A three-time All-Star, Nathan bowed out Sunday after experiencing soreness in his pitching shoulder the previous five days.
"I think we backed off it early enough to where it won't be an issue," said Nathan, who aggravated the AC joint, which connects the collarbone and clavicle at the top of the shoulder.
With Nathan and Ryan out, a number of relievers were added to the roster.
"It's going to be really cool to have USA on the front of my jersey," Bell said.
The right-hander got the word shortly before the Padres played the Milwaukee Brewers. He said he checked with manager Bud Black and pitching coach Darren Balsley to make sure it was OK with them before he accepted the assignment.
"Bud said, 'Have fun. You know how important you are to the Padres,' and Bals just said, 'Hey, be smart.'
Said Grabow: "I wanted to make sure myself that I'm ready to flip the switch and get after it in meaningful games. I know my limits, and I think I'm ready."
Ryan, a two-time All-Star, decided to stay in spring training with Toronto and tune up for the regular season.
"This was an especially tough decision because of the honor of playing for my country, but I feel it is [in] the best interest of Team USA and the Toronto Blue Jays organization to not participate," the left-hander said in a statement released by USA Baseball early Monday. "I do not see it as being fair to my USA teammates, my Blue Jay teammates or myself to try to compete when my mechanics and delivery are not where they need to be in order to perform at the highest level."
Nathan also called the decision a hard one.
"It's going to be difficult to watch it, for sure," Nathan said of the Classic. "At some time, I have a responsibility for the Twins. It was a decision everybody agreed upon. It was a tough decision to make."
Outfielders Grady Sizemore and Brad Hawpe also have been removed from the U.S. squad since final rosters were announced last week. Picked as replacements were outfielder Shane Victorino, outfielder-first baseman Adam Dunn and right-hander Joel Hanrahan.
The 34-year-old Nathan was 1-2 with a 1.33 ERA and 39 saves last season. He has averaged 39.8 saves over the past five years.
Nathan said he felt fine after a bullpen session Sunday morning before the Twins played the Boston Red Sox in a Grapefruit League game. But he said he wanted to be extra cautious, and playing in the WBC wouldn't allow him to do so.
"That's the one advantage I have of being here," Nathan said. "If there's a day I can back off, I can. Being there wouldn't allow me to stay on the schedule I need. I think I'm on the right track now. If things go well, I can be in a game on Thursday."
After missing nearly all of 2007 with an arm injury that required surgery, Ryan saved 32 games last year and went 2-4 with a 2.95 ERA in 60 appearances.
Information from The Associated Press is included in this report