Biocomputing Toolbox
Memory units,
Multiplexer and Demultiplexer, Filters

This research project is conducted in a close collaboration with Prof. Vladimir Privman

PI: Evgeny Katz, Co-PI: Vladimir Privman

Title: "Biochemical Computing: Experimental and Theoretical Development of Error Correction and Digitalization Concepts"

Agency: National Science Foundation (NSF)

Award No: CCF-0726698

Time Period: 09/15/07 - 08/31/10

Title: "SHF: Small: Experimental and Theoretical Development of Error Correction and Digitalization Concepts for Multi-Enzyme Biomolecular Computing Networks"

Agency: National Science Foundation (NSF)

Award No: CCF-1015983

Time Period: 09/01/10 - 08/31/13

The need for a “toolbox” of non-Boolean network elements:
Why are non-Boolean network elements, hopefully those with modular properties (that can be reused in various network designs), needed? There are actually several different aspects of networking that require such functionalities: Digital error correction for larger networks (which for biochemical logic sometimes means networks involving as few as order 10 information processing steps), is based on redundancy and therefore requires at least the elements for splitting the signal, for signal amplification and intensity-balancing, which, for biochemical logic is easier accomplished by utilizing signal attenuation. Filtering is obviously useful for control of analog errors, by resetting the signals to their reference digital values. Signal resetting is more generally a useful function if we were to attempt to “clock” the biocomputing processes, in future information processing designs. Finally, converters between various types of chemical “signals” will also be useful for networking. Among the more risky research directions that we hope to explore, are bio-inspired network elements involving time-delay and memory.

Set-Reset Flip-Flop Memory Based on Enzyme Reactions:
Towards Memory Systems Controlled by Biochemical Pathways

The enzyme-based set-reset flip-flop memory system was designed with the core part composed of horseradish peroxidase and diaphorase biocatalyzing oxidation and reduction of redox species (2,6-dichloroindophenol or ferrocianide). The biocatalytic redox transformations were activated by H2O2 and NADH produced in situ by different enzymatic reactions allowing transformation of various biochemical signals (glucose, lactate, D-glucose-6-phosphate, ethanol) into reduced or oxidized states of the redox species. The current redox state of the system, controlled by the set and reset signals, was read out by optical and electrochemical means. The multi-well setup with the flip-flop units separately activated by various set/reset signals allowed encoding of complex information. For illustrative purposes, the words “Clarkson” and then “University” were encoded using ASCII character codes. The present flip-flop system will allow additional functions of enzyme-based biocomputing systems, thus enhancing the performance of multi-signal biosensors and actuators controlled by logically processed biochemical signals. The integrated enzyme logic systems and flip-flop memories associated with signal-responsive chemical actuators are envisaged as basic elements of future implantable biomedical devices controlled by immediate physiological conditions.

M. Pita, G. Strack, K. MacVittie, J. Zhou, E. Katz, Set-reset flip-flop memory based on enzyme reactions: Towards memory systems controlled by biochemical pathways. J. Phys. Chem. B 2009, 113, 16071-16076.

(left) The enzyme biocatalytic system mimicking set-reset flip-flop memory operations using HRP and Diaph as the components of the core part and GOx and AlcDH as terminal biocatalysts converting primary set-reset signals (glucose and ethanol) to H2O2 and NADH inputs controlling the switchable core part.

(above) Words encoded using ASCII character codes upon application of different set-reset signals (H2O2-NADH, respectively) to the multi-well flip-flop system composed of HRP and Diaph as the biocatalysts and K4[Fe(CN)6] as the redox species. Optical read out of the words Clarkson (A) and University (B) at 415 nm. Color photo of the multi-well reactor with the encoded word University (C) and the respective ASCII codes for the used characters (D).

It should be noted that an undergraduate student Kevin MacVittie participated in the project working in a team of graduate students/postdocs.

Enzyme-Based Multiplexer and Demultiplexer

Digital 2-to-1 multiplexer and 1-to-2 demultiplexer were mimicked by biocatalytic reactions involving concerted operation of several enzymes. Using glucose oxidase (GOx) and laccase (Lac) as the data input signals and variable pH as the addressing signal, ferrocyanide oxidation in the output channel was selectively activated by one from two inputs, thus mimicking the multiplexer operation. Demultiplexer based on the enzyme system composed of GOx, glucose dehydrogenase (GDH) and horseradish peroxidase (HRP) allowed selective activation of different output channels (oxidation of ferrocyanide or reduction of NAD+) by the glucose input. The selection of the output channel was controlled by the addressing input of NAD+. The designed systems represent important novel components of future branched enzyme networks processing biochemical signals for biosensing and bioactuating.

M.A. Arugula, V. Bocharova, M. Pita, J. Halámek, E. Katz, Enzyme-based multiplexer and demultiplexer. J. Phys. Chem. B 2010, 114, 5222-5226.

(left) The biocatalytic system mimicking the 2-to-1 multiplexer, where glucose oxidase (GOx) and laccase (Lac) are the data input signals (Input1 and Input2, respectively) and the pH change is the addressing signal (Address). The same Output, K3[Fe(CN)6] is produced in the both reacting pathways.

(above) The electronic equivalent circuitry of the 2-to-1 multiplexer based on the enzyme catalyzed reactions.

(left) The biocatalytic system mimicking the 1-to-2 demultiplexer, where glucose is the data input signal (Input) and NAD+ is the addressing signal (Address). Two different output channels (Output1 and Output1) are represented by ABTSox and NADH, which production is triggered by the same data input and selected by the addressing input.

(above) The electronic equivalent circuitry of the 1-to-2 demultiplexer based on the enzyme catalyzed reactions.

Biochemical Filter with Sigmoidal Response to pH Changes
We realize a biochemical filtering process based on the introduction of a buffer in a biocatalytic signal-transduction logic system based on the function of an enzyme, esterase. The input, ethyl butyrate, is converted into butyric acid—the output signal, which in turn is measured by the drop in the pH value. The developed approach offers a versatile "network element" for increasing the complexity of biochemical information processing systems. Evaluation of an optimal regime for quality filtering is accomplished in the framework of a kinetic rate-equation model.

(left) Schematic presentation of the buffering-based pH-signal "logic filter." The reaction biocatalyzed by an enzyme, here esterase, results in the hydrolysis of ethyl butyrate (the logic Input) to yield butyric acid which releases H+ ions upon dissociation. A limited quantity of a buffer, here HEPES, if introduced, consumes most of the biocatalytically produced H+ ions when the input is applied at a low concentration. The pH change (the logic Output, measured by the pH drop, as indicated by an arrow) sets in when the biocatalytically produced H+ ions overwhelm the buffer. The biocatalytic process and buffering combined, yield a sigmoidal dependence of the pH change as a function of the input concentration. The inset illustrates the onset of the sigmoidal response in our experimental system. The solid curves show the output, y, vs. the input, x, properly redefined/rescaled to vary in the "binary-logic ranges" from 0 to 1, as explained in the text. Experimental data were fitted by using rate equations appropriate for the processes involved, and the results are shown, here for the reaction time 120 min, for increasing buffer (HEPES) concentrations. The top (red) curve corresponds to [HEPES] = 0; middle (blue): [HEPES] = 50 mM, bottom (green): [HEPES] = 100 mM. The dashed black curve does not correspond to experimental data but rather illustrates a desirable, "ideal" filter response with small slopes at both binary logic points 0 and 1, and with a steep, symmetrically positioned inflection region in the middle.

M. Pita, V. Privman, M.A. Arugula, D. Melnikov, V. Bocharova, E. Katz, Towards biochemical filter with sigmoidal response to pH changes: Buffered biocatalytic signal transduction. PhysChemChemPhys 2011, 13, 4507-4513.

Measured pH values at the reaction time t = 120 min, shown vs. the initial substrate concentration, for different amounts of HEPES. Red (bottom) symbols/curve correspond to [HEPES] = 0, blue (middle): [HEPES] =50 mM, green (top): [HEPES] = 100 mM. The circular symbols are the actual pH values, whereas the solid curves are the theoretical model fits. (These curves were shown in the inset in the figure above, rescaled in terms of the logic-range variables).

Top: Experimental dependence of pH on the initial substrate concentration (ethyl butyrate) and reaction time, for [HEPES] = 100 mM. Bottom: Numerically computed dependence for this system, based on the kinetic model.

Dr. Marcos Pita
developed the system.

Prof. Vladimir Privman suggested the filter concept and analyzed the experimental results.

Mary Arugula performed most of the experiments.

Biochemical Filter with Sigmoidal Response: Increasing the Complexity of Biomolecular Logic

The first realization of a designed, rather than natural, biochemical filter process is reported and analyzed as a promising network component for increasing the complexity of biomolecular logic systems. Key challenge in biochemical logic research has been achieving scalability for complex network designs. Various logic gates have been realized, but a "toolbox" of analog elements for interconnectivity and signal processing has remained elusive. Filters are important as network elements that allow control of noise in signal transmission and conversion. We report a versatile biochemical filtering mechanism designed to have sigmoidal response in combination with signal-conversion process. Horseradish peroxidase-catalyzed oxidation of chromogenic electron donor by H2O2, was altered by adding ascorbate, allowing to selectively suppress the output signal, modifying the response from convex to sigmoidal. A kinetic model was developed for evaluation of the quality of filtering. The results offer improved capabilities for design of scalable biomolecular information processing systems.

(left) The convex and sigmoidal response for the "identity" logic gate mapping 0 to 0, and 1 to 1. The inset illustrates an "ideal" sigmoidal curve passing through the two logic points, with a steep and symmetrically positioned central inflection part, surrounded by broad small-slope regions at the logic points, and with no measurable noise in the curve itself (unlike in the actual experimental data). The extensions of the curve indicate that the response could also be considered and measured somewhat beyond the logic points, if physically relevant. The schematic outlines the experimental system, "color-coded" to the plots. The Red and Ox labels refer to the redox states of the chromogen, TMB; DHA referes to dehydroascorbic acid — the product of irreversible oxidation of ascorbate (Asc).

V. Privman, J. Halámek, M.A. Arugula, D. Melnikov, V. Bocharova, E. Katz, Biochemical filter with sigmoidal response: Increasing the complexity of biomolecular logic. J. Phys. Chem. B 2010, 114, 14103-14109.

Experimental dependence of the concentration of the charge transfer species (the blue product), measured by the absorbance, A, on the initial concentration of H2O2, for varying reaction time, tg, with different initial amounts of ascorbate, the concentration of which is shown above each plot.

Theoreticl fit of the experimental data shown in the figure at the left with the model rate equations.

updated on February 26, 2011