Symmetry breaking from physics to biology
Philip Ball
What is the developmental source of biological form? The question
preoccupied natural philosophers from Aristotle to William Harvey
to Rudolf Virchow, and it remains debated today. Early ideas assumed
that biological form was either already manifest in some way within
the embryo – the preformationist idea, famously illustrated by theDutch mathematician and microscopist Nicolaas Hartsoeker’s
drawing of the homunculus in a sperm in the seventeenth century –or emerged via the guidance of a kind of life force or soul, as Aristotle asserted: theessentially teleological position called epigenesis. We might now regard both theories
as sleights of hand designed to circumvent rather than to explain what is now seen as
an example of symmetry breaking.

With the emergence of modern genetics, questions about form in biology became
questions about genes: the phenotype of the developing organism was considered to beprogrammed by the genotype. DNA could in this view be regarded as a kind of
informational homunculus: form already existed in the embryo, but in an encoded
format, which Erwin Schrodinger famously called the “code-script” of life.

In his approach to the origins of embryogenesis, Alan Turing was thus going against thegrain. It may be partly for this reason that his 1952 paper on morphogenesis had little
impact for several decades. His approach follows the physical scientist’s instinct toexpress the problem at hand in the simplest possible terms, and then to explore what
the minimal requirements are of a model that captures the essential phenomena. Turing
pointed out that the question of how an embryo develops and acquires shape and form– bilateral symmetry, say, and the budding of limbs – seemed indeed to be one of
spontaneous symmetry-breaking.
In this presentation I shall set out to explore how, by expressing the question in thismanner, Turing aligned it with what is arguably the major theme of twentieth-century
physics.

Perhaps the first intimation of the role of symmetry in physical processes wasexpressed in 1894 by Pierre Curie in a paper titled “On symmetry in physicalphenomena”. Here he asked the question: what is the relationship between the physicaland the symmetry properties of a system? Curie stated the fundamental principle ofsymmetry breaking by saying that some phenomena occur when a symmetry isremoved: he said that “asymmetry is what creates the phenomenon”.
In Curie’s doctorate in the early 1890s on magnetism, he reported that ferromagnets
such as iron will lose their magnetism when heated: this falls to zero at a temperature
now called the Curie temperature. The onset of spontaneous magnetization by coolingthrough the Curie temperature occurs when random orientations of the atomic spins
due to thermal motion switch to a collective state of mutual alignment.

This phase transition was studied in the 1920s using the Ising model, a lattice model
developed by Wilhelm Lenz and his student Ernst Ising. It was soon appreciated that thesame model could be used to represent the transition between the gaseous and liquidstates of matter, as investigated in the 1870s by Johannes Diderik van der Waals. Herethe presence of a particle at a point in the lattice denotes the liquid, while its absence
denotes a gas. Cooling a magnet through its Curie temperature then looks equivalent tocooling a fluid through its critical point, where the uniform symmetry of thesupercritical state breaks to permit two distinct phases of differing density.

This connection was arguably the first glimpse of universality in physics: the idea that
there is a deep parallel between systems that look superficially as though they sharenothing in common. It stems from the fact that many-body behaviour often does notdiscriminate between the fine differences in the natures of those bodies: all that matters
are the general features of how they interact, such as how many neighbours feel theinfluence of each body and the dimensionality of the system.
The 1956 proposal by Tsung Dao Lee and Chen Ning Yang that the weak interaction
might break left-right symmetry (parity violation), experimentally confirmed by ChienShiung Wu that same year in experiments on beta decay, opened the path for theunification of the electromagnetic and weak interactions. The idea was developed in the1960s by Sheldon Glashow and Abdus Salam, who had to introduce the symmetry
breaking by hand. Their theory predicted three massive new bosons, later identifiedwith the W and Z bosons that mediate the weak force, along with the massless photon.
In the later 1960s Steven Weinberg showed how this symmetry breaking could happen
spontaneously. The theory was verified by the discovery of the W and Z bosons in
CERN’s Proton-Antiproton Collider in 1983.

This Nobel-winning work on electroweak symmetry breaking was intimately tied up
with the theory of the Higgs field and the Higgs boson. The fundamental insight herecame in the late 1950s from theoretical physicist Yoichiro Nambu, who saw an analogy
between the theory of superconductivity and quantum field theory. The idea wonNambu the 2008 Nobel prize for “the discovery of the mechanism of spontaneous
broken symmetry in subatomic physics”. But Nambu’s work raised new problems, and it
was by resolving them in the early 1960s that Peter Higgs and others concluded thatspace is permeated by the Higgs field, which exerts a drag on the particles and soaffords them mass.
Turing’s work on morphogenesis takes on a different complexion when consideredagainst this context. Symmetry breaking is, one might say, nature’s way of making manyfrom one: of developing complexity out of simplicity. In this way it offers a kind of orderand form for free: a distinction between a here and a there in what was initially ahomogeneous system. Biology, it is now clear, exploits this source of organization toproduce structure at scales well beyond the molecular. Turing’s mechanism is just one
among several now known to feature in the living world at scales ranging from thecellular to the ecological.
The broader question is how the palette of shapes and patterns available fromspontaneous symmetry breaking interacts with natural selection. To what extent canevolution adapt and modify Turing structures, for example? Are all such structures
necessarily adaptive at all? Or are we too readily tempted, when we see order andregularity in biology, to attribute a function to it? Might some of it, at least, represent
nothing more than the intrinsic creative potential in the natural world?