Towards computing with proteins

pH-Controlled enzymatic computing for digital circuits and neural networks

Unconventional computing paradigms explore new methods for processing information beyond the capabilities of traditional electronic architectures. In this work, we present our approach to digital computation through enzymatic reactions in chemically buffered environments. A key aspect of this approach is its reliance on pH-sensitive enzymatic reactions, with the direction of the reaction controlled by maintaining pH levels within a specific range. When the pH crosses a defined threshold, the reaction moves forward and vice versa, akin to the switching action of electronic switches in digital circuits. The binary signals (0 and 1) are encoded as different concentrations of strong acids or bases, offering a bio-inspired method for computation. The final readout is done using UV-vis spectroscopy after applying detection reactions to indicate whether the output is 1 (indicated by the presence of the enzymatic reaction's product) or 0 (indicated by the absence of the enzymatic reaction's product). We build and evaluate a set of digital circuits in the lab using our proposed methodology to model the circuits using chemical reactions. In addition, we demonstrate the implementation of a neural network classifier using our framework.

Chemical Logic Gates on Active Colloids

Recent studies have shown that active colloidal motors using enzymatic reactions for propulsion hold special promise for applications in fields ranging from biology to material science. It will be desirable to have active colloids with capability of computation so that they can act autonomously to sense their surroundings and alter their own dynamics. It is shown how small chemical networks that make use of enzymatic chemical reactions on the colloid surface can be used to construct motor-based chemical logic gates. The basic features of coupled enzymatic reactions that are responsible for propulsion and underlie the construction and function of chemical gates are described using continuum theory and molecular simulation. Examples are given that show how colloids with specific chemical logic gates, can perform simple sensing tasks. Due to the diverse functions of different enzyme gates, operating alone or in circuits, the work presented here supports the suggestion that synthetic motors using such gates could be designed to operate in an autonomous way in order to complete complicated tasks.

The art of molecular computing: Whence and whither

An astonishingly diverse biomolecular circuitry orchestrates the functioning machinery underlying every living cell. These biomolecules and their circuits have been engineered not only for various industrial applications but also to perform other atypical functions that they were not evolved for-including computation. Various kinds of computational challenges, such as solving NP-complete problems with many variables, logical computation, neural network operations, and cryptography, have all been attempted through this unconventional computing paradigm. In this review, we highlight key experiments across three different ''eras'' of molecular computation, beginning with molecular solutions, transitioning to logic circuits and ultimately, more complex molecular networks. We also discuss a variety of applications of molecular computation, from solving NP-hard problems to self-assembled nanostructures for delivering molecules, and provide a glimpse into the exciting potential that molecular computing holds for the future. Also see the video abstract here: https://youtu.be/9Mw0K0vCSQw.

Not-XOR (NXOR) Logic Gate Realized with Enzyme-Catalyzed Reactions: Optical and Electrochemical Signal Transduction

The studied enzyme-based biocatalytic system mimics NXOR Boolean logic gate, which is a logical operator that corresponds to equality in Boolean algebra. It gives the functional value true (1) if both functional arguments (input signals) have the same logical value (0,0 or 1,1), and false (0) if they are different (0,1 or 1,0). The output signal producing reaction is catalyzed by pyrroloquinoline quinone-dependent glucose dehydrogenase (PQQ-GDH), which is inhibited at acidic and basic pH values. Two other reactions catalyzed by esterase and urease produce acetic acid and ammonium hydroxide, respectively, shifting solution pH from the optimum pH for PQQ-GDH to acidic and basic values (1,0 and 0,1 input combinations, respectively), thus switching the enzyme activity off (output 0). When the input signals are not applied (0,0 combination) or both applied compensating each other (1,1 combination) the optimum pH is preserved, thus keeping PQQ-GDH running at the high rate (output 1). The biocatalytic cascade mimicking the NXOR gate was characterized optically and electrochemically. In the electrochemical experiments the PQQ-GDH enzyme communicated electronically with a conducting electrode support, thus resulting in the electrocatalytic current when signal combinations 0,0 and 1,1 were applied. The logic gate operation, when it was realized electrochemically, was also extended to the biomolecular release controlled by the gate. The release system included two electrodes, one performing the NXOR gate and another one activated for the release upon electrochemically stimulated alginate hydrogel dissolution. The studied system represents a general approach to the biocatalytic realization of the NXOR logic gate, which can be included in different catalytic cascades mimicking operation of concatenated gates in sophisticated logic circuitries.

Experimental Realization of a High-Quality Biochemical XOR Gate

We report an experimental realization of a biochemical XOR gate function that avoids many of the pitfalls of earlier realizations based on biocatalytic cascades. Inputs-represented by pairs of chemicals-cross-react to largely cancel out when both are nearly equal. The cross-reaction can be designed to also optimize gate functioning for noise handling. When not equal, the residual inputs are further processed to result in the output of the XOR type, by biocatalytic steps that allow for further gate-function optimization. The quality of the realized XOR gate is theoretically analyzed.

Computational Biosensors: Molecules, Algorithms, and Detection Platforms

Advanced nucleic acid-based sensor-applications require computationally intelligent biosensors that are able to concurrently perform complex detection and classification of samples within an in vitro platform. Realization of these cutting-edge computational biosensor systems necessitates innovation and integration of three key technologies: molecular probes with computational capabilities, algorithmic methods to enable in vitro computational post processing and classification, and immobilization and detection approaches that enable the realization of deployable computational biosensor platforms. We provide an overview of current technologies, including our contributions towards the development of computational biosensor systems.

Enzyme-based logic gates and circuits-analytical applications and interfacing with electronics

The paper is an overview of enzyme-based logic gates and their short circuits, with specific examples of Boolean AND and OR gates, and concatenated logic gates composed of multi-step enzyme-biocatalyzed reactions. Noise formation in the biocatalytic reactions and its decrease by adding a "filter" system, converting convex to sigmoid response function, are discussed. Despite the fact that the enzyme-based logic gates are primarily considered as components of future biomolecular computing systems, their biosensing applications are promising for immediate practical use. Analytical use of the enzyme logic systems in biomedical and forensic applications is discussed and exemplified with the logic analysis of biomarkers of various injuries, e.g., liver injury, and with analysis of biomarkers characteristic of different ethnicity found in blood samples on a crime scene. Interfacing of enzyme logic systems with modified electrodes and semiconductor devices is discussed, giving particular attention to the interfaces functionalized with signal-responsive materials. Future perspectives in the design of the biomolecular logic systems and their applications are discussed in the conclusion. Graphical Abstract Various applications and signal-transduction methods are reviewed for enzyme-based logic systems.

An Enzyme-based 1:2 Demultiplexer Interfaced with an Electrochemical Actuator

An enzyme-based 1:2 demultiplexer is designed in a flow system composed of three cells where each one is modified with a different enzyme: hexokinase, glucose dehydrogenase and glucose-6-phosphate dehydrogenase. The Input signal activating the biocatalytic cascade is represented by glucose, while the Address signal represented by ATP is responsible for directing the Input signal to one of the output channels, depending on the logic value of the Address. The biomolecular 1:2 demultiplexer is extended to include two electrochemical actuators releasing entrapped DNA molecules in the active output channel. The modular design of the system allows for easy exchange and extension of the functional elements. The present demultiplexer can be easily integrated in various biomolecular logic systems, including different logic gates based on the enzyme- or DNA-based reactions, as well as containing different chemical actuators, for example, with a biomolecular release function.

Enzyme-based logic systems interfaced with signal-responsive materials and electrodes

Enzyme-based biocomputing systems were interfaced with signal-responsive membranes and electrodes resulting in bioelectronic devices switchable by logically processed biomolecular signals. "Smart" membranes, electrodes, biofuel cells, memristors and substance-releasing systems were activated by various combinations of biomolecular signals in the pre-programmed way implemented in biocatalytic cascades mimicking logic networks.

Enzyme-based logic gates switchable between OR, NXOR and NAND Boolean operations realized in a flow system

The enzyme-based system performing a biocatalytic cascade reaction was realized in a flow device and was used to mimic Boolean logic operations. Chemical inputs applied to the system resulted in the activation of additional reaction steps, allowing the reversible switch of the logic operations between OR, NXOR and NAND gates for processing of two other biomolecular inputs.

Notes on stochastic (bio)-logic gates: computing with allosteric cooperativity

Recent experimental breakthroughs have finally allowed to implement in-vitro reaction kinetics (the so called 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. However, as biochemical systems are always affected by the presence of noise (e.g. thermal), standard logic is not the correct theoretical reference framework, rather we show that statistical mechanics can work for this scope: 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 noisy logical operators and/or perform stochastic logical operations. Mixing statistical mechanics with logics, and testing quantitatively the resulting findings on 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).

Programming the quorum sensing-based AND gate in Shewanella oneidensis for logic gated-microbial fuel cells

A modularly structured, flexible, and reprogrammable AND logic gate gene circuit-controlled microbial fuel cell.

Creation of a gated antibody as a conditionally functional synthetic protein

The ability to conditionally direct antibodies is a potentially powerful application for Synthetic Biology in Medicine. Here we show that control of antibody binding through site-specific, chemical phosphorylation of a recognition domain creates a ‘gated’ antibody (Ab). This displays a crude Boolean logic where binding is induced in an enzyme-AND-antigen dependent manner. This ‘AND-Ab’ is therefore active only in the presence of two biomarker inputs: the simultaneous expression of a (cell surface) antigen and secreted enzyme to generate function in vitro, on cells and in mammalian tissue. Such gated Abs, either alone or in combination, could allow the application of logic strategies to enhance precision in biological interrogation, modulation and in therapy.

The ability to control antibody binding could have important medical implications. Here, the authors present a method to engineer phosphatase-controllable antibodies that bind to a specific recognition site in the presence of two biomarker inputs.

Majority and minority gates realized in enzyme-biocatalyzed systems integrated with logic networks and interfaced with bioelectronic systems

Biocatalytic reactions operating in parallel and resulting in reduction of NAD(+) or oxidation of NADH were used to mimic 3-input majority and minority logic gates, respectively. The substrates corresponding to the enzyme reactions were used as the input signals. When the input signals were applied at their high concentrations, defined as logic 1 input values, the corresponding biocatalytic reactions were activated, resulting in changes of the NADH concentration defined as the output signal. The NADH concentration changes were dependent on the number of parallel reactions activated by the input signals. The absence of the substrates, meaning their logic 0 input values, kept the reactions mute with no changes in the NADH concentration. In the system mimicking the majority function, the enzyme-biocatalyzed reactions resulted in a higher production of NADH when more than one input signal was applied at the logic 1 value. Another system mimicking the minority function consumed more NADH, thus leaving a smaller residual output signal, when more than one input signal was applied at the logic 1 value. The performance of the majority gate was improved by processing the output signal through a filter system in which another biocatalytic reaction consumed a fraction of the output signal, thus reducing its physical value to zero when the logic 0 value was obtained. The majority gate was integrated with a preceding AND logic gate to illustrate the possibility of complex networks. The output signal, NADH, was also used to activate a process mimicking drug release, thus illustrating the use of the majority gate in decision-making biomedical systems. The 3-input majority gate was also used as a switchable AND/OR gate when one of the input signals was reserved as a command signal, switching the logic operation for processing of the other two inputs. Overall, the designed majority and minority logic gates demonstrate novel functions of biomolecular information processing systems.

A biocatalytic cascade with several output signals--towards biosensors with different levels of confidence

The biocatalytic cascade based on enzyme-catalyzed reactions activated by several biomolecular input signals and producing output signal after each reaction step was developed as an example of a logically reversible information processing system. The model system was designed to mimic the operation of concatenated AND logic gates with optically readable output signals generated at each step of the logic operation. Implications include concurrent bioanalyses and data interpretation for medical diagnostics.

Biocomputing, Biosensing and Bioactuation Based on Enzyme Biocatalyzed Reactions

The focus of this review paper is on the design and implementation of smart ‘Sense-and-Treat’ systems using enzyme-biocatalytic systems. These systems were used to perform biomolecular computing and they were functionally integrated with signal responsive materials aiming towards their biomedical use. Electrode interfaces, functionalized with signal-responsive materials, find applications in biocomputing, biosensing, and, specifically, triggered release of bioactive substances. ‘Sense-and-Treat’ systems require multiple components working together, including biosensors, actuators, and filters, in order to achieve closed-loop and autonomous operation. In general, biochemical logic networks were developed to process single biochemical or chemical inputs as well as multiple inputs, responding to nonphysiological (for concept demonstration purposes) and physiological signals (for injury detection or diagnosis). Actuation of drug-mimicking release was performed using the responsive material iron-cross-linked alginate with entrapped biomolecular species, responding to physical, chemical or biochemical signals.

Enzymatic AND logic gate with sigmoid response induced by photochemically controlled oxidation of the output

We report a study of a system which involves an enzymatic cascade realizing an AND logic gate, with an added photochemical processing of the output, allowing the gate's response to be made sigmoid in both inputs. New functional forms are developed for quantifying the kinetics of such systems, specifically designed to model their response in terms of signal and information processing. These theoretical expressions are tested for the studied system, which also allows us to consider aspects of biochemical information processing such as noise transmission properties and control of timing of the chemical and physical steps.

Enzyme-based D-flip-flop memory system

The enzyme system was used to mimic the D-flip-flop memory unit. The reversible conversion of NAD(+) and NADH cofactors was used to encode the states of the memory unit, while a mixture of inhibitors was used as the Clock input and the substrates were used as the Data input.

Realization of Associative Memory in an Enzymatic Process: Toward Biomolecular Networks with Learning and Unlearning Functionalities

We report a realization of an associative memory signal/information processing system based on simple enzyme-catalyzed biochemical reactions. Optically detected chemical output is always obtained in response to the triggering input, but the system can also "learn" by association, to later respond to the second input if it is initially applied in combination with the triggering input as the "training" step. This second chemical input is not self-reinforcing in the present system, which therefore can later "unlearn" to react to the second input if it is applied several times on its own. Such processing steps realized with (bio)chemical kinetics promise applications of bioinspired/memory-involving components in "networked" (concatenated) biomolecular processes for multisignal sensing and complex information processing.

Biomolecular filters for improved separation of output signals in enzyme logic systems applied to biomedical analysis

Biomolecular logic systems processing biochemical input signals and producing "digital" outputs in the form of YES/NO were developed for analysis of physiological conditions characteristic of liver injury, soft tissue injury, and abdominal trauma. Injury biomarkers were used as input signals for activating the logic systems. Their normal physiological concentrations were defined as logic-0 level, while their pathologically elevated concentrations were defined as logic-1 values. Since the input concentrations applied as logic 0 and 1 values were not sufficiently different, the output signals being at low and high values (0, 1 outputs) were separated with a short gap making their discrimination difficult. Coupled enzymatic reactions functioning as a biomolecular signal processing system with a built-in filter property were developed. The filter process involves a partial back-conversion of the optical-output-signal-yielding product, but only at its low concentrations, thus allowing the proper discrimination between 0 and 1 output values.

Integrating multiple signals into cell decisions by networks of protein modification cycles

Posttranslational protein modifications play a key role in regulating cellular processes. We present a general model of reversible protein modification networks and demonstrate that a single protein modified by several enzymes is capable of integrating multiple signals into robust digital decisions by switching between multiple forms that can activate distinct cellular processes. First we consider two competing protein modification cycles and show that in the saturated regime, the protein is concentrated into a single form determined by the enzyme activities. We generalize this to protein modification networks with tree structure controlled by multiple enzymes that can be characterized by their phase diagram, which is a partition of the space of enzyme activities into regions corresponding to different dominant forms. We show that the phase diagram can be obtained analytically from the wiring diagram of the modification network by recursively solving a set of balance equations for the steady-state distributions and then applying a positivity condition to determine the regions corresponding to different responses. We also implement this method in a computer algebra system that automatically generates the phase diagram as a set of inequalities. Based on this theoretical framework, we determine some general properties of protein modification systems.

Multi-enzyme logic network architectures for assessing injuries: digital processing of biomarkers

A multi-enzyme biocatalytic cascade processing simultaneously five biomarkers characteristic of traumatic brain injury (TBI) and soft tissue injury (STI) was developed. The system operates as a digital biosensor based on concerted function of 8 Boolean AND logic gates, resulting in the decision about the physiological conditions based on the logic analysis of complex patterns of the biomarkers. The system represents the first example of a multi-step/multi-enzyme biosensor with the built-in logic for the analysis of complex combinations of biochemical inputs. The approach is based on recent advances in enzyme-based biocomputing systems and the present paper demonstrates the potential applicability of biocomputing for developing novel digital biosensor networks.

Enzyme logic gate associated with a single responsive microparticle: scaling biocomputing to microsize systems

A microsize biocomputing system based on enzyme logic processing biochemical signals was developed. Optical transduction of pH signals generated in situ by the enzyme OR logic gate was achieved with the use of a single optode microparticle.