Mounting experimental evidence suggests the hypothesis that brain-state-specific neural mechanisms, supported by the connectome shaped by evolution, could play a crucial role in integrating past and contextual knowledge with the current, incoming flow of evidence (e.g., from sensory systems). These mechanisms would operate across multiple spatial and temporal scales, necessitating dedicated support at the levels of individual neurons and synapses. A notable feature within the neocortex is the structure of large, deep pyramidal neurons, which exhibit a distinctive separation between an apical dendritic compartment and a basal dendritic/perisomatic compartment. This separation is characterized by distinct patterns of incoming connections and three brain-state-specific activation mechanisms, namely, apical-amplification, -isolation, and drive, which have been proposed to be associated - with wakefulness, deeper NREM sleep stages, and REM sleep, respectively. The cognitive roles of apical mechanisms have been supported by experiments in behaving animals. In contrast, classical models of learning in spiking networks are based on single-compartment neurons, lacking the ability to describe the integration of apical and basal/somatic information. This work provides the computational community with a two-compartment spiking neuron model that supports the proposed forms of brain-state-specific activity. A machine learning evolutionary algorithm, guided by a set of fitness functions, selected parameters defining neurons that express the desired apical dendritic mechanisms. The resulting spiking model can be further approximated by a piece-wise linear transfer function (ThetaPlanes) for use in large-scale bio-inspired artificial intelligence systems.