What can a neuron compute

Cortical pyramidal neurons possess elaborate dendritic trees with diverse nonlinear membrane conductances and thousands of plastic synapses, suggesting substantial computational capabilities at the single-cell level. Yet, what can a neuron compute remains an open question, largely due to the lack of a systematic framework to quantify its computational capabilities. We introduce TwinProp, a digital-twin-based backpropagation algorithm that enables gradient-based optimization of synaptic strengths and dendritic locations in detailed neuron models via a millisecond-accurate deep neural network (DNN). Using TwinProp, we demonstrate that a detailed model of rat layer 5 pyramidal cell (L5PC) can perform naturalistic image and audio classification tasks at a remarkably high accuracy, significantly surpassing perceptron and leaky integrate-and-fire baselines. The same neuron solves high-dimensional nonlinear problems, including exclusive-or (XOR), 10-bit parity, and random Boolean tasks, demonstrating capabilities typically attributed to multilayer networks. Mechanistically, increasing task complexity recruits distributed dendritic nonlinearities, including NMDA- and voltage-dependent mechanisms; removing these or collapsing dendritic structure markedly impairs performance. These findings identify dendrites as a substrate for high-order feature binding and position single cortical pyramidal neurons as powerful, noise-robust, general-purpose analog computational units. Our results offer testable in vivo predictions and provide a systematic framework linking cellular morpho-electrical properties to computation in both brains and artificial systems.