We develop an approach aimed at optimizing the parameters of a network of biochemical logic gates for reduction of the "analog" noise buildup. Experiments for three coupled enzymatic AND gates are reported, illustrating our procedure. Specifically, starch - one of the controlled network inputs - is converted to maltose by beta-amylase. With the use of phosphate (another controlled input), maltose phosphorylase then produces glucose. Finally, nicotinamide adenine dinucleotide (NAD+) - the third controlled input - is reduced under the action of glucose dehydrogenase to yield the optically detected signal. Network functioning is analyzed by varying selective inputs and fitting standardized few-parameters "response-surface" functions assumed for each gate. This allows a certain probe of the individual gate quality, but primarily yields information on the relative contribution of the gates to noise amplification. The derived information is then used to modify our experimental system to put it in a regime of a less noisy operation.
Electrode-immobilized glucose-6-phosphate dehydrogenase is used to catalyze an enzymatic reaction which carries out the AND logic gate. This logic function is considered here in the context of biocatalytic processes utilized for the biocomputing applications for "digital" (threshold) sensing/actuation. We outline the response functions desirable for such applications and report the first experimental realization of a sigmoid-shape response in one of the inputs. A kinetic model is developed and utilized to evaluate the extent to which the experimentally realized gate is close to optimal.
The complete characterization of enzymatic activities between molecules remains incomplete, hindering biological engineering and limiting biological discovery. We develop in this work a technique, Enzymatic Link Prediction (ELP), for predicting the likelihood of an enzymatic transformation between two molecules. ELP models enzymatic reactions catalogued in the KEGG database as a graph. ELP is innovative over prior works in using graph embedding to learn molecular representations that capture not only molecular and enzymatic attributes but also graph connectivity. We explore both transductive (…
We report the first systematic study of designed two-input biochemical systems as information processing gates with favorable noise-transmission properties accomplished by modifying the gate's response from convex shape to sigmoid in both inputs. This is realized by an added chemical "filter" process which recycles some of the output back into one of the inputs. We study a system involving the biocatalytic function of the enzyme horseradish peroxidase, functioning as an AND gate. We consider modularity properties, such as the use of three different input chromogens that, when oxidized yield si…
We report an experimental evaluation of the "input-output surface" for a biochemical AND gate. The obtained data are modeled within the rate-equation approach, with the aim to map out the gate function and cast it in the language of logic variables appropriate for analysis of Boolean logic for scalability. In order to minimize "analog" noise, we consider a theoretical approach for determining an optimal set for the process parameters to minimize "analog" noise amplification for gate concatenation. We establish that under optimized conditions, presently studied biochemical gates can be concaten…
Biochemical computing is an emerging field of unconventional computing that attempts to process information with biomolecules and biological objects using digital logic. In this work we survey filtering in general, in biochemical computing, and summarize the experimental realization of an AND logic gate with sigmoid response in one of the inputs. The logic gate is realized with electrode-immobilized glucose-6-phosphate dehydrogenase enzyme that catalyzes a reaction corresponding to the Boolean AND functions. A kinetic model is also developed and used to evaluate the extent to which the perform…
Computing based on biochemical processes is a newest rapidly developing field of unconventional information and signal processing. In this paper we present results of our research in the field of biochemical computing and summarize the obtained numerical and experimental data for implementations of the standard two-input OR and AND gates with double-sigmoid shape of the output signal. This form of response was obtained as a function of the two inputs in each of the realized biochemical systems. The enzymatic gate processes in the first system were activated with two chemical inputs and resulte…
We describe modeling approaches to a "network" of connected enzyme-catalyzed reactions, with added (bio)chemical processes that introduce biochemical filtering steps into the functioning of such a biocatalytic cascade. Theoretical expressions are derived that allow simple, few-parameter modeling of processes concatenated in such cascades, both with and without filtering. The modeling approach captures and explains features identified in earlier studies of enzymatic processes considered as potential "network components" for multi-step information/signal processing systems.
Biochemical computing attempts to process information with biomolecules and biological objects. In this work we review our results on analysis and optimization of single biochemical logic gates based on enzymatic reactions, and a network of three gates, for reduction of the "analog" noise buildup. For a single gate, optimization is achieved by analyzing the enzymatic reactions within a framework of kinetic equations. We demonstrate that using co-substrates with much smaller affinities than the primary substrate, a negligible increase in the noise output from the logic gate is obtained as compa…
Experimental and theoretical analyses of the lactate dehydrogenase and glutathione reductase based enzymatic AND logic gates in which the enzymes and their substrates serve as logic inputs are performed. These two systems are examples of the novel, previously unexplored, class of biochemical logic gates that illustrate potential biomedical applications of biochemical logic. They are characterized by input concentrations at logic 0 and 1 states corresponding to normal and abnormal physiological conditions. Our analysis shows that the logic gates under investigation have similar noise characteri…
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 to make the gate's response 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 chemic…
In this work we demonstrate both experimentally and theoretically that the analog noise generation by a single enzymatic logic gate can be dramatically reduced to yield gate operation with virtually no input noise amplification. This is achieved by exploiting the enzyme's specificity when using a co-substrate that has a much lower affinity than the primary substrate. Under these conditions, we obtain a negligible increase in the noise output from the logic gate as compared to the input noise level. Experimental realizations of the AND logic gate with the enzyme horseradish peroxidase using hyd…
Biochemical reactions are fundamentally noisy at a molecular scale. This limits the precision of reaction networks, but also allows fluctuation measurements which may reveal the structure and dynamics of the underlying biochemical network. Here, we study non-equilibrium reaction cycles, such as the mechanochemical cycle of molecular motors, the phosphorylation cycle of circadian clock proteins, or the transition state cycle of enzymes. Fluctuations in such cycles may be measured using either of two classical definitions of the randomness parameter, which we show to be equivalent in general mic…
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 pro…
We report the first study of a network of connected enzyme-catalyzed reactions, with added chemical and enzymatic processes that incorporate the recently developed biochemical filtering steps into the functioning of this biocatalytic cascade. New theoretical expressions are derived to allow simple, few-parameter modeling of network components concatenated in such cascades, both with and without filtering. The derived expressions are tested against experimental data obtained for the realized network's responses, measured optically, to variations of its input chemicals' concentrations with and w…
We study the problem of computing outer bounds for the region of steady states of biochemical reaction networks modelled by ordinary differential equations, with respect to parameters that are allowed to vary within a predefined region. Using a relaxed version of the corresponding feasibility problem and its Lagrangian dual, we show how to compute certificates for regions in state space not containing any steady states. Based on these results, we develop an algorithm to compute outer bounds for the region of all feasible steady states. We apply our algorithm to the sensitivity analysis of a Go…
The Michaelis-Menten equation has played a central role in our understanding of biochemical processes. It has long been understood how this equation approximates the dynamics of irreversible enzymatic reactions. However, a similar approximation in the case of networks, where the product of one reaction can act as an enzyme in another, has not been fully developed. Here we rigorously derive such an approximation in a class of coupled enzymatic networks where the individual interactions are of Michaelis-Menten type. We show that the sufficient conditions for the validity of the total quasi stead…
Nature presents multiple intriguing examples of processes which proceed at high precision and regularity. This remarkable stability is frequently counter to modelers' experience with the inherent stochasticity of chemical reactions in the regime of low copy numbers. Moreover, the effects of noise and nonlinearities can lead to "counter-intuitive" behavior, as demonstrated for a basic enzymatic reaction scheme that can display stochastic focusing (SF). Under the assumption of rapid signal fluctuations, SF has been shown to convert a graded response into a threshold mechanism, thus attenuating t…
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 filterin…
An information processing circuit must be flexible to perform multiple tasks: biochemical information processing circuits in living systems can have multiple functions, requiring them to perform distinct computational tasks in different scenarios. Here, we describe a tunable dynamical system that performs different logical operations (such as AND, OR, and XOR) depending on which basin of attraction the dynamics resides in. We analyze the robustness of these dynamically switchable logic gates, and characterize the trade-off between reliability and efficiency in their function.
The present study aims at integrating drug-releasing materials with signal-processing biocomputing systems. Enzymes alanine transaminase (ALT) and aspartate transaminase (AST)---biomarkers for liver injury---were logically processed by a biocatalytic cascade realizing Boolean AND gate. Citrate produced in the system was used to trigger a drug-mimicking release from alginate microspheres. In order to differentiate low vs. high concentration signals, the microspheres were coated with a protective shell composed of layer-by-layer adsorbed poly(L-lysine) and alginate. The alginate core of the micr…
After being considered as a nuisance to be filtered out, it became recently clear that biochemical noise plays a complex role, often fully functional, for a genetic network. The influence of intrinsic and extrinsic noises on genetic networks has intensively been investigated in last ten years, though contributions on the co-presence of both are sparse. Extrinsic noise is usually modeled as an unbounded white or colored gaussian stochastic process, even though realistic stochastic perturbations are clearly bounded. In this paper we consider Gillespie-like stochastic models of nonlinear networks…
The inherent behavioral variability exhibited by stochastic biochemical systems makes it a challenging task for human experts to manually analyze them. Computational modeling of such systems helps in investigating and predicting the behaviors of the underlying biochemical processes but at the same time introduces the presence of several unknown parameters. A key challenge faced in this scenario is to determine the values of these unknown parameters against known behavioral specifications. The solutions that have been presented so far estimate the parameters of a given model against a single sp…
Cellular signaling involves the transmission of environmental information through cascades of stochastic biochemical reactions, inevitably introducing noise that compromises signal fidelity. Each stage of the cascade often takes the form of a kinase-phosphatase push-pull network, a basic unit of signaling pathways whose malfunction is linked with a host of cancers. We show this ubiquitous enzymatic network motif effectively behaves as a Wiener-Kolmogorov (WK) optimal noise filter. Using concepts from umbral calculus, we generalize the linear WK theory, originally introduced in the context of c…
The first realization of a biomolecular OR gate function with double-sigmoid response (sigmoid in both inputs) is reported. Two chemical inputs activate the enzymatic gate processes resulting in the output signal: chromogen oxidation, which occurs when either one of the inputs or both are present (corresponding to the OR binary function), and can be optically detected. High-quality gate functioning in handling of sources of noise is enabled by "filtering" involving pH control with an added buffer. The resulting gate response is sigmoid in both inputs when proper system parameters are chosen, a…
We review enzymatic systems which involve biocatalytic reactions utilized for information processing (biocomputing). Extensive ongoing research in biocomputing, mimicking Boolean logic gates has been motivated by potential applications in biotechnology and medicine. Furthermore, novel sensor concepts have been contemplated with multiple inputs processed biochemically before the final output is coupled to transducing "smart-material" electrodes and other systems. These applications have warranted recent emphasis on networking of biocomputing gates. First few-gate networks have been experimental…
We consider a realization of the XOR logic gate in a process biocatalyzed by an enzyme (here horseradish peroxidase: HRP), the function of which can be inhibited by a substrate (hydrogen peroxide for HRP), when the latter is inputted at large enough concentrations. A model is developed for describing such systems in an approach suitable for evaluation of the analog noise amplification properties of the gate. The obtained data are fitted for gate quality evaluation within the developed model, and we discuss aspects of devising XOR gates for functioning in "biocomputing" systems utilizing biomol…
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 bei…
Motivation: Protein interactions are fundamental building blocks of biochemical reaction systems underlying cellular functions. The complexity and functionality of such systems emerge not from the protein interactions themselves but from the dependencies between these interactions. Therefore, a comprehensive approach for integrating and using information about such dependencies is required. Results: We present an approach for endowing protein networks with interaction dependencies using propositional logic, thereby obtaining protein hypernetworks. First we demonstrate how this framework straig…
Information processing and decision making is based upon logic operations, which in cellular networks has been well characterized at the level of transcription. In recent years however, both experimentalists and theorists have begun to appreciate that cellular decision making can also be performed at the level of a single protein, giving rise to the notion of protein logic. Here we systematically explore protein logic using a well known statistical mechanical model. As an example system, we focus on receptors which bind either one or two ligands, and their associated dimers. Notably, we find t…
A ubiquitous building block of signaling pathways is a cycle of covalent modification (e.g., phosphorylation and dephosphorylation in MAPK cascades). Our paper explores the kind of information processing and filtering that can be accomplished by this simple biochemical circuit. Signaling cycles are particularly known for exhibiting a highly sigmoidal (ultrasensitive) input-output characteristic in a certain steady-state regime. Here we systematically study the cycle's steady-state behavior and its response to time-varying stimuli. We demonstrate that the cycle can actually operate in four diff…
The design and synthesis of complex and large mimicked biochemical networks de novo is an unsolved problem in synthetic biology. To address this limitation without resorting to ad hoc computations and experiments, a predictive mathematical theory is required to reduce these complex chemical networks into natural physico-chemical expressions. Here we provide a theory that offers a physico-chemical expression for a large chemical network that is almost arbitrarily both nonlinear and complex. Unexpectedly, the theory demonstrates that such networks can be decomposed into reactions based solely on…
CANA: A python package for quantifying control and canalization in Boolean Networks
School of Informatics, Computing, and Engineering Indiana University（印第安纳大学信息学、计算与工程学院）；CAPES Foundation, Ministry of Education of Brazil（巴西教育部CAPAS基金会）；Center for Complex Networks Research, Northeastern University（东北大学复杂网络研究中心）
The study of biochemical pathways usually focuses on a small section of a protein interactions network. Two distinct sources contribute to the noise in such a system: intrinsic noise, inherent in the studied reactions, and extrinsic noise generated in other parts of the network or in the environment. We study the effect of extrinsic noise entering the system through a nonlinear uptake reaction which acts as a nonlinear filter. Varying input noise intensity varies the mean of the noise after the passage through the filter, which changes the stability properties of the system. The steady-state d…
