Barack Obama and Xi Jinping will meet in Beijing at this week's Apec leaders' gathering, at a time when their careers are on very different trajectories and bilateral relations have turned sour.
Hamstrung by the Democratic party's poor showing in last week's mid-term elections, Mr Obama is limping into the final two years of his presidency while Mr Xi can look forward to another eight years in office, during which time China is set to overtake the US as the world's biggest economy.
Mr Obama and Mr Xi will emphasize that a stable bilateral relationship is essential to both countries and downplay the many instances of friction between the two as so much surface noise. But the strategic divide between the world's two largest economies – on everything from cyber security issues to trade policy – is enormous and both leaders are under pressure to be even tougher with each other.
"A heightened level of tension is the new normal [in Sino-US relations]," says Mike Green, former Asia director at the US National Security Council. "The challenge for the president is to continue framing the relationship in a win-win way because on broad economic issues, management of North Korea and regional integration, we're still generally on the same side."
Further disagreements have arisen over China's allegations of "foreign involvement" in the ongoing pro-democracy protests in Hong Kong. Beijing also recently established a rival to the US and Japanese-led Asian Development Bank and, excluded from Washington's Trans-Pacific Partnership trade agreement, is pushing for a more inclusive Free Trade Area of the Asia Pacific.
US officials deny suggestions that they have played any role in the Hong Kong unrest – or that they tried to sabotage China's new development bank – but trade tensions between the two countries were evident over the weekend.
As China's foreign and trade ministers briefed reporters on their ambitions for FTAAP on Saturday, the US was simultaneously hosting a TPP negotiating session at its embassy in Beijing. Mr Obama is scheduled to host another TPP leaders meeting – again snubbing his hosts – in the Chinese capital on Monday.
According to one person familiar with deliberations between Beijing and Washington, the world's most important bilateral relationship grew so fraught over the summer that US diplomats spoke of trying to re-establish a "civil tone" at Apec.
The potential for a miscalculation, accident or worse was dramatically illustrated in August when the Pentagon accused China's air force of a dangerous intercept of a US Navy surveillance plane off the Chinese coast – in a near replay of the 2001 collision that left one People's Liberation Army pilot dead and forced an American spy plane to make an emergency landing on Hainan island.
While Chinese military officials rejected the Pentagon's characterisation of the August encounter, it featured prominently in talks a month later when Susan Rice, US national security adviser, visited Beijing.
"When it comes to unsafe and unprofessional intercepts, we talk to the Chinese regularly and at high levels because this is risky behaviour that could imperil the relationship," one administration official said on the sidelines of Ms Rice's visit. "The Chinese heard very clearly the nature of our concerns."
"The administration and the president need to take a tougher line over China's growing assertiveness," adds Elbridge Colby, an Asia expert at the Center for a New American Security. "If you listen to the Pentagon, there is increasing concern and in some ways a real outcry for help. They are saying this is a really severe problem and we need to face up to it."
For its part, China feels hemmed in by Washington's military alliances with Japan and South Korea, its close relationship with the Philippines and Mr Obama's policy "pivot" towards the Asia Pacific, which Beijing officials see as an effort to contain China's emergence as a global power in its own right.
"With regards to strategic issues such as the East and South China seas, China's relations with the US are very antagonistic," says Shi Yinhong, an international relations expert at Beijing's Renmin University. "There can be no substantial agreement in that regard."
During her visit to Beijing, Ms Rice spent eight hours with Chinese state councillor Yang Jiechi, who later paid a reciprocal visit to US secretary of state John Kerry's home in Boston.
Senior administration officials described the national security adviser's intensive meetings with Chinese officials as "cordial, amicable and straightforward" and say they will pave the way for a constructive meeting between the two countries' leaders this week.
But they also struggled to point to any real breakthroughs. In an attempt to accentuate the positive, the administration official noted that "most of [Ms Rice's] meetings were held in some very unique and special villas".
In Washington's effort to find common ground with Beijing, US officials have more recently emphasised the two countries' mutual interest in stabilising Afghanistan and also in the fight against Isis rebels in Iraq and Syria.
Substantive cooperation in these areas remains elusive, however, given China's reluctance to participate in any US-led initiatives.
"A lack of mutual trust has led to further misunderstandings," says Wang Yiwen at Renmin University's Institute of International Affairs. "In principle we are also against Isis extremism and can cooperate with the US, but prefer to do so under the framework of the UN."