Exploring the Programmability of Autocatalytic Chemical Reaction Networks

Exploring the Programmability of Autocatalytic Chemical Reaction Networks | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Physical Sciences - Article Exploring the Programmability of Autocatalytic Chemical Reaction Networks Albert Wong, Dmitrii Kriukov, Jurriaan Huskens This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-4379130/v1 This work is licensed under a CC BY 4.0 License Status: Published Journal Publication published 27 Sep, 2024 Read the published version in Nature Communications → Version 1 posted You are reading this latest preprint version Abstract Chemical reaction networks (CRNs) could offer chemical complexity 1 to contribute to future intelligent material design 2 or neuromorphic computing technologies 3,4 . Recent advances in systems chemistry use the complex Belousov–Zhabotinsky 5-7 and Formose reactions 8,9 , or simpler chemical systems with fewer feedback loops 10-12 , to demonstrate that (spatio)temporal patterns can be harnessed to emulate properties important for intelligent behavior ( i.e. , the ability to perceive information and retain it as knowledge to execute complex tasks 13 ). In all examples, autocatalysis appears an essential element for facilitating a nonlinear response. How this chemical analogue of a positive feedback mechanism 14,15 can be reconfigured in a programmable manner is, however, unknown. Here, we developed a strategy that uses metal ions (Ca 2+ , La 3+ , and Nd 3+ ) to control the rate of a trypsin-catalysed autocatalytic reaction network. A flow setup is employed to sustain the reaction network under out-of-equilibrium conditions and demonstrate that various kinetically controllable responses can be mapped onto polynomial and Boolean functions. Remarkably, these functions cannot only be programmed but their temporal and history-dependent nature bestows them with neuromorphic properties, promising novel strategies in designing intelligent chemical systems. Beyond, the easy-to-use method to control autocatalysis will impact future development focusing on biocatalysis, nanobiotechnology, and the chemical origin of life. Physical sciences/Chemistry/Supramolecular chemistry Biological sciences/Biochemistry/Enzyme mechanisms Physical sciences/Nanoscience and technology/Nanobiotechnology Physical sciences/Chemistry/Chemical origin of life Physical sciences/Chemistry/Biochemistry/Biocatalysis Figures Figure 1 Figure 2 Figure 3 Figure 4 Introduction Living systems, from a simple slime mold to a more complex Venus flytrap to a highly sophisticated cephalopod, exhibit intelligent behavior 16 . That is, they have the ability to perceive information and retain it as knowledge to execute complex tasks 13 . Decision making on the molecular level is, arguably, driven by chemical reaction networks (CRNs) 17 , and have inspired chemists to design artificial systems 18,19 capable of bistability 20-22 , oscillations 23-25 , and homeostasis 26 . How feedback loops in CRNs can be tuned, scaled, and reconfigured in a programmable manner ( i.e. , accept instructions to perform a range of tasks, rather than just one), however, remains elusive. Autocatalysis—a chemical process in which the product acts as the catalyst for its own formation—is at the core of the mechanisms of the aforementioned examples of CRNs, facilitating a fast and nonlinear response to stimuli from the environment 27 . Significant progress has been made in the de-novo synthesis of autocatalytic networks 14,15 . Current design strategies to control autocatalysis for chemical functions that arise from signal amplification rely heavily on the incorporation of a component that triggers the network to release the first catalyst ( e.g. , through delay or inhibition) 10,20,25,28,29 . CRNs that use the rate of autocatalysis (changing the strength of the positive feedback) for the translation of autocatalytic systems into programmable molecular systems are unexplored. We recently reported how an autocatalytic network under out-of-equilibrium conditions could display behaviour ( e.g. , hysteresis and adaptation) important for neuromorphic systems 29 . It was shown that history-dependent behaviour could be established by controlling the amount of inhibitor present in its preceding state. Specifically, trypsinogen, Tg , is converted into trypsin, Tr , when the trypsin activation peptide (TAP) in Tg is cleaved. This conversion was regulated by an inhibitor that could control the release of the first Tr (the catalyst for this reaction). Importantly, Ca 2+ , were used to promote autocatalysis and prevent degradation of both Tg and Tr 30 . According to literature, trivalent lanthanide ions employ the same binding sites on Tg and Tr as Ca 2+ 31,32 , but can enhance the rate of trypsin autocatalysis to a greater extent than Ca 2+ 32 . Here, we explore how the use of metal ions (Ca 2+ , La 3+ , and Nd 3+ ) could allow for the design of kinetically programmable functions based on the trypsin autocatalytic network ( Fig. 1 ). A polydimethylsiloxane (PDMS)-based continuous stirred-tank reactor (CSTR) was employed to continuously feed the CSTR and remove all reactants and products. Such a flow setup not only allows for sustaining out-of-equilibrium conditions but also for introducing input sequences for the purpose of demonstrating how the ions, or mixtures thereof, can affect the rate of autocatalysis. Particularly, we show that Nd 3+ could accelerate as well as decelerate the conversion of Tg into Tr , establishing a nonlinear control over the rate of Tr autocatalysis. Using simulations and experiments, we demonstrate that input sequences with one or more metal ions allow for logical operations with defined output sequences that can be mapped onto mathematical functions ( i.e. , polynomial functions with different degrees and various logic gates). We demonstrate not only that such functions are kinetically programmable but that their temporal and history-dependent nature bestows them with properties important for the design of future intelligent chemical systems ( i.e. , long-term depression and history dependency). Results and Discussion Influencing the rate of autocatalysis We first examined the influence of the metal ions (Ca 2+ , La 3+ , and Nd 3+ ) on the rate of trypsin autocatalysis under batch conditions. Tg (100 µM), Tr (1 µM), and Ca 2+ (20 mM) were initially mixed, and we monitored the change in the concentration of Tr , [ Tr ], using a standard assay with Na-Benzoyl-DL-arginine 4-nitroanilide, BAPNA. Figure 2 a depicts a typical sigmoidal curve—a sharp transition that is characteristic to an autocatalytic conversion—can be initiated earlier when La 3+ or Nd 3+ was added to the mixture. In greater detail, Fig. 2b-d depicts the [ Tr ] at three specific time points of a set of experiments wherein we varied the concentration of the three metal ions ( Extended data Fig. 1 ). Two important effects were observed in the examined range of concentrations of the ions: i) La 3+ can accelerate the rate of autocatalysis, and the acceleration is much stronger than when Ca 2+ was used. Figure 2 b-c show that [ Tr ] increases until it saturates as [Ca 2+ ] 0 and [La 3+ ] 0 are increased. ii) Nd 3+ , in contrast, can accelerate and decelerate the rate of autocatalysis. Figure 2 d shows that the [ Tr ] increases when [Nd 3+ ] 0 increases from 0 to 0.3 mM. Upon further increase of [Nd 3+ ] 0 , however, the [ Tr ] decreases. This pattern was established in any of the three time points. Overall, the observations suggest that all examined ions change the apparent rate of autocatalysis, affecting the rate to a different extent. How the metal ions ( X ) affect Tr autocatalysis is proposed in Scheme 1 . Based on these batch experiments, we assume that i) autocatalysis cannot occur without any of the metal ions; ii) binding of the ions to Tr (depicted as [ TrX ]) can ‘activate’ autocatalysis, changing the apparent rate constant for the conversion of Tg into Tr (indicated by k x ); iii) binding of Nd 3+ to Tg (depicted as [Nd 3+ Tg ]) can ‘de-activate’ autocatalysis, inhibiting the conversion of Tg into Tr . Notably, this inhibitory effect was not observed when La 3+ or Ca 2+ were used. We performed control experiments using gel electrophoresis ( i.e. , SDS-PAGE) for samples from the reaction mixtures to examine the product distribution as a function of [Nd 3+ ] 0 ( Extended data Fig. 2 ). The gels revealed that, only at optimal [Nd 3+ ] 0 (0.3–0.4 mM), Tg is fully hydrolysed after 16 min of the reaction. Intrigued by this observation, we investigated if the effect of [Nd] 0 on autocatalysis can be explained using a Michaelis-Menten model. Extended data Fig. 3 , however, shows that both kinetic parameters ( K M and k cat ) change as a function of [Nd 3+ ] 0 , and led us to the conclusion that the Michaelis-Menten approach could not provide a straightforward explanation for the observed nonlinear effect. Alternatively, a first-order degradation of Tr was also investigated but Extended data Fig. 4 showed that such degradation step could not explain the nonlinear effect either. Considering these limitations, we developed a mathematical model based on the set of ordinary differential equations according to the processes in Scheme 1 . Quadratic equations are incorporated to account for the binding of the ions to the proteins. Details of the mathematical model is appended to Supplementary Information . Nonlinear effect of Nd 3+ in flow Next, we establish control over trypsin concentration in time under flow conditions. Figure 3 a depicts a flow experiment wherein we changed the [Nd 3+ ] 0 (from 0 to 0.7 mM and back in steps of 0.05 mM per 30 min) and monitored [ Tr ] continuously. Essentially, the residence time in the CSTR, t (determined by the volume of the CSTR divided over the total flow rate), was comparable to our batch experiments with a reaction time of 6 min. In accordance with our batch experiments, a maximum in [ Tr ] could indeed be reached when the input satisfied the condition 0.20 ≤ [Nd 3+ ] 0 ≤ 0.40. Outside this range, we found that [ Tr ] was significantly lower. Figure 3 b summarizes how the use of t as a flow parameter could tune the behaviour of the system, characterized by an apparent non-equilibrium steady state, [ Tr ]*, which we determined as the average [ Tr ] over the last 5 min before [Nd 3+ ] 0 was changed. The use of a higher residence time (t = 10 min) could maintain the nonlinear response but with an elevate values of [ Tr ]. Hence, while a change in the flow parameter changes the absolute concentrations in [ Tr ]*, the nonlinear effect of Nd 3+ on Tr autocatalysis remains. We increase the level of control by forcing competitive binding ( 30 ) among several ions. Figure 3 c illustrates our approach wherein five different values of [Nd 3+ ] 0 were used to change the rate of Tr autocatalysis in the presence of a second ion (La 3+ or Ca 2+ ). The addition of a ‘slower’ ion [Ca 2+ ] 0 (20 mM) resulted in the same nonlinear response as in the absence of a second ion (black line) but changed in the position of its local maximum (dashed line). That is, the maximum [ Tr ]* remained around 35 µM but moved towards slightly higher [Nd 3+ ] 0 compared to the systems without Ca 2+ . Similarly, the addition of the ‘faster’ [La 3+ ] also resulted in the same nonlinear response but led to a change in the position of its local maximum into the direction of a lower [Nd 3+ ] 0 (dotted line). We used our model to confirm the observation that the local maximum can shift in different directions in the presence of the metal ions ( Extended data Fig. 5 ). The opposing effects that the mixtures of ions induce can be mapped onto polynomial functions with different degrees ( Fig. 3d ). The relation between [ Tr ]* and [Nd 3+ ] 0 can be approximated with a quadratic function in the absence of an additional ion, and the degree of the polynomial function is therefore 2. In the presence of Ca 2+ , this relation changes but only at higher concentrations of [Nd 3+ ] 0 and therefore the nature of the polynomial function, its degree, does not change and remains 2. In the presence of La 3+ , however, the behaviour can change from a quadratic to a linear relation, and the degree of the polynomial function becomes 1. An experiment with both La 3+ and Ca 2+ shows that the competition for different binding sites allows for a combination of two opposing effects, creating a mechanism to maintain [ Tr ]* within the narrow range of [Nd 3+ ] 0 . In the presence of Ca 3+ and La 3+ , the behaviour became close to constant ( i.e. , a polynomial function with the degree 0). The mapping of a chemical output onto polynomial functions as demonstrated here underscores the flexibility of using metal ions in controlling the autocatalytic network. Nd 3+ -induced temporal logic operations Next, we developed a procedure to obtain Boolean functions for [ Tr ]* by varying only [Nd 3+ ] 0 . Figure 4 a illustrates our concept wherein three different values for [Nd 3+ ] 0 of a given range (a minimum, maximum, and a value in between) correspond to four binary combinations (0|0; 0|1; 1|1; 1|0). The notation [Nd 3+ ] A|B is used to represent the input sequence [Nd 3+ ] 0|0 ; [Nd 3+ ] 1|0 ; [Nd 3+ ] 1|1 ; [Nd 3+ ] 0|1 . As an example, Fig. 4b shows the output sequences for the gates NAND and XOR. We chose the not-AND (NAND) and exclusive-OR (XOR) gates because they are exemplary for functional completeness 34 and nonlinear classification 35 , and are considered difficult to construct using chemical systems 36,37 . The differences between the two gates reside on the range of [Nd 3+ ] 0 that was applied: the maximum [Nd 3+ ] 0 in both cases is 0.6 mM but minimum [Nd 3+ ] 0 is 0.2 and 0 mM, respectively. The top graph in Fig. 4b , shows five conditions wherein [Nd 3+ ] 0 is changed in steps of 45 min. The first four conditions represent the input 0|0; 0|1; 1|1; 1|0, with the corresponding response in Tr for the two sequences demonstrated in the below graph. A threshold [ Tr ] with an arbitrary value (20 µM), was used to determine if the observed values in the sequence were true, ‘1’ or false, ‘0’. For the first sequence, [ Tr ]* exceeded the threshold (red line) at all conditions, except for [Nd 3+ ] 1|1 . Hence, the input combination resulted in an output sequence representing the NAND-gate: [ Tr ] 0|0 = 1 ; [ Tr ] 0|1 = 1 ; [ Tr ] 1|0 = 1 ; [ Tr ] 1|1 = 0 . For XOR, [ Tr ]* exceeded the threshold at two conditions, namely for [Nd 3+ ] 0|1 and [Nd 3+ ] 1|0 , yielding the sequence representing the XOR-gate: [ Tr ] 0|0 = 0 ; [ Tr ] 0|1 = 1 ; [ Tr ] 1|0 = 1 ; [ Tr ] 1|1= 0 . The initial value was recovered in the final condition ([ Tr ]* at [Nd 3+ ] 0|0 ), demonstrating that the output signal can be reset. Other gates (AND, OR, NOR) can be developed using a similar procedure ( Extended data Fig. 6 ). Figure 4 c summarizes these experiments by plotting the output concentration as a function of [Nd 3+ ] 0 . The results underline that a change in the minimum and maximum of [Nd 3+ ] 0 is sufficient to create different logic operations. We, thus, showed that the autocatalytic reaction can accept instructions (in this case, encoded as an input sequence based on [Nd 3+ ]) to perform a range of logic operations. We used our mathematical model to simulate the response of this autocatalytic network based on changes in the residence time and the concentration of the metal ion. A procedure was developed to discriminate between the different types of logic. Briefly, the ratio [Tr] 1|1 :[Tr] 1|0 was used to distinguish AND, OR and XOR and the ratio ([ Tr ] 1|1 +[ Tr ] 1|0 ):[Tr] 0|0 was used to distinguish NAND and NOR ( Supplementary Information ). Figure 4 d depicts the simulated phase space of the autocatalytic network and shows that the regions of AND, NAND, NOR, XOR and OR can be found in a narrow range of parameters, and depending on the [Nd 3+ ] 0|0 the regions can overlap. Each grid in the phase space represents a predicted response in [ Tr ] ss as a function of input sequence (0|0; 0|1; 1|1; 1|0), and [Nd 3+ ] 1|1 is placed on the Y axis. [Nd 3+ ] 0|0 on Fig. 4d for AND, OR, XOR equals 0 mM, and for NAND and NOR equals 0.2 mM. A comparison between the simulated areas for, and experimentally observed, logic gates (open symbols) demonstrates that the model is in good agreement with the experiments. The method of creating logic gates is not restricted to Nd 3+ , and ions can be combined to change the phase space ( Extended data Fig. 7) . More importantly, we show that lowering the residence time during the experiment (indicated with the red symbols) could change the output sequence from a XOR or an AND into an OR gate, demonstrating that the Boolean functions can be readily tuned ( Extended data Fig. 8) . Bistability in temporal logic operations The use of an external component such as an inhibitor for thresholding provides further control over the network properties. Figure 4 e shows a sequence wherein the [Nd 3+ ] 0 was changed from a low to a high value, and vice versa, in the presence of a trypsin inhibitor ( I , at a concentration of 8, 4, and 2 µM). Overall, [ Tr ] changes from a high to a low concentration when [Nd 3+ ] 0 was changed from 0.3 to 0.8 mM. At an inhibitor concentration that appeared to be too high ([ I ] 0 =8 µM), we observed that original [ Tr ]* cannot be recovered and instead remains low when [Nd 3+ ] 0 was changed in the opposite direction (from 0.8 to 0.3 mM). The observation that a pulse in [Nd 3+ ] 0 ( i.e. , the sequence 0.3-0.8-0.3 mM) enabled a retention of the low [ Tr ]* demonstrates that the autocatalytic network, in the presence of the inhibitor, is capable of a so-called long-term depression of the input. This effect disappeared when the inhibitor concentration was lowered to [ I ] 0 = 4 µM but notably [ Tr ]* remains to depend on the amount of inhibitor present in its preceding state, i.e. , the response is history dependent. Validations in Extended data Fig. 9 supports the observation that the XOR-gate is (and perhaps other logic gates are) history dependent. The history dependency was lost when [ I ] 0 = 2 µM was applied and, instead, the response became bistable. That the signal could fully recover, however, shows that a trace of inhibitor allows for an increased robustness of the output signal. Hence, while the metal ion provides control for tuning and switching of the logic operation, an inhibitor was introduced as an additional control parameter for strengthening or weakening its history dependency. Conclusion This work shows that achieving control over a single positive feedback mechanism can offer sufficient complexity to develop kinetically controllable functions. Metal ions were used to target the activity of the catalyst in a feedback element—a strategy which is potentially achievable through a range of physical and chemical strategies—and provided the necessary control over the autocatalytic conversion of trypsinogen into trypsin. We demonstrated that trypsin autocatalysis can be controlled to emulate polynomial functions with different degrees and Boolean functions with various outcomes ( e.g. , AND, OR, XOR, NAND, NOR). Additionally, a trypsin inhibitor was incorporated into the network to create a bistable system capable of long-term depression of the input and history dependency in the output ( i.e. , characteristics for neuromorphic behaviour). We envision that this work will offer novel strategies to exploit the programmability of small and simple chemical reaction networks for building artificial systems with responsive 38 , adaptive 39 , and other life-like properties 2 characteristic for intelligent systems. Such a prospect will undoubtably impact many scientific domains including those that focus on the exploration of out-of-equilibrium chemical systems, synthesis of artificial life, and design of autonomous molecular materials. Methods Materials Bovine trypsinogen (Type I; ~10,000 BAEE units/mg), bovine trypsin (≥ 7,500 BAEE units/mg solid), Nα-Benzoyl-DL-arginine 4-nitroanilide hydrochloride (BAPNA), and Ln(NO 3 ) 3 *6H2O salts (99.9% purity) were purchased from Sigma. Trypsin inhibitor from soybean (STI) was purchased from Roche. Water is purified using a Millipore Milli-Q lab water system. Other solvents and buffers (i.e., Dimethyl sulfoxide (DMSO), Dimethylformamide (DMFA), tris(hydroxymethyl)aminomethane (TRIS) were obtained commercially and were used without purification. Polydimethylsiloxane (PDMS), 184 Silicon Elastomer and 184 Curing Agent, was purchased from SYLGARD. For 3D printer Vero Clear material and SUP706b supporting material were purchased from Stratasys. Hamilton gastight glass syringes (1000 series) which have volume of 1 mL, 2.5 mL, 10 mL and 25 mL, and were purchased from Hamilton. Polytetrafluoroethylene (PTFE) tubings (I.D. x O.D. 0.5 x 1 mm; 1/16 x 0.010 inch) were purchased from Inacom. For bovine trypsinogen Type I from Sigma Aldrich, we found significant differences between batches of this product. We suspect inconsistency in the purity of the product because the time of complete auto-activation in same conditions was varying from flask to flask. Traces of trypsin and Ca 2+ are suspected sources of impurity. Reported data is collected from two chemically closest batches. It is important, that all stock solutions of trypsin and trypsinogen were not stronger that 0.4 mM and had 4 mM HCl added to decrease the degradation rate. In experiments with Ca 2+ all stock solutions also contained 20 mM CaCl 2 for the same purpose. Equipment A Stratasys Objet Pro 30 3D printer was used for printing continuous-flow stirred-tank reactors (CFSTRs) master molds. BINDER E 28 oven was used for PDMS curing. ZEPTO plasma oven from Diener Electronic was used for PDMS and glass surface activation. Batch experiments for samples for SDS-PAGE were performed in separate vials with mixing and temperature control by Eppendorf Thermomixer Comfort. PerkinElmer EnSpire 2300 plate reader was used for absorbance detection for other batch experiments. Flow experiments were performed with Nemesys low pressure pumps from CETONI with Qmix Lambda custom absorbance detector with LED light source and 8 mm length flow cell. Trypsin assay Reaction mixtures containing trypsin were diluted 1:10, 1:20 or 1:50 with freshly prepared detection mixture (1 mM BAPNA from 50 mM stock in DMSO, 100 mM TRIS-HCl pH = 7.8 with 20 mM CaCl 2 ) and put inside the absorbance plate reader for initial shaking and further absorbance measurement. Initial slopes of absorbance at 405 nm were transformed into trypsin concentration by a linear calibration curve. SDS PAGE protocol Aliquots of reaction mixture were quenched 1:3 by 0.2 M KHSO4. 4 µL of Laemmle 4X buffer + 10 µl of an aliquot + 2 µL NaOH 5M were put on a gel and ran at 30 mA with 250 mM TRIS-HCl, 1.92M Glycine, 1% SDS running buffer. Stacking gel: 120 mM TRIS-HCl pH = 6, 1.5% acrylamide 30:0.8, 0.001% SDS, 0.0012% APS, 0.001% TEMED. Running gel: 370 mM TRIS-HCl pH = 8.8, 60% acrylamide 30:0.8, 0.002% SDS, 0.001% APS, 0.0008% TEMED. Proteins were stained by Bradford technique, namely, 2g of Coomassie Blue R250 in 10% acetic acid and 40% ethanol solution. Fabrication of the CSTR 3D models of 90 ml CSTRs were 3D-printed. PDMS CSTRs upper parts were prepared by covering prints with degassed 1:10 mixture of curing agent with silicone elastomer base. PDMS mixture was polymerized at 75°C for 30 minutes. Holes for tubings in solidified CSTRs upper parts were made by Harris Uni-Core 1.00 puncher. Glass slide was cleaned with isopropanol and scotch tape, and then treated in oxygen plasma oven for 2–4 minutes within PDMS CSTRs upper parts before attaching surfaces. For continuous stirring 3 mm diameter Teflon coated spherical magnetic stirrers were incorporated inside reactor. Final working volume of CSTR was 76 µl (after volume occupied by the magnetic stirrer was subtracted). Flow experiments Low pressure pumps (CETONI Nemesys) were controlled by CETONI Elements software and connected to two CSTRs (experiment CSTR and reporting CSTR) sequentially connected by PTFE tubings ( Supplementary Fig. 1 ). First reactor served as a main reaction chamber whereas the second was receiving its outflow and reporting solution at the constant (2:1) ratio. Reporting solution consisted of 4 mM BAPNA in mixture of MQ:DMSO:DMFA (0.2:0.08:0.72). The outflow through the sequence of reactors was passing through the Qmix Lambda flow detector after which the solution was collected in the waste container. The result of the measurement was visualized using the online plotting function of CETONI Elements software. We used two wavelength bands to detect pNA: 620-630nm (internal standard wavelengths, where pNA does not absorb light) and 400-450nm (detection wavelengths, where pNA absorbs light). Result of division of internal standard signal by detection signal was calibrated for the concentration of trypsin in the reaction chamber. Artifacts from air bubbles were removed manually, then 60 or 180 pts FFT smoothing procedure was implemented to results in OriginPro2021. More detailed information can be found in literature 27 . Mathematical modelling Our mathematical model (see Supplementary Materials ) uses ordinary differential equations (script compdeq ) and quadratic equations (script compsqeq ) to simulate reaction trajectories of our network in flow. The model is designed for determining the steady state and transient concentrations of Tr as a function of the initial conditions: concentrations of species and inflow concentrations of species. Specifically, the model (script comp ) recalculates equilibrium concentrations of the complexes (script compsqeq ) after each step in the numerical integration (script compdeq ). The list of reactions and complexes used can be found in Supplementary Table S1 . All kinetic and thermodynamic constants were estimated from published data 29,30 to support experimental results. The assumptions required for developing the mathematical model are appended to Supplementary Information . Software Origin Pro 2021 was used for processing raw data. CETONI Elements software (v. 20210406) was used for programming low pressure pumps. SOLIDWORKS 2022 was used for designing 3D models. MATLAB 2023a was used for mathematical modelling. Declarations Author contributions : ASYW conceived and planned the project. ASYW and JH supervised the project. DVK performed the experiments, designed the mathematical model, performed the simulations. ASYW and DVK wrote the manuscript. All authors contributed to revising the manuscript. (In CrediT terms, Conceptualization: ASYW and DVK. Methodology: ASYW and DVK. Investigation: DVK. Visualization: ASYW and DVK. Funding acquisition: ASYW. Project administration: ASYW. Supervision: ASYW and JH. Writing – original draft: ASYW and DVK. Writing – review & editing: ASYW, DVK and JH). Supplementary Information is available for this paper. Correspondence and requests for materials should be addressed to [email protected] Peer review information includes the names of reviewers who agree to be cited and is completed by Nature staff during proofing Reprints and permissions information is available at www.nature.com/reprints . Funding The project is supported by the Netherlands Organization for Scientific Research (NWO, Veni Grant 202.155 to A.S.Y.W). Competing interests: Authors declare that they have no competing interests. Additional information Data integral to the work is provided in Extended data . Scripts are provided as separate files in Supplementary Materials Funding The project is supported by the Netherlands Organization for Scientific Research (NWO, Veni Grant 202.155 to A.S.Y.W). Competing interests: Authors declare that they have no competing interests. Additional information Data integral to the work is provided in Extended data . 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Nature 577, 341–345 (2020). Samiappan, M., Dadon, Z., Ashkenasy, G. Replication NAND gate with light as input and output. Chem. Commun . 47 , 710–712 (2010). Katz, E. Boolean Logic Gates Realized with Enzyme‐catalyzed Reactions – Unusual Look at Usual Chemical Reactions. ChemPhysChem 20 , 9–22 (2019). Lancia, F., Ryabchun, A., Katsonis, N. Life-like motion driven by artificial molecular machines. Nat. Rev. Chem . 3 , 536–551 (2019). Lerch, M. M., Grinthal, A., Aizenberg, J. Viewpoint: Homeostasis as Inspiration—Toward Interactive Materials. Adv. Mater . 32 , 1905554 (2020). Schemes Scheme 1 is available in the Supplementary Files section Additional Declarations There is NO Competing Interest. Supplementary Files 20240506DKProgrammabilitySI.pdf Supplementary Information 20240506DKProgrammabilityExtData.pdf Extended Data Scheme1.png Scheme 1:Proposed mechanism for the cation-induced activation of Tr autocatalysis. 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Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-4379130","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Physical Sciences - Article","associatedPublications":[],"authors":[{"id":305561868,"identity":"4a2982c5-0b08-4241-b3b9-78a58efa5694","order_by":0,"name":"Albert Wong","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA8ElEQVRIiWNgGAWjYDACdh44k/EBQrgAjxZmkJYECNMAzGADsQ2I08ImQZQW/mbeg48rfzAk9ku3X6vm/XFYzly++QBzAR4tEof5kg3PJDAkzpxzpuw2T8JhY8s2tgTmGfgcdpjHTLIhgSF3w42cNKCW24kbjvEYMPPg0SJ/mMf8J0xLMVBL/YZj/B/wajEA2sII0ZJ+jBmoJcHgGA8DXi2GQL9INqRJ1M+ckcMsOSftv+GGY2lAc/BokTvee/Bjg42NMb9E+sMPb2zS5A0OH374mKcCj/chQAKIkUw+QFADBLA/IFLhKBgFo2AUjDQAAGkNTHqU6p3TAAAAAElFTkSuQmCC","orcid":"https://orcid.org/0000-0001-6484-9087","institution":"University of Twente","correspondingAuthor":true,"prefix":"","firstName":"Albert","middleName":"","lastName":"Wong","suffix":""},{"id":305561869,"identity":"136ae012-4a64-4801-aaa1-499000414c81","order_by":1,"name":"Dmitrii Kriukov","email":"","orcid":"https://orcid.org/0009-0006-6465-6844","institution":"University of Twente","correspondingAuthor":false,"prefix":"","firstName":"Dmitrii","middleName":"","lastName":"Kriukov","suffix":""},{"id":305561870,"identity":"f119156f-f50d-458d-ad04-8f4563ac45e3","order_by":2,"name":"Jurriaan Huskens","email":"","orcid":"https://orcid.org/0000-0002-4596-9179","institution":"University of Twente","correspondingAuthor":false,"prefix":"","firstName":"Jurriaan","middleName":"","lastName":"Huskens","suffix":""}],"badges":[],"createdAt":"2024-05-06 21:55:10","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-4379130/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-4379130/v1","draftVersion":[],"editorialEvents":[{"content":"https://doi.org/10.1038/s41467-024-52649-z","type":"published","date":"2024-09-27T04:00:00+00:00"}],"editorialNote":"","failedWorkflow":false,"files":[{"id":57821023,"identity":"8df0d88c-2976-415a-847b-9db96813253c","added_by":"auto","created_at":"2024-06-06 05:50:06","extension":"png","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":148741,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eA programmable autocatalytic network under out-of-equilibrium conditions. \u003c/strong\u003eTrypsin, \u003cem\u003eTr\u003c/em\u003e, acts as a catalyst for the conversion of its precursor trypsinogen, \u003cem\u003eTg\u003c/em\u003e, into \u003cem\u003eTr\u003c/em\u003e, resulting in autocatalysis (highlighted in yellow). The rate and onset of the autocatalysis can be controlled by the metal ion, \u003cem\u003eX\u003c/em\u003e, and the inhibitor, \u003cem\u003eI\u003c/em\u003e. Together, they form a chemical reaction network (CRN) which is maintained under out-of-equilibrium conditions using a continuously stirred tank reactor. The CRN accepts instructions encoded in a defined sequence of concentrations of metal ions, and/or inhibitor—the INPUT—and performs a range of tasks as a defined sequence that could be mapped onto a mathematical function—the OUTPUT.\u003c/p\u003e","description":"","filename":"image1.png","url":"https://assets-eu.researchsquare.com/files/rs-4379130/v1/e327aef13b5c3fe4634bf357.png"},{"id":57820582,"identity":"7393d833-aafc-4042-8695-eb3d19162f55","added_by":"auto","created_at":"2024-06-06 05:42:06","extension":"png","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":138330,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eCation-dependent control over the rate of trypsinogen autocatalysis. a\u003c/strong\u003e,\u003cstrong\u003e \u003c/strong\u003eInfluence\u003cstrong\u003e \u003c/strong\u003eof\u003cstrong\u003e \u003c/strong\u003eCa\u003csup\u003e2+\u003c/sup\u003e on the autocatalytic conversion of \u003cem\u003eTg\u003c/em\u003e into \u003cem\u003eTr\u003c/em\u003e. The addition of La\u003csup\u003e3+ \u003c/sup\u003eand\u003csup\u003e \u003c/sup\u003eNd\u003csup\u003e3+ \u003c/sup\u003esignificantly increase the rate of \u003cem\u003eTr\u003c/em\u003e autocatalysis. \u003cstrong\u003ea-d\u003c/strong\u003e, Concentration of trypsin, [\u003cem\u003eTr\u003c/em\u003e], as a function of the metal ion and its concentration. Depicted are data at three time points (see \u003cstrong\u003eExtended data Fig. 1\u003c/strong\u003e). Initial conditions: [\u003cem\u003eTg\u003c/em\u003e]\u003csub\u003e0\u003c/sub\u003e=100µM and [\u003cem\u003eTr\u003c/em\u003e]\u003csub\u003e0\u003c/sub\u003e=1µM. Initial conditions,\u003cstrong\u003ea-d\u003c/strong\u003e: [TRIS-HCl] =100 mM (pH 7.8), T=21-23\u003csup\u003eo\u003c/sup\u003eC.\u003c/p\u003e","description":"","filename":"image2.png","url":"https://assets-eu.researchsquare.com/files/rs-4379130/v1/1ab1a3239129be9057bca7e3.png"},{"id":57821630,"identity":"a999661c-6ecd-40d5-a118-76515f6f7280","added_by":"auto","created_at":"2024-06-06 05:58:06","extension":"png","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":133365,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eControl over\u003c/strong\u003e \u003cstrong\u003eNd\u003c/strong\u003e\u003csup\u003e\u003cstrong\u003e3+\u003c/strong\u003e\u003c/sup\u003e\u003cstrong\u003e-induced nonlinearity under continuous flow conditions.\u003c/strong\u003e \u003cstrong\u003ea\u003c/strong\u003e,\u003cstrong\u003e \u003c/strong\u003eInfluence of [Nd\u003csup\u003e3+\u003c/sup\u003e]\u003csub\u003e0\u003c/sub\u003e on the autocatalytic conversion of \u003cem\u003eTg\u003c/em\u003e into \u003cem\u003eTr\u003c/em\u003e in a CSTR (76 uL). [Nd]\u003csub\u003e0\u003c/sub\u003e was changed at regular intervals, and programmed by changing [Nd\u003csup\u003e3+\u003c/sup\u003e]\u003csub\u003efeed\u003c/sub\u003e synchronously with an additional syringe containing TRIS-HCl buffer, pH=7.8. \u003cstrong\u003eb\u003c/strong\u003e, Biphasic control over\u003cstrong\u003e \u003c/strong\u003e\u003cem\u003eTr \u003c/em\u003eautocatalysis using [Nd\u003csup\u003e3+\u003c/sup\u003e]\u003csub\u003e0\u003c/sub\u003e. [\u003cem\u003eTr\u003c/em\u003e]* is the average [\u003cem\u003eTr\u003c/em\u003e] over the last 5 min before [Nd\u003csup\u003e3+\u003c/sup\u003e]\u003csub\u003e0\u003c/sub\u003e was changed in \u003cstrong\u003e3a\u003c/strong\u003e. Extended data based on a t=10 min are appended to \u003cstrong\u003eExtended data Fig. 10\u003c/strong\u003e. \u003cstrong\u003ec\u003c/strong\u003e, Influence of [Nd\u003csup\u003e3+\u003c/sup\u003e]\u003csub\u003e0\u003c/sub\u003e on the autocatalytic conversion of \u003cem\u003eTg\u003c/em\u003e into \u003cem\u003eTr\u003c/em\u003e in a CSTR, in the presence of an additional ion (Ca\u003csup\u003e2+\u003c/sup\u003e and La\u003csup\u003e3+\u003c/sup\u003e). \u003cstrong\u003ed\u003c/strong\u003e, Additional metal ions allow for manipulations with the shape of [Nd\u003csup\u003e3+\u003c/sup\u003e]\u003csub\u003e0\u003c/sub\u003e effect, that can be mapped onto polynomial functions with different degrees (indicated with n). Extended simulated data is appended to \u003cstrong\u003eExtended data Fig. 5\u003c/strong\u003e. For\u003cstrong\u003e a-d\u003c/strong\u003e, [\u003cem\u003eTr\u003c/em\u003e] was determined using Na-Benzoyl-DL-arginine 4-nitroanilide (BAPNA). Other initial conditions: [\u003cem\u003eTg\u003c/em\u003e]\u003csub\u003efeed\u003c/sub\u003e=0.25 mM, [\u003cem\u003eTr\u003c/em\u003e]\u003csub\u003efeed\u003c/sub\u003e=0.01 mM, and [Nd\u003csup\u003e3+\u003c/sup\u003e]\u003csub\u003efeed\u003c/sub\u003e=5 mM. For \u003cstrong\u003eb\u003c/strong\u003e and \u003cstrong\u003ed\u003c/strong\u003e conditions were: [TRIS-HCl]\u003csub\u003e0\u003c/sub\u003e=60-100 mM (pH 7.8), T=21-23\u003csup\u003eo\u003c/sup\u003eC, [\u003cem\u003eTg\u003c/em\u003e]\u003csub\u003e0\u003c/sub\u003e=100 µM, [\u003cem\u003eTr\u003c/em\u003e]\u003csub\u003e0\u003c/sub\u003e=1 µM, t=5 min.\u003c/p\u003e","description":"","filename":"image3.png","url":"https://assets-eu.researchsquare.com/files/rs-4379130/v1/3fae2ca2769a9b46a6098494.png"},{"id":57820586,"identity":"61adb876-c01a-451d-a64f-d2e2260b0b88","added_by":"auto","created_at":"2024-06-06 05:42:07","extension":"png","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":335703,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eNd\u003c/strong\u003e\u003csup\u003e\u003cstrong\u003e3+\u003c/strong\u003e\u003c/sup\u003e\u003cstrong\u003e-induced Boolean logic functions.a\u003c/strong\u003e,\u003cstrong\u003e \u003c/strong\u003eConceptual scheme of the approach towards Boolean logic functions implementation.\u003cstrong\u003e b\u003c/strong\u003e, Demonstrations of a NAND and XOR gate. Top panel shows the input sequence encoded in [Nd\u003csup\u003e3+\u003c/sup\u003e]\u003csub\u003eA|B\u003c/sub\u003e. Bottom panel shows the system’s response observed as [\u003cem\u003eTr\u003c/em\u003e](t). Initial conditions: [TRIS-HCl]\u003csub\u003e0\u003c/sub\u003e=60-100 mM (pH 7.8), T=21-23\u003csup\u003eo\u003c/sup\u003eC, [Tg]\u003csub\u003e0\u003c/sub\u003e=100 µM, [Tr]\u003csub\u003e0\u003c/sub\u003e=1 µM, t=5 min. The average from triplicated sequence showed for XOR.\u003cstrong\u003e c\u003c/strong\u003e, Boolean functions determined by an input sequence of [Nd\u003csup\u003e3+\u003c/sup\u003e]\u003csub\u003e0\u003c/sub\u003e. The minima and maxima of [Nd\u003csup\u003e3+\u003c/sup\u003e]\u003csub\u003e0\u003c/sub\u003e are changed gradually in the demonstrations from top to bottom to create five logic gates. [\u003cem\u003eTr\u003c/em\u003e]*\u003csub\u003e \u003c/sub\u003eis determined\u003csub\u003e \u003c/sub\u003ebased on the time series appended to \u003cstrong\u003eExtended Data Fig. 6\u003c/strong\u003e. \u003cstrong\u003ed\u003c/strong\u003e, Computational investigation of the phase space wherein the logic gates can be defined. The ratio between steady states of [\u003cem\u003eTr\u003c/em\u003e]\u003csub\u003e0|0\u003c/sub\u003e\u003cstrong\u003e, \u003c/strong\u003e[\u003cem\u003eTr\u003c/em\u003e]\u003csub\u003e0|1 \u003c/sub\u003eand\u003cstrong\u003e \u003c/strong\u003e[\u003cem\u003eTr\u003c/em\u003e]\u003csub\u003e1|1\u003c/sub\u003e determines the type of gate (\u003cstrong\u003eSupplementary Information\u003c/strong\u003e). The bottom part of the Fig. indicates transformation of gates when residence time was changed (for time series, see \u003cstrong\u003eExtended Data Fig. 8\u003c/strong\u003e). Additional simulated phase spaces in the presence of La\u003csup\u003e3+\u003c/sup\u003e and Ca\u003csup\u003e2+\u003c/sup\u003e are appended to\u003cstrong\u003e Extended Data Fig. 7\u003c/strong\u003e.\u003cstrong\u003e e\u003c/strong\u003e,\u003cstrong\u003e \u003c/strong\u003eAdditional control using Soybean Trypsin inhibitor, \u003cem\u003eI\u003c/em\u003e, at a concentration of 8, 4, and 2 µM. Experimental conditions: [TRIS-HCl]\u003csub\u003e0\u003c/sub\u003e=75-100 mM (pH 7.8), T=21-23\u003csup\u003eo\u003c/sup\u003eC, [Tg]\u003csub\u003e0\u003c/sub\u003e=100 µM, [Tr]\u003csub\u003e0\u003c/sub\u003e=1 µM, 20 mM CaCl\u003csub\u003e2\u003c/sub\u003e, t =4.5 min.\u003c/p\u003e","description":"","filename":"image4.png","url":"https://assets-eu.researchsquare.com/files/rs-4379130/v1/cc70e66c9ab022a68943f867.png"},{"id":65485027,"identity":"9be64c4f-fd4b-4237-91c4-75a78099c1d2","added_by":"auto","created_at":"2024-09-28 07:14:20","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":1476297,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-4379130/v1/7e2cf1b6-844f-40b9-9c5e-d952cb469cf1.pdf"},{"id":57821025,"identity":"45edc305-851e-4fb4-a117-15c68c59b121","added_by":"auto","created_at":"2024-06-06 05:50:06","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"supplement","size":324763,"visible":true,"origin":"","legend":"Supplementary Information","description":"","filename":"20240506DKProgrammabilitySI.pdf","url":"https://assets-eu.researchsquare.com/files/rs-4379130/v1/7b47ef101ce7ad40c4b56a6d.pdf"},{"id":57820585,"identity":"a3937adc-15a4-4df7-9c7a-3a87983cfc84","added_by":"auto","created_at":"2024-06-06 05:42:07","extension":"pdf","order_by":2,"title":"","display":"","copyAsset":false,"role":"supplement","size":1285977,"visible":true,"origin":"","legend":"Extended Data","description":"","filename":"20240506DKProgrammabilityExtData.pdf","url":"https://assets-eu.researchsquare.com/files/rs-4379130/v1/d417fd533be51136adc19f6f.pdf"},{"id":57820580,"identity":"01195de3-49b5-43f7-9d76-6b15869d65ae","added_by":"auto","created_at":"2024-06-06 05:42:06","extension":"png","order_by":3,"title":"","display":"","copyAsset":false,"role":"supplement","size":20510,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eScheme 1:\u003c/strong\u003eProposed mechanism for the cation-induced activation of \u003cem\u003eTr\u003c/em\u003eautocatalysis.\u003c/p\u003e","description":"","filename":"Scheme1.png","url":"https://assets-eu.researchsquare.com/files/rs-4379130/v1/7e990703431a2f09596f83cf.png"}],"financialInterests":"There is \u003cb\u003eNO\u003c/b\u003e Competing Interest.","formattedTitle":"Exploring the Programmability of Autocatalytic Chemical Reaction Networks","fulltext":[{"header":"Introduction","content":"\u003cp\u003eLiving systems, from a simple slime mold to a more complex Venus flytrap to a highly sophisticated cephalopod, exhibit intelligent behavior\u003csup\u003e16\u003c/sup\u003e. That is, they have the ability to perceive information and retain it as knowledge to execute complex tasks\u003csup\u003e13\u003c/sup\u003e. Decision making on the molecular level is, arguably, driven by chemical reaction networks (CRNs)\u003csup\u003e17\u003c/sup\u003e, and have inspired chemists to design artificial systems\u003csup\u003e18,19\u003c/sup\u003e capable of bistability\u003csup\u003e20-22\u003c/sup\u003e, oscillations\u003csup\u003e23-25\u003c/sup\u003e, and homeostasis\u003csup\u003e26\u003c/sup\u003e. How feedback loops in CRNs can be tuned, scaled, and reconfigured in a programmable manner (\u003cem\u003ei.e.\u003c/em\u003e, accept instructions to perform a range of tasks, rather than just one), however,\u0026nbsp;remains elusive.\u003c/p\u003e\n\u003cp\u003eAutocatalysis\u0026mdash;a chemical process in which the product acts as the catalyst for its own formation\u0026mdash;is at the core of the mechanisms of the aforementioned examples of CRNs, facilitating a fast and nonlinear response to stimuli from the environment\u003csup\u003e27\u003c/sup\u003e. Significant progress has been made in the \u003cem\u003ede-novo\u003c/em\u003e synthesis of autocatalytic networks\u003csup\u003e14,15\u003c/sup\u003e. Current design strategies to control autocatalysis for chemical functions that arise from signal amplification rely heavily on the incorporation of a component that triggers the network to release the first catalyst (\u003cem\u003ee.g.\u003c/em\u003e, through delay or inhibition)\u003csup\u003e10,20,25,28,29\u003c/sup\u003e.\u0026nbsp;CRNs that\u0026nbsp;use\u0026nbsp;the rate of autocatalysis (changing the strength of the positive feedback) for\u0026nbsp;the translation of autocatalytic systems into programmable\u0026nbsp;molecular systems are unexplored.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eWe recently reported how an autocatalytic network under out-of-equilibrium conditions could display behaviour (\u003cem\u003ee.g.\u003c/em\u003e, hysteresis and adaptation) important for neuromorphic systems\u003csup\u003e29\u003c/sup\u003e. It was shown that history-dependent behaviour could be established by controlling the amount of inhibitor present in its preceding state. Specifically, trypsinogen, \u003cem\u003eTg\u003c/em\u003e, is converted into trypsin, \u003cem\u003eTr\u003c/em\u003e, when the trypsin activation peptide (TAP) in \u003cem\u003eTg\u003c/em\u003e is cleaved. This conversion was regulated by an inhibitor that could control the release of the first \u003cem\u003eTr\u003c/em\u003e (the catalyst for this reaction). Importantly, Ca\u003csup\u003e2+\u003c/sup\u003e, were used to promote autocatalysis and prevent degradation of both \u003cem\u003eTg\u003c/em\u003e and \u003cem\u003eTr\u003c/em\u003e\u003csup\u003e30\u003c/sup\u003e. According to literature, trivalent lanthanide ions employ the same binding sites on \u003cem\u003eTg\u003c/em\u003e and \u003cem\u003eTr\u003c/em\u003e as Ca\u003csup\u003e2+ 31,32\u003c/sup\u003e, but can enhance the rate of trypsin autocatalysis to a greater extent than Ca\u003csup\u003e2+ 32\u003c/sup\u003e.\u003c/p\u003e\n\u003cp\u003eHere, we explore how the use of metal ions (Ca\u003csup\u003e2+\u003c/sup\u003e, La\u003csup\u003e3+\u003c/sup\u003e, and Nd\u003csup\u003e3+\u003c/sup\u003e) could allow for the design of kinetically programmable functions based on the trypsin autocatalytic network (\u003cstrong\u003eFig. 1\u003c/strong\u003e). A polydimethylsiloxane (PDMS)-based continuous stirred-tank reactor (CSTR) was employed to continuously feed the CSTR and remove all reactants and products. Such a flow setup not only allows for sustaining out-of-equilibrium conditions but also for introducing input sequences for the purpose of demonstrating how the ions, or mixtures thereof, can affect the rate of autocatalysis. Particularly, we show that Nd\u003csup\u003e3+\u003c/sup\u003e could accelerate as well as decelerate the conversion of \u003cem\u003eTg\u003c/em\u003e into \u003cem\u003eTr\u003c/em\u003e, establishing a nonlinear control over the rate of \u003cem\u003eTr\u003c/em\u003e autocatalysis. Using simulations and experiments, we demonstrate that input sequences with one or more metal ions allow for logical operations with defined output sequences that can be mapped onto mathematical functions (\u003cem\u003ei.e.\u003c/em\u003e, polynomial functions with different degrees and various logic gates). We demonstrate not only that such functions are kinetically programmable but that their temporal and history-dependent nature bestows them with properties important for the design of future intelligent chemical systems (\u003cem\u003ei.e.\u003c/em\u003e, long-term depression and history dependency).\u003c/p\u003e"},{"header":"Results and Discussion","content":"\u003cp\u003e\u003cem\u003eInfluencing the rate of autocatalysis\u003c/em\u003e\u003c/p\u003e\u003cp\u003eWe first examined the influence of the metal ions (Ca\u003csup\u003e2+\u003c/sup\u003e, La\u003csup\u003e3+\u003c/sup\u003e, and Nd\u003csup\u003e3+\u003c/sup\u003e) on the rate of trypsin autocatalysis under batch conditions. \u003cem\u003eTg\u003c/em\u003e (100 \u0026micro;M), \u003cem\u003eTr\u003c/em\u003e (1 \u0026micro;M), and Ca\u003csup\u003e2+\u003c/sup\u003e (20 mM) were initially mixed, and we monitored the change in the concentration of \u003cem\u003eTr\u003c/em\u003e, [\u003cem\u003eTr\u003c/em\u003e], using a standard assay with Na-Benzoyl-DL-arginine 4-nitroanilide, BAPNA. Figure\u0026nbsp;2\u003cb\u003ea\u003c/b\u003e depicts a typical sigmoidal curve\u0026mdash;a sharp transition that is characteristic to an autocatalytic conversion\u0026mdash;can be initiated earlier when La\u003csup\u003e3+\u003c/sup\u003e or Nd\u003csup\u003e3+\u003c/sup\u003e was added to the mixture. In greater detail, \u003cb\u003eFig.\u0026nbsp;2b-d\u003c/b\u003e depicts the [\u003cem\u003eTr\u003c/em\u003e] at three specific time points of a set of experiments wherein we varied the concentration of the three metal ions (\u003cb\u003eExtended data Fig.\u0026nbsp;1\u003c/b\u003e). Two important effects were observed in the examined range of concentrations of the ions: \u003cem\u003ei)\u003c/em\u003e La\u003csup\u003e3+\u003c/sup\u003e can accelerate the rate of autocatalysis, and the acceleration is much stronger than when Ca\u003csup\u003e2+\u003c/sup\u003e was used. Figure\u0026nbsp;2\u003cb\u003eb-c\u003c/b\u003e show that [\u003cem\u003eTr\u003c/em\u003e] increases until it saturates as [Ca\u003csup\u003e2+\u003c/sup\u003e]\u003csub\u003e0\u003c/sub\u003e and [La\u003csup\u003e3+\u003c/sup\u003e]\u003csub\u003e0\u003c/sub\u003e are increased. \u003cem\u003eii)\u003c/em\u003e Nd\u003csup\u003e3+\u003c/sup\u003e, in contrast, can accelerate and decelerate the rate of autocatalysis. Figure\u0026nbsp;2\u003cb\u003ed\u003c/b\u003e shows that the [\u003cem\u003eTr\u003c/em\u003e] increases when [Nd\u003csup\u003e3+\u003c/sup\u003e]\u003csub\u003e0\u003c/sub\u003e increases from 0 to 0.3 mM. Upon further increase of [Nd\u003csup\u003e3+\u003c/sup\u003e]\u003csub\u003e0\u003c/sub\u003e, however, the [\u003cem\u003eTr\u003c/em\u003e] decreases. This pattern was established in any of the three time points. Overall, the observations suggest that all examined ions change the apparent rate of autocatalysis, affecting the rate to a different extent.\u003c/p\u003e\u003cp\u003eHow the metal ions (\u003cem\u003eX\u003c/em\u003e) affect \u003cem\u003eTr\u003c/em\u003e autocatalysis is proposed in \u003cb\u003eScheme 1\u003c/b\u003e. Based on these batch experiments, we assume that \u003cem\u003ei)\u003c/em\u003e autocatalysis cannot occur without any of the metal ions; \u003cem\u003eii)\u003c/em\u003e binding of the ions to \u003cem\u003eTr\u003c/em\u003e (depicted as [\u003cem\u003eTrX\u003c/em\u003e]) can \u0026lsquo;activate\u0026rsquo; autocatalysis, changing the apparent rate constant for the conversion of \u003cem\u003eTg\u003c/em\u003e into \u003cem\u003eTr\u003c/em\u003e (indicated by \u003cem\u003ek\u003c/em\u003e\u003csub\u003ex\u003c/sub\u003e); \u003cem\u003eiii)\u003c/em\u003e binding of Nd\u003csup\u003e3+\u003c/sup\u003e to \u003cem\u003eTg\u003c/em\u003e (depicted as [Nd\u003csup\u003e3+\u003c/sup\u003e\u003cem\u003eTg\u003c/em\u003e]) can \u0026lsquo;de-activate\u0026rsquo; autocatalysis, inhibiting the conversion of \u003cem\u003eTg\u003c/em\u003e into \u003cem\u003eTr\u003c/em\u003e. Notably, this inhibitory effect was not observed when La\u003csup\u003e3+\u003c/sup\u003e or Ca\u003csup\u003e2+\u003c/sup\u003e were used. We performed control experiments using gel electrophoresis (\u003cem\u003ei.e.\u003c/em\u003e, SDS-PAGE) for samples from the reaction mixtures to examine the product distribution as a function of [Nd\u003csup\u003e3+\u003c/sup\u003e]\u003csub\u003e0\u003c/sub\u003e (\u003cb\u003eExtended data Fig.\u0026nbsp;2\u003c/b\u003e). The gels revealed that, only at optimal [Nd\u003csup\u003e3+\u003c/sup\u003e]\u003csub\u003e0\u003c/sub\u003e (0.3\u0026ndash;0.4 mM), \u003cem\u003eTg\u003c/em\u003e is fully hydrolysed after 16 min of the reaction.\u003c/p\u003e\u003cp\u003eIntrigued by this observation, we investigated if the effect of [Nd]\u003csub\u003e0\u003c/sub\u003e on autocatalysis can be explained using a Michaelis-Menten model. \u003cb\u003eExtended data Fig.\u0026nbsp;3\u003c/b\u003e, however, shows that both kinetic parameters (\u003cem\u003eK\u003c/em\u003e\u003csub\u003eM\u003c/sub\u003e and \u003cem\u003ek\u003c/em\u003e\u003csub\u003ecat\u003c/sub\u003e) change as a function of [Nd\u003csup\u003e3+\u003c/sup\u003e]\u003csub\u003e0\u003c/sub\u003e, and led us to the conclusion that the Michaelis-Menten approach could not provide a straightforward explanation for the observed nonlinear effect. Alternatively, a first-order degradation of \u003cem\u003eTr\u003c/em\u003e was also investigated but \u003cb\u003eExtended data Fig.\u0026nbsp;4\u003c/b\u003e showed that such degradation step could not explain the nonlinear effect either. Considering these limitations, we developed a mathematical model based on the set of ordinary differential equations according to the processes in \u003cb\u003eScheme 1\u003c/b\u003e. Quadratic equations are incorporated to account for the binding of the ions to the proteins. Details of the mathematical model is appended to \u003cb\u003eSupplementary Information\u003c/b\u003e.\u003c/p\u003e\u003cp\u003e\u003cem\u003eNonlinear effect of Nd\u003c/em\u003e \u003csup\u003e \u003cem\u003e3+\u003c/em\u003e \u003c/sup\u003e \u003cem\u003ein flow\u003c/em\u003e\u003c/p\u003e\u003cp\u003eNext, we establish control over trypsin concentration in time under flow conditions. Figure\u0026nbsp;3\u003cb\u003ea\u003c/b\u003e depicts a flow experiment wherein we changed the [Nd\u003csup\u003e3+\u003c/sup\u003e]\u003csub\u003e0\u003c/sub\u003e (from 0 to 0.7 mM and back in steps of 0.05 mM per 30 min) and monitored [\u003cem\u003eTr\u003c/em\u003e] continuously. Essentially, the residence time in the CSTR, t (determined by the volume of the CSTR divided over the total flow rate), was comparable to our batch experiments with a reaction time of 6 min. In accordance with our batch experiments, a maximum in [\u003cem\u003eTr\u003c/em\u003e] could indeed be reached when the input satisfied the condition 0.20 \u003cspan type=\"Underline\" class=\"Underline\" name=\"Emphasis\"\u003e\u0026le;\u003c/span\u003e [Nd\u003csup\u003e3+\u003c/sup\u003e]\u003csub\u003e0\u003c/sub\u003e \u003cspan type=\"Underline\" class=\"Underline\" name=\"Emphasis\"\u003e\u0026le;\u003c/span\u003e 0.40. Outside this range, we found that [\u003cem\u003eTr\u003c/em\u003e] was significantly lower. Figure\u0026nbsp;3\u003cb\u003eb\u003c/b\u003e summarizes how the use of t as a flow parameter could tune the behaviour of the system, characterized by an apparent non-equilibrium steady state, [\u003cem\u003eTr\u003c/em\u003e]*, which we determined as the average [\u003cem\u003eTr\u003c/em\u003e] over the last 5 min before [Nd\u003csup\u003e3+\u003c/sup\u003e]\u003csub\u003e0\u003c/sub\u003e was changed. The use of a higher residence time (t\u0026thinsp;=\u0026thinsp;10 min) could maintain the nonlinear response but with an elevate values of [\u003cem\u003eTr\u003c/em\u003e]. Hence, while a change in the flow parameter changes the absolute concentrations in [\u003cem\u003eTr\u003c/em\u003e]*, the nonlinear effect of Nd\u003csup\u003e3+\u003c/sup\u003e on \u003cem\u003eTr\u003c/em\u003e autocatalysis remains.\u003c/p\u003e\u003cp\u003eWe increase the level of control by forcing competitive binding (\u003cem\u003e30\u003c/em\u003e) among several ions. Figure\u0026nbsp;3\u003cb\u003ec\u003c/b\u003e illustrates our approach wherein five different values of [Nd\u003csup\u003e3+\u003c/sup\u003e]\u003csub\u003e0\u003c/sub\u003e were used to change the rate of \u003cem\u003eTr\u003c/em\u003e autocatalysis in the presence of a second ion (La\u003csup\u003e3+\u003c/sup\u003e or Ca\u003csup\u003e\u003cem\u003e2+\u003c/em\u003e\u003c/sup\u003e). The addition of a \u0026lsquo;slower\u0026rsquo; ion [Ca\u003csup\u003e\u003cem\u003e2+\u003c/em\u003e\u003c/sup\u003e]\u003csub\u003e0\u003c/sub\u003e (20 mM) resulted in the same nonlinear response as in the absence of a second ion (black line) but changed in the position of its local maximum (dashed line). That is, the maximum [\u003cem\u003eTr\u003c/em\u003e]* remained around 35 \u0026micro;M but moved towards slightly higher [Nd\u003csup\u003e3+\u003c/sup\u003e]\u003csub\u003e0\u003c/sub\u003e compared to the systems without Ca\u003csup\u003e2+\u003c/sup\u003e. Similarly, the addition of the \u0026lsquo;faster\u0026rsquo; [La\u003csup\u003e3+\u003c/sup\u003e] also resulted in the same nonlinear response but led to a change in the position of its local maximum into the direction of a lower [Nd\u003csup\u003e3+\u003c/sup\u003e]\u003csub\u003e0\u003c/sub\u003e (dotted line). We used our model to confirm the observation that the local maximum can shift in different directions in the presence of the metal ions (\u003cb\u003eExtended data Fig.\u0026nbsp;5\u003c/b\u003e).\u003c/p\u003e\u003cp\u003eThe opposing effects that the mixtures of ions induce can be mapped onto polynomial functions with different degrees (\u003cb\u003eFig.\u0026nbsp;3d\u003c/b\u003e). The relation between [\u003cem\u003eTr\u003c/em\u003e]* and [Nd\u003csup\u003e3+\u003c/sup\u003e]\u003csub\u003e0\u003c/sub\u003e can be approximated with a quadratic function in the absence of an additional ion, and the degree of the polynomial function is therefore 2. In the presence of Ca\u003csup\u003e2+\u003c/sup\u003e, this relation changes but only at higher concentrations of [Nd\u003csup\u003e3+\u003c/sup\u003e]\u003csub\u003e0\u003c/sub\u003e and therefore the nature of the polynomial function, its degree, does not change and remains 2. In the presence of La\u003csup\u003e3+\u003c/sup\u003e, however, the behaviour can change from a quadratic to a linear relation, and the degree of the polynomial function becomes 1. An experiment with both La\u003csup\u003e3+\u003c/sup\u003e and Ca\u003csup\u003e\u003cem\u003e2+\u003c/em\u003e\u003c/sup\u003e shows that the competition for different binding sites allows for a combination of two opposing effects, creating a mechanism to maintain [\u003cem\u003eTr\u003c/em\u003e]* within the narrow range of [Nd\u003csup\u003e3+\u003c/sup\u003e]\u003csub\u003e0\u003c/sub\u003e. In the presence of Ca\u003csup\u003e3+\u003c/sup\u003e and La\u003csup\u003e3+\u003c/sup\u003e, the behaviour became close to constant (\u003cem\u003ei.e.\u003c/em\u003e, a polynomial function with the degree 0). The mapping of a chemical output onto polynomial functions as demonstrated here underscores the flexibility of using metal ions in controlling the autocatalytic network.\u003c/p\u003e\u003cp\u003e\u003cem\u003eNd\u003c/em\u003e \u003csup\u003e \u003cem\u003e3+\u003c/em\u003e \u003c/sup\u003e \u003cem\u003e-induced temporal logic operations\u003c/em\u003e\u003c/p\u003e\u003cp\u003eNext, we developed a procedure to obtain Boolean functions for [\u003cem\u003eTr\u003c/em\u003e]* by varying only [Nd\u003csup\u003e3+\u003c/sup\u003e]\u003csub\u003e0\u003c/sub\u003e. Figure\u0026nbsp;4\u003cb\u003ea\u003c/b\u003e illustrates our concept wherein three different values for [Nd\u003csup\u003e3+\u003c/sup\u003e]\u003csub\u003e0\u003c/sub\u003e of a given range (a minimum, maximum, and a value in between) correspond to four binary combinations (0|0; 0|1; 1|1; 1|0). The notation [Nd\u003csup\u003e3+\u003c/sup\u003e]\u003csub\u003eA|B\u003c/sub\u003e is used to represent the input sequence [Nd\u003csup\u003e3+\u003c/sup\u003e]\u003csub\u003e0|0\u003c/sub\u003e; [Nd\u003csup\u003e3+\u003c/sup\u003e]\u003csub\u003e1|0\u003c/sub\u003e; [Nd\u003csup\u003e3+\u003c/sup\u003e]\u003csub\u003e1|1\u003c/sub\u003e; [Nd\u003csup\u003e3+\u003c/sup\u003e]\u003csub\u003e0|1\u003c/sub\u003e. As an example, \u003cb\u003eFig.\u0026nbsp;4b\u003c/b\u003e shows the output sequences for the gates NAND and XOR. We chose the not-AND (NAND) and exclusive-OR (XOR) gates because they are exemplary for functional completeness\u003csup\u003e34\u003c/sup\u003e and nonlinear classification\u003csup\u003e35\u003c/sup\u003e, and are considered difficult to construct using chemical systems\u003csup\u003e36,37\u003c/sup\u003e. The differences between the two gates reside on the range of [Nd\u003csup\u003e3+\u003c/sup\u003e]\u003csub\u003e0\u003c/sub\u003e that was applied: the maximum [Nd\u003csup\u003e3+\u003c/sup\u003e]\u003csub\u003e0\u003c/sub\u003e in both cases is 0.6 mM but minimum [Nd\u003csup\u003e3+\u003c/sup\u003e]\u003csub\u003e0\u003c/sub\u003e is 0.2 and 0 mM, respectively. The top graph in \u003cb\u003eFig.\u0026nbsp;4b\u003c/b\u003e, shows five conditions wherein [Nd\u003csup\u003e3+\u003c/sup\u003e]\u003csub\u003e0\u003c/sub\u003e is changed in steps of 45 min. The first four conditions represent the input 0|0; 0|1; 1|1; 1|0, with the corresponding response in \u003cem\u003eTr\u003c/em\u003e for the two sequences demonstrated in the below graph. A threshold [\u003cem\u003eTr\u003c/em\u003e] with an arbitrary value (20 \u0026micro;M), was used to determine if the observed values in the sequence were true, \u0026lsquo;1\u0026rsquo; or false, \u0026lsquo;0\u0026rsquo;. For the first sequence, [\u003cem\u003eTr\u003c/em\u003e]* exceeded the threshold (red line) at all conditions, except for [Nd\u003csup\u003e3+\u003c/sup\u003e]\u003csub\u003e1|1\u003c/sub\u003e. Hence, the input combination resulted in an output sequence representing the NAND-gate: [\u003cem\u003eTr\u003c/em\u003e]\u003csub\u003e0|0\u003c/sub\u003e = \u003cb\u003e1\u003c/b\u003e; [\u003cem\u003eTr\u003c/em\u003e]\u003csub\u003e0|1\u003c/sub\u003e = \u003cb\u003e1\u003c/b\u003e; [\u003cem\u003eTr\u003c/em\u003e]\u003csub\u003e1|0\u003c/sub\u003e = \u003cb\u003e1\u003c/b\u003e; [\u003cem\u003eTr\u003c/em\u003e]\u003csub\u003e1|1\u003c/sub\u003e = \u003cb\u003e0\u003c/b\u003e. For XOR, [\u003cem\u003eTr\u003c/em\u003e]* exceeded the threshold at two conditions, namely for [Nd\u003csup\u003e3+\u003c/sup\u003e]\u003csub\u003e0|1\u003c/sub\u003e and [Nd\u003csup\u003e3+\u003c/sup\u003e]\u003csub\u003e1|0\u003c/sub\u003e, yielding the sequence representing the XOR-gate: [\u003cem\u003eTr\u003c/em\u003e]\u003csub\u003e0|0\u003c/sub\u003e=\u003cb\u003e0\u003c/b\u003e; [\u003cem\u003eTr\u003c/em\u003e]\u003csub\u003e0|1\u003c/sub\u003e=\u003cb\u003e1\u003c/b\u003e; [\u003cem\u003eTr\u003c/em\u003e]\u003csub\u003e1|0\u003c/sub\u003e=\u003cb\u003e1\u003c/b\u003e; [\u003cem\u003eTr\u003c/em\u003e]\u003csub\u003e1|1=\u003c/sub\u003e\u003cb\u003e0\u003c/b\u003e. The initial value was recovered in the final condition ([\u003cem\u003eTr\u003c/em\u003e]* at [Nd\u003csup\u003e3+\u003c/sup\u003e]\u003csub\u003e0|0\u003c/sub\u003e), demonstrating that the output signal can be reset.\u003c/p\u003e\u003cp\u003eOther gates (AND, OR, NOR) can be developed using a similar procedure (\u003cb\u003eExtended data Fig.\u0026nbsp;6\u003c/b\u003e). Figure\u0026nbsp;4\u003cb\u003ec\u003c/b\u003e summarizes these experiments by plotting the output concentration as a function of [Nd\u003csup\u003e3+\u003c/sup\u003e]\u003csub\u003e0\u003c/sub\u003e. The results underline that a change in the minimum and maximum of [Nd\u003csup\u003e3+\u003c/sup\u003e]\u003csub\u003e0\u003c/sub\u003e is sufficient to create different logic operations. We, thus, showed that the autocatalytic reaction can accept instructions (in this case, encoded as an input sequence based on [Nd\u003csup\u003e3+\u003c/sup\u003e]) to perform a range of logic operations.\u003c/p\u003e\u003cp\u003eWe used our mathematical model to simulate the response of this autocatalytic network based on changes in the residence time and the concentration of the metal ion. A procedure was developed to discriminate between the different types of logic. Briefly, the ratio [Tr]\u003csub\u003e1|1\u003c/sub\u003e:[Tr]\u003csub\u003e1|0\u003c/sub\u003e was used to distinguish AND, OR and XOR and the ratio ([\u003cem\u003eTr\u003c/em\u003e]\u003csub\u003e1|1\u003c/sub\u003e+[\u003cem\u003eTr\u003c/em\u003e]\u003csub\u003e1|0\u003c/sub\u003e):[Tr]\u003csub\u003e0|0\u003c/sub\u003e was used to distinguish NAND and NOR (\u003cb\u003eSupplementary Information\u003c/b\u003e). Figure\u0026nbsp;4\u003cb\u003ed\u003c/b\u003e depicts the simulated phase space of the autocatalytic network and shows that the regions of AND, NAND, NOR, XOR and OR can be found in a narrow range of parameters, and depending on the [Nd\u003csup\u003e3+\u003c/sup\u003e]\u003csub\u003e0|0\u003c/sub\u003e the regions can overlap. Each grid in the phase space represents a predicted response in [\u003cem\u003eTr\u003c/em\u003e]\u003csub\u003ess\u003c/sub\u003e as a function of input sequence (0|0; 0|1; 1|1; 1|0), and [Nd\u003csup\u003e3+\u003c/sup\u003e]\u003csub\u003e1|1\u003c/sub\u003e is placed on the Y axis. [Nd\u003csup\u003e3+\u003c/sup\u003e]\u003csub\u003e0|0\u003c/sub\u003e on \u003cb\u003eFig.\u0026nbsp;4d\u003c/b\u003e for AND, OR, XOR equals 0 mM, and for NAND and NOR equals 0.2 mM. A comparison between the simulated areas for, and experimentally observed, logic gates (open symbols) demonstrates that the model is in good agreement with the experiments. The method of creating logic gates is not restricted to Nd\u003csup\u003e3+\u003c/sup\u003e, and ions can be combined to change the phase space (\u003cb\u003eExtended data Fig.\u0026nbsp;7)\u003c/b\u003e. More importantly, we show that lowering the residence time during the experiment (indicated with the red symbols) could change the output sequence from a XOR or an AND into an OR gate, demonstrating that the Boolean functions can be readily tuned (\u003cb\u003eExtended data Fig.\u0026nbsp;8)\u003c/b\u003e.\u003c/p\u003e\u003cp\u003e\u003cem\u003eBistability in temporal logic operations\u003c/em\u003e\u003c/p\u003e\u003cp\u003eThe use of an external component such as an inhibitor for thresholding provides further control over the network properties. Figure\u0026nbsp;4\u003cb\u003ee\u003c/b\u003e shows a sequence wherein the [Nd\u003csup\u003e3+\u003c/sup\u003e]\u003csub\u003e0\u003c/sub\u003e was changed from a low to a high value, and vice versa, in the presence of a trypsin inhibitor (\u003cem\u003eI\u003c/em\u003e, at a concentration of 8, 4, and 2 \u0026micro;M). Overall, [\u003cem\u003eTr\u003c/em\u003e] changes from a high to a low concentration when [Nd\u003csup\u003e3+\u003c/sup\u003e]\u003csub\u003e0\u003c/sub\u003e was changed from 0.3 to 0.8 mM. At an inhibitor concentration that appeared to be too high ([\u003cem\u003eI\u003c/em\u003e]\u003csub\u003e0\u003c/sub\u003e=8 \u0026micro;M), we observed that original [\u003cem\u003eTr\u003c/em\u003e]* cannot be recovered and instead remains low when [Nd\u003csup\u003e3+\u003c/sup\u003e]\u003csub\u003e0\u003c/sub\u003e was changed in the opposite direction (from 0.8 to 0.3 mM). The observation that a pulse in [Nd\u003csup\u003e3+\u003c/sup\u003e]\u003csub\u003e0\u003c/sub\u003e (\u003cem\u003ei.e.\u003c/em\u003e, the sequence 0.3-0.8-0.3 mM) enabled a retention of the low [\u003cem\u003eTr\u003c/em\u003e]* demonstrates that the autocatalytic network, in the presence of the inhibitor, is capable of a so-called long-term depression of the input. This effect disappeared when the inhibitor concentration was lowered to [\u003cem\u003eI\u003c/em\u003e]\u003csub\u003e0\u003c/sub\u003e= 4 \u0026micro;M but notably [\u003cem\u003eTr\u003c/em\u003e]* remains to depend on the amount of inhibitor present in its preceding state, \u003cem\u003ei.e.\u003c/em\u003e, the response is history dependent. Validations in \u003cb\u003eExtended data Fig.\u0026nbsp;9\u003c/b\u003e supports the observation that the XOR-gate is (and perhaps other logic gates are) history dependent. The history dependency was lost when [\u003cem\u003eI\u003c/em\u003e]\u003csub\u003e0\u003c/sub\u003e= 2 \u0026micro;M was applied and, instead, the response became bistable. That the signal could fully recover, however, shows that a trace of inhibitor allows for an increased robustness of the output signal. Hence, while the metal ion provides control for tuning and switching of the logic operation, an inhibitor was introduced as an additional control parameter for strengthening or weakening its history dependency.\u003c/p\u003e"},{"header":"Conclusion","content":"\u003cp\u003eThis work shows that achieving control over a single positive feedback mechanism can offer sufficient complexity to develop kinetically controllable functions. Metal ions were used to target the activity of the catalyst in a feedback element\u0026mdash;a strategy which is potentially achievable through a range of physical and chemical strategies\u0026mdash;and provided the necessary control over the autocatalytic conversion of trypsinogen into trypsin. We demonstrated that trypsin autocatalysis can be controlled to emulate polynomial functions with different degrees and Boolean functions with various outcomes (\u003cem\u003ee.g.\u003c/em\u003e, AND, OR, XOR, NAND, NOR). Additionally, a trypsin inhibitor was incorporated into the network to create a bistable system capable of long-term depression of the input and history dependency in the output (\u003cem\u003ei.e.\u003c/em\u003e, characteristics for neuromorphic behaviour). We envision that this work will offer novel strategies to exploit the programmability of small and simple chemical reaction networks for building artificial systems with responsive\u003csup\u003e38\u003c/sup\u003e, adaptive\u003csup\u003e39\u003c/sup\u003e, and other life-like properties\u003csup\u003e2\u003c/sup\u003e characteristic for intelligent systems. Such a prospect will undoubtably impact many scientific domains including those that focus on the exploration of out-of-equilibrium chemical systems, synthesis of artificial life, and design of autonomous molecular materials.\u003c/p\u003e"},{"header":"Methods","content":"\u003cp\u003e\u003cem\u003eMaterials\u003c/em\u003e\u003c/p\u003e\u003cp\u003eBovine trypsinogen (Type I; ~10,000 BAEE units/mg), bovine trypsin (\u0026ge;\u0026thinsp;7,500 BAEE units/mg solid), Nα-Benzoyl-DL-arginine 4-nitroanilide hydrochloride (BAPNA), and Ln(NO\u003csub\u003e3\u003c/sub\u003e)\u003csub\u003e3\u003c/sub\u003e*6H2O salts (99.9% purity) were purchased from Sigma. Trypsin inhibitor from soybean (STI) was purchased from Roche. Water is purified using a Millipore Milli-Q lab water system. Other solvents and buffers (i.e., Dimethyl sulfoxide (DMSO), Dimethylformamide (DMFA), tris(hydroxymethyl)aminomethane (TRIS) were obtained commercially and were used without purification. Polydimethylsiloxane (PDMS), 184 Silicon Elastomer and 184 Curing Agent, was purchased from SYLGARD. For 3D printer Vero Clear material and SUP706b supporting material were purchased from Stratasys. Hamilton gastight glass syringes (1000 series) which have volume of 1 mL, 2.5 mL, 10 mL and 25 mL, and were purchased from Hamilton. Polytetrafluoroethylene (PTFE) tubings (I.D. x O.D. 0.5 x 1 mm; 1/16 x 0.010 inch) were purchased from Inacom. For bovine trypsinogen Type I from Sigma Aldrich, we found significant differences between batches of this product. We suspect inconsistency in the purity of the product because the time of complete auto-activation in same conditions was varying from flask to flask. Traces of trypsin and Ca\u003csup\u003e2+\u003c/sup\u003e are suspected sources of impurity. Reported data is collected from two chemically closest batches. It is important, that all stock solutions of trypsin and trypsinogen were not stronger that 0.4 mM and had 4 mM HCl added to decrease the degradation rate. In experiments with Ca\u003csup\u003e2+\u003c/sup\u003e all stock solutions also contained 20 mM CaCl\u003csub\u003e2\u003c/sub\u003e for the same purpose.\u003c/p\u003e\u003cp\u003e\u003cem\u003eEquipment\u003c/em\u003e\u003c/p\u003e\u003cp\u003eA Stratasys Objet Pro 30 3D printer was used for printing continuous-flow stirred-tank reactors (CFSTRs) master molds. BINDER E 28 oven was used for PDMS curing. ZEPTO plasma oven from Diener Electronic was used for PDMS and glass surface activation. Batch experiments for samples for SDS-PAGE were performed in separate vials with mixing and temperature control by Eppendorf Thermomixer Comfort. PerkinElmer EnSpire 2300 plate reader was used for absorbance detection for other batch experiments. Flow experiments were performed with Nemesys low pressure pumps from CETONI with Qmix Lambda custom absorbance detector with LED light source and 8 mm length flow cell.\u003c/p\u003e\u003cp\u003e\u003cem\u003eTrypsin assay\u003c/em\u003e\u003c/p\u003e\u003cp\u003eReaction mixtures containing trypsin were diluted 1:10, 1:20 or 1:50 with freshly prepared detection mixture (1 mM BAPNA from 50 mM stock in DMSO, 100 mM TRIS-HCl pH\u0026thinsp;=\u0026thinsp;7.8 with 20 mM CaCl\u003csub\u003e2\u003c/sub\u003e) and put inside the absorbance plate reader for initial shaking and further absorbance measurement. Initial slopes of absorbance at 405 nm were transformed into trypsin concentration by a linear calibration curve.\u003c/p\u003e\u003cp\u003e\u003cem\u003eSDS PAGE protocol\u003c/em\u003e\u003c/p\u003e\u003cp\u003eAliquots of reaction mixture were quenched 1:3 by 0.2 M KHSO4. 4 \u0026micro;L of Laemmle 4X buffer\u0026thinsp;+\u0026thinsp;10 \u0026micro;l of an aliquot\u0026thinsp;+\u0026thinsp;2 \u0026micro;L NaOH 5M were put on a gel and ran at 30 mA with 250 mM TRIS-HCl, 1.92M Glycine, 1% SDS running buffer. Stacking gel: 120 mM TRIS-HCl pH\u0026thinsp;=\u0026thinsp;6, 1.5% acrylamide 30:0.8, 0.001% SDS, 0.0012% APS, 0.001% TEMED. Running gel: 370 mM TRIS-HCl pH\u0026thinsp;=\u0026thinsp;8.8, 60% acrylamide 30:0.8, 0.002% SDS, 0.001% APS, 0.0008% TEMED. Proteins were stained by Bradford technique, namely, 2g of Coomassie Blue R250 in 10% acetic acid and 40% ethanol solution.\u003c/p\u003e\u003cp\u003e\u003cem\u003eFabrication of the CSTR\u003c/em\u003e\u003c/p\u003e\u003cp\u003e3D models of 90 ml CSTRs were 3D-printed. PDMS CSTRs upper parts were prepared by covering prints with degassed 1:10 mixture of curing agent with silicone elastomer base. PDMS mixture was polymerized at 75\u0026deg;C for 30 minutes. Holes for tubings in solidified CSTRs upper parts were made by Harris Uni-Core 1.00 puncher. Glass slide was cleaned with isopropanol and scotch tape, and then treated in oxygen plasma oven for 2\u0026ndash;4 minutes within PDMS CSTRs upper parts before attaching surfaces. For continuous stirring 3 mm diameter Teflon coated spherical magnetic stirrers were incorporated inside reactor. Final working volume of CSTR was 76 \u0026micro;l (after volume occupied by the magnetic stirrer was subtracted).\u003c/p\u003e\u003cp\u003e\u003cem\u003eFlow experiments\u003c/em\u003e\u003c/p\u003e\u003cp\u003eLow pressure pumps (CETONI Nemesys) were controlled by CETONI Elements software and connected to two CSTRs (experiment CSTR and reporting CSTR) sequentially connected by PTFE tubings (\u003cb\u003eSupplementary Fig.\u0026nbsp;1\u003c/b\u003e). First reactor served as a main reaction chamber whereas the second was receiving its outflow and reporting solution at the constant (2:1) ratio. Reporting solution consisted of 4 mM BAPNA in mixture of MQ:DMSO:DMFA (0.2:0.08:0.72). The outflow through the sequence of reactors was passing through the Qmix Lambda flow detector after which the solution was collected in the waste container. The result of the measurement was visualized using the online plotting function of CETONI Elements software. We used two wavelength bands to detect pNA: 620-630nm (internal standard wavelengths, where pNA does not absorb light) and 400-450nm (detection wavelengths, where pNA absorbs light). Result of division of internal standard signal by detection signal was calibrated for the concentration of trypsin in the reaction chamber. Artifacts from air bubbles were removed manually, then 60 or 180 pts FFT smoothing procedure was implemented to results in OriginPro2021. More detailed information can be found in literature\u003csup\u003e27\u003c/sup\u003e.\u003c/p\u003e\u003cp\u003e\u003cem\u003eMathematical modelling\u003c/em\u003e\u003c/p\u003e\u003cp\u003eOur mathematical model (see \u003cb\u003eSupplementary Materials\u003c/b\u003e) uses ordinary differential equations (script \u003cem\u003ecompdeq\u003c/em\u003e) and quadratic equations (script \u003cem\u003ecompsqeq\u003c/em\u003e) to simulate reaction trajectories of our network in flow. The model is designed for determining the steady state and transient concentrations of \u003cem\u003eTr\u003c/em\u003e as a function of the initial conditions: concentrations of species and inflow concentrations of species. Specifically, the model (script \u003cem\u003ecomp\u003c/em\u003e) recalculates equilibrium concentrations of the complexes (script \u003cem\u003ecompsqeq\u003c/em\u003e) after each step in the numerical integration (script \u003cem\u003ecompdeq\u003c/em\u003e). The list of reactions and complexes used can be found in \u003cb\u003eSupplementary Table \u003cspan refid=\"MOESM1\" class=\"InternalRef\"\u003eS1\u003c/span\u003e\u003c/b\u003e. All kinetic and thermodynamic constants were estimated from published data\u003csup\u003e29,30\u003c/sup\u003e to support experimental results. The assumptions required for developing the mathematical model are appended to \u003cb\u003eSupplementary Information\u003c/b\u003e.\u003c/p\u003e\u003cp\u003e\u003cem\u003eSoftware\u003c/em\u003e\u003c/p\u003e\u003cp\u003eOrigin Pro 2021 was used for processing raw data. CETONI Elements software (v. 20210406) was used for programming low pressure pumps. SOLIDWORKS 2022 was used for designing 3D models. MATLAB 2023a was used for mathematical modelling.\u003c/p\u003e"},{"header":"Declarations","content":"\u003cp\u003e\u003cstrong\u003eAuthor contributions\u003c/strong\u003e:\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eASYW conceived and planned the project. ASYW and JH supervised the project. DVK performed the experiments, designed the mathematical model, performed the simulations. ASYW and DVK wrote the manuscript. All authors contributed to revising the manuscript. (In CrediT terms, Conceptualization: ASYW and DVK. Methodology: ASYW and DVK. Investigation: DVK. Visualization: ASYW and DVK. Funding acquisition: ASYW. Project administration: ASYW. Supervision: ASYW and JH. Writing \u0026ndash; original draft: ASYW and DVK. Writing \u0026ndash; review \u0026amp; editing: ASYW, DVK and JH).\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eSupplementary Information\u003c/strong\u003e is available for this paper.\u003c/p\u003e\n\u003cp\u003eCorrespondence and requests for materials should be addressed to [email protected]\u003c/p\u003e\n\u003cp\u003ePeer review information includes the names of reviewers who agree to be cited and is completed by Nature staff during proofing\u003c/p\u003e\n\u003cp\u003eReprints and permissions information is available at \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ewww.nature.com/reprints\u003c/span\u003e\u003c/span\u003e.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eFunding\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThe project is supported by the Netherlands Organization for Scientific Research (NWO, Veni Grant 202.155 to A.S.Y.W).\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eCompeting interests:\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eAuthors declare that they have no competing interests.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eAdditional information\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eData integral to the work is provided in \u003cstrong\u003eExtended data\u003c/strong\u003e. Scripts are provided as separate files in \u003cstrong\u003eSupplementary Materials\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eFunding\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThe project is supported by the Netherlands Organization for Scientific Research (NWO, Veni Grant 202.155 to A.S.Y.W).\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eCompeting interests:\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eAuthors declare that they have no competing interests.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eAdditional information\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eData integral to the work is provided in \u003cstrong\u003eExtended data\u003c/strong\u003e. Scripts are provided as separate files in \u003cstrong\u003eSupplementary Materials\u003c/strong\u003e\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\n\u003cli\u003eWhitesides, G. M. \u0026amp; Ismagilov, R. F. 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Mater\u003c/em\u003e. \u003cstrong\u003e32\u003c/strong\u003e, 1905554 (2020).\u003c/li\u003e\n\u003c/ol\u003e"},{"header":"Schemes","content":"\u003cp\u003eScheme 1 is available in the Supplementary Files section\u003c/p\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":true,"hideJournal":false,"highlight":"","institution":"","isAcceptedByJournal":true,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"nature-portfolio","isNatureJournal":true,"hasQc":false,"allowDirectSubmit":false,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"","title":"Nature Portfolio","twitterHandle":"","acdcEnabled":false,"dfaEnabled":false,"editorialSystem":"ejp","reportingPortfolio":"","inReviewEnabled":true,"inReviewRevisionsEnabled":false},"keywords":"","lastPublishedDoi":"10.21203/rs.3.rs-4379130/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-4379130/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eChemical reaction networks (CRNs) could offer chemical complexity\u003csup\u003e1\u003c/sup\u003e to contribute to future intelligent material design\u003csup\u003e2\u003c/sup\u003e or neuromorphic computing technologies\u003csup\u003e3,4\u003c/sup\u003e. Recent advances in systems chemistry use the complex Belousov–Zhabotinsky\u003csup\u003e5-7\u003c/sup\u003e and Formose reactions\u003csup\u003e8,9\u003c/sup\u003e, or simpler chemical systems with fewer feedback loops\u003csup\u003e10-12\u003c/sup\u003e, to demonstrate that (spatio)temporal patterns can be harnessed to emulate properties important for intelligent behavior (\u003cem\u003ei.e.\u003c/em\u003e, the ability to perceive information and retain it as knowledge to execute complex tasks\u003csup\u003e13\u003c/sup\u003e). In all examples, autocatalysis appears an essential element for facilitating a nonlinear response. How this chemical analogue of a positive feedback mechanism\u003csup\u003e14,15\u003c/sup\u003e can be reconfigured in a programmable manner is, however, unknown. Here, we developed a strategy that uses metal ions (Ca\u003csup\u003e2+\u003c/sup\u003e, La\u003csup\u003e3+\u003c/sup\u003e, and Nd\u003csup\u003e3+\u003c/sup\u003e) to control the rate of a trypsin-catalysed autocatalytic reaction network. A flow setup is employed to sustain the\u003cem\u003e \u003c/em\u003ereaction network under out-of-equilibrium conditions and demonstrate that various kinetically controllable responses can be mapped onto polynomial and Boolean functions. Remarkably, these functions cannot only be programmed but their temporal and history-dependent nature bestows them with neuromorphic properties, promising novel strategies in designing intelligent chemical systems. Beyond, the easy-to-use method to control autocatalysis will impact future development focusing on biocatalysis, nanobiotechnology, and the chemical origin of life.\u003c/p\u003e","manuscriptTitle":"Exploring the Programmability of Autocatalytic Chemical Reaction Networks","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2024-06-06 05:42:02","doi":"10.21203/rs.3.rs-4379130/v1","editorialEvents":[],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"nature-communications","isNatureJournal":true,"hasQc":false,"allowDirectSubmit":false,"externalIdentity":"NCOMMS","sideBox":"Learn more about [Nature Communications](http://www.nature.com/ncomms/)","snPcode":"","submissionUrl":"https://mts-ncomms.nature.com/","title":"Nature Communications","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"ejp","reportingPortfolio":"Nature Communications","inReviewEnabled":true,"inReviewRevisionsEnabled":false}}],"origin":"","ownerIdentity":"cf0b3e57-0f24-4793-920b-1709cb8e0fc3","owner":[],"postedDate":"June 6th, 2024","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"published-in-journal","subjectAreas":[{"id":32266691,"name":"Physical sciences/Chemistry/Supramolecular chemistry"},{"id":32266692,"name":"Biological sciences/Biochemistry/Enzyme mechanisms"},{"id":32266693,"name":"Physical sciences/Nanoscience and technology/Nanobiotechnology"},{"id":32266694,"name":"Physical sciences/Chemistry/Chemical origin of life"},{"id":32266695,"name":"Physical sciences/Chemistry/Biochemistry/Biocatalysis"}],"tags":[],"updatedAt":"2024-09-28T07:14:15+00:00","versionOfRecord":{"articleIdentity":"rs-4379130","link":"https://doi.org/10.1038/s41467-024-52649-z","journal":{"identity":"nature-communications","isVorOnly":false,"title":"Nature Communications"},"publishedOn":"2024-09-27 04:00:00","publishedOnDateReadable":"September 27th, 2024"},"versionCreatedAt":"2024-06-06 05:42:02","video":"","vorDoi":"10.1038/s41467-024-52649-z","vorDoiUrl":"https://doi.org/10.1038/s41467-024-52649-z","workflowStages":[]},"version":"v1","identity":"rs-4379130","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-4379130","identity":"rs-4379130","version":["v1"]},"buildId":"qtupq5eGEP_6zYnWcrvyt","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}