One must work harder to obtain oxygen, primarily by breathing faster. This is particularly noticeable with exertion, such as walking uphill. Being out of breath with exertion is normal, as long as the sensation of shortness of breath resolves rapidly with rest. As the amount of oxygen in the lungs decreases, the blood becomes less and less efficient at acquiring and transporting oxygen . This means that no matter how fast one breathes, attaining normal blood levels of oxygen is not possible at high altitude.
Dramatic changes take place in the body's chemistry and fluid balance during acclimatization.
This results in an altitude diuresis as the kidneys dump fluid. It is normal at altitude to be urinating several times per night. If you are not, you may be dehydrated, or you may not be acclimatizing well. Periodic breathing consists of cycles of normal breathing, breath-holding, and accelerated breathing. This is not correlated with altitude sickness.