Turing, von Neumann, and the computational architecture of biological machines

Abstract

In the mid-1930s, the English mathematician and logician Alan Turing invented an imaginary machine which could emulate the process of manipulating finite symbolic configurations by human computers. His machine launched the field of computer science and provided a foundation for the modern-day programmable computer. A decade later, building on Turing's machine, the American-Hungarian mathematician John von Neumann invented an imaginary self-reproducing machine capable of open-ended evolution. Through his machine, von Neumann answered one of the deepest questions in Biology: Why is it that all living organisms carry a self-description in the form of DNA? The story behind how two pioneers of computer science stumbled on the secret of life many years before the discovery of the DNA double helix is not well known, not even to biologists, and you will not find it in biology textbooks. Yet, the story is just as relevant today as it was eighty years ago: Turing and von Neumann left a blueprint for studying biological systems as if they were computing machines. This approach may hold the key to answering many remaining questions in Biology and could even lead to advances in computer science.

Keywords: DNA polymerase; biological computation; finite state machine; molecular computation; structural biology.

Fig. 1.

(Left) Flier used to advertise the Hixon symposium in 1948. (Right) Photograph of the participants. From left to right in the back row are Henry W. Brosin, Jeffress, Paul Weiss, Donald B Lindsley, John von Neumann, J. M. Nielsen, R. W. Gerard, H. S. Liddell. Front row Ward C Halstead, K. S. Lashley, Heinrich Klüver, Wolfgang Köhler, and R. Lorente de No. Images kindly provided by Loma Karklins, archivist at Caltech.

Fig. 2.

(Left) Canonical Watson–Crick base pairs form a rectangular shape, referred to as the “Watson–Crick geometry.” (Middle) Noncanonical mismatches such as G–T and A–C form non-Watson–Crick geometries referred to as the “wobble” conformation. (Right) Mismatches can adopt a Watson–Crick-like geometries through tautomerization of the bases (indicated with a star).

Fig. 3.

Mechanism of nucleotide incorporation by a high-fidelity DNA polymerase. Note that the mechanism can vary from polymerase to polymerase. The given example typifies the mechanisms of polymerase β and ε (–25). (A) Correct incorporation of Watson–Crick base-pairs. (B) The induced-fit subroutine increases the fidelity of nucleotide incorporation by high-fidelity polymerases. (C) Nucleotide misincorporation through tautomeric shifts of nucleobases can lead to copying errors which if uncorrected can result in mutations.

Fig. 4.

DNA polymerase a finite-state machine. (A) State diagram for the DNA polymerase nucleotide incorporation finite-state machine. q₀, q₁, q₂, q₃, and q₄ refer to the states of DNA polymerase, open, closed, catalytic, ajar, and halt, respectively. The inputs are MA = match (rectangular); MM = mismatch (irregular); IN = incorporated; and BL = blank. Note that q₀ processes the input “IN” by translocating (Trans) and reverting back to the state q₀. (B) Graphical description of DNA polymerase as a computational machine.

Fig. 5.

Hierarchical organization of automata and biocomputing machines.