We present a computational, biophysical model of neuron-astrocyte-vessel interaction. Unlike other cells, neurons convey “hunger” signals to the vascular network via an intervening layer of glial cells (astrocytes); vessels dilate and release glucose which fuels neuronal firing. Existing computational models focus on only parts of this loop (neuron→astrocyte→vessel→neuron), whereas the proposed model describes the entire loop. Neuronal firing causes release of a neurotransmitter like glutamate which triggers release of vasodilator by astrocytes via a cascade of biochemical events. Vasodilators released from astrocytic endfeet cause blood vessels to dilate and release glucose into the interstitium, part of which is taken up by the astrocyticendfeet. Glucose is converted into lactate in the astrocyte and transported into the neuron. Glucose from the interstitium and lactate (produced from glucose) influx from astrocyte are converted into ATP in the neuron. Neuronal ATP is used to drive the $Na^+$/$K^{+}$ATPase pumps, which maintain ionic gradients necessary for neuronal firing. When placed in the metabolic loop, the neuron exhibits sustained firing only when the stimulation current is more than a minimum threshold. For various combinations of initial neuronal [ATP] and external current, the neuron exhibits a variety of firing patterns including sustained firing, firing after an initial pause, burst firing etc. Neurovascular interactions under conditions of constricted vessels are also studied. Most models of cerebral circulation describe neurovascular interactions exclusively in the “forward” neuron→vessel direction. The proposed model indicates possibility of “reverse” influence also, with vasomotion rhythms influencing neural firing patterns. Another idea that emerges out of the proposed work is that brain’s computations may be more comprehensively understood in terms of neuro-glial-vascular dynamics and not in terms of neural firing alone.