by David Orrell
At the Institute for Systems Biology in Seattle, our computational group—a biologist, an ex-astrophysicist, a mathematician, and an ex-electrical engineer (the group leader, Hamid Bolouri)— produced a dynamical model of the galactose network.65 The model included fifty-five types of reactions between a range of chemical species, including DNA, RNA, and proteins; stochastic simulations, which tracked interactions between millions of individual molecules, took days to run on a cluster of computers.66 Complex processes—such as the regulation of DNA transcription, the interior dynamics of the cell, and so on—were represented by simple parameterizations. Such models are useful in the scientific process: like an architectural model of a complicated structure, they help the scientist see how things fit together and test whether her assumptions are reasonable.
The aim of our model was to view the galactose network as a piece of engineering and “predict” the role of various features (many of which are also employed in our own bodies). It appeared, for example, that the intricate combination of feedback loops made the yeast less erratic in its response to galactose. This hypothesis was backed up by a laboratory experiment that compared the metabolic responses of two types of yeast: the regular baker’s yeast, and a mutant version whose feedback loops had been disabled using the techniques of genetic engineering.67 For both strains, there was a spread owing to random stochasticity, or noise, with some individual cells reacting more and others less; however, the simpler mutant strain showed a broader, more erratic response, while the regular yeast was more controlled and robust (see figure 5.6 below). If these were archery scores, we would say that the regular strain was a steadier shot.
FIGURE 5.6. Histograms comparing the reaction of regular (wild) and mutant yeast to galactose. The horizontal scale indicates the metabolic response six hours after the yeast was exposed to galactose. The mutant strain has a broad distribution, indicating that some cells underreact and others overreact, while the regular type is less erratic. If the distance from the centre of the horizontal scale denoted the distance from a target, the regular strain would be more consistently accurate.
GLOW-IN-THE-DARK YEAST
Its robustness makes yeast hard to model but very convenient for experimentalists and bakers, who can starve it, store it in the fridge, and subject it to all kinds of abuse before miraculously reviving it by putting it in a more welcoming environment (like a petri dish full of nutrients or a bread dough). Biotechnologists go so far as to inject foreign DNA into the yeast genome, to alter certain genes or show when they are being expressed.
Such experiments show the Promethean nature of modern biology. Stretches of DNA can be bought ready-made from biotech companies and inserted into the cell nucleus. One method uses a jolt of electricity, Frankenstein-style, to shock the yeast into opening its pores. In some cases, the DNA is then taken up by the cell’s own mechanisms and incorporated into the genome. These cells are then bred in petri dishes to create a modified yeast strain.
One way to tell whether a gene is being expressed is to insert the gene for green fluorescent protein (GFP), taken from a type of jellyfish, and ensure that its expression is regulated like that of the gene in question. To produce figure 5.6, the GFP gene was turned on at the same time as one of the genes in the galactose network. When cells eat and metabolize the galactose, they glow green under ultraviolet light. It is also possible to knock out particular genes so they are not expressed at all, or to make them express at specified levels. Such experiments can be used to test predictions about the function of biological systems.
With simple organisms like yeast, it is possible to do controlled experiments to test hypotheses. However, we must distinguish between this type of general prediction and more accurate “point predictions” for individual cells or groups of cells. The positive and negative feedbacks of the galactose network are in dynamic, non-linear balance, and any system that places powerful forces in opposition to each other is inherently hard to model, because an error modelling one of the forces would throw the system out of balance. Small changes in the model produce large effects. The problem is not sensitivity to initial condition (the galactose model is not chaotic), but sensitivity to small changes in parameterization. This property is illustrated for a simple mathematical system in Appendix III (see figure A.5 on page 360).
Because the galactose model parameters could not be precisely known, they had to be selected and balanced against one another to give plausible behaviour in the first place. Changing them randomly, by even a small amount, would throw the model off course and give unrealistic protein concentrations. If a skeptic had insisted that we quantify the uncertainty in the model, by running an ensemble of forecasts with random changes to the parameters, for example, this would have been a misuse of the model, because the very feature that made it robust—the balance of positive and negative feedback loops—also forced us to carefully adjust (i.e., fix) the parameters.68 The model could be used to propose testable hypotheses about the function of the network, which was its aim, but it could not be taken literally as an exact simulation of the real system. As we’ll see in the third part of the book, similar issues are encountered when modelling the positive and negative feedbacks that regulate the earth’s climate.
While the complexity of the galactose pathway is inconvenient for mathematical modellers, it seems entirely reasonable when we consider that yeast cells have evolved over billions of years to survive in a harsh, unpredictable environment. Complex organisms like yeast depend on homeostasis, which keeps their systems in balance.69 Their rate of metabolism, for example, cannot be allowed to vary over too wide a range. To maintain such stability and direction in a shifting, unpredictable environment—to be a steady shot—they must develop sophisticated systems to control noise and must be able to respond in a flexible way to external perturbations. Positive feedbacks (which allow rapid reaction) must be balanced by negative feedbacks (which pull back towards equilibrium). From the outside, while at rest, it may appear that there is little going on, but in fact this peace is the result of a truce between powerful internal forces. The situation was perhaps best described by Heraclitus (who was a critic of the Pythagoreans and their good– evil polarity): “what is at variance comes to terms with itself—a harmony of opposite tensions, as in the bow or the lyre.”70 This tug of war leads in the organism to a balance between creativity and stability, and in models to sensitivity to parameterization. Because complex molecular processes are computationally irreducible, any model parameterization will include errors, which this sensitivity will magnify.
The sense of a dynamic balance also gives an understanding of why individual genes, or even groups of genes, are only partially useful for predicting an organism’s traits. What counts is the behaviour of the whole organism. If any one part is out of balance, then the organism may either adjust itself internally or modify its behaviour to compensate.
One could therefore say that complex organisms are unpredictable because they have evolved to be that way. It’s in their nature. As Pasteur Institute biologist Antoine Danchin writes, a fascinating quality of life is that “even if we do not deny its deterministic character, what we can know about it does not enable us to predict its future. Life is simply the one material process that has discovered that the only way to deal with an unpredictable future is to be able to produce the unexpected itself ” (his italics).71
This does not imply that all organisms evolve towards greater sophistication—the preponderance of life on this planet is unicellular. Still, simple organisms like bacteria can retain the element of surprise, but only by constantly shifting and changing shape. Nowhere is the race for prediction seen more clearly than in the struggle between the human immune system and its microscopic invaders. We return to this subject in Chapter 7.
WATCHING FOR STORMS
Since the development of most human traits from the genotype cannot be predicted either from first principles or from observed trends and correlations, it follows that geneti
c information can provide only a hazy and incomplete picture of human health. Human traits are like the emergent properties of Class IV systems, which defy computation.72 Still, advances in biology will be immensely useful for making certain types of very exact predictions. Just as a new communication technology (the telegraph) led to the development of synoptic weather forecasting, new medical technologies will advance the detection and diagnosis of diseases such as cancer.
Cancers occur when mutations in a cell’s DNA cause it to grow and divide in an unregulated fashion. The particular type depends on the cell (e.g., a skin cell or a blood cell) and on the exact mutation. Microarray technology, which uses nucleic acids to fish for a range of RNA molecules or DNA segments in a prepared sample, can automatically determine what genes are being expressed by a cancer.73 Its DNA can be identified just like a criminal’s. The newer field of proteomics aims to do the same thing for proteins. In some cases, this knowledge will help determine who will benefit from particular therapies. This is valuable to doctors and patients, as well as drug companies (especially since the cost of developing a new drug can be hundreds of millions of dollars).74 Cancer is nature’s reductionist, and increasingly it can be confronted and cured using reductionist science. It is the medical equivalent of looking over the horizon for storms—and it has the same promise to save lives.
It is already possible to purchase a genetic risk-assessment test that predicts our susceptibility to a wide range of diseases. These predictions are based on statistical correlations of certain gene forms with conditions like heart disease or cancer; they may also help doctors tailor treatments or diets to the genetic profile of a particular patient.75 Such advice should be interpreted with care. Broad statistics don’t necessarily apply to an individual with a unique history, environment, and mix of genes. As the late biologist and science writer Stephen Jay Gould said, while himself fighting cancer, “If both genes and culture interact—of course they do—you can’t then say it’s 20 percent genes and 80 percent environment. . . . The emergent property is the emergent property and that’s all you can ever say about it.”76 Also, risk assessments become relevant (rather than something to obsess over) only if—like the dangers of smoking or not wearing seatbelts—they are large enough to make it worth modifying our behaviour.
Personal genetic information will have to be closely protected— like any other medical or identifying data—but the current anxiety about the potential misuse of genetic testing seems to be based on an exaggerated idea of its effectiveness. As Columbia University’s Joseph Terwilliger has said, “In many ways, scientists overhyped the information in the genome, or at least what we know about it, to the point where now people are getting unnecessarily nervous about societal implications.”77 Genes are not destiny, and their
omens and portents are usually vague and sometimes deceiving. Their role is similar to that which Johannes Kepler assigned to the stars: “In what manner does the countenance of the sky at the moment of a man’s birth determine his character? It acts on the person during his life in the manner of the loops which a peasant ties at random around the pumpkins in his field: they do not cause the pumpkin to grow, but they determine its shape. The same applies to the sky: it does not endow man with his habits, history, happiness, children, riches or a wife, but it moulds his condition.”78 Like astrology and other forms of prediction, genetic testing and counselling will undoubtedly make extremely good business. A 2003 article in Nature Genetics observed that “the predictive power and mystique associated with genetics, consumers’ desire to take control of their health and be proactive, and the ease of advertising and ordering tests on the Internet combine to create a powerful incentive for companies to continue developing and promoting genomic profiling regardless of whether the tests have been validated and proven useful.”79
Most diseases that have a hereditary component are influenced in their development by a broad range of genetic and environmental factors (two of the most important are hunger and poverty—health often depends more on economics than on genetics). These interact and develop in complex, unpredictable, and often antagonistic ways. We shouldn’t anticipate the arrival of a magical machine that will fly into someone’s future and predict whether he will drop dead of a heart attack in seventeen years. Traits such as personality are even harder to pin down. My newborn child may have a quarter of my father’s genes, but I have no idea whether she will have 25 percent of his sense of humour, or even what that would mean. Uncertainty, it seems, is in our blood.
This may seem disappointing. As Lewontin wrote, “Saying that our lives are the consequences of a complex and variable interaction between internal and external causes does not concentrate the mind nearly so well as a simplistic claim; nor does it promise anything in the way of relief for individual and social miseries. It takes a certain moral courage to accept the message of scientific ignorance and all that it implies.”80 As we will see, uncomputability is a stern and unforgiving companion. On the other hand, perhaps it is no bad thing if nature maintains a little mystery—after all, past attempts at genetic prediction have a long, dark shadow side.81
Like weather forecasting, the prediction of complex traits or diseases appears to defy our computational ability: there is no Apollo’s arrow to fly into an organism’s future. We cannot model the trajectory of a life the way we can the arc of a planet across the sky. The issues are perhaps best summarized by John Maynard Keynes, who wrote in 1933, “We are faced at every turn with the problems of Organic Unity, of Discreteness, of Discontinuity—the whole is not equal to the sum of the parts, comparisons of quantity fail us, small changes produce large effects, and the assumptions of a uniform and homogeneous continuum are not satisfied.”82 But Keynes, an economist, wasn’t talking about genetics. He was talking about the Great Depression. In the next chapter, we examine how mathematicians and scientists have modelled another great biological system, the economy.
6 BULLS AND BEARS
PREDICTING OUR ECONOMY
Rules by their nature are simple. Our problem is not the complexity of our models but the far greater complexity of a world economy whose underlying linkages appear to be in a continual state of flux.
—Alan Greenspan, chairman of the U.S. Federal Reserve (1987–2006)
To me our knowledge of the way things work, in society or in nature, comes trailing clouds of vagueness.
—Kenneth Arrow, Nobel laureate in economics
ANATOMY OF A STORM
In 1720, an entrepreneur set up a company in England for the mysterious purpose of “carrying on an undertaking of great advantage, but nobody to know what it is.” Five thousand shares of £100 would be issued. The public could get in at the ground floor by making a deposit of £2 per share. In a month’s time, the technical details of the project would be filled in and a call made for the remaining £98. The promised payoff was generous: £100 per year, per share.
The next morning, the man opened his office in London’s financial district to admit the deluge of investors who were waiting outside. At the end of the day, he counted his takings, saw he had sold a thousand shares, and promptly left for Europe.1
In the same year, other company prospectuses offered even less investor value. One tried to raise a million pounds to fund the development of a “wheel of perpetual motion”; others promoted techniques for “extracting silver from lead,” and for turning “quicksilver into a malleable fine metal.” But the one that caused the most damage, and created the almost hysterical environment for these “bubble” investments, as they came to be known, was a much larger project that was sanctioned by the highest levels of government, all the way up to King George I.
The South Sea Company was established in 1711 by Robert Harley, Earl of Oxford, to help fund the national debt. In return, it was granted a permanent monopoly on trade with Mexico and South America. Everyone knew these places harboured inexhaustible supplies of gold, and investors were easily found. The actual trading was slow to get started—
the king of Spain restricted traffic to only one ship per year, and the first didn’t set sail until 1717—but the less that was delivered, the more enormous seemed the potential.
None of the company directors had experience with South Seas trade. Safely ensconced in their London office, they managed to arrange some slave-trade voyages, but these weren’t particularly profitable. Preferring to concentrate on financial schemes, and fuelled by the public’s love of gold, they made a bid to triple their share of the national debt to almost the full amount, at better terms than those offered by the Bank of England. Robert Walpole from the bank protested against the scheme, telling the House of Commons that it would “decoy the unwary to their ruin, by making them part with the earnings of their labour for a prospect of imaginary wealth.”
His Cassandra-like warnings went unheeded. Eased along by a number of large bribes, in the form of offerings of stock to politicians and influential people like King George’s mistresses, the company’s proposal was accepted by the government. Rumours of increasing Latin American trade spread like wildfire through the coffeehouses in Cornhill and Lombard streets, and in 1720 the stock rose yeastily, from £175 in February to over £1,000 by June. By then, scores of other businesses had been set up to cash in on the growing public interest in stock-market investment, which seemed to be making so many rich. As Charles Mackay, in his book Extraordinary Popular Delusions and the Madness of Crowds, commented: “The public mind was in a state of unwholesome fermentation. Men were no longer satisfied with the slow but sure profits of cautious industry.”
