Why do we sleep?

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Adults sleep less than babies. Sperm whales sleep less again. A new mathematical theory unlocks the mysteries of slumber

‘That we come to this earth to live is untrue. We come but to sleep, to dream.’
– Aztec poem

Humans have long wondered why we sleep. A well-rested prehistoric mind probably pondered the question, long before Galileo thought to predict the period of the pendulum or to understand how fast objects fall. Why must we put ourselves into this potentially endangering state, one that consumes about a third of our adult lives and even more of our childhood? And we don’t do it grudgingly – why do we, along with dogs, lions and virtually every other animal, apparently enjoy it? Unlike measuring the period of the pendulum, scientists would have to wait much longer to obtain reliable answers, since it’s not so easy to sleep while strangers watch. Doing so involves building sleep disorder clinics for humans and elaborate structures such as platypusariums to observe the REM (rapid eye movement) repose of platypuses.

Over the past few decades, huge amounts of data about the duration of sleep states have been gathered across species, as well as from birth to adulthood in humans. These findings have also been tallied with potential correlates such as melatonin, brain size, metabolic rate, lifespan, and sleep-promoting genes and neurons. Even so, until very recently we’ve lacked a quantitative theory that can predict, for example, why mice sleep roughly 10 times more per day than whales; why baby humans sleep roughly twice as long as adults; why REM and total sleep times change much faster as a baby grows in size than they do with similar size differences across species; and why temperature affects sleep times in cold-blooded animals such as fruit flies. Although great progress has been made in developing sophisticated models and explaining phenomena such as circadian rhythms, jetlag and details of EEG recordings of the sleeping brain, these advances are belied by the difficulty of developing a general quantitative theory for why we sleep.

Our work has started to fill this gap. Armed with a new, mathematical approach to the question of why we sleep, our framework leads to entirely new ways of understanding sleep data and responding to its basic questions. Many earlier studies might have foundered because they were more preoccupied with cataloguing the myriad aspects and properties of sleep, rather than pinning down what it was for. By contrast, the regular patterns predicted by our equations, and supported by empirical data, flow from our focus on determining the primary function of sleep. Equipped with insights into the role of the metabolism and the special status of the brain, we’ve discovered an abrupt and surprising shift in the function of sleep from infancy to adulthood, and expected across much of the animal kingdom – a phase transition as swift as water freezing to become ice.

In 1894, Marie de Manacéine, one of the first female physicians in Russia, published a remarkable paper showing that when puppies were completely deprived of sleep they died after just a few days. Her experiments were performed on 10 puppies, ranging from two to four months old, who were fed by their mothers and otherwise well cared for. As a control measure, she deprived other puppies of food but not sleep. These dogs could be restored to good health after being starved for 20 to 25 days, whereas those deprived of sleep were ‘irreparably lost’ after only four to six days. Her conclusions were clear: ‘the total absence of sleep is more fatal for the animals than the total absence of food’.

Although her methodology doesn’t meet modern-day ethical or experimental standards, her results have been confirmed by other observations and more rigorous studies in the intervening years: prolonged sleep deprivation can lead to death not only in dogs but in rats, fruit flies and possibly even humans due to a disease known as fatal insomnia. This terrifying syndrome involves a progressively worsening state of insomnia that leads to death within a year or two. It’s the result of a mutation of the prion protein encoding gene, similar to the much better known ‘mad cow disease’. There is no known cure.

A person who sleeps less than six hours each night has a 13 per cent higher mortality risk

As Manacéine remarked in the opening paragraph of her paper: ‘Facts of this kind clearly demonstrate that sleep deprivation produces a most noxious influence.’ Short of fatal insomnia, sleep deprivation invariably leads to an altered state of consciousness that manifests as dysfunctionalities such as memory loss, confusion, irritability, hallucinations, depression and even dementia. Examination of animals that have died from sleep deprivation shows severe brain-tissue damage including local haemorrhages and cerebral ganglion degeneration. Yet sleep deprivation continues to be used as a tool of interrogation, with its proponents claiming that it isn’t ‘torture’.

The idea that getting adequate sleep is a crucial ingredient for good health – as crucial as good nourishment – is one that many societies have been slow to embrace. The pressures and pace of modern lifestyles certainly don’t encourage healthy sleep practices, whether it’s from the pressures of work or the ubiquitous increase of anxiety-induced insomnia. Perhaps one of the few positives to have emerged from the COVID-19 pandemic is that physicians and health experts have been publicly urging people to get adequate sleep in order to maintain and promote a robust immune system.

Whether individually or collectively, many of us have been reluctant to acknowledge the centrality of sleep for our long-term health. On average, a person who sleeps less than six hours each night has a 13 per cent higher mortality risk than someone sleeping between seven and nine hours. Pervasive sleep deprivation is estimated to cost the US economy more than $400 billion a year as a result of higher mortality and lower productivity. In light of these impacts, it’s surprising that none of the 28 institutes comprising the US National Institutes of Health is explicitly devoted to sleep, with some of the most substantial support coming from one national centre devoted to sleep disorders research housed within the US National Heart, Lung, and Blood Institute. This reflects the relatively minor role that sleep research has played in the academic and medical communities, at least until recently. Although there is no ‘National Institute of Sleep’, at least sleep research is beginning to be more vigorously supported and pursued across the globe.

In recent years, neurobiological research has revealed many of the underlying mechanisms involved in sleep. Hormones, cells and enzymes – whose levels of activity and expression vary during sleep and between sleeping and waking states – have all been identified. We’ve learned a great deal about the physiology, anatomy and biochemistry of sleep. In this sense, when we say we understand why we sleep, what we really mean is that we understand what makes us sleepy, how we sleep, and what dysfunctions are caused by lack of sleep.

But all of this leaves unanswered the more fundamental question of why we need to sleep in the first place. What, in fact, is sleep’s function? We spend approximately a third of our life sleeping, yet we don’t know why we need to. And if we try not to, dire consequences follow. Why do we need approximately eight hours of sleep a night, and can’t get by with just three to four, like an elephant, or less than two, like a sperm whale? And as we progress from childhood to adulthood, why do our sleep needs decrease from a whopping 16 hours or so a day when we’re babies (comparable with the sleep of a much smaller mouse or shrew), down to the canonical eight hours at maturity? Where do these various timescales come from, and why?

Understanding the origins of sleep is particularly vexing since sleep hardly seems to confer any evolutionary advantage. Quite the opposite: why would an organism go into an unconscious, vulnerable state for several hours if it didn’t need to? There is the problem of coping with night-time, so maybe sleep evolved just to adapt to the challenges of darkness. On the other hand, many animals are nocturnal. Furthermore, mammals such as mice and shrews sleep much longer than the length of the night; others, such as elephants and whales, much less. Finally, the length of the night varies significantly across seasons and latitude, so why should human sleep time have settled on an approximately ‘universal’ value of about eight hours?

One intuitive explanation for sleep that’s easy to reject is that it’s needed to conserve energy, to rest and restore our bodies. We do lower our average metabolic rate while asleep but only by about 15 per cent – a measly 100 food calories a night, the equivalent of a slice of bread and butter. That seems hardly enough to justify the complexities, vulnerabilities and challenges of sleep.

There needs to be a dedicated downtime. After all, it would be foolhardy to make repairs to your car while driving it

Nevertheless, it’s generally believed that one of the two major functions of sleep is to repair the wear and tear of living, the damage that’s a byproduct of the metabolic processes keeping us alive. From humans to hermit crabs, life is sustained through networks – such as the cardiovascular system – that transport metabolic energy across all scales, servicing and feeding cells, mitochondria, genomes and other intracellular units. And just as the friction from cars and trucks on highways or the movement of water through pipes lead to continuous damage and decay, so it is with the blood, resources, cells and energy that flow through our networks. In addition to the familiar circulatory system, there are analogous networks of biochemical reactions in mitochondria – the fundamental source of our energy – that harm our bodies by producing free radicals. A free radical is any atom or molecule that has an unpaired electron that, in turn, makes it highly volatile and destructive. Antioxidants such as dark chocolate and blueberries serve as a protective buffer for this type of damage. So the damage that sleep helps to repair results from both blood flow and biochemical forces. Indeed, it’s sobering to realise that the very systems that sustain us are also continually degrading our bodies.

Another major function of sleep is reorganising and reconfiguring the neural connections in our brains to respond to the myriad sensory inputs we continuously receive. These come from both the external environment as well as from stimuli within our own bodies, such as our heartbeat and signals from our gut. This ongoing daily processing is a fundamental component of learning and memory. To stay efficient and effective, it also involves the pruning of seldom-used synapses, the rearranging and discarding of old pathways and connections, and the construction of new ones. Consequently, every fleeting thought, every dream, every new idea is a potential reconfiguration of your brain that can happen only by using metabolic energy.

Although these two functions – repair and reorganisation of the brain – reflect different reasons for why we need to sleep, they share two major properties. First, they’re both directly connected with metabolism, since metabolic energy fuels both the reorganisation of neural networks and also the repair of damage that itself is caused by byproducts of energy production and delivery. A second shared feature is that they’re both happening in a brain that essentially never replaces neurons (unlike most other organs and tissues whose cells are being continually replaced and regenerated). Because damaged neurons are almost never replaced, they must be faithfully repaired, in order to enable and preserve memory and learning while maintaining the integrity of a multicomponent brain.

For these reasons, efficient repair and reorganisation of neurons in the brain can’t occur without disrupting the organism’s normal functions. Consequently, there needs to be a dedicated downtime. After all, it would be foolhardy and probably dangerous to make repairs to your car while driving it. That’s why you stop the motor and take it to a mechanic. Similarly, major repairs to downtown roads or subway systems, clearing city trash, and upgrades to computer systems and networks are usually conducted on nights or weekends when there are significantly fewer users. This rationale is why our brains and bodies seemingly ‘shut down’ when carrying out the majority of the necessary repairs and reorganisation, leaving less chance for potential conflicts and disruptions to our day-to-day operations. And that’s why we need time to sleep.

In terms of your brain, you remain ‘you’ for most of your life. But this can be assured only if cellular damage to the brain is faithfully repaired so as to maintain its long-term integrity and identity. If not, ‘you’ will begin to transform into someone or something else – as indeed you do quite quickly if you’re significantly sleep-deprived. In contrast, it’s not as important to repair our other organs and tissues so conscientiously. Indeed, it was the brain lesions and haemorrhages that cropped up in the initial studies by Manacéine and others that gave us the first hints that sleep is primarily for the brain. Further support comes from the fact that the brain sucks up more than 20 per cent of all the energy used by our entire body, even though it constitutes only about 2 per cent of its mass. The brain takes more than its share because it needs to process sensory information and operate our bodies, as well as to repair and reorganise those neural networks while we sleep.

The demands of faithful repair and of neural reorganisation provide a powerful starting point for developing a quantitative theory for sleep because of how they relate to metabolic rate. The increasing interest in sleep and the recognition of its central role in good health has stimulated many studies that have illuminated the nature of how and why we fall asleep. What’s been much slower to emerge, though, has been a comprehensive theoretical framework – one that’s both quantitative and predictive – for understanding why we need to sleep. What sets the timescales of sleep that explain why humans need eight hours, but an elephant needs only three? What are the relative roles of repair and neural reorganisation? How do these change as we grow from a baby to an adult? We need a framework to begin chipping away at these mysteries.

Metabolism is fuelled by oxygen that’s delivered from our lungs to our cells via our cardiovascular system. Across all animals from mice to elephants, and throughout development from babies to adults, there are common features of cardiovascular systems that make it possible to describe and understand them within a general framework. These features arise because of fundamental biological properties – such as minimising the power for pumping blood, the need for branching networks to span the body and feed all cells, and for having capillaries of similar size and structure through which red blood cells flow to deliver oxygen to cells. Together, these properties conspire to create one of the most pervasive patterns in all of biology that’s known as biological or allometric scaling.

Big animals need less sleep than small ones, and adults need less than babies

In a nutshell, this means that almost all physiological rates and times – from lifespan to population growth to cell-turnover to pregnancies – change with body weight in a systematic predictive way, referred to mathematically as ‘quarter-power scaling’. For instance, an elephant is 10,000 times heavier than a squirrel so, as a consequence of these scaling laws, it lives roughly 10 times longer, grows about 10 times slower, has cells that are replaced about 1/10th as often, and spends about 10 times longer being pregnant before giving birth. Whales, giraffes, humans and cats might look quite different and live in quite different environments, but we all follow these same basic rules, constraints and tradeoffs with regard to our sizes, due to the continuous process of natural selection and shared ancestry. Consequently, the bigger the mammal, the slower its pace of life: times get longer and rates get slower with body size in a systematic and predictable way.

Despite the ubiquity of these scaling relationships, sleep is a notable exception – and in fact, that’s what first clued us into new insights about the function of sleep and the need to analyse the data in fresh ways. Specifically, although total sleep time changes with the body size of different animals or as babies grow, it doesn’t follow the pattern above: sleep times do not increase with body size, they decrease! For instance, a naive extrapolation of the scaling laws would lead us to expect that an elephant sleeps 10 times longer than a squirrel. But not only do elephants sleep substantially less than squirrels, the difference is by a factor of about four or five, not 10. Similarly, a toddler sleeps less than a newborn, not more.

This extremely puzzling result runs in the opposite direction, and at a different rate, to all the biological timings we and others have studied for decades. After much scratching of heads, we arrived at two paradigm-shifting hypotheses for potentially explaining this dilemma.

First, the inversion of the relationship between size and sleep time makes sense if we remember how sleep links to metabolism. Sleep works to counteract damage caused by energy production, and sleep is also reactive to stimuli via the neural reorganisation needed to encode information processed from the environment. Moreover, the counteracting work of repair, and reactive work of reorganisation, each occur at rates that are themselves determined by metabolism. Although the metabolic rate of the whole body increases with an animal’s size – either looking across species of different sizes, or as size increases as we grow up – according to allometric scaling relationships, it does so such that the metabolic rate per gram of tissue decreases with body size. Consequently, when an animal is larger, it suffers less damage to a fixed volume of tissue or cells. It therefore requires less energy and consequently less sleep time to accomplish the repair.

Second, the fact that the rate of change doesn’t follow a quarter-power scaling pattern can be explained if the metabolic rate were not set by the whole body, but instead by some part of the body that scales in an unusual way relative to body size. Which brings us back to the brain: unlike most other organs and tissues such as the heart, it has long been observed that brain size varies non-linearly with body size across species and as babies grow. That means, for example, the brain of an elephant is only about 1,000 times bigger than that of a squirrel, and not the 30,000 times bigger that we’d expect from the linear scaling of their body weights, as observed for other organs and tissues such as the heart.

With these two insights, we did a back-of-the-envelope calculation to see if repair and reorganisation being reactionary to metabolic processes in the brain (which scales more slowly than the whole body) could explain the longstanding puzzle of how sleep times change – why big animals need less sleep than small ones, and why adults need less than babies. We were delighted to see that the results were in the right ballpark, and that’s when we started taking these ideas seriously to derive a rigorous, quantitative and predictive theory of sleep.

Because of our past research, we were well positioned to develop the equations to express the role of metabolism in repair and reorganisation while asleep. Previously, while working on theories of ageing and lifespan, we’d calculated estimates for how much damage is done by metabolism. Our new theory for sleep was an outgrowth of this: any damage we incurred while awake had to be balanced by the energy required to repair that damage during sleep. We contextualised this insight by looking at both the brain and the body, in order to figure out what the scaling relationships revealed about which one played the dominant role in accounting for sleep.

This allowed us to derive the fundamental equation that related sleep time to awake time. From there, it was simple algebraic manipulation to discover that the best way to express and test the new theory was to focus on how the ratio of total sleep time to total awake time changed with brain (or body) size. This represented a significant departure, since prior research had focused only on either sleep time or awake time in absolute, not relative, terms. Moreover, our equations also demanded that in testing our theory, the proper space to plot data was logarithmic – a space in which the step from one to 10 is the same distance as from 10 to 100, or from 100 to 1,000. These simple mathematical manipulations and transformations – ratios of times, and logarithms of variables – meant we’d be plotting the data in a completely different way than researchers had done before us.

To test our theory, we began by analysing the largest existing dataset of sleep times of adult mammals that ranged from mice to elephants. When these data were plotted according to our theory, we were delighted to find that they scaled just as we predicted for the case that sleep is primarily for repair in the brain. And this wasn’t just true for total sleep time. Across species, we could also predict the fraction of REM sleep and the scaling of sleep cycle time – how long it takes to cycle between REM and non-REM sleep. This was very satisfying, and gave us confidence that we’d found the correct mechanism and correct theory for why we need to sleep. Indeed, we had derived a mathematical formula for how long adult animals sleep.

As a further test, we later wondered whether the theory would also apply to how sleep changes as individuals grow. We all know that newborns and children sleep much longer than adults – but does that map on to the rates and magnitudes of changes we see across species? Does the decrease of sleep times during growth mirror the decrease of sleep times across mammals of increasing size? After the theory was developed, new data appeared on total sleep times, REM sleep times, brain size, and other properties from human birth through adulthood, as interest in understanding sleep gained broader scientific and popular appeal.

The purpose of sleep shifts from neural reorganisation in children to repair once we’re grown

With great anticipation we and our collaborators plotted the new data – and were disappointed to find that the scaling of sleep times of children is substantially different from the results we had found across species. Clearly, our theory wasn’t correct when applied to growing children. Our confusion grew when we observed further that the amount of REM sleep changes profoundly as we grow. That’s a marked contrast to the way that REM sleep time hardly changes at all across species. As a final surprise, we also found that brain metabolic rate and the rate of synapse formation (the connections among neurons) scaled radically differently than we expected.

These findings reinforced our fascination with what a curious and biologically unusual process sleep is. However, they also made it clear, and essentially ‘proved’, that the reason we need sleep when we grow appears to be fundamentally different from the reason we need sleep as adults, and why sleep varies across species. So, working with our collaborators Junyu Cao, Alex Herman and Gina Poe, who are experts in sleep and statistics, we returned to an alternative version of the theory, based on the idea that sleep was primarily for neural reorganisation to process incoming information from the day. From this perspective, sleep is still about the brain and its metabolic activity – much like in the repair theory for adult animals. The big divergence that manifests during early childhood is because the way the brain grows in our early years is itself highly unusual compared with processes in the adult brain. In particular, synapse formation and brain metabolic rate increase incredibly fast in these early stages: a doubling in brain size results in a near quadrupling of synapse density and brain metabolic rate.

Based on these insights, we extended our theory so that the primary function of sleep during early life is for neural reorganisation rather than just for repair. And, voilà, we were able to predict the observed relationships for how total sleep time and REM sleep time change with brain size and metabolic rate during early development.

Comparing our findings across species with those across growth led us to a final question. If the purpose of sleep shifts from being about neural reorganisation as children to being about repair once we’re grown, when exactly does that transition occur, and how sudden is it? Armed with our new theory plus human developmental data, we could answer this question with surprising accuracy: the transition occurs when we’re extremely young – at about 2.5 years of age – and it happens extremely abruptly, like water freezing at 0°C.

We were delighted with this stunning result. First, it gave us an even greater appreciation for the critical importance of sleep: never again would we underestimate its importance for our children, especially in their first few years of life when their sleep is doing something so fundamentally different and extraordinarily important, something that seemingly can’t be made up for later in life. Second, we had discovered that these two states of sleep, while they looked remarkably similar from the outside, are actually analogous to completely different states of matter before and after the stark dividing line of 2.5 years of age. Before 2.5 years, our brains are more fluid and plastic, enabling us to learn and adapt quickly, similar to the state of water flowing around obstacles. After 2.5 years, our brains are much more crystalline and frozen, still capable of learning and adapting but more like glaciers slowly pushing across a landscape.

Many questions still remain. How much does sleep vary across humans and across species? Can this early fluid phase of sleep be extended? Is this phase already extended or shortened in some individuals, and what costs or benefits are associated with that? What other functions of sleep have piggybacked on to the primary functions of repair and neural reorganisation? How do the different reasons for sleep compete for or share sleep time, either across ages or even within a single night? It will take much more work to fully unravel the mysteries of sleep, but our recent insights – about age-based shifts in the purpose of sleep and the mathematical, predictive theories that quantify them – represent an essential tool to plumb these depths even further.

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