Aperiodic crystal

An aperiodic crystal is a solid in which the atoms are arranged in an orderly way that does not repeat by simple translation. The phrase has two histories. In 1944 the physicist Erwin Schrödinger used it for the material of heredity, which he thought must be a molecule with a different atomic role at each position, and nine years later the structure of DNA showed a molecule that fits the description in one respect and in another does not. Since the 1980s crystallographers have used the same two words, with a precise meaning, for solids such as quasicrystals.

Schrödinger gave the lectures behind the book What Is Life? in February 1943 at Trinity College, Dublin, under the Dublin Institute for Advanced Studies, and the book appeared the next year from Cambridge University Press.^[1] His problem was that the hereditary material is small and must also last. From a paper by Delbrück, Timofeeff-Ressovsky and Zimmer he took an estimate that a gene fills a cube about ten atomic distances on a side, which holds roughly a thousand atoms. A structure so small survives the jostling of heat only if it is a solid held together by chemical bonds.^[1]

An ordinary crystal is such a solid, but it is built by repetition. Schrödinger set two kinds of order side by side: "an ordinary wallpaper in which the same pattern is repeated again and again in regular periodicity", and a masterpiece of embroidery that "shows no dull repetition". Organic chemistry had already come close to the second kind, in molecules where "every atom, and every group of atoms, plays an individual role". He wrote that the chromosome fiber "may suitably be called an aperiodic crystal", and later put the hypothesis in a sentence that begins "We believe a gene" and ends "to be an aperiodic solid". Because every position can differ, the structure could hold what he called a "code-script" for the whole development of the organism.^[1]

The book sold more than 100,000 copies.^[2] Maurice Wilkins had studied electrons in perfect and irregular crystals for his doctorate, and the aperiodic crystal "struck a chord" with him; in 1946 John Randall recruited him to a biophysics laboratory at King's College London. Francis Crick thought parts of the argument flawed, was impressed anyway, and after reading it left wartime military research for the Cavendish Laboratory. James Watson said later that "the notion that life might be perpetuated by means of an instruction book inscribed in a secret code appealed to me".^[2]

In 1953 the second paper of Watson and Crick, on the genetic implications of the double helix, said of the new structure that the sugar and phosphate backbone "is completely regular, but any sequence of the pairs of bases can fit into the structure". It added that "the precise sequence of the bases is the code which carries the genetical information".^[3]

The standing of the book among biologists declined. Max Perutz, who solved the structure of hemoglobin, wrote an assessment for Schrödinger's centenary in 1987 and judged that what was true in the book was not original.^[4]

In 1984 Dan Shechtman and colleagues reported an aluminum-manganese alloy whose electron diffraction showed sharp spots with icosahedral symmetry, a symmetry no periodic lattice can have.^[5] Either such solids were not crystals, or the definition of a crystal had to change. The International Union of Crystallography took the second course. In a report published in 1992 it defined a crystal as any solid with an essentially discrete diffraction diagram, and an aperiodic crystal as a crystal in which three-dimensional lattice periodicity can be considered absent.^[6][7] Quasicrystals, incommensurately modulated structures and incommensurate composites come under it. Shechtman received the Nobel Prize in Chemistry in 2011 for the discovery of quasicrystals.^[8]

The crystallographers' term describes how a solid diffracts, and Schrödinger's describes how a molecule carries a message. X-ray patterns of DNA fibers report mainly on the repeat of the helix, and the sequence, which holds the message, does not show in them.

A nanopore reads an aperiodic polymer in Schrödinger's sense. Threaded through the pore one unit at a time, the polymer lets the ionic current record which units are inside at each moment. Single strands of DNA and RNA were first detected this way in 1996, in a protein channel,^[9] and nanopore sequencing now reads the order of the bases directly.

The stated purpose of the Church of Sequence Space, a cultural side project of Molecular Reality Corporation associated with its mascot Keltar, is "to promote understanding of aperiodic polymers like DNA as the key to solving biology to free our species from disease".^[10] Here a polymer is aperiodic if its units differ along the chain, as they do in DNA, RNA and proteins.

• Church of Sequence Space
• DNA
• Nanopore sequencing