The smallest and lowest part of the brain is called the medulla.The medulla lies beneath the cerebellum.It connects the brain to the spinal cord ,which runs down the neck and back.It controls involuntary actions i.e the ones that work automatically,without us even thinking about them.When the rest part of the brain sleep,its the medulla that keeps the part of the brain working.
While not smallest brain region, there is a really tiny part of the brain responsible for lots of really important roles managing different systems in our body. It is the Hypothalamus.
It contains different nuclei (groups of specialized neurons working together), each one with a different function:
Preoptic and Paraventricular Nuclei - Regulation os thirst, sexual development and behavior, sleep, growth;
Supraoptic Nucleus - Regulation of body water distribution and excretion, secretion of oxitocine (the love hormone);
Anterior Nucleus - Regulation of internal temperature (it induces fever as a protective response to infection/inflammation), sweating;
Suprachiasmatic Nucleus - Regulates the Circadian Rhythm;
Dorsomedial Nucleus - Regulates blood pressure, heart rate and gastrointestinal function;
Ventromedial Nucleus - Regulates hunger, also has controls lots of neuroendocrine responses;
Mammillary Nucleus - Participates in memory processing;
Posterior Nucleus - Regulates blood pressure, pupillary dilation, induces shivering;
Tuberomammillary Nucleus - Regulates awareness, energy balance and sleep. Also participates in memory acquisition and learning.
As you can see, a really tiny little part of our brain is involved in countless vital roles.
While not the smallest, it is probably one of the most important small structures!