Sequence space

In evolutionary biology and molecular engineering, sequence space is the set of all possible sequences of a given length for a chain molecule such as DNA, RNA or protein, arranged so that two sequences that differ at a single position are neighbors. A mutation is a step to a neighboring point, and evolution is a walk through the space. The idea was introduced by John Maynard Smith in 1970 under the name "protein space".^[1]

A chain of length L built from an alphabet of k letters has k^L possible sequences. Each has L(k − 1) neighbors, one for each other letter at each position, and the distance between two sequences is the number of positions at which they differ, the Hamming distance used in coding theory. For binary strings the space is a hypercube: the eight strings of length three sit at the corners of an ordinary cube, and strings of length L at the corners of a cube in L dimensions. The spaces of biology have the same structure with four letters for nucleic acids and twenty for proteins.

The spaces are very large and very high-dimensional, which makes them unlike any space a person can picture. A protein of 100 amino acids can be written in 20¹⁰⁰, about 1.3 × 10¹³⁰, ways, and a typical protein of 300 in about 2 × 10³⁹⁰. Yet any two of the 100-residue sequences are at most 100 steps apart, and each has only 1,900 neighbors.^[a] Most points in the space are not proteins at all in the useful sense: they fold into nothing and do nothing.

Maynard Smith's letter answered an objection published in Nature the year before by the plant physiologist Frank Salisbury, who calculated that the number of possible genes was so vast that natural selection could never have found working ones by chance.^[2] Maynard Smith replied that evolution does not search the space at random. It only needs a connected network of functional proteins, each one mutation from the next, along which selection can move without crossing a gap. He illustrated the idea with a word game, changing WORD to GENE one letter at a time through words that all mean something: WORD, WORE, GORE, GONE, GENE.^[1]

The geometry soon gained more uses. Manfred Eigen's theory of the quasispecies (1971) treats a population of replicating molecules, such as an RNA virus, as a cloud of related sequences around a master sequence, and calculates how high a mutation rate can be before the cloud spreads out and loses its center.^[3] Giving each point a fitness turns the space into a fitness landscape, the picture Sewall Wright had drawn in 1932, of peaks and valleys. Studies of RNA in the 1990s found that very many sequences fold into the same shape, and that the sequences sharing a shape form networks that reach across the whole space, so that a population can drift a long way without losing its function.^[4]

Experiments can sample only a vanishing fraction of the space. In 2001 Anthony Keefe and Jack Szostak made a library of 6 × 10¹² random proteins, each 80 amino acids long, and selected the ones that bind ATP. They found four new families of ATP-binding proteins, unrelated to one another or to any known protein.^[5] The space of 80-residue proteins holds about 10¹⁰⁴ sequences, so the library covered roughly one point in 10⁹¹. Directed evolution, for which Frances Arnold shared the 2018 Nobel Prize in Chemistry, searches the other way: it starts from a protein that works and walks outward through its neighbors, keeping the best variant of each round.

Writers have pictured the same space as a library. Jorge Luis Borges's story "The Library of Babel" (1941) describes a library containing every possible book of 410 pages, almost all of them gibberish. Daniel Dennett, in Darwin's Dangerous Idea (1995), named the corresponding collection of every possible genome the Library of Mendel.

The phrase gives its name to the Church of Sequence Space, a side project of Molecular Reality Corporation whose stated purpose is "to promote understanding of aperiodic polymers like DNA as the key to solving biology to free our species from disease".^[6] "Aperiodic" comes from Erwin Schrödinger's description of the gene as an aperiodic crystal. The church's mascot, Keltar, is said on his profile page to have "traversed the sequence spaces of the multiverse to guide civilizations toward life-saving technological singularities".^[7]

The church's founding text of 2013, the Book of the Church of Sequence Space, uses the words only in proper names, such as Sequence Space Explorer, the first of its five modules. That module later became a character path in a draft of the company's quiz dungeon, with the titles "The Cartographer of Codons, The Architect of Aperiodic Polymers, The Voyager to Xenobiology's Edge".^[6] The company's science quiz, JeoPOREdy!, has a category called Aliens of Sequence Space, and one of the congratulations its host may offer after a correct answer is "By the sequence space, you nailed it!"^[6]

• Nanopore sequencing
• Protein sequencing
• AlphaFold