Scale: The Universal Laws of Life and Death in Organisms, Cities and Companies

by Geoffrey West

Since the production of ATP is common to almost all animals, this exponential dependence is universal, much as quarter-power scaling with mass is. Its overall scale is governed by just a single “universal” parameter: the average activation energy needed to produce an ATP molecule via the oxidative chemical process

I discussed in the previous chapter. This is approximately 0.65 eV (electron volts, introduced in chapter 2), which is typical of chemical reactions and re...

leads to the fascinating conclusion that across the spectrum of life all biological rates and times such as those associated with growth, embryonic development, longevity, and evolutionary processes are determined by a joint universal scaling law in terms of just two parameters: the number 1⁄4, arising from the network constraints that control the depe...

The two most important events in an organism’s life, its birth and its death, which are usually thought of as being independent, are intimately related to each other: the slopes of these two graphs are determined by exactly the same parameter, the 0.65 eV, representing the average energy needed to produce an ATP molecule.

The exponential dependence of ATP production, which is governed by the 0.65 eV activation energy, can be translated into the simple statement that for every 10°C rise in temperature the production rate doubles. Consequently, a relatively small increase of only 10°C leads to a doubling of metabolic rate and therefore to a doubling of the rate of living. By the way, this is why you don’t see many insects in the morning when it’s cool—they have to wait till it warms up to increase their metabolism.

More pertinent, a modest 2°C change in ambient temperature leads to a 20 percent to 30 percent change in growth and mortality rates.11 This is huge and therein lies our problem. If global warming induces a temperature increase of around 2°C, which it is on track to do, then the pace of almost all biological life across all scales will increase by a whopping 20 percent to 30 percent. This is highly nontrivial and will potentially wreak havoc with the ecosystem.

Of greater significance is that he was the first scientist to calculate how changes in the levels of carbon dioxide in the atmosphere could alter the surface temperature of the Earth through the greenhouse effect,

predicting that the burning of fossil fuels was large enough to cause significant global warming.

The fact that almost everything dies plays a central role in the evolutionary process because it allows new adaptations, designs, and innovations to emerge and flourish.

Improved housing, public health programs, immunization, antiseptics, and, most important, the development of sanitation, sewage systems, and access to clean running water played an enormous role in overcoming and containing childhood diseases and infections.

The city as the engine for social change and increasing well-being is one of the truly great triumphs of our amazing ability to form social groups and collectively take advantage of economies of scale.

One of the surprising results that emerges is that the mortality rate for most organisms remains approximately unchanged with age. In other words, the relative number of individuals that die in any time period is the same at any age.

Physicists use the term decay rate, rather than mortality rate, to quantify the decay of radioactive material in which “individual” atoms change their state by emitting particles (alpha, beta, or gamma rays) and “die.”

Physicists also use the term half-life

to characterize decay rates: this is the time it takes for half of the original radioactive atoms to have decayed. Half-life is a very useful metric for thinking about decay processes in general and has migrated into many fields, including medicine, where it is used to quantify the time efficacy of drugs, isotopes, and other substances that the body processes.

the data show that the half-life of publicly traded companies in the United States is only about ten years.

The leading causes of death are overwhelmingly associated with damage, whether in organs and tissue (as in heart attacks or stroke) or in molecules (as in cancer)—infectious diseases play a relatively minor role. (2) Even if every cause of death were eliminated, all human beings are destined to die before they reach 125 years old, and the vast majority of us will do so well before we reach that ripe old age.

Natural selection only needs to ensure that the majority of individuals in a species survive sufficiently long to produce enough offspring to maximize their evolutionary fitness.

The number of heartbeats in a lifetime is approximately the same for all mammals,

shrews have heart rates of roughly 1,500 beats a minute and live for about two years, whereas heart rates of elephants are only about 30 beats a minute but they live for about seventy-five years. Despite their vast difference in size, both of their hearts beat approximately one and a half billion times during an average lifetime.

the total amount of energy used in a lifetime to support a gram of tissue is approximately the same for all mammals and, more generally, for all animals within a specific

For mammals it’s about 300 food calories per gram per lifetime.

Quantities that do not change when other parameters of the system change play a special role in science because they point the way to generic underlying principles that transcend the detailed dynamics and structure of a system.

conservation of energy and the conservation of electric charge are two famous examples of this in physics: no matter how complicated and convoluted the evolution of a system might be as it transforms and interchanges energy and electric charge, the total amount of energy and the total electric charge remain the same.

you add up all of the energy and all of the electric charge in a system at some initial time, then these maintain the same value at any later time no matter what has happened—provided, of course, that you have ...

take an extreme example: the total mass-energy in the universe today is exactly the same as it was at the Big Bang more than 13 billion years ago when it was just a compact minuscule point, despite the subsequent evol...

For instance, the horsepower rating of these engines (the analog to their metabolic rate) scales linearly with their weight, so to double their power output, you have to double their weight.

These are in distinct contrast to the 1⁄4 power scaling laws obeyed by organisms, which result from their optimized fractal-like network structures: their metabolic rates (their horsepower) scale with an exponent of 3⁄4 and their heart rates (their RPMs) with an exponent of -1⁄4.

alive. Like all organisms, we metabolize energy and resources in a highly efficient way in order to combat the continuous fight against the inevitable production of entropy in the form of waste products and dissipative forces that cause physical damage.

A central feature of how life is sustained is the transportation of metabolic energy through space-filling networks across all scales to service and feed cells, mitochondria, respiratory complexes, genomes, and other functional intracellular units,

in organisms the damage with the most serious consequences occurs at the cellular and intracellular levels, which are terminal units of these networks where energy and resources are exchanged as,

Damage occurs across multiple scales through many different mechanisms associated with physical or chemical transport phenomena, but loosely speaking it can be separated into two categories: (1) Classic physical wear and tear due to the viscous drag in the flow, analogous to the wear and tear resulting from ordinary friction when two physical objects move over each other like wearing out your shoes or the tires of your car. (2) Chemical damage from free radicals, which are by-products of the production of ATP in respiratory metabolism.

A free radical is any atom or molecule that has lost an electron and consequently has a positive electric charge, making it highly volatile. Most of this kind of damage is caused by oxygen radicals that react with vital cellular components. Oxidative damage to DNA may be particularly deleterious, because in nonreplicating cells such as in the brain and musculature, it causes permanent damage to transcriptional, and perhaps most important, regulatory regions of the genome. Although the detailed role and extent of oxidative damage in aging remains unclear, it has...

The details of the damage mechanism are not important for understanding many of the general features of aging and mortality because the most relevant damage occurs in invariant terminal units of networks (capillaries and mitochondria, for example) whose properties do not appreciably change with the size of the organism. Consequently, the damage per capillary or mitochondrion is approximately the same regardless of the animal.

Because these networks are space filling, meaning that they service all cells and mitochondria throughout the body of the organism, damage occurs approximately uniformly and relentlessly throughout the organism, explaining why aging is approximately spatially uniform and progresses approximately linearly with age.

Because larger animals metabolize at higher rates following the 3⁄4 power scaling law, they suffer greater production of entropy and therefore greater overall damage,

the most significant damage occurs at the terminal units of networks in capillaries, mitochondria, and cells, and their metabolic rates decrease with the size of the organism following power law scaling with an exponent of 1⁄4.

Cells in larger animals are systematically processing energy at a slower rate than cells in smaller ones.

at the critical cellular level cells suffer systematically less damage at a slower rate the larger the animal, and this resul...

the number of terminal units increasing only as the 3⁄4 power of mass,

Driven by metabolism, the accumulation of damage relentlessly degrades the entire organism.

ultimate threshold for death is reached when the fraction of damaged cells (or molecules such as DNA) relative to the total number in the organ or body reaches a critical value, which is approximately the same for all organisms of the same taxonomic

life span is proportional to the total number of cells divided by the number of terminal units. But the number of terminal units scales with mass with a 3⁄4 power exponent, while the number of cells scales linearly, resulting in life span scaling as the 1⁄4 power of mass, consistent with data.

the mismatch between the scaling of the sources of energy and therefore the sources of damage (the terminal units) and the scaling of the sinks of energy (cells that need to be sustained) has enormous consequences.

the one case, it ensures that we cease growing, and in the other it ensures that larger anima...

Because metabolic rate is proportional to the number of terminal units and these are where most damage occurs,

life span as the ratio of the body mass to its metabolic rate.

life span is inversely proportional to the metabolic rate per unit mass of the organism and therefore inversely proportional to the average metabolic rate of its cells.

that life span can in principle be extended by lowering the body temperature because this lowers cellular metabolic rate and therefore the rate at which damage is incurred. This is a very large effect: I remind you that a modest 2°C decrease in body temperature can result in a 20 percent to 30 percent increase in life span.

Because the theory for the cardiovascular system predicts that heart rates decrease with a 1⁄4 power of mass,