Enzyme-Based Reversible Logic Gates Operated in Flow Cells

Abstract

Reversible logic gates, such as Feynman gate (Controlled NOT), Double Feynman gate, Toffoli gate and Peres gate, with 2-input/2-output and 3-input/3-output channels, were realized using reactions biocatalyzed by enzymes and performed in flow systems. The flow devices were constructed using a modular approach, where each flow cell was modified with one enzyme that biocatalyzed one chemical reaction. Assembling the biocatalytic flow cells in different networks, with different pathways for transporting the reacting species, allowed the multi-step processes mimicking various reversible logic gates. The chapter emphasizes “logic” reversibility but not the “physical” reversibility of the constructed systems. Their advantages and disadvantages are discussed and potential use in biosensing systems, rather than in computing devices, is suggested.

Appendix

This section is addressed to the readers interested in technical details of the experimental realization of the reversible logic gates described above.

2.1.1 Chemicals and Materials

Enzymes and their substrates used in the biocatalytic reactions were specified in Sect. 2.2. Results and Discussion (second paragraph).

Other chemicals used for the immobilization procedure and being components of reacting solutions: pepsin (E.C. 232.629.3) from porcine gastric mucosa, glutaric dialdehyde, poly(ethyleneimine) solution (PEI) (average M$_{\text {w}}$ ca. 750,000), 2-amino-2-hydroxymethyl-propane-1,3-diol (Tris-buffer), $2,2'$-azino-bis(3-ethylbenzothiazoline-6-sulfonic acid) diammonium salt (ABTS), K$_{3}$[Fe(CN)$_{6}$] and K$_{4}$[Fe(CN)$_{6}$]. The chemicals listed above and other standard inorganic/organic reactants were purchased from Sigma-Aldrich and used as supplied. Ultrapure water (18.2 M$\Omega \cdot$ cm) from NANOpure Diamond (Barnstead) source was used in all of the experiments.

2.1.2 Instruments and Devices

Flow cells ($\upmu$-Slide III 3in1 Flow Kit; ibidi GmbH) were used for the biocatalytic reactions. A Shimadzu UV-2450 UV-Vis spectrophotometer with flow-through quartz cuvettes (1 cm optical pathway) connected to the tubing of the flow device was used for all optical measurements. The reacting solutions were pumped through the flow cells and spectrophotometer cuvettes with the help of a peristaltic pump (Gilson Minipuls 3) connected with polyethylene tubing, 1 mm internal diameter.

2.1.3 Immobilization of Enzymes in the Flow Cells

Before any experimental data were realized, the flow cells were flushed with concentrated sulfuric acid to remove residual physical adsorption of PEI left on the cell surface from previous experiments. After this initial preparatory step, all subsequent cleanings were conducted with the following method. The flow cells were washed with a minimum of 10 mL of deionized water and then reacted with pepsin solution, 0.5 mg/mL, in 0.1 M phosphate buffer, pH 2.0, for 1 h. Then, the cells were washed with a minimum of 10 mL of deionized water. These cleaning steps aimed at removing remnant enzymes from previous experiments and prepared the cell surface for adsorption of PEI. Then, the flow cells were treated with a PEI solution (2 % v/v) for 1 h and then, thoroughly washed with 5 mL of deionized water, resulting in physical adsorption of PEI on polystyrene and providing the amino groups needed for the enzyme immobilization. Then, the amino-functionalized surface was reacted with glutaric dialdehyde (5 % v/v) for 1 h; after that, the surface was washed with 5 mL of deionized water to remove non-reacted glutaric dialdehyde. The enzyme solutions were reacted with the flow cells and the wells that were activated with glutaric dialdehyde for 1 h and then, the cells were thoroughly washed with Tris-buffer (0.1 M, pH 7.1) to remove non-reacted enzymes from the cells. The following enzyme concentrations were used for preparing the logic gates: (i) Feynman gate: AP ca. 500 units/mL; G6PDH ca. 280 units/mL; LDH ca. 600 units/mL, (ii) Double Feynman gate: GDH ca. 46 units/mL; G6PDH ca. 14 units/mL; LDH ca. 30 units/mL, (iii) Toffoli gate: GDH ca. 140 units/mL; G6PDH ca. 280 units/mL; LDH ca. 340 units/mL; GOx ca. 140 units/mL; HRP ca. 120 units/mL, (iv) Peres gate: GDH ca. 190 units/mL; GOx ca. 665 units/mL; LDH ca. 343 units/mL; HRP ca. 400 units/mL; Diaph ca. 66 units/mL. This procedure resulted in the enzymes covalently bound to the adsorbed PEI through Schiff-base bonds. The flow cell devices with the immobilized enzymes demonstrated reproducible performance for at least two days allowing pumping of the input solutions over long period of time, thus proving stable immobilization of the enzymes and preserving their biocatalytic activity.

2.1.4 Optimization of the Input Concentrations

The input concentrations were experimentally optimized for the specific enzyme activity in the flow cells. The optimization was aimed at the output signals with the comparable intensity upon application of different combinations of the input signals. Balancing output signals for XOR gates, when optimizing the reversible gates, was particularly important.

The following optimized input concentrations were considered as logic 1 values:

Feynman gate: Input A (PNPP + Pyr) 10 mM $+$ 1 mM, respectively, Input B (G6P) 6 mM.

Double Feynman gate: Input A (Pyr) 1.46 mM, Input B (G6P) 2.22 mM, Input C (Glc) 0.6 mM.

Toffoli gate: Input A (Glc) 0.6 mM, Input B (NAD$^{+})$ 2.75 mM, Input C (Pyr) 1.1 mM.

Peres gate: Input A (NADH) 0.02 mM, Input B (Glc) 10 mM, Input C (H$_{2}$O$_{2})$ 0.7 mM.

Logic 0 value for all input signals was defined as the absence of the corresponding chemicals (meaning their zero physical concentration in the background solutions).

2.1.5 Flow Cell Performance and the Output Signal Measurements

The enzyme-modified flow cells were activated with solutions containing the input signals applied in all possible logic combinations (4 variants for Feynman gate and 8 variants for all other gates). The solutions also included non-variable reacting components which had the same initial concentrations for all combinations of the inputs signals. The solution compositions used for different gate are listed below:

Feynman gate

The input signals (represented with PNPP + Pyr and G6P solutions also containing non-variable NADH (0.4 mM) and NAD$^{+}$ (10 mM) cofactors were pumped through the flow system with the volumetric rate of 50 $\upmu$L/min. Optical absorbance measurements were performed for the Identity gate channel (Output P) at $\lambda = 420$ nm characteristic of p-nitrophenol (PNP) and for the XOR gate channel (Output Q) at $\lambda = 340$ nm characteristic of NADH. The reference channel (cuvette) of the spectrophotometer was filled with the background (“machinery”) solution containing NADH (0.4 mM) and NAD$^{+}$ (10 mM), thus allowing the absorbance change measurements versus the composition of the background solution.

Double Feynman gate

The input signals (represented with Pyr, G6P and Glc solutions also containing non-variable NADH, 0.4 mM, and NAD$^{+}$, 5.0 mM) were pumped through the flow system with the volumetric rate of 50 $\upmu$L/min. Optical absorbance measurements were performed for the Identity and two XOR gate channels at $\lambda = 340$ nm characteristic of NADH. The reference channel (cuvette) of the spectrophotometer was filled with the background (“machinery”) solution containing NADH (0.4 mM) and NAD$^{+}$ (5.0 mM), thus allowing the absorbance change measurements versus the composition of the background solution.

Toffoli gate

The input signals (represented with Pyr, Glc and NAD$^{+}$ solutions also containing non-variable NADH, 0.375 mM, G6P, 0.4 mM, ABTS, 4.0 mM) were pumped through the flow system with the volumetric rate of 50 $\upmu$L/min. Optical absorbance measurements were performed for the GOx/HRP Identity gate at $\lambda = 415$ nm characteristic of the oxidized form of ABTS (ABTS$_{\text {ox}})$, while the G6PDH Identity gate and the AND/XOR gate channels were measured at $\lambda = 340$ nm characteristic of NADH. The reference channel (cuvette) of the spectrophotometer was filled with the background (“machinery”) solution containing NADH (0.375 mM), G6P (0.4 mM) and ABTS (4.0 mM), thus allowing the absorbance change measurements versus the composition of the background solution.

Peres gate

The input signals (represented with NADH, Glc and H$_{2}$O$_{2 }$solutions also containing non-variable K$_{4}$[Fe(CN)$_{6}$] 2.0 mM, K$_{3}$[Fe(CN)$_{6}$] 1.0 mM and Pyr 0.065 mM) were pumped through the flow system with the volumetric rate of 25 $\upmu$L/min. Optical absorbance measurements were performed at $\lambda = 420$ nm characteristic of K$_{3}$[Fe(CN)$_{6}$]. The reference channel (cuvette) of the spectrophotometer was filled with the background (“machinery”) solution containing K$_{4}$[Fe(CN)$_{6}$] 2.0 mM, K$_{3}$[Fe(CN)$_{6}$] 1.0 mM and Pyr 0.065 mM, thus allowing the absorbance change measurements versus the composition of the background solution.