This time, Dr. Melgen’s contract dispute went unresolved.

And when Dr. Melgen was accused of overbilling Medicare for $8.9 million, he reached out to Mr. Menendez, who asked his chief of staff to see who had the most “juice” at the Department of Health and Human Services. Eventually, Mr. Menendez went through one of his close friends in the Senate, Harry Reid, a Democrat from Nevada, to convene a meeting.

“It was unusual for Senator Reid to ask me to come to a meeting involving another member of Congress,” Kathleen Sebelius, the health and human services secretary at the time, testified. “I think this was the only time in five and a half years that that occurred.”

In return for his assistance, Mr. Menendez was rewarded with free flights on Dr. Melgen’s private jet (Dr. Melgen’s personal pilot recalled flying the senator 16 times), a luxurious weekend stay in Paris (paid for by 650,000 of Dr. Melgen’s American Express Rewards points), rounds of golf, dinners and more than $700,000 in contributions to various political committees likely to be supportive of Mr. Menendez.

“This is what bribery looks like,” Peter Koski, the lead prosecutor in the case, said in his opening statement. “Friends can commit crimes together. Friends can bribe each other.”

At one point, another prosecutor, Amanda Vaughn, tried to tie the alleged scheme together on a whiteboard in front of the jury. She carefully wrote the date of each action and the date of each gift.

The whiteboard was quite likely a helpful aid; the methodical parsing of every detail — hotel receipts, credit card statements and passports, among other things — mixed with constant interruptions over legal points left many jurors inattentive, with some even nodding off, as the trial has dragged on at a sluggish pace.

For its part, the defense does not dispute many of the facts laid out by the prosecution. Dr. Melgen was generous and bestowed many gifts on Mr. Menendez. But the reason was simple. They were friends and that is what friends do.