Spiking neural networks exploit spatiotemporal processing, spiking sparsity, and high interneuron bandwidth to maximize the energy efficiency of neuromorphic computing. While conventional silicon-based technology can be used in this context, the resulting neuron-synapse circuits require multiple transistors and complicated layouts that limit integration density. Here, we demonstrate unprecedented electrostatic control of dual-gated Gaussian heterojunction transistors for simplified spiking neuron implementation. These devices employ wafer-scale mixed-dimensional van der Waals heterojunctions consisting of chemical vapor deposited monolayer molybdenum disulfide and solution-processed semiconducting single-walled carbon nanotubes to emulate the spike-generating ion channels in biological neurons. Circuits based on these dual-gated Gaussian devices enable a variety of biological spiking responses including phasic spiking, delayed spiking, and tonic bursting. In addition to neuromorphic computing, the tunable Gaussian response has significant implications for a range of other applications including telecommunications, computer vision, and natural language processing.