Jiang_Riedel_Parhi_Digital_Logic_with_Molecular_Reactions

Jiang_Riedel_Parhi_Digital_Logic_with_Molecular_Reactions -...

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Digital Logic with Molecular Reactions Hua Jiang, Marc D. Riedel and Keshab K. Parhi Department of Electrical and Computer Engineering, University of Minnesota { hua, mriedel, parhi } @umn.edu Abstract —This paper presents a methodology for implement- ing digital logic with molecular reactions based on a bistable mechanism for representing bits. The value of a bit is not deter- mined by the concentration of a single molecular type; rather, it is the comparison of the concentrations of two complementary types that determines if the bit is “0” or “1”. This mechanism is robust: any small perturbation or leakage in the concentrations quickly gets cleared out and the signal value is not affected. Based on this bistable bit representation, a constituent set of logical components are implemented. These include combinational components – AND, OR, and XOR – as well as sequential components – D latches and D flip-flops. Using these components, two full-fledged design examples are given: a binary counter and a linear feedback shift register. All the constructs consist of sets of coupled chemical reactions with only coarsely specified rate categories (“fast” and “slow”). Given such categories, the computation is robust regardless of the specific reaction rates. The designs are validated through simulations of the chemical kinetics. The simulations show that the constructs produce nearly perfect digital signal values. I. I NTRODUCTION Just as electronic systems implement computation in terms of voltage ( energy per unit charge ), molecular systems com- pute in terms of chemical concentrations ( molecules per unit volume ). Indeed, the field of molecular computation strives for molecular implementations of computational processes – that is to say processes that transform input concentrations of chemical types into output concentrations of chemical types [1], [2], [3], [4], [5], [6]. Yet the impetus of the field is not computation per se ; chemical systems will never be useful for number crunch- ing. Rather the field aims for the design custom, embedded biological “sensors” and “controllers” – viruses and bacteria that are engineered to perform useful tasks in situ , such as cancer detection and drug therapy. Exciting work in this vein includes [7], [8], [9], [10]. As one might expect, the success of these endeavors has mostly been attributable to the experimental expertise of the practitioners in specific domains of biology. However, the field has reached a stage where it is beneficial to bring in expertise from computer engineering and from circuit design. Indeed, there have been several attempts to apply concepts from digital circuit theory to biological engineering. The view that the presence of a type of molecule, such as a protein, corresponds to logical one and its absence corresponds to logical zero, is contained in much of this prior work, either explicitly or implicitly. Numerous types of genetic gates have been proposed [11], [12], [13], [14], [15], [16], [17], This work is supported by an NSF EAGER Grant, #CCF0946601.
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