What helped influence the Japanese to eventually open their country to trade with the US?

They wanted the Japanese to open their ports to American trade and they organised the Perry expedition

Explanation:

The Perry Expedition was a diplomatic expedition to Bakumatsu period Japan, involving two separate trips by warships of the United States Navy, which took place during 1853–54. The goals of this expedition included exploration, surveying, and the establishment of diplomatic relations and negotiation of trade agreements with various nations of the region; opening contact with the government of Japan was considered a top priority of the expedition, and was one of the key reasons for its inception.

The expedition was commanded by Commodore Matthew Calbraith Perry, under orders from American President Millard Fillmore.

Perry’s primary goal was to force an end to Japan’s 220-year-old policy of isolation and to open Japanese ports to American trade, through the use of gunboat diplomacy if necessary. The Perry Expedition led directly to the establishment of diplomatic relations between Japan and the western "Great Powers", and eventually to the collapse of the ruling Tokugawa shogunate.

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