consistent with experimental observations of the orientation of the capsid in the pore and mutation studies that inhibit translocation.