Concatenated logic gates using four coupled biocatalysts operating in series

Abstract

The assembly of three concatenated enzyme-based logic gates consisting of OR, AND, XOR is described. Four biocatalysts, acetylcholine esterase, choline oxidase, microperoxidase-11, and the NAD⁺-dependent glucose dehydrogenase, are used to assemble the gates. Four inputs that include acetylcholine, butyrylcholine, O₂, and glucose are used to drive the concatenated-gates system. The cofactor NAD⁺, and its reduced 1,4-dihydro form, NADH, are used as a reporter couple, and these provide an optical output for the gates. The modulus of the absorbance changes of NADH is used as a readout signal.

The hardware of computers consists of parallel and serial logic-gate operations that are triggered by electronic inputs. These functions may be duplicated by appropriately designed chemical or biological systems. Different molecular and supramolecular assemblies that operate as logic gates and perform molecular-scale arithmetic operations were discussed (1–9). Similarly, biomolecules such as nucleic acids or proteins were used as active components that perform logic-gate operations (10–15). Gene-based artificial circuits acting as bistable toggle switches (16) or oscillators (17) were developed, and coupled enzyme/DNA systems that perform programmable biochemical transformations that mimic basic computing of finite automaton were reported (17). The use of enzymes as the active components for logic gate functions is specifically intriguing because numerous biocatalytic cycles in nature rely on information processing, revealing similarities to computer devices. Although the function of enzyme networks as mimics of Boolean logic gates was discussed (18), and the potential use of enzymes as building units of high-density computing architectures was addressed (19), the experimental work that validates biocatalyst-stimulated logic gate operations is quite scarce, and lacks the desired complexity that resembles computers. Single enzyme-based logic-gate operations were reported. For example, the dynamic conformational changes of malate dehydrogenase in response to Mg⁺ and Ca²⁺ ions acting as inputs was used to develop a XOR gate (20). Also, a modified enzyme and its inhibitor were used as inputs that activated an AND gate (21). Recently, we have reported on the assembly of coupled biocatalytic systems that mimic OR, XOR, AND, or InhibAND logic-gate functions (22), and the use of these systems for elementary arithmetic operations (half-adder and half-subtractor) was demonstrated (23). In none of these systems was the consecutive operation of several gates that operate in series demonstrated. This feature is, however, essential to develop any future “computer-like” function of enhanced complexity. Here, we report on the assembly of a four-enzyme-coupled system that includes four inputs and performs in series three logic-gate operations OR, AND, and XOR.

Results and Discussions

The system and its operation is depicted in Fig. 1A and consists of the four biocatalysts, acetylcholine esterase (AChE), choline oxidase, microperoxidase-11 (MP-11), and glucose dehydrogenase (GDH), coupled to its cofactor pair NAD⁺/NADH. Acetylcholine (input A) or butyrylcholine (input B) are hydrolyzed by AChE to form choline that acts as the output of the first OR gate, Fig. 1B. Choline generated by the OR gate and O₂ (input C) activate the AND gate that yields betaine aldehyde and H₂O₂ as products. Note that H₂O₂ is formed only in the presence of O₂ (Fig. 1B). The two biocatalysts MP-11 and GDH perform the most complicated XOR gate, where two “1” inputs yield a “0” output. The inputs for the XOR gate are H₂O₂, the product of the AND gate, and glucose (input D). The operation of the sequence of gates is read out by following the concentration ratio of the NAD⁺/NADH cofactors by following the absorbance at λ = 340 nm. That is, if only H₂O₂ is activating the system and no glucose is added, MP-11 catalyzes the oxidation of NADH to NAD⁺, and NADH is depleted. Similarly, when only glucose is added and the AND gate does not generate H₂O₂, the GDH-biocatalyzed oxidation of glucose reduces NAD⁺ to NADH, and the absorbance of NADH increases. When H₂O₂ and glucose (input D) are activating the MP-11/GDH couple, the MP-11-catalyzed oxidation of NADH to NAD⁺ is compensated by the GDH/glucose-mediated reduction of NAD⁺ to NADH. Thus, no net change in the NADH concentration would be detected (as required from an XOR gate). The modulus of absorbance ‖A‖ of the NADH acts as the readout signal for the XOR gate operation.

Fig. 1.

Scheme describing the operation of concatenated logic gates based on four coupled biocatalysts (A) and circuitry for the concatenated four-enzyme system (B).

Fig. 2 shows the absorbance changes of NADH as a result of the operation of the series of gates in the presence of the four inputs. Note that these results represent the properties of an optimized composition of the concentrations of the different biocatalysts and the respective inputs that take into account the specific activities of the different biocatalysts. Fig. 2A, curve a, shows the absorbance features of the NADH in the system before the activation of the different biocatalysts by any of the inputs. This absorbance may be considered as a reference for the operation of the different gates. Fig. 2A, curve b, shows the absorbance features upon activation of the OR gate by acetylcholine and, thus, activation of the AND gate by choline and O₂ to yield H₂O₂. The two biocatalysts MP-11 and GDH are activated by H₂O₂ and glucose as inputs. Because the MP-11-catalyzed oxidation of NADH is compensated by the GDH-catalyzed oxidation of glucose with the concomitant generation of NADH, no significant change in the absorbance of NADH is detected. Thus, the system inputs (1, 0, 1, 1) lead to a “0” output in the XOR gate. Fig. 2B presents the output of the concatenated gates in the form of an absorbance bar presentation. The output for state (1, 0, 1, 1) is thus given by bar b. Similarly, exchange of acetylcholine with butyrylcholine as the input of the OR gate yields the choline product that, together with O₂, activates the AND gate, leading to the H₂O₂ product. As before, the MP-11-catalyzed oxidation of NADH by H₂O₂ is compensated by the GDH-mediated oxidation of NAD⁺, and, thus, no significant net change in the NADH absorbance is detected. Accordingly, the system state (0, 1, 1, 1) yields a “0” output (Fig. 2B, bar c). When both inputs of the OR gate are introduced and all other inputs activate the respective gates, state (1, 1, 1, 1), no significant change in the absorbance of NADH is observed, as expected (Fig. 2A, curve d, and 2B, bar d). Naturally, when only O₂ acts as input and no other input triggers any of the gates, state (0, 0 1, 0), none of the biocatalyzed reactions occurs, no change in the absorbance of NADH is observed, and, thus, the output of the system is “0” (Fig. 2A, curve e, and 2B, bar e). When no inputs trigger the “OR” gate and only the O₂ and glucose act as inputs, system state (0, 0, 1, 1), no choline is formed, and, thus, no H₂O₂ is generated. As a result, only the GDH-catalyzed oxidation of glucose proceeds, with the concomitant formation of NADH, as evidenced by the increase in the absorbance of the system (Fig. 2A, curve f, and 2B, bar f). Thus, the output of the XOR gate is “1.” Activation of the system by the acetylcholine, or butyrylcholoine, in the presence of O₂ but in the absence of glucose, states (1, 0, 1, 0) or (0, 1, 1, 0) lead to the formation of choline (in the OR gate) and the subsequent generation of H₂O₂ (in the AND gate). The H₂O₂ that is generated activates the MP-11-catalyzed oxidation of NADH. In the absence of glucose as input, this condition leads to the depletion of the NADH absorbance (Fig. 2A, curves g and h, respectively) yielding a change in the absorbance modules values, as presented in Fig. 2B, bars g and h, respectively. Thus, these states lead to an output “1” of the XOR gate. Naturally, when the two inputs, acetylcholine and butyrylcholine, activate the OR gate, and the AND gate is activated by O₂, the formation of H₂O₂ proceeds. In the absence of glucose, however, the generated H₂O₂ depletes the absorbance of NADH, leading to a “1” output (Fig. 2A, curve i, and 2B, bar i). Note that, in Fig. 2A, curves a, f, and e, in addition to the absorbance band of NADH at λ = 340 nm, an additional band at 410 nm is observed. This band is attributed to the absorbance of the heme center present in MP-11. In Fig. 2A, curves b–d and g–i, the band at λ = 410 nm is depleted. This result is consistent with the fact that the biocatalytically generated H₂O₂ forms an oxocomplex with the heme center of MP-11 as an intermediate species that oxidizes NADH. The latter oxocomplex lacks an absorbance in this spectral region (24). The truth table for the concatenated gates system that operates in the presence of O₂ (input C = 1) using the three other inputs is displayed in Fig. 2C.

Fig. 2.

Operation and analysis of the concatenated biocatalytic gates in the presence of four inputs. (A) Absorbance features of NADH in the concatenated four-enzyme system in the presence of O₂. (B) Bar presentation of the output of the concatenated gates, derived from the absorbance modulus changes. For all, spectra inputs correspond to: a, the absorbance of the biocatalytic system before activation by the inputs, and b–i, the activation of the system by inputs A, B, C, and D, where b = 1,0,1,1; c = 0,1,1,1; d = 1,1,1,1; e = 0,0,1,0; f = 0,0,1,1; g = 1,0,1,0; h = 0,1,1,0; and i = 1,1,1,0. The threshold absorbance values of 0.14 and 0.24 are marked for all bar presentations. (C) Truth table for the concatenated gates in the presence of O₂. Imp, input.

Fig. 3 depicts the operation of the concatenated gates while excluding O₂ from the system (O₂ input always “0”). Under these conditions, an output “1” of the OR gate will not lead to the formation of H₂O₂, and, thus, the output of the AND gate will always be “0.” Accordingly, the changes in the absorbance of the NADH will be controlled only by the glucose input in the XOR gate. Fig. 3A, curves b, c, and d, show the absorbance changes of the systems in all three configurations where the OR gate yields an out “1,” namely, configurations (1, 0, 0, 1), (0, 1, 0, 1), and (1, 1, 0, 1), respectively. Evidently, for all of these configurations, a net increase in the absorbance of NADH is observed because of the noncompensated bioelectrocatalyzed oxidation of glucose and the formation of NADH. Naturally, the system configuration (0, 0, 0, 1), where the inputs of the OR gate are “0,” and, thus, the output of the AND is also forced to be “0,” results in the presence of a glucose input “1,” leading to a net increase in the NADH formation (output “1” of the XOR gate) (Fig. 3A, curve e). Fig. 3B depicts the outputs of the respective concatenated gates in a form of bar presentation, bars b, c, and e. Fig. 3A, curves f–i, shows the absorbance features of the system for all three concatenated gates that involve a “0” glucose input for the XOR gate. Evidently, no absorbance change for NADH is observed, and, thus, for all four configurations: (1, 0, 0, 0), (0, 1, 0, 0), (1, 1, 0, 0), and (0, 0, 0, 0), the output of the XOR gate is “0.” These results are presented in Fig. 3B, bars f–i, respectively. These results are consistent with the fact that exclusion of the O₂ from the system always results in a “0” output of the AND gate. Because no glucose is present in the system, neither the biocatalyzed oxidation of glucose nor the MP-11-catalyzed oxidation of NADH proceeds, and no change in the NADH concentration is observed. It should be noted that in all of the curves shown in Fig. 3A, the absorbance band of the MP-11 at λ = 410 nm is visible. This finding is consistent with the fact that no H₂O₂ is generated in any of the systems, and thus no intermediate oxocomplex is formed (24). The truth table for the concatenated gates system that operates in the absence of O₂ (input C = 0), using the three other inputs, A, B, and D, is displayed in Fig. 3C.

Fig. 3.

Operation and analysis of the lower concatenated biocatalytic gates in the absence of O₂. (A) Absorbance features of NADH in the concatenated four-enzyme system in the absence of O₂. (B) Bar presentation of the output of the concatenated gates, derived from the absorbance modulus changes. For all spectra, inputs correspond to: a, the absorbance of the biocatalytic system before activation by the inputs and b–i, the activation of the system by inputs A, B, C, and D, where b = 1,0,0,1; c = 0,1,0,1; d = 1,1,0,1; e = 0,0,0,1; f = 1,0,0,0; g = 0,1,0,0; h = 1,1,0,0; and i = 0,0,0,0. The threshold absorbance values of 0.14 and 0.24 are marked for all bar presentations. (C) Truth table for the concatenated gates in the absence of O₂. Inp, input.

It should be noted that we defined two regions for the absorbance modulus changes of the different concatenated gates. One region was defined as an absorbance modulus change from 0 to 0.14 and is considered as the low-level output that corresponds to “0.” The second region for absorbance modulus changes was defined in the range 0.24 to 0.5, and corresponds to a high-level output or logic “1.” We also note that the presentation of absorbance changes in the form of a modulus can be implemented by available electronic circuits that could be integrated into the analyzing spectrophotometer. Furthermore, we wish to emphasize that, upon defining the absorbance modulus changes regions for TRUE/FALSE, “1”/“0,” outputs, we identified a “gray” region that lacks any definite response. This situation is analogous to the identification of “0”/“1” states in electronic computers, where appropriate voltage regions are defined for the logic functions. The comprehensive truth table corresponding to the operation of the three concatenated biocatalytic gates in the presence of the four inputs A, B, C, and D is depicted in Table 1.

Table 1.

Truth table corresponding to the operation of three concatenated gates in Fig. 1

Inp A	Inp B	Inp C	Inp D	Output
0	0	0	0	0
0	0	0	1	1
0	0	1	0	0
0	0	1	1	1
0	1	0	0	0
0	1	0	1	1
0	1	1	0	1
0	1	1	1	0
1	0	0	0	0
1	0	0	1	1
1	0	1	0	1
1	0	1	1	0
1	1	0	0	0
1	1	0	1	1
1	1	1	0	1
1	1	1	1	0

The four inputs used are A, acetylcholine; B, butyrylcholine; C, O₂; D, glucose; Inp, input.

The unique aspect of this system rests on the fact that four biocatalysts form three concatenated logic gates that operate in series. The operation of the integrated system is “read out” by the output of the last gate. In contrast to our previous enzyme-based computing systems, where each biocatalytic gate operated as a separate unit, this study demonstrates the information transfer from one gate to the other by the produced chemical stimuli. We do not consider enzyme-based logic gates as substitutes for electronic circuitry and computers. We feel, however, that such systems might find future utility as “diagnostic computers” that would follow biological transformations, such as in metabolic pathways or drug interactions. The availability of numerous enzymes in nature, and the demonstration that multiplexed biocatalytic cascades can be harnessed to yield logic operations, support our vision for future enzyme-based computers.

Conclusions

To summarize, this study has demonstrated the successful application of enzymes to design a scheme of concatenated logic gates. It is important to state that the operation of the concatenated gates in the presence of oxygen, Fig. 2, or in the absence of oxygen, Fig. 3, required numerous optimization experiments when the concentrations of the inputs and the concentrations of the different biocatalysts had to be balanced. These experiments required the detailed characterization of each of the gates, the tuning of the respective concentrations of the biocatalysts/inputs, to the extent that the system operates as an integrated assembly. The availability of numerous other enzymes (and their respective substrates) suggested that concatenated gates of enhanced complexity might be designed in the future. Furthermore, the ability to immobilize enzymes on solid supports, such as magnetic particles or membranes, may allow the “resetting” of the biocatalytic gates.

Materials and Methods

All chemicals and enzymes were purchased from Aldrich (Metuchen, NJ) or Sigma (St. Louis, MO). The enzymes that were used are glucose dehydrogenase from Thermoplasma acidophilum (E.C. 1.1.1.47), microperoxidase-11 sodium salt from equine heart cytochrome c, choline oxidase from Alcaligenes species (E.C. 1.1.3.17), and acetylcholine esterase from Electrophorus electricus type VI-S (E.C. 3.1.1.7). For each gate, the amounts of enzymes and substrates were optimized to keep the same concentrations of inputs for all of the gates and to yield a significant difference of ‖ΔA‖ between the “0” and “1” states. The absorbance measurements were performed by using a UV-2401PC UV-visible spectrophotometer (Shimadzu, Tokyo, Japan). All measurements were performed at 25 ± 2°C.

Composition of the Four-Enzyme System.

The system is composed of a 350-μl solution of 1.5 μM microperoxidase-11 sodium salt, 7.7 units of glucose dehydrogenase, 6 units of choline oxidase, 10 units of acetylcholinesterase, 1 × 10⁻⁴ M NAD⁺ and 1 × 10⁻⁴ M NADH in 0.1 M phosphate buffer, pH = 7.4. The experiments were conducted in a 1- × 1-cm quartz cuvette, and a 1-ml volume of solution. The enzyme choline oxidase was purified by filtration through a centrifugation filtration device (Centricon Millipore, Bedford, MA) with a molecular mass cut-off of 50,000 Da. For the systems where O₂ was excluded, the reaction mixture was degassed with argon that was purified from traces of oxygen by bubbling the gas through an alkaline aqueous solution of methyl viologen that was reduced electrochemically. The absorbance variations correspond to the difference of absorbance before and after the enzymatic reaction took place. The inputs defined as “0” correspond to the lack of activating chemicals. The inputs defined as “1” correspond to an addition of 40 mM acetylcholine chloride (input A) or 4 mM butyrylcholine iodide (input B), oxygen from the air (8.2 ppm; 25°C, 1 bar) (input C), and 20 mM β-D(+)glucose (input D). For the experiments where inputs A and B are applied both as “1,” their concentrations corresponded to 13 mM and 1 mM, respectively. The modulus of absorbance change, ‖ΔA‖, was measured after a time interval of 20 min. A TRUE output corresponds to ‖ΔA‖ > 0.24 arbitrary units (a.u.) at 340 nm, whereas a FALSE output corresponds to ‖ΔA‖ < 0.14 a.u.

Abbreviations

MP-11

microperoxidase-11

GDH

glucose dehydrogenase.