Mark McCrea has replaced Fijian winger Timoci Nagusa, who suffered a hamstring injury against Munster, in the province's starting line-up.
David Pollock has been promoted to the back row in place of last week's stand-in captain Kieron Dawson, who has dropped to the bench.
Regular captain Rory Best is back to don the number 2 jersey, while Nigel Brady, who slotted in for Best last Saturday, is on the bench.
Commenting on the trip to the Scottish capital, Williams said: "My heart rate won't change. We'll walk through the door and go out and do what we have to do. It's not about me, it's about the boys.
"Edinburgh are a powerful team of great professionals, and we will give them the respect they deserve.
"The bad news for our opposition is that there were so many aspects of our game I wasn't happy with against Munster on Saturday night.
"We can improve a lot in three or four areas, tactical and technically."
He added: "We're in a really positive frame of mind and we have to take that on the road, but that shouldn't be a worry for us and there is no reason why we can't win away from home.
"We proved that at Thomond Park. Before it was just about convincing people and now we have got the proof.
"We threw points away earlier in the year and now it is up to us to get them back. If we can win on Friday, it's incredible how close to the top of the table we can come. So we're going to give it a go."
Ulster are currently one point behind Edinburgh in the Magners League table heading into their floodlit clash. The last time the two teams met in October, Ulster claimed a 13-9 win at Ravenhill.
ULSTER (v Edinburgh): Clinton Schifcofske; Andrew Trimble, Darren Cave, Paddy Wallace, Mark McCrea; Ian Humphreys, Isaac Boss; Tom Court, Rory Best (capt), BJ Botha, Ed O'Donoghue, Matt McCullough, Stephen Ferris, David Pollock, Robbie Diack.
Replacements: Nigel Brady, Justin Fitpzatrick, Filo Paulo, Kieron Dawson, Paul Marshall, Paul Steinmetz, Bryn Cunningham.