The pneumotaxic center, also known as the pontine respiratory group, is a critical component of the brain's respiratory control mechanism. It is located in the upper part of the brainstem known as the pons. This center primarily functions to regulate the duration of inspiration by sending inhibitory impulses to the medullary inspiratory center. By doing so, it helps in fine-tuning the breathing pattern, ensuring that each breath is smooth and appropriately timed. This regulation is essential to maintain the rhythm of breathing and to prevent over-inflation of the lungs. In contrast, the cerebellum and cerebrum are primarily involved in coordination and higher-order brain functions respectively, while the medulla also plays a role in respiration but houses the inspiratory and expiratory centers, not the pneumotaxic center.