More than Biology
I'd say your brain is simply part of your body. Now your mind? That's something altogether different. I think of our bodies as the equipment, but there are some safety features already wired in--you don't have to chose to blink and we probably wouldn't ever live to reproduce if our brains didn't automatically signal the heart to beat. Literally, every single beat. But it's not a one way signal. The heart speaks too.
So, what is the dialogue between your brain and mind? In a panic attack your mind starts running some subconscious programing (based on prior experiences) and your body starts playing along. A little blood pressure hear, a little blood sugar there. Then your mind notices the shortness of breath, the sweaty hands, the narrowing of focus. Now with your conscious mind on the train your body says, "Oh, crap! This is serious!" and escalates it's end. Everybody is playing so nice! "Drive her over the edge!" Wash. Rinse. Repeat. Until the world caves in.
But to your question. Yeah, we are more than the brain. If your body didn't have the sensitivities, anomalies, preferences, and limitations it does, your brain would operate differently. But it's a dance and you can't always tell who is in the lead!