Notes on stochastic (bio)-logic gates: the role of allosteric cooperativity

Recent experimental breakthroughs have finally allowed to implement in-vitro reaction kinetics (the so called {\em enzyme based logic}) which code for two-inputs logic gates and mimic the stochastic AND (and NAND) as well as the stochastic OR (and NOR). This accomplishment, together with the already-known single-input gates (performing as YES and NOT), provides a logic base and paves the way to the development of powerful biotechnological devices. The investigation of this field would enormously benefit from a self-consistent, predictive, theoretical framework. Here we formulate a complete statistical mechanical description of the Monod-Wyman-Changeaux allosteric model for both single and double ligand systems, with the purpose of exploring their practical capabilities to express logical operators and/or perform logical operations. Mixing statistical mechanics with logics, and quantitatively our findings with the available biochemical data, we successfully revise the concept of cooperativity (and anti-cooperativity) for allosteric systems, with particular emphasis on its computational capabilities, the related ranges and scaling of the involved parameters and its differences with classical cooperativity (and anti-cooperativity)

Optimization of Enzymatic Logic Gates and Networks for Noise Reduction and Stability

Biochemical computing attempts to process information with biomolecules and biological objects. In this work we review our results on analysis and optimization of single biochemical logic gates based on enzymatic reactions, and a network of three gates, for reduction of the "analog" noise buildup. For a single gate, optimization is achieved by analyzing the enzymatic reactions within a framework of kinetic equations. We demonstrate that using co-substrates with much smaller affinities than the primary substrate, a negligible increase in the noise output from the logic gate is obtained as compared to the input noise. A network of enzymatic gates is analyzed by varying selective inputs and fitting standardized few-parameters response functions assumed for each gate. This allows probing of the individual gate quality but primarily yields information on the relative contribution of the gates to noise amplification. The derived information is then used to modify experimental single gate and network systems to operate them in a regime of reduced analog noise amplification.Comment: 7 pages in PD