There was a special kind of exhaustion that only came after several days of trying to keep up with Sherlock as he rushed from place to place, realisations and deductions sparking off him as he unravelled what anyone else would have declared an impossible case. It wasn't just an exhaustion of the body, but of the mind too, a weariness that sank as deeply into John's brain as it did into his bones, until thinking seemed almost as impossible as moving.
Trying to keep up with Sherlock's brain was an impossible task. No matter how hard John tried, he was always 15 steps behind and usually heading in the wrong direction, but he kept trying anyway. It might have been easier to just leave the thinking to Sherlock and follow him without trying to understand why they were heading to a library in Clapham, or trying to find the victim's rental DVD, but John wasn't prepared to give up that easily. If nothing else, it was worth it for the brief flash of pleasure and affection that Sherlock gave him on the rare occasion that he was able to contribute something, or make a connection that Sherlock hadn't explained yet.
It sapped him though, so that all he was able to do after it was all over was collapse into the chair outside the DI's office (not Lestrade this time - some bloke with an impossibly large moustache who clearly thought Sherlock had been sent to plague him by the Devil) while Sherlock went in to explain it all in words of one syllable. It took quite a while and John was left sitting alone, head resting against the wall behind him and his eyelids drooping. He could feel his mind shutting down as he slumped there, until it was as blank as the wall he was staring at.
The only thing that really made it through the fog was a distant and blurred vision of his bed. The idea of having to stand up again and find the energy to make the journey home seemed almost insurmountable, though. How was he ever even going to manage to make it down the corridor to the lift? Or just stand up, come to that? Maybe they'd let him just sleep in the chair for now.
Sherlock exited the DI's office with a bang of the door, exclaiming loudly enough to be heard in most of the surrounding offices, "We're never working with that unspeakable cretin again, John. He makes amoebae look like Nobel laureates."
John found the strength to bend his neck so that he could look at Sherlock, and blinked. "Right," he said slowly, weariness stretching the word out.
Sherlock looked at him. "Ah," he said in a quieter voice. "I've left you sitting down too long."
That required a response. John thought for a moment. "It's a comfy chair," he said eventually.
"Your bed will be comfier," Sherlock pointed out.
"It's a long way away," said John, and the thought made him sad. Why did it have to be so far away?
"You're not staying here," said Sherlock. "That idiot might infect you." He bent down and took hold of John's biceps. "Up," he commanded, lifting John's weight with ease and pulling him to his feet in one go.
John stumbled for a moment, surprised by the speed of it, and Sherlock kept hold of him until he'd found his feet.
"Come on, John," he said. "One last effort and then you can sleep for as long as you want."
"Oh, that sounds beautiful," said John, forcing himself to wake up a bit more so that he could remember how to walk.
Sherlock's arm went around his shoulders, holding him steady as they headed down to the lifts, and the only thing in John's mind was a surge of affection and gratitude for the man walking beside him, who took him on wild chases and incredible adventures, stretching his body and brain to their limits, and then took him home afterwards so that he could sleep curled up beside him.