Exploring the programmability of autocatalytic chemical reaction networks

Abstract

Networks of chemical reactions exhibit emergent properties under out-of-equilibrium conditions. Recent advances in systems chemistry demonstrate that networks with sufficient chemical complexity can be harnessed to emulate properties important for neuromorphic computing. In all examples, autocatalysis appears an essential element for facilitating the nonlinear integration of the input and self-regulatory abilities in the output. How this chemical analogue of a positive feedback mechanism can be controlled in a programmable manner is, however, unexplored. Here, we develop a strategy that uses metal ions (Ca²⁺, La³⁺, and Nd³⁺) to control the rate of a trypsin-catalysed autocatalytic reaction network. We demonstrate that this type of control allows for tuning the kinetics in the network, thereby changing the nature of the positive feedback. The simulations and experiments reveal that an input with one or more metal ions allow for temporal and history-dependent outputs that can be mapped onto a variety of mathematical functions.

Networks of chemical reactions exhibit emergent properties under out-of-equilibrium conditions and can be utilized to emulate properties important for neuromorphic computing. Here, the authors report a strategy that uses metal ions (Ca²⁺, La³⁺, and Nd³⁺) to control the rate of a trypsin catalysed autocatalytic reaction network, with temporal and history dependent outputs that can be mapped onto a variety of mathematical functions.

Introduction

Living systems, from a simple slime mould to a more complex Venus flytrap to a highly sophisticated cephalopod, exhibit intelligent behaviour¹. That is, they have the ability to perceive information and retain it as knowledge to execute complex tasks². The underlying processes by which decisions are made are fundamentally different from conventional (digital) computing, as they rely on complex, decentralised networks of biochemical reactions that operate in parallel². Artificial neuromorphic systems take inspiration from natural and biological processes³, particularly from how neurons process and transmit signals in the brain⁴. Rethinking the design of neuromorphic systems do not necessarily restrict to neural architectures⁵ and opportunities may lie in using analogue and approximate computing that arise from purely (bio)chemical processes⁶.

Chemical reaction networks (CRNs) could offer chemical complexity⁷ to contribute to the design of neuromorphic computing technologies⁴ and intelligent materials⁸. Decision making on the molecular level in biological systems is, arguably, driven by CRNs, and have inspired chemists to design artificial systems^9,10 capable of bistability^11–13, oscillations^14–16 and homoeostasis¹⁷. Recent advances in systems chemistry use the complex Belousov–Zhabotinsky^18–20 and Butlerov reactions^21,22, or simpler chemical systems with fewer feedback loops^23–25, to demonstrate that (spatio)temporal patterns can be harnessed to emulate properties important for intelligent behaviour. How feedback loops in CRNs can be tuned, scaled and reconfigured (rewired)²⁶ 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 environment²⁶. The nonlinearity of artificial neurons can, essentially, be resembled by the kinetic feature of autocatalytic reactions^23,24_. Significant progress has been made in the de novo synthesis of autocatalytic networks^27,28. 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)^{11,16,23,29,30}. 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. Can autocatalysis, a chemical analogue of a positive feedback mechanism^27,28, be controlled to enable fundamentals of natural computing³?

We recently reported how an autocatalytic network under out-of-equilibrium conditions could display behaviour (e.g., hysteresis and adaptation) important for neuromorphic systems³⁰. 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, Ca²⁺, were used to promote autocatalysis and prevent degradation of both Tg and Tr³¹. According to literature, trivalent lanthanide ions employ the same binding sites on Tg and Tr as Ca^2+32,33 but can enhance the rate of trypsin autocatalysis to a greater extent than Ca²⁺³⁴.

Here, we explore how the use of metal ions (Ca²⁺, La³⁺ and Nd³⁺) 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 Nd³⁺ 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).

Fig. 1. A programmable autocatalytic chemical network under out-of-equilibrium conditions.

Trypsin, Tr, acts as a catalyst for the conversion of its precursor trypsinogen, Tg, into Tr, resulting in autocatalysis. The rate and onset of the autocatalysis can be controlled by the metal ion, X, and the inhibitor, I. Together, they form a chemical reaction network (CRN), which is maintained under out-of-equilibrium conditions using a continuous stirred-tank reactor (CSTR). The CRN accepts instructions encoded in a defined sequence of initial concentrations of metal ions ([X]₀), 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. [Tr] denotes concentration of Tr in CSTR; t and τ denote time and residence time in CSTR, respectively.

Results

Influencing the rate of autocatalysis

We first examined the influence of the metal ions (Ca²⁺, La³⁺ and Nd³⁺) on the rate of trypsin autocatalysis under batch conditions. Tg (100 μM), Tr (1 μM) and Ca²⁺ (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, Nα-Benzoyl-DL-arginine 4-nitroanilide hydrochloride (BAPNA). Figure 2a depicts a typical sigmoidal curve—a sharp transition that is characteristic to an autocatalytic conversion—can be initiated earlier when La³⁺ or Nd³⁺ 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 (Supplementary Fig. 3). Two important effects were observed in the examined range of concentrations of the ions: (I) La³⁺ can accelerate the rate of autocatalysis, and the acceleration is much stronger than when Ca²⁺ was used. Figure 2b, c show that [Tr] increases until it saturates as the initial concentration of Ca²⁺ and La³⁺ ([Ca²⁺]₀ and [La³⁺]₀) are increased. (II) Nd³⁺, in contrast, can accelerate and decelerate the rate of autocatalysis. Figure 2d shows that the [Tr] increases when the initial concentration of Nd³⁺ ([Nd³⁺]₀) increases from 0 to 0.3 mM. Upon further increase of [Nd³⁺]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.

Fig. 2. Cation-dependent control over the rate of trypsinogen autocatalysis.

a Autocatalytic conversion of Tg into Tr in the presence of Ca²⁺. The addition of La³⁺ and Nd³⁺ significantly increase the rate of Tr autocatalysis. b–d Concentration of trypsin, [Tr], as a function of the metal ion and its concentration at fixed time after start of the reaction. Depicted are data at three time points (for extended data see Supplementary Fig. 3). SD bars are based on independent measurements (n = 2). Initial conditions: [Tg]₀ = 100 µM and [Tr]₀ = 1 µM. Initial conditions for a–d: [TRIS-HCl] = 100 mM (pH 7.8), T = 21–23 ^oC.

How the metal ions (X) affect Tr autocatalysis is proposed in Fig. 3. Based on the 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 Nd³⁺ to Tg (depicted as [Nd³⁺Tg]) can ‘de-activate’ autocatalysis, slowing down the conversion of Tg into Tr. Notably, this effect was not observed when La³⁺ or Ca²⁺ 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 [Nd³⁺]₀ (Supplementary Fig. 4). The gels revealed that, only at optimal [Nd³⁺]₀ (0.3–0.4 mM), Tg is fully hydrolysed after 16 min of the reaction.

Fig. 3. Proposed mechanism for the cation-induced activation of Tr autocatalysis.

Both Tr and Tg form 1:1 complexes with metal ions but only Tg has a second binding step for Nd³⁺. For a detailed description of the mechanism, see Supplementary Methods Mathematical modelling.

Intrigued by this observation, we investigated if the effect of [Nd]₀ on autocatalysis can be explained using a Michaelis–Menten model. Supplementary Fig. 6, however, shows that both kinetic parameters (K_M and k_cat) change as a function of [Nd³⁺]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 Supplementary Fig. 7 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 Fig. 3. Arithmetic equations are incorporated to account for the binding of the ions to the proteins. Details of the mathematical model is appended to Supplementary Methods Mathematical modelling section.

Nonlinear effect of Nd³⁺ in flow

Next, we establish control over trypsin concentration in time under flow conditions. Figure 4a depicts a flow experiment wherein we changed the [Nd³⁺]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, τ (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 ≤ [Nd³⁺]₀ ≤ 0.40 mM. Outside this range, we found that [Tr] was significantly lower. Figure 4b summarises how the use of τ as a flow parameter could tune the behaviour of the system, characterised by an apparent non-equilibrium steady state, [Tr]*, which we determined as the average [Tr] over the last 5 min before [Nd³⁺]₀ was changed. The use of a higher residence time (τ = 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 Nd³⁺ on Tr autocatalysis remains.

Fig. 4. Control over Nd³⁺-induced nonlinearity under continuous flow conditions.

a Influence of [Nd³⁺]₀ on the autocatalytic conversion of Tg into Tr in a CSTR. [Nd]₀ is changed at regular intervals, programmed by changing [Nd³⁺]_feed (see Methods section). b Nonlinear control over Tr autocatalysis using [Nd³⁺]₀. [Tr]* is the average [Tr] determined based on the time series in a. Error bars are based on the average [Tr] over the last 5 min before [Nd³⁺]₀ was changed. Time series based on τ = 10 min is appended to Supplementary Fig. 13. c Influence of [Nd³⁺]₀ on the autocatalytic conversion of Tg into Tr in a CSTR, in the presence of an additional metal ion (Ca²⁺ and La³⁺). d Effect of additional metal ions on the [Nd³⁺]₀-induced nonlinearity, shown by mapping the dependence of [Tr]* onto polynomial functions with different degrees (indicated with n). Simulated data (bold lines) are appended to Supplementary Fig. 8. Initial conditions: [TRIS-HCl]₀ = 60–100 mM (pH 7.8), T = 21–23 ^oC, [Tg]₀ = 100 µM, [Tr]₀ = 1 µM. For a residence time, τ = 10 min. For c, d residence time, τ = 5 min.

We increase the level of control by forcing competitive binding^32–34 among several ions. Figure 4c illustrates our approach wherein five different values of [Nd³⁺]₀ was used to change the rate of Tr autocatalysis in the presence of a second ion (La³⁺ or Ca²⁺). The addition of a slower catalysing ion [Ca²⁺]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 [Nd³⁺]₀ compared to the systems without Ca²⁺. Similarly, the addition of the faster acting catalyst [La³⁺] 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 [Nd³⁺]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 (Supplementary Fig. 8).

The opposing effects that the mixtures of ions induce can be mapped onto polynomial functions with different degrees (Fig. 4d). The relation between [Tr]* and [Nd³⁺]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 Ca²⁺, this relation changes but only at higher concentrations of [Nd³⁺]₀ and therefore the nature of the polynomial function, its degree, does not change and remains 2. In the presence of La³⁺, 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 La³⁺ and Ca²⁺ 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 [Nd³⁺]₀. In the presence of Ca³⁺ and La³⁺, 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.

Nd³⁺-induced temporal logic operations

Next, we developed a procedure to obtain Boolean functions for [Tr]* by varying only [Nd³⁺]₀. Figure 5a illustrates our concept wherein three different values for [Nd³⁺]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 [Nd³⁺]_A|B is used to represent the input sequence [Nd³⁺]_0|0; [Nd³⁺]_1|0; [Nd³⁺]_1|1; [Nd³⁺]_0|1. As an example, Fig. 5b 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 completeness³⁵ and nonlinear classification³⁶, and are considered difficult to construct using chemical systems^37,38. The differences between the two gates reside on the range of [Nd³⁺]₀ that was applied: the maximum [Nd³⁺]₀ in both cases is 0.6 mM but minimum [Nd³⁺]₀ is 0.2 and 0 mM, respectively. The top graph in Fig. 5b, shows five conditions wherein [Nd³⁺]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 [Nd³⁺]_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 [Nd³⁺]_0|1 and [Nd³⁺]_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 [Nd³⁺]_0|0), demonstrating that the output signal can be reset.

Fig. 5. Nd³⁺-induced Boolean logic functions.

a Conceptual scheme for implementing Boolean logic functions. b Experimental time series of a NAND and a XOR gate. Top panel: input sequence encoded in [Nd³⁺]_A|B. Bottom panel: System’s response observed as [Tr](t). The time series for XOR is based on an average from a triplicated experiment (n = 3). c Boolean functions determined as a function of an input sequence of [Nd³⁺]₀ at τ=5 min. [Tr]* is the average [Tr] determined based on the time series in Supplementary Fig. 9. Data points, and error bars, are based on the average over the last 5 min of each condition. d Simulated phase space wherein logic gates can be defined. The ratio between steady states of [Tr]_0|0, [Tr]_0|1 and [Tr]_1|1 determines the type of gate (Supplementary Methods Criteria for distinguishing logic gates section): AND (white circle), OR (white square), XOR (white star), NAND (white hexagon) and NOR (white triangle). The nature of the gate changes when τ=5 min is changed to 10 min (for time series, see Supplementary Fig. 11): from AND to OR (red circle); from XOR to OR (red star). Initial conditions for b and c: [TRIS-HCl]₀ = 100 mM (pH 7.8), T = 21–23 ^oC, [Tg]₀ = 100 µM, [Tr]₀ = 1 µM, residence time, τ = 5 min.

Other gates (AND, OR, NOR) can be developed using a similar procedure (Supplementary Fig. 9). Figure 5c summarises these experiments by plotting the output concentration as a function of [Nd³⁺]₀. The results underline that a change in the minimum and maximum of [Nd³⁺]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 [Nd³⁺]) 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 Methods Criteria for distinguishing logic gates section). Figure 5d 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 [Nd³⁺]_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 [Nd³⁺]_1|1 is placed on the Y axis. [Nd³⁺]_0|0 on Fig. 5d for AND, OR, XOR equals 0 mM and for NAND and NOR equals 0.2 mM. The phase plot shows that a parameter window exists to maintain each logic operation, ensuring that the desired functions of the system are robust³⁹. This robustness, however, differs per operation. 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 Nd³⁺, and ions can be combined to change the phase space (Supplementary Fig. 10). 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 (Supplementary Fig. 11).

Increasing the control over temporal logic operations

The use of an external component such as an inhibitor for thresholding provides further control over the network properties (Fig. 6a). Without the inhibitor, the low steady state was stabilised by continuously depleting Tr using flow, which leads to an unstable steady state. The incorporation of the inhibitor enables a stable and low steady state (as Tr becomes inactive) but does not change the stability of the high steady state, which is supported by autocatalytic production of Tr³⁰. Figure 6b shows a sequence wherein the [Nd³⁺]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 [Nd³⁺]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 [Nd³⁺]₀ was changed in the opposite direction (from 0.8 to 0.3 mM). The observation that a pulse in [Nd³⁺]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 Supplementary Fig. 12 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.

Fig. 6. History dependence in Nd³⁺-induced Boolean logic functions.

a Schematic representation of autocatalysis controlled by the metal ion, Nd³⁺, and Soybean Trypsin inhibitor, I. b Experimental time series with [I]₀ = 8, 4 and 2 µM. Initial conditions: [TRIS-HCl]₀ = 100 mM (pH 7.8), T = 21–23 ^oC, [Tg]₀ = 100 µM, [Tr]₀ = 1 µM, 20 mM CaCl₂, τ = 4.5 min.

Discussion

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 showed 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), demonstrating that autocatalytic reactions can be programmable. Furthermore, we demonstrated that (i) the output signal can be reset, (ii) multiple ions can be combined to change the phase space and (iii) Boolean functions can be readily tuned and modelled mathematically and (iv) the history-dependent nature of autocatalysis in flow can retain information. That a range of logic are tuneable and controllable based on a kinetic parameter sets this work apart from traditional molecular logic gates⁴⁰.

Additionally, a trypsin inhibitor was incorporated into the network to create a system capable of long-term depression of the input and history dependency in the output (i.e., characteristics for neuromorphic behaviour). In this regard, the XOR gate can be considered as a primitive nonlinear operation³⁶. Building on this foundation, future work could include the introduction of spike-driven conditions to perform other nonlinear operations under out-of-equilibrium conditions²². The implementation of different configurations of multiple autocatalytic systems (based on series-, parallel- or array-coupled CSTRs) will be a crucial next step to systematically increase the number of collective feedback loops in the system. It will provide the potential to bestow CRNs with the capacity to perceive and retain information and apply it towards adaptive behaviour. Hence, we envision that this work will offer novel strategies to exploit the programmability of small and simple CRNs for building artificial systems with responsive⁴¹, adaptive⁴² and other life-like properties⁷ 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 (≥7500 BAEE units/mg solid), BAPNA and Ln(NO₃)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. 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 tubing’s (I.D. × O.D. 0.5 × 1 mm; 1/16 × 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 Ca²⁺ 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 Ca²⁺ all stock solutions also contained 20 mM CaCl₂ for the same purpose.

Equipment

A Stratasys Objet Pro 30 3D printer was used for printing CSTRs master moulds. 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 CaCl₂) 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. In all, 4 μL of Laemmle 4× buffer + 10 μl of an aliquot + 2 μL NaOH 5 M were put on a gel and ran at 30 mA with 250 mM TRIS-HCl, 1.92 M 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, 2 g of Coomassie Blue R250 in 1 L of 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 polymerised at 75 °C for 30 minutes. Holes for tubing’s 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 polytetrafluoroethylene tubing’s (Supplementary Fig. 2). First reactor served as a main reaction chamber whereas the second was receiving its outflow and reporting solution at the constant (2:1) ratio. The residence time in the second reactor was deliberately made twice as small as the first reactor to ensure that we could detect the output signal as pseudo-online. Reporting solution consisted of 4 mM BAPNA in mixture of MQ:DMSO:DMFA (0.2:0.08:0.72). The mixture of DMSO and DMFA was used to dissolve the detection molecule (BAPNA) and reduce the rate of trypsinogen conversion. Hence, the second reactor was engineered to allows for a fast detection of [Tr] by converting BAPNA into pNA (detectable moiety at 405 nm) without any side processes.

In our setup, we use stock solutions of the components of the system and store them in glass syringes, which content is connected by polytetrafluoroethylene tubing’s to the CSTR. The low-pressure pumps are used to independently control the syringes and feed each stock solution into the CSTR. The feeding concentrations for the components (Tg, Tr, I and X) are abbreviated as [Tg]_feed, [Tr]_feed, [I]_feed, [X]_feed, respectively. Initial concentration ([Tg]₀, [Tr]₀, [I]₀, [X]₀) reported in the figure captions and legends are calculated based on the feeding concentration and flow rate of each component. The total flow rate is kept constant throughout the experiments.

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 visualised using the online plotting function of CETONI Elements software. We used two wavelength bands to detect pNA: 620–630 nm (internal standard wavelengths, where pNA does not absorb light) and 400–450 nm (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.

Mathematical modelling

Our mathematical model (see Supplementary Methods Mathematical modelling section) 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 Tables 1 and 2. All kinetic and thermodynamic constants were estimated from published data^31–34 to support experimental results.

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.

Reporting summary

Further information on research design is available in the Nature Portfolio Reporting Summary linked to this article.

Author contributions

A.S.Y.W. conceived and planned the project. A.S.Y.W. and J.H. supervised the project. D.V.K. performed the experiments, designed the mathematical model, performed the simulations. A.S.Y.W. and D.V.K. wrote the manuscript. All authors contributed to revising the manuscript.

Peer review

Peer review information

Nature Communications thanks Jerzy Gorecki, István Szalai and the other, anonymous, reviewer(s) for their contribution to the peer review of this work. A peer review file is available.

Data availability

We present the data as figures in the main text and Supplementary Information. The data generated in this study (both experimentally obtained as well as simulated data) are available in the 4TU repository with 10.4121/0ef4bcb9-09e0-4a74-9fa1-21d467f951f4.

Code availability

Data simulated in MATLAB 2023a are used in this paper. Source codes for the simulated data are provided as Matlab (*.m) files and can be downloaded from 10.4121/0ef4bcb9-09e0-4a74-9fa1-21d467f951f4. The readme file provides instructions to run the codes, and produce the full dataset used in this work.

Competing interests

The authors declare no competing interests.

Supplementary information

The online version contains supplementary material available at 10.1038/s41467-024-52649-z.