Computational functions in biochemical reaction networks

Abstract

In prior work we demonstrated the implementation of logic gates, sequential computers (universal Turing machines), and parallel computers by means of the kinetics of chemical reaction mechanisms. In the present article we develop this subject further by first investigating the computational properties of several enzymatic (single and multiple) reaction mechanisms: we show their steady states are analogous to either Boolean or fuzzy logic gates. Nearly perfect digital function is obtained only in the regime in which the enzymes are saturated with their substrates. With these enzymatic gates, we construct combinational chemical networks that execute a given truth-table. The dynamic range of a network's output is strongly affected by "input/output matching" conditions among the internal gate elements. We find a simple mechanism, similar to the interconversion of fructose-6-phosphate between its two bisphosphate forms (fructose-1,6-bisphosphate and fructose-2,6-bisphosphate), that functions analogously to an AND gate. When the simple model is supplanted with one in which the enzyme rate laws are derived from experimental data, the steady state of the mechanism functions as an asymmetric fuzzy aggregation operator with properties akin to a fuzzy AND gate. The qualitative behavior of the mechanism does not change when situated within a large model of glycolysis/gluconeogenesis and the TCA cycle. The mechanism, in this case, switches the pathway's mode from glycolysis to gluconeogenesis in response to chemical signals of low blood glucose (cAMP) and abundant fuel for the TCA cycle (acetyl coenzyme A).

Strong Turing Completeness of Continuous Chemical Reaction Networks and Compilation of Mixed Analog-Digital Programs

“…Then we derive from the proof of these results a compiler of behavioural specifications 6 into elementary reaction systems, without prejudging of their biochemical implementation, by enzymatic reactions [37], DNA [13] or RNA for instance.…”

“…These constraints are necessary conditions for the existence of a set of biochemically realizable reactions that react according to the dynamics y = p(y). Note however that we shall not discuss here the choice of their possible implementations by particular biochemical devices, such as DNA polymers [40], DNA double strands [33] or enzymatic reactions [19,37] as this is beyond the scope of this paper.…”

Implementing Arithmetic and Other Analytic Operations by Transcriptional Regulation

“…The lac operon, for example, is often described as implementing a simple logical rule-the gene is on when lactose is present and glucose is absent [6]. Theoretically, a variety of nonlinear chemical systems, including gene regulatory systems, are capable of implementing arbitrary logical rules [7][8][9][10][11]. Networks of such systems can implement finite state machines [12], and families of such networks of increasing size can be said to implement arbitrary Turing-computable functions [13,14].…”

Computation in Gene Networks

“…In a related series of papers it is shown both theoretically and experimentally that chemical reactions can be used to implement Boolean logic and neural networks ͑see Ref. 11 and references therein͒.…”