J. Phys. Chem. B 2010, 114, 14059–14063
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Base-Catalyzed Feedback in the Urea-Urease Reaction Gang Hu,† John A. Pojman,*,† Stephen K. Scott,‡ Magdalena M. Wrobel,‡ and Annette F. Taylor*,‡ Department of Chemistry, Louisiana State UniVersity, Baton Rouge, Louisiana 70803, United States, and School of Chemistry, UniVersity of Leeds, Leeds LS2 9JT, United Kingdom ReceiVed: July 14, 2010; ReVised Manuscript ReceiVed: September 24, 2010
The bell-shaped rate-pH curve coupled to production of base in the urea-urease reaction was utilized to give feedback-driven behavior: an acid-to-base pH clock (a kinetic switch), bistability and hysteresis between an acid/base state when the initial pH was adjusted by a strong acid, and aperiodic pH oscillations when the initial pH was adjusted by a weak acid in an open reactor. A simple model of the reaction reproduced most of the experimental results and provided insight into the role of self-buffering in the dynamics. This reaction suggests new possibilities in the development of biocompatible feedback to couple to pH-sensitive processes for bioinspired applications in medicine, engineering, or materials science. Introduction Feedback is the process by which a system is regulated by its output and is responsible for emergent phenomena in biological systems such as homeostasis, signal amplification, bistable switches, memory, and rhythms.1 Current research in biology has uncovered some of the feedback loops underlying such phenomena and resulted in the genetic manipulation of cellular systems to produce a specific behavior, providing valuable contributions to the field of systems/synthetic biology that seeks to understand and manipulate the complex interactions leading to biological structure and function.2,3 There is an associated emerging field of systems chemistry,4 which may be considered to be the interplay between complex chemical reaction and physical processes to create a macroscopic function or property in a chemical system. One avenue of research involves exploiting feedback for potential applications in product selectivity,5 drug-delivery devices,6 and structured or active materials.7-11 Feedback may arise through mechanical means, such as hysteresis in gel volume with pH, or chemical means, such as autocatalytic production of a chemical species. Autocatalysis has been mainly studied in inorganic systems involving halogen oxidation of species such as sulfite and displaying large REDOX changes.12 There is a need for increasing the range of autocatalytic reactions for biocompatible applications, and enzyme-catalyzed reactions provide an obvious route. However, to date, there are relatively few reproducible and robust examples of feedback in enzyme systems in vitro.13-15 The hydrolysis of urea by the enzyme urease results in the production of a weak base, ammonia, and carbon dioxide, which hydrolyses to give bicarbonate.16 The base-producing properties of the reaction have been used for enzyme logic systems in biofuel cells17 and in the rapid urease test for the bacteria H. pylori, which produces this enzyme to raise its pH locally to protect itself against the strongly acidic (HCl) environment in the stomach.18 An important and unexplored aspect of the reaction is the dynamic behavior under nonbuffered conditions. * To whom correspondence should be addressed. E-mail: A.F.Taylor@ leeds.ac.uk (A.F.T.);
[email protected] (J.A.P.). † Louisiana State University. ‡ University of Leeds.
The typical bell-shaped rate-pH curve of enzyme reactions coupled to the production of acid/base may result in rate acceleration and feedback-driven behavior under such conditions.19 In this Article, we show that the production of base and the pH dependence of the urea-urease reaction gives rise to basecatalyzed feedback and associated emergent behavior. An interesting feature of the reaction is that the behavior was found to depend on whether the initial pH was adjusted using a weak or strong acid. A sharp switch from low (∼4) to high pH (∼9) was observed up to 1 h after the reactants were mixed with sulfuric acid. In the presence of acetic acid, rate acceleration was suppressed by the formation of the acetic acid/acetate buffer, resulting in a slower acid-base switch. In both cases, the clock time is controlled by the initial concentrations, and the final pH is governed by the internal ammonia-ammonium buffer formed. Under open conditions in a flow reactor, bistability between the low and high pH states was observed over a large range of flow rates with an inflow of sulfuric acid, and aperiodic oscillations between pH 4 and 7 were observed with acetic acid. A simple model of the reaction reproduced the experimental results, with good quantitative match for a wide range of experimental conditions; however, it failed to show oscillations. It is suggested that the latter arise from imperfect mixing20 or noise-induced bistable switching.21 This reaction involves only urea, acid, and a single enzyme urease and was modeled using Michaelis-Menten kinetics and several acid-base equilbria. Therefore, it is possibly one of the simplest and most benign enzymatic reactions to display emergent behavior and provides a prototype for the investigation of pH-driven feedback in enzyme-catalyzed reactions. The urea-urease reaction creates exciting new possibilities in the development of less aggressive, biocompatible feedback to couple to pH-sensitive processes for bioinspired applications in medicine, engineering, or materials science. Experimental Section For the clock reactions, stock solutions were prepared of acetic acid (Fisher, Glacial), sulfuric acid (Fisher), urea, and urease (Sigma, Type III, from Jack Beans, typically 40 100 units/g solid). The urease solution was freshly prepared daily.
10.1021/jp106532d 2010 American Chemical Society Published on Web 10/18/2010
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The reactants were mixed to give the final concentrations quoted in the text, with a total reaction volume of 30 mL. Stirring was achieved using magnetic stirrer bar (600 rpm), and the pH was monitored using a HANNA pH electrode and digital meter. Experiments were performed with an open air interface at a temperature of 20 °C. In the flow experiments, a cylindrical continuous-flow stirred tank reactor (CSTR) was used of diameter 2.5 cm, height 2.1 cm, and total free volume 9.1 mL and thermostatted with a water jacket at 20 °C. Two stock solutions were exploited: an acid/ urea solution and a urease solution. The inflow concentrations quoted are the concentrations in the reactor in the absence of reaction. The reactants were pumped into the reactor using a Gilson peristaltic pump. The stirring rate was maintained constant at 600 rpm with a magnetic stirrer bar of length 1.8 cm, and the pH was monitored using a HANNA pH electrode and a HI9000 digital meter. Modeling Section The enzyme-catalyzed hydrolysis of urea yields ammonia and carbon dioxide urease
CO(NH2)2 + H2O 98 2NH3 + CO2
(1)
(
V′ ) 1 +
Kes2 [H+]
+
[H+] Kes1
)
-1
(8)
This relationship arises from the dependence of the rate on the formation of an active protonated form of the enzyme-substrate complex (Kes2) and inactive biprotontated form (Kes1). When the reaction is performed under open (flow) conditions, the following term is added to each rate equation: k0([X]0 [X]), where k0 is the flow rate (inverse residence time) and [X]0 is the inflow concentration of species X. The total amount of enzyme remains constant in the reactor ([E]T ) inflow concentration), and [X]0 ) 0 for all species except urea and acetic/ sulfuric acid. We note that in flow KM ) (kd + k1 + k0)/ka, where ka is the formation and kd is the decomposition of the enzyme-substrate complex. However, it is reasonable to assume that k0 (with values up to 10-2 s-1 in this work) is small compared with kd (on the order of 102 s-1)23 such that this term can be ignored. The rate constants and enzyme parameters are included in Table 1. Rate constants for reactions 2-6 are taken directly from the literature,24,25 and the enzyme rate and equilibrium constants are within the ranges quoted in the literature, with values taken to best match the experimental results.26,27 The rate equations were solved using XPPaut with integration method CVODE.28
The pH is determined by the following equilibria Results and Discussion +
+
NH4 h NH3 + H
pKa ) 9.25
CO2 + H2O h H+ + HCO3HCO3- h CO32- + H+
pKa ) 6.5
pKa ) 10.25
H2O h H+ + OH-
(2) (3) (4) (5)
For the addition of acetic acid and for the second dissociation of sulfuric acid, the following reaction is included
HA h A- + H+
(6)
where HA is the weak acid. Reactions 1-6 result in 10 coupled rate equations with mass action kinetics for equilibria 2-6, and the enzyme rate V is of the Michaelis-Menten form (incorporating substrate inhibition, product inhibition, and pH dependence22)
V)
(
(
U KM + U 1 + KS
))(
VmaxU
)(
)
[NH4+] Kes2 [H+] 1+ 1+ + + KP Kes1 [H ] (7)
where the maximum rate Vmax ) k1[E]T, [E]T is the total amount of enzyme, U is urea, KM is the Michaelis constant, Ku is the equilibrium constant for uncompetitive substrate inhibition, and Kp is the equilibrium constant for noncompetitive product inhibition. The relationship between the rate in eq 7 and the acid concentration is given by V ) AV′ where A is independent of acid concentration and V′ is given by
pH Clock. A pH “clock” reaction refers to a reaction that displays a maximum rate of production of acid or base at some nonzero extent of reaction. Therefore, a kinetically driven switch in pH is observed after a period of time, referred to as the induction period or clock time. This scenario often arises because of the presence of feedback: rate acceleration due to the base/acid-catalyzed production of base/acid. It has been proposed that the pH dependence of an enzymecatalyzed reaction might be exploited to generate feedbackdriven behavior if the reaction produces base or acid.19 In the case of a base-producing reaction, when the initial pH is adjusted by the addition of acid such that the rate is initially low, then as base is produced, the rate will accelerate until it reaches the maximum given by the bell-shaped rate-pH curve. The rate-pH curve for urea-urease reaction is plotted in Figure 1a inset; the form agrees well with that observed experimentally.27 Base-catalyzed feedback and a pH clock are observed in this reaction by adjusting the initial pH to ∼4. Because reaction produces base (through ammonia), the rate accelerates as the reaction proceeds, reaching a maximum at pH ∼7 and falling to zero at pH ∼10. The change in pH in time is shown in Figure 1 during typical clock reactions with the initial pH adjusted by (a) acetic acid and (b) sulfuric acid. It can be seen that the maximum rate of change of pH is decreased in the case of acetic acid compared with sulfuric acid. The form of the pH profiles can be explained by examination of the individual species using the model. The experimental and simulated data for the pH clock reaction are shown in Figure 2 with (a) sulfuric acid and (b) acetic acid. The main difference between (a) and (b) is that in the case of acetic acid there is a decrease in the rate of removal of [H+] between pH 4 and 5 (Figure 1f). This is because a buffer is formed when acetic acid is converted to acetate (Figure 1c,e). At ∼500 s, the pH ) pKa(acetic acid) ) 4.8, [CH3COOH] ) [CH3COO-], and the buffering capacity is at a maximum. At ∼650 s, the pH 7, all CH3COOH is converted to CH3COO-, and the buffering
Base-Catalyzed Feedback in the Urea-Urease Reaction
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TABLE 1: Rate Constants (25 °C) for the Urease-Urea Reaction rate constants24,25
k2/s-1 24
enzyme constants26,27
a
k-2/M-1 s-1 4.3 × 10
10
k3/s-1
k-3/M-1 s-1
0.037
7.9 × 10
k4/s-1
4
k-4/M-1 s-1 5 × 10
2.8
10
k5/M s-1 1 × 10
k-5/M-1 s-1
-3
1 × 10
11
k6/s-1 b
1.2 × 10 7.8 × 105
a
k1/unit-1 mL M-1 s-1
KM/M
Kes1
Kes2
Ku
Kp
3.7 × 10-6
3 × 10-3
5 × 10-6
2 × 10-9
3
2 × 10-3
k-6/M-1 s-1 9
b 1 × 1011 4.5 × 1010
a
CH3COOH. b HSO4-.
Figure 1. Experimental pH-time profiles obtained in the urea-urease reaction. Inset: Relative enzyme rate V′ as a function of pH calculated from eq 8. Initial concentrations are: [CO(NH2)2]0 ) 5 mM, [urease]0 ) 1.4 units mL-1. (a) [CH3COOH]0 ) (i) 0.2, (ii) 0.58, and (iii) 0.93 mM. (b) [H2SO4]0 ) (i) 0.05, (ii) 0.11, and (iii) 0.18 mM.
Figure 2. (a-e) Experiment (points) and model (line) kinetic profiles in the urea-urease reaction. (f) Simulated rate of change of acid as a function of pH. Initial concentrations are: [CO(NH2)2]0 ) 5 mM; [urease]0 ) 1.4 units mL-1. (a,f) [H2SO4]0 ) 0.22 mM. (b-f) [CH3COOH]0 ) 5.8 mM.
capacity is lost. With increasing initial concentrations of acetic acid, the rate of change of pH becomes progressively more damped because a stronger buffer (higher buffering capacity) is formed. Therefore, adjusting the initial pH with a weak acid with a pKa > 3 will result in weak feedback (low maximum rate of change of pH) in the urea-urease reaction.
Figure 3. (a-c) Experiment (points) and model (line) clock times in the urea-urease reaction as a function of the initial concentrations where (a) [urea]0 ) 5 mM, [urease]0 ) 1.4 units mL-1. (b) Acetic acid: [CH3COOH]0 ) 0.58 mM and [urea]0 ) 5 mM, sulphuric acid: [H2SO4]0 ) 0.06 mM and [CO(NH2)2]0 ) 15 mM. (c) Acetic acid: [CH3COOH]0 ) 0.58 mM and [urease]0 ) 1.4 units mL-1, sulfuric acid: [H2SO4]0 ) 0.06 mM and [urease]0 ) 0.7 units mL-1. (d) The final pH as a function of the initial concentration of urea with other concentrations as in part c. Inset shows pH-time profiles for sulfuric acid.
The main characteristics of the pH clock reaction are the clock time, defined here as the time taken for the system to reach pH 7, which increases with decreasing maximum reaction rate, and the final pH, which is governed mainly by the amount of ammonia relative to ammonium ion (and therefore the initial pH). In contrast with other pH clock reactions,29,30 there is a self-buffering effect in the urea-urease reaction at high pH due to the formation of the ammonia-ammonium buffer (Figure 2c). The effect of the initial concentrations on the clock time and final pH is shown in Figure 3. As expected, the clock time increases, and the final pH decreases with increasing initial acid concentration and decreasing initial urea or urease concentration. Power law dependencies for the experimental clock times (tclock ) [X]0a) give reasonable fits in the case of X ) acid where a(sulfuric) ) 1.9 ( 0.2, a(acetic) ) 1.6 ( 0.1, and X ) urease where a(acetic) ) -1.0 ( 0.04. Very long clock times can be obtained, up to several thousand seconds, and as seen in Figure 2a, the change from acid to base is still sharp when the initial acid is adjusted using sulfuric acid. The simulations reproduced the experimental trends, but quantitative agreement is lacking, particularly for low urea concentrations. Michaelis-Menten kinetics may not be appropriate under these conditions.16 For simplicity, we have not included several steps here, including the formation of carbonic acid,31 the reaction25 of CO2 with OH-, and the transfer of CO2/ NH3 to the gas phase. Preliminary investigations suggest that they have little signifi-
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Figure 4. Urea-urease reaction under open (flow) conditions with inflow concentrations: [CO(NH2)2]0 ) 5 mM; [urease]0 ) 1.4 units mL-1. (a) Experiment (points) and model (line) bistability in pH with flow rate where [H2SO4]0 ) 0.7 mM. (b) Simulated phase diagram showing regions of bistability (BS), the thermodynamic state (TS, high pH), and the flow state (FS, low pH) as a function of inflow sulfuric acid concentration and flow rate.
cance in the dynamical results reported here; the influence of these processes on the reaction will be reported elsewhere. Bistability and Hysteresis. The coexistence of two steady states for the same conditions can occur when a clock reaction is maintained far-from-equilibrium under open conditions. Bistability is observed experimentally when the urea-urease reaction is performed in a CSTR with an inflow of urea, sulfuric acid, and urease. A typical bifurcation diagram is plotted in Figure 4a showing the steady-state value of pH as a function of the flow rate, k0. There is excellent agreement between the experiment (points) and simulation (line) in the example shown. The upper thermodynamic branch of pH is followed as the flow rate is increased from the low flow (reacted) state, whereas the lower flow branch is followed starting from the high flow (unreacted) state. Therefore, a low (pH ∼4) and a high pH state (pH 7.5 to 9) coexist for values of the flow rate between 0.007 and 0.35 s-1 with the pH observed depending on whether the reaction was started from low or high flow rates: this is the phenomenon known as hysteresis. The regions of bistability (BS), a single thermodynamic steady state (TS), and a single flow state (FS) are plotted in a phase diagram of inflow acid concentration versus flow rate in Figure 4b for sulfuric acid. There is a wide range of flow rates over which bistability is observed, particularly at low acid concentrations; the range decreases with increasing initial acid concentration and hence increasing clock time. The region of bistability also shifts to lower flow rates. Oscillations. With an inflow of acetic acid, bistability is predicted over a much smaller range of flow rates in the model than with sulfuric acid (Figure 5a). This might be attributed to the weaker feedback in the case of acetic acid. However, in the experiments, an interesting feature was observed: rather than coexistence of a stable low or high pH state, aperiodic oscillations between pH ∼4 and 7 were observed. The maximum and minimum pH observed are plotted in the bifurcation diagram in Figure 5b, and example traces of the time variation in pH are shown in Figure 5c. This behavior occurs at the transition between the low and high pH states, over a narrow range of flow rates. The model does not show oscillations for any of the parameter values explored; however, it assumes a homogeneous reaction mixture. It is well known that random fluctuations21 or mixing effects20 may strongly influence the behavior of autocatalytic systems. Experimentally, the clock time and regions of bistability in the urea-urease system are found to be sensitive to stirring rate and thus to mixing effects.32 We attempted to reduce macromixing effects (large-scale spatial inhomogeneities) by using a reactor with height and diameter of similar values and relatively
Figure 5. (a) Simulated phase diagram showing regions of bistability (BS), the thermodynamic state (TS, high pH), and the flow state (FS, low pH) as a function of inflow acetic acid concentration and flow rate. The inflow concentrations are: [CO(NH2)2]0 ) 5 mM; [urease]0 ) 1.4 units mL-1. (b,c) Experimental results for the urea-urease reaction in a flow reactor with inflow concentrations: [CO(NH2)2]0 ) 5 mM; [urease]0 ) 1.4 units mL-1; [CH3COOH]0 ) 0.58 mM. (b) Maximum/minimum in pH with flow rate. (c) Time variations in pH for three different flow rates.
high stirring rate (given the small volume of the reactor). Imperfect micromixing33 (small-scale spatial inhomogeneities) can lead to shifts in bifurcation points and the appearance of oscillations, although it is unlikely to yield periodic sustained oscillations in a chemical system that does not already display oscillations in any region of phase space. However, micromixing effects might explain aperiodic, transient oscillations in bistable systems.34 The influence of the addition of micromixing or noise to the reaction model will be the subject of further study. Insight into the different response of the sulphuric acid and acetic acid systems to noise or imperfect micromixing might be provided by examination of the simulated response of the reaction to perturbations. Under flow conditions in the region of bistability, the addition of a supercritical concentration of acid or base results in a transition from one pH state to the other. The response of the system to perturbations is shown in Figure 6 for sulfuric acid (a,c) and acetic acid (b,d). For the examples shown, the flow state is less stable than the thermodynamic state in that a much larger perturbation is required to initiate a transition. With sulfuric acid, the response to a perturbation is extremely rapid (tclock ) 310 s here, but even for clock times up to 3000 s fast transitions were observed). In the experiments, the region of bistability was sometimes smaller than that predicted in simulations, which may be attributed to the fact that any perturbations result in a rapid switch from the flow to the thermodynamic state. However, with acetic acid, a slow return to the thermodynamic state is observed in the case of a subcritical perturbation of this state (Figure 6b), and a slow transition from the flow state to the thermodynamic state is observed following a supercritical perturbation of this state (Figure 6d). This slow evolution following perturbation might again be attributed to the formation of the acetic acid-acetate buffer with a maximum buffering capacity at pH ∼5. The transition time depends on the size of the perturbation and the flow rate. The system becomes sensitive to fluctuations in acid/ base at the transition points from the thermodynamic to the flow branch (and vice versa).35 Conclusions In this Article, we have demonstrated how the bell-shaped rate-pH curve of the urea-urease reaction might be exploited
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Figure 6. Simulated response of the bistable urea-urease reaction to (i) a subcritical perturbation and (ii) a supercritical perturbation from the thermodynamic state in (a,b) and the flow state in (c,d). The dotted line indicates the threshold for a transition between states. The inflow concentrations and flow rates are: [CO(NH2)2]0 ) 5 mM; [urease]0 ) 1.4 units mL-1. (a,c) [H2SO4]0 ) 0.7 mM, k0 ) 0.02 s-1; (b,d) [CH3COOH]0 ) 0.58 mM, k0 ) 0.005 s-1.
to give feedback-driven behavior. The experimental results were supported with a model containing Michaelis-Menten kinetics for the enzyme-catalyzed reaction. A switch from low to high pH was observed in a closed reactor after clock times of up to several thousand seconds. The rate acceleration was dampened in the presence of the weak acid (acetic) compared with a strong acid (sulfuric) as a result of the formation of an internal buffer. When the reaction was performed in an open (flow) reactor, a wide range of bistability and hysteresis was observed in the presence of sulfuric acid. Aperiodic oscillations were observed in the acetic acid experiments, and it was demonstrated that this system undergoes largeamplitude slow transitions between pH states in response to perturbations in acid/base. It was suggested that the time variations in pH observed arise as a result of mixing effects or noise-induced bistable switching. The reaction might be exploited for the development of new biocompatible pH oscillators.36,37 To obtain periodic oscillations, a negative feedback agent that removes OH- at high pH must be added to the system. Possible candidates include the basecatalyzed hydrolysis of gluconolactone, which produces acid.38 Gluconolactone is the product in the glucose-oxidase-glucose reaction, and the coupling of these two enzymatic reactions will be explored in future work. To date, all known pH systems oscillate only under open conditions because one of the substrates is usually entirely consumed during the initial pH switch. A batch pH oscillator might be used to drive periodic changes in the morphology of pH-sensitive polymers in chemomechanical devices39,40 or the motion of molecular machines.41,42 The urea-urease enzymecatalyzed reaction might be used in the development of a batch pH oscillator because the substrate urea is only partially consumed during the pH switch. The possibility of pH fronts, waves, and patterns43 in this system also makes the urea-urease reaction an attractive reaction for further investigation. Acknowledgment. Financial support for this work from National Science Foundation (CHE-0719099) is greatly appreciated. G.H. acknowledges the China Scholarship Council for partial support.
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JP106532D
