Trying to figure that out right now :), there is a tension between an algorithm like this and the biophysical reality of actual brains. My intuition is that whatever the brain does is not so much an approximation of any known algorithm, but rather an analog of such an algorithm. Now that we know how in a spiking neural network gradient computation looks like, we can ask what assumptions are violated in the brain, just like people have done before for the vanilla backpropagation algorithm. There is some recent concrete experimental evidence that points towards a solution.