The dominant model for sleep regulation today is the two-process model. The two processes – the homeostatic process and the circadian process – sometimes work together and sometimes against each other, and the situation and wishes of the person can often override the process and keep us awake when we should be sleeping.
Homeostatic just means the body tries to maintain itself in a narrow range. Body temperature is regulated in a homeostatic process – the body stays with a few degrees. So are the pH and salinity of bodily fluids. This is a little simplistic, but sleep homeostasis can be modeled by assuming there is a quantitative need for sleep that builds while a person is awake and declines during sleep. The homeostatic pressure to sleep depends not only on how long you are awake but on how active you are while awake. What constitutes this need for sleep in a biochemical sense is still a subject for research. Discovery of orexins and unraveling of some of the neurotransmitter soup in recent decades have helped paint part of the picture but even the top neuroscientists confess they don't know.
The circadian process helps keep the homeostatic process in line. It helps us sleep through the night and not drop off during the day. Without the circadian process we would sleep intermittently in a manner more like polyphasic sleep. Physiologists who use this model often call the homeostatic process "Process S" and the circadian one "Process C."
The two-process model gets some support when you look at the stages of sleep in a typical night. Earlier in the night the periods of deep sleep (stage 3) are longer and more frequent than they are later in the night. Likewise, a person’s behavior and cognitive functioning depends on the body’s position in those two phases.
When you sleep extra time after being deprived of sleep, the extra is called recovery sleep and it is a consequence of the homeostatic process. In fact, during the sleep period after deprivation, EEG readings show a decline in the magnitude of delta waves over time during NREM. This suggests the magnitude is related to how tired the brain is in the homeostatic process.
Sleep has a quantitative dimension – how long it lasts - and a qualitative dimension – how intense the NREM sleep is. (Physiologists can measure intensity of NREM sleep, but REM sleep seems to have no quantitative dimension.) The two-process model explicitly names regulation of variables:
The model also sheds light on how smart you are during the day. Upon waking, you may not be at the peak of your cognitive abilities due to sleep inertia, but almost everyone shakes off that inertia and is at maximum mental capability in a couple hours. The longer we stay awake, the more the homeostatic sleep propensity builds and if the circadian cycle didn’t provide a boost, mental performance would decline across the waking day. As it is, many or most people experience a dip in cognitive ability in the mid-afternoon before rebounding in late afternoon into the evening. This dip may be because the circadian cycle is not yet strong enough to counteract the decline from the homeostatic process.
Genes identified as controlling the circadian rhythms (called clock genes) have been found to play a part in the homeostatic process,. The longer a person has been awake (the homeostatic process) and the more strain the person is under, the more the clock genes are active. Circadian processes in the body influence the homeostatic process and if the circadian impulse is strong enough it prevents the sleep deprived person from catching up in one night.
Circadian circuits in the forebrain do seem to influence the homeostatic process and if the circadian impulse is strong enough it prevents the sleep deprived person from catching up in one night.
Likewise, in the other direction, sleep deprivation can influence the circadian cycle by lowering the strength of the signal to the body from the suprachiasmatic nucleus.
Army researchers have recently been able to fit a biomathematical model of sleep-related performance impairment using a two-phase process.
When sleep quality declines as people get older, the cause can be a slip in either or both of the processes. Here's a talk from a couple scientists at the University of Surrey about various sleep issues, incorporating a background of the two-process understanding: http://www.youtube.com/watch?v=OCranah_01k.
The two phase model can be fitted to explain a biphasic sleep pattern, but it is not synonymous.
Remember, the two-process model is only a model. It assumes Process S and Process C are independent, and in reality they are not. It is a simplifying model that can help us in some situations. But there is an interplay between homeostasis and the circadian cycle. Sleep deprivation (an artificial intervention in Process S) suppresses some circadian genes. And some genetic transcripts in the cerebral cortex are influenced by circadian time even though we would tend to classify them as part of Process S.
So the simple model of two separate systems - circadian and homeostatic - doesn't represent reality, and the two systems are connected. However, it is useful to look the two-process model to describe and explain much of sleep and waking behavior, as long as we keep in mind it is overly simple.