The second MESSENGER flyby of Venus on 5 June 2007 provided a new opportunity to study the response of the induced magnetosphere of the planet to changes in the direction of the interplanetary magnetic field (IMF). At the time of the MESSENGER flyby, the European Space Agency's Venus Express spacecraft was located outside the magnetosphere and provided a monitor of solar wind conditions. Measurements by the Venus Express magnetometer show that the IMF underwent four major changes in direction and magnitude while MESSENGER was traveling through the inner magnetosphere of Venus. The response of the magnetosphere to each of these IMF changes was determined with a semi-time-dependant global magnetohydrodynamic (MHD) model, and the results were compared with magnetic and compositional measurements by the Magnetometer (MAG) and the Energetic Particle and Plasma Spectrometer (EPPS) on MESSENGER. Our modeling results show that this semi-time-dependant MHD technique produces magnetic field profiles that can account for both of the field reversals seen by MAG and the peak in the pick-up ion density measured by EPPS. Moreover, these results reveal that the plasma sheet that confines most of the pick-up ions has a barred disk shape and continuously rotates along the Sun-planet axis to align its smallest dimension with the transverse direction of the IMF.