Characterizing metalloendonuclease mixed metal complexes by global kinetic analysis

  • Charulata B. Prasannan
  • Fuqian Xie
  • Cynthia M. Dupureur
Original Paper

Abstract

To test the role of a secondary metal ion in a two metal ion metallonuclease mechanism, some groups have introduced a nonsupportive metal ion [usually Ca(II)] in cleavage reactions. Stimulation of Mg(II)- or Mn(II)-supported activity has been taken as evidence that the second metal ion is regulatory. However, this activity has yet to be dissected to determine what processes and species contribute to this observation. Here, we test global kinetic analysis as an approach to this problem. Taking advantage of the various binding and cleavage constants established for PvuII endonuclease, we apply cleavage data obtained under a range of Mg(II) and Ca(II) concentrations to a number of kinetic models which specify A and B sites for both metal ions and various active species. The data are best fit and simulated with models which feature Ca(II) being held more strongly in the B (or secondary) site. This mixed metal enzyme species is the only one which forms appreciably and exhibits a cleavage rate constant similar to that observed when there is only one Mg(II) per active site (approximately 0.01 s−1). Thus, in the case of PvuII endonuclease, Ca(II) does not stimulate cleavage. However, a simulated increase in activity at moderate Ca(II) concentrations can be rationalized with a cleavage rate constant for the mixed species similar to that when two Mg(II) ions are present in the active site. This provides an important insight into the underlying basis for the Ca(II)-stimulated activity observed for some metallonucleases that is not accessible by any other means.

Keywords

Structure–function relationship Enzyme kinetics Nucleic acid Thermodynamics Binding affinity 

Introduction

Metallonucleases are enzymes that conduct the metal-ion-dependent cleavage of nucleic acids. The majority of these enzymes utilize Mg(II) as the native cofactor [1]; such activity is often supported in vitro by Mn(II), a metal ion very similar to Mg(II) in its properties. However, Ca(II) does not support activity alone and has been used to good effect in substrate binding and crystallographic studies [1].

Although the active-site architecture can vary, the hydrolysis of nucleic acids by many metal-ion-dependent nucleases has been proposed to involve more than one metal ion. This mechanism has been most widely supported by X-ray crystal structures which feature two metal ions in the metallonuclease active sites [1, 2]. In this mechanism (Fig. 1), metal ion A ligates the attacking water molecule and the scissile phosphate; metal ion B also ligates the scissile phosphate, but in addition coordinates a water molecule that donates a proton to the leaving group.
Fig. 1

General two-metal-ion mechanism for the hydrolysis of DNA by a protein metallonuclease. In the most accepted two metal ion mechanism model, metal ion A ligates the scissile phosphate and coordinates the attacking water molecule. Metal ion B also interacts with the DNA, but is modeled to also coordinate a water molecule which donates a proton to the leaving group. X refers to the uncertain means by which the attacking water molecule is activated. (Adapted from [1])

Challenging this evidence are a number of solution and computational studies [3, 4, 5, 6] which support the requirement of only one metal ion for metallonuclease activity [typically Mg(II)], with the second metal ion modulating or regulating nuclease activity. One such experiment involves adding to the reaction mixture a second metal ion, usually Ca(II), which does not support cleavage activity. The idea is that Ca(II) will occupy one of the metal ion binding sites (Fig. 2); if the role of the metal ion in that site is simply to contribute charge to the active site, then it will not matter which metal ion occupies that site.
Fig. 2

Mixed metal enzyme complexes. A and B refer to the metal ion binding sites indicated in the mechanism (Fig. 1)

For reasons that will be addressed in this paper, the patterns observed with different enzymes and cofactors vary. For EcoRV endonuclease activity supported by Mn(II), Ca(II) stimulates steady-state reaction rates. In the cleavage of noncognate DNA supported by Mg(II), steady-state EcoRV activity was stimulated at low Ca(II) concentrations and was inhibited at higher Ca(II) concentrations (above 2 mM) [7]. Ca(II) stimulates the Mn(II)-dependent single-turnover activity of endonuclease V as characterized by single-point rates [8]. Ca(II) also stimulates the Mg(II)-dependent activity of ApeI endonuclease [9] and the Mn(II)-supported activity of TaqI endonuclease [10].

Although stimulation of activity by Ca(II) is often observed when the nonnative Mn(II) is substituted for Mg(II), a review of the literature will indicate that an apparent increase in cleavage activity upon the addition of Ca(II) to a Mn(II)-supported reaction is generally taken as evidence for a two metal ion mechanism in which the role of one metal ion is regulatory in nature.

Although they are certainly more convenient than X-ray crystallography and in-depth thermodynamic studies, these “mixed metal” experiments suffer from some serious limitations: the observed increase in cleavage rate as a function of Ca(II) concentration depends not only on which metal ions are present, but also on which site they occupy (A or B; Fig. 2), and with what affinities they are held relative to the other site and the other metal ion. These affinities can and often do differ between sites and among metal ions. For example, it is very common for Mg(II)-dependent metallonucleases to bind Mn(II) more strongly than Mg(II) [1]; Ca(II) can also bind these enzymes more strongly than Mg(II) [1]. These differences in affinity affect the distribution of species such that one cannot rely on simple statistics to estimate the distribution of species. Further, it is not clear how much these species contribute to activity, both in terms of population distribution and in terms of actual rates of cleavage by each species. In interpreting the effect of adding Ca(II) on cleavage activity, it would be helpful to understand how these factors contribute to the Ca(II) dependence of cleavage.

Recently we demonstrated that global kinetic analysis has the power to dissect the contributions of various species in a metallonuclease kinetic reaction mixture [11]. In this approach, one leverages existing information about metal ion [both Ca(II) and Mg(II)] and substrate binding equilibria to obtain constants which are not accessible via direct experiment. Although clearly there are a number of metallonuclease enzymes of interest when considering mixed metal behavior, the homodimeric PvuII endonuclease is the only metalloenzyme for which these data exist in sufficient abundance to support the quantitative analysis of mixed metal enzyme species undertaken here. Previous characterization of these equilibria for this system indicates that there are two metal ion binding sites per active site, and substrate binding is strongly metal ion dependent [12]. The equilibrium and rate constants emerging from these earlier studies are combined with cleavage rate constants and applied to various mechanistic models. Global fits of these data yield unknown rate constants for binding and cleavage, the distribution of species, and the appropriateness of various models. For example, with use of this approach, it was possible to ascertain the Mg(II) binding, substrate binding, and cleavage constants for the enzyme species which binds only one metal ion per active site while it exists in equilibrium with other species [11]. Indeed, global analysis is the only means by which such mixtures can be examined quantitatively without introducing a mutation or cofactor substitution, both of which can complicate interpretation.

Dissecting the activities of mixed metal enzyme–substrate complexes of a metallonuclease is an ideal problem for global analysis. To that end, single-turnover rate constants were obtained as a function of Mg(II) and Ca(II) concentrations in turn, and then subsequently applied to various kinetic models to determine to what extent mixed metal enzyme species form and execute cleavage of substrate. This analysis provides unprecedented detail about the mixtures that dominate such reactions.

Materials and methods

Materials

Chelex resin was purchased from Bio-Rad (Hercules, CA, USA). Puratronic MgCl2 was purchased from Alfa Aesar (Ward Hill, MA, USA). Concentrations of stock solutions were determined by flame atomic absorption spectroscopy using a GBC 904 BT 700 spectrophotometer (GBC Scientific). All buffers were applied to a Chelex column to remove adventitious metal ions. Metal-free nitric acid was used to make all subsequent pH adjustments. All solutions were determined by atomic absorption spectroscopy to be metal-free to the limits of detection [13].

Preparation of PvuII endonuclease

Purification of PvuII endonuclease was achieved using phosphocellulose chromatography and heparin Sepharose affinity chromatography as previously described [14]. Adventitious metal ions were removed via exhaustive dialysis against metal-free buffer [15]. Enzyme was quantitated using ε280 = 36,900 M−1 cm−1 for the monomer subunit and handled with sterile plasticware and metal-free sterile pipet tips to prevent contamination.

Preparation of oligonucleotides

The non-self-complementary 14mer strand 5′-CAGGCAGCTGCGGA-3′ and its complement were purchased high performance liquid chromatography purified from IDT (Coralville, IA, USA). DNA was quantitated using ε260 values provided by the vendor. All oligonucleotide concentrations are expressed with respect to the strand or duplex as indicated. DNAs were rendered metal-free through at least two exchanges of more than 90% volume with deionized distilled water using Centricon filters. Subsequent handling was accomplished with metal-free pipet tips and sterile plasticware. Duplexes were formed by heating to 95 °C a mixture of 1 equiv of one strand with 1 equiv of complementary strand and permitting the sample to cool to room temperature overnight. Samples were stored in sterile water at 4 °C for immediate use or were lyophilized for storage.

Radiolabeling was accomplished with 17 pmol of duplex DNA and 32P-γATP (33 pmol of a 6,000 Ci mmol−1 stock) (PerkinElmer, Boston, MA, USA) and polynucleotide kinase (1 U) as per the manufacturer’s instructions (New England Biolabs, Ipswich, MA, USA). Following incubation for 2 h at 37 °C, the duplex was purified using Sephadex G-50 resin (Sigma, St. Louis, MO, USA).

Single-turnover kinetics

Suitable single-turnover conditions, that is, the enzyme concentration is in sufficient excess of the substrate for kobs to be independent of the enzyme concentration, were determined previously [11]. Relatively high enzyme and substrate concentrations make working at low metal ion concentrations, where the reaction rates are slow, more feasible. 32P end-labeled 14mer duplex DNA added to 300 nM unlabeled DNA was incubated with 2 μM PvuII endonuclease dimers in 50 mM tris(hydroxymethyl)aminomethane (Tris), pH 7.5, 37 °C. Mg(II) and Ca(II) concentrations were varied independently, and NaCl was adjusted uniquely at varying the metal ion concentration to maintain constant ionic strength (130 mM) across all experiments. Slower reactions were initiated by addition of metal-free enzyme at the bench. At various metal ion concentrations, changes in the order of addition did not significantly affect the measured single-turnover rate constants [11] (and data not shown). At the indicated time, the reaction was quenched with an equal volume of 250 mM EDTA in 50% glycerol. The product was separated from the substrate using a 20% polyacrylamide/8 M urea/1× Tris–borate–EDTA (TBE) gel with 1× TBE as the running buffer. This assay does not require product release to ascertain how much DNA has been cleaved. EDTA stops the reaction, and polyacrylamide gel electrophoresis proceeds under denaturing conditions. Therefore, any DNA that is cut is counted as product, whether it is still bound to the enzyme or not at the time of quenching. Relative amounts of substrate and product were visualized with a Storm phosphorimager, which converts radioactivity into a digital image. ImageQuant was used to convert the fraction of product formed to concentration, which is plotted versus incubation time. These data were plotted and fit using Kaleidagraph 3.6 (Synergy, Reading, PA, USA) to the first-order-exponential equation \( \left[ P \right]_{t} = \left[ P \right]_{0} \left( {1 - {\text{e}}^{{ - k_{\text{obs}} t}} } \right), \) where [P]t is the concentration of product at time t, [P]0 is the concentration of product at time 0, and kobs is the single-turnover rate constant. The entire data set comprises 28 curves and 379 points over 20 different Mg(II)/Ca(II) concentration conditions.

Quenched flow experiments

Faster reactions [i.e., high Mg(II) and low Ca(II) concentrations] required the use of a Biologic SFM4/Q quench-flow instrument (Claix, France). Equivalent volumes of solutions containing 600 nM DNA and 4 μM enzyme were loaded into the instrument. Most experiments were conducted with both solutions containing the required metal ion concentration(s) in the reaction buffer. However, experiments in which 4 μM metal-free enzyme was mixed with 600 nM substrate and double the required metal ion concentration yielded the same binding constants within experimental error. At appropriate time intervals (250 ms to 30 s), the reaction was quenched by mixing it with 140 μL of 100 mM EDTA solution. The collected samples were analyzed via polyacrylamide gel electrophoresis as described in the previous section.

Global fitting and simulation of kinetic data using DynaFit

The program DynaFit [16] was used to globally fit reaction progress data to various mechanistic models. Input includes arrays of progress curves (product vs. time) as a function of Mg(II) or Ca(II) concentration at fixed DNA and enzyme concentrations. DynaFit converts a reaction scheme, consisting of individual reversible and irreversible reactions involving metal ion binding, substrate binding, and product conversion, into a series of differential equations. Starting parameters (equilibrium or rate constants for dissociation and association) are provided and either fixed or permitted to float during the fit. Output from DynaFit includes values for floated parameters with errors, standard deviations for the global fits as well as for each progress curve, and plots of the experimental data with the curves generated by nonlinear regression. Percent errors refer to specific parameters. To simulate experimental kobs versus metal ion concentration plots, data points generated from the fits were used to obtain kobs. Rate constants and equilibrium constants for various steps were readily interconverted using the relation Kd = koff/kon, where koff for metal ion binding was always 1,000 s−1 [11] and koff for DNA binding was always 1 × 10−3 s−1 [12].

Results

Single-turnover cleavage kinetics in the presence of both Mg(II) and Ca(II)

In this analysis, our objectives are to determine if enzyme species bound to both Ca(II) and Mg(II) are capable of cleavage, compare their activities with those of enzyme species bound only by Mg(II), and use the results in simulations to understand the contributions to the Ca(II) concentration dependence of cleavage rate constants. As will be described, these goals will be met via global analysis of kinetic cleavage data, which allows us to dissect an observed rate into contributions by individual species.

It is first necessary to acquire arrays of cleavage data for fitting to various candidate models. This multidimensional data “space” consists of as many possible combinations of Mg(II) and Ca(II) concentrations as permit the determination of distinct and reliable cleavage rates. That is, the Mg(II) concentration must be high enough and the Ca(II) concentration low enough to generate a rate which can be measured. Further, although some of the aforementioned studies on other systems involved Mn(II), we confined our measurements to Mg(II) because (1) it is the native cofactor, and Mn(II) is not, and (2) the relevant metal ion binding, substrate binding, and cleavage parameters are characterized for Mg(II) and not for Mn(II) [11, 17]. This is necessary to reduce the number of unknown parameters in the scheme.

Next, although some of the previous mixed metal metallonuclease studies used single-turnover kinetics and others used steady-state kinetics, we chose the former, a condition under which the enzyme is in large excess over the substrate. There are a number of advantages in the application of single-turnover kinetics, provided one works in a concentration range in which the observed rate is independent of enzyme concentration. Rates are determined by the chemical step and/or any preceding events which determine the concentration of active complexes which conduct the actual cleavage step. Under single-turnover conditions, product release does not limit what is observed, since any one enzyme molecule acts on no more than one substrate molecule. This eliminates the need to use parameters in the global analysis that characterize product release (shown in multiple metallonuclease systems to be rate-limiting [17]). All other events, including binding steps, are accessible via global fitting using these data [11, 17]. In addition, here it is necessary to measure very slow reactions; this is more reliably accomplished via single-turnover kinetics. The effect of multiple-turnover conditions is examined by simulation in “Discussion.”

We measured single-turnover rate constants at fixed Mg(II) concentrations (5 and 10 mM) as a function of Ca(II) concentration and vice versa at 50 μM Ca(II) (Fig. 3). As summarized in Fig. 3a, the Ca(II) concentration has a very dramatic impact on these rate constants: At 10 mM Mg(II), only 50 μM Ca(II) is required to observe a twofold reduction in the rate constant. The effect is more dramatic against a 5 mM Mg(II) background (Fig. 3b), where the rate at 50 μM Ca(II) reduces the rate tenfold. This is consistent with Ca(II) binding the enzyme more strongly than Mg(II), making it a particularly effective competitive inhibitor. This is reasonable, since we have already established that in the absence of DNA, Ca(II) fills one metal ion binding site on PvuII endonuclease with a Kd of 120 ± 80 μM [18], an affinity which is 15-fold stronger than for Mg(II) [19].
Fig. 3

Summary of mixed metal PvuII endonuclease cleavage data. The Ca(II) concentration dependence of the single-turnover cleavage rate constant (kobs) in the presence of a 10 mM MgCl2 and b 5 mM MgCl2 and c the Mg(II) concentration dependence of the rate constant in the presence of 50 μM CaCl2. The conditions were as follows: 2 μM PvuII endonuclease dimers, 300 nM 14 mer cognate DNA substrate, 50 mM tris(hydroxymethyl)aminomethane, pH 7.5, 37 °C, and NaCl adjusted to a constant ionic strength of 130 mM

Global analysis of mixed metal single-turnover data

To do this analysis, one must take into consideration a wide variety of species: two different metal ions binding to two different sites, in addition to species which form with only Mg(II) or only Ca(II). The fact that PvuII endonuclease is a homodimer [20] can introduce additional complexity. However, here we assume that when metal ions fill their sites, they do so simultaneously in both monomer subunits of the dimer. More specifically, if two metal ions bind a dimer, it is assumed that there is one metal ion per subunit and that it occupies the same site (A or B) in both subunits. Although more sophisticated models which account for subunit heterogeneity can be written, this involves more unknown binding constants, which makes the global analysis less reliable in the context of mixed metal species. We feel this is a reasonable assumption. Cleavage of both DNA strands in most restriction enzymes appears concerted under many standard assay conditions [21]: it often requires special care to observe nicking by homodimeric restriction enzymes. This is consistent with it being unlikely that metals bind in one subunit without metals binding the other subunit. A companion assumption is that the subunits have very tight binding constants and do not exchange with each other on the experimental timescale. Although this has not been investigated for PvuII endonuclease, there is experimental support that this is the case for the structurally related EcoRV endonuclease [22].

An important clarification is that there are two binding sites per monomer (A and B). Although there is no way to access a specific metal ion binding site using direct experimental techniques, through global analysis we were previously able to extract binding constants for Mg(II) binding to site A and site B (KM2A 2.5 and KM2B 3.4 mM, respectively, from model C2 in [17]). Similarly, experimentally determined Ca(II) binding constants are also not site-specific; in other words, from observed binding behavior one can get two Ca(II) binding constants (i.e., 120 μM and 2 mM [18]), but from these data alone one cannot specifically assign a constant to a particular site. As will be described below, this will be dealt with using fit trials.

With these issues in mind, the presence of two metal ions in the reaction mixture, only one of which can support cleavage alone, can theoretically result in the formation of a number of enzyme species: EM2A, EM2B, EC2A, EC2B, EM2AM2B, EC2AC2B, EM2AC2B, and EC2AM2B, where M and C denote Mg(II) and Ca(II), respectively, and A and B indicate individual metal ion binding sites. All of these species have the potential to bind and cleave DNA, but not necessarily with the same affinities and rates.

The approach is to apply the above kinetic data to a series of model schemes, leveraging a number of established equilibrium and rate constants. Enclosed in the solid box in Fig. 4 is the scheme established by previous work with cleavage data. Target (cognate) DNA affinity is much greater in the presence of metal ions than in their absence [23]; this is due to a dramatic difference in association rates [12]. Consequently, global kinetic analysis of cleavage data indicates that a route in which metal ion binding precedes substrate binding is kinetically preferred [11], and the data fit better to models which do not feature substrate binding preceding metal ion binding [11]. The rate (k) and equilibrium (K) constants resulting from this work and relevant earlier studies are summarized in Table 1. Depending on the occupancy of metal ion binding sites, DNA binding parameters are in the nanomolar to picomolar range. DNA binding association and dissociation rate constants were previously measured by fluorescence anisotropy and substrate-trap experiments [12]. The dissociation rate constant for DNA is 1 × 10−3 s−1 and is metal-ion-independent [12]. This value permits facile conversion between rate (k) and equilibrium (K) DNA binding constants. In contrast, the metal ion binding parameters are in the millimolar to high micromolar range. Association rate constants for metal ion binding were calculated from the experimental equilibrium constants using the dissociation rate constant of 1,000 s−1 [11]. For the binding of 2 equiv of metal ion per enzyme dimer (one per monomer), the appropriate kon is obtained from the square of Kd, which is presented here for facility in units of millimolar or micromolar. Finally, global analysis indicates that species with either one or two Mg(II) ions per active site are active [11].
Fig. 4

Summary of kinetic schemes. The solid box indicates the Mg(II)-dependent portion of the scheme characterized previously [11]. The dashed box indicates binding equilibria involving Ca(II) which have been previously established [11, 12]. Gray text is excluded for model I (three species active). Small numbers near the arrows index the equilibrium and rate constants, which are interconverted using koff 1,000 s−1 for metal ions and 1 × 10−3 s−1 for substrate. Circular graphics indicate filling of sites by Mg(II) (black) and Ca(II) (gray) in the homodimer. Table 1 summarizes the indicated constants

Table 1

Parameters used in the models and their sources

Parameters (reaction)

Values used/fit

Source for the parameter values

kM2A (E + 2M → EM2A)

1.6 × 108 M−2 s−1

Xie and Dupureur [17]

KM2A (EM2B + 2M → EM2AM2B and EC2B + 2M → EM2AC2B)

2.5 mMa

Fixed

kM2B (E + 2M → EM2B)

8.7 × 107 M−2 s−1

Xie and Dupureur [17]

KM2B (EM2A + 2M → EM2AM2B and EC2A + 2M → EC2AM2B)

3.4 mMa

Fixed

kC2A (E + 2C → EC2A)

2.5 × 108 M−2 s−1

José et al. [18] and this work

KC2A (EC2B + 2C → EC2AC2B and EM2B + 2C → EC2AM2B)

2 mMa

Fixed in trial 1 model I

kC2B (E + 2C → EC2B)

2.8 × 1011 M−2 s−1

Fixed in trial 2 model I

KC2B (EC2A + 2C → EC2AC2B and EM2A + 2C → EM2AC2B)

60 μMa

120 ± 80 μM in José et al. [18] fixed and optimized in this work; see the text

k5 (EM2A + S → EM2AS)

3.7 × 104 M−1 s−1

Xie et al. [11]

K5 (EM2B + S → EM2BS)

27 nM

Fixed

k6 (EM2AM2B + S → EM2AM2BS)

2 × 105 M−1 s−1

Xie et al. [11]

K6 (EM2AM2B + S → EM2AM22BS)

5 nM

Fixed

k7 (EC2A + S → EC2AS)

1 × 105 M−1 s−1

Fixed

K7 (EC2B + S → EC2BS)

10 nM

Xie et al. [11]

k8 (EC2AC2B + S → EC2AC2BS)

2 × 107 M−1 s−1

Optimized in this work and fixed

K8 (EC2AC2B + S → EC2AC2BS)

5 pM

56 ± 22 pM in Conlan and Dupureur [23]; see the text

k9 (EM2AC2B + S → EM2AC2BS)

1.2 × 106 M−1 s−1

Optimized in this work and fixed

K9 (EC2AM2B + S → EC2AM2BS)

0.8 nM

 

k10 (EM2AS → P + EM2A)

0.01 s−1

Xie et al. [11]; fixed

k11 (EM2BS → P + EM2B)

≈0 s−1

This work; floated

k12 (EM2AM2BS → P + EM2AM2B)

1.1 s−1

Xie et al. [11]; fixed

k13 (EM2AC2BS → P + EM2AC2B)

0.0084 s−1

This work; floated

k14 (EC2AM2BS → P + EC2AM2B)

≈0 s−1

This work; floated

koff metal (1,000 s−1 [11]) and koff DNA (1 × 10−3 s−1 [12]). See Fig. 4 and text for the definitions of the reactions and other details

aObtained by taking the square root of Kd calculated from the association and dissociation rate constants and which has units of millimolar squared or micromolar squared in this reaction. See the text for further details

To this scheme, equilibria including Ca(II) are added (dashed box in Fig. 4). The constants which characterize this part of the scheme were also previously determined [12, 18] and are also summarized in Table 1. To the models, these constants were either submitted as resolutely fixed or varied as indicated.

This leaves the binding constants for the mixed metal species. Since there is ample evidence that metal binding sites A and B do not interact energetically [17, 18], we apply the same binding constant for a metal ion whether the adjacent site is occupied or not. In other words, Ca(II) binding to EM2A to form EM2AC2B (KC2B) has the same constant as enzyme binding Ca(II) into its B site with site A empty (KC2B); the same principle applies to Mg(II) binding. Next, we have previously observed that for both Mg(II) and Ca(II), metal ion equivalents contribute nearly equivalent energy to DNA binding ([11, 18]). Therefore, the DNA binding constants for EM2A and EM2B are equivalent (K5) (and likewise for EC2A and EC2B; K7). Finally, for DNA binding by the mixed metal enzyme species (i.e., EM2AC2BS and EC2AM2BS, K9), we used a common constant that is intermediate in value between that for binding supported by Ca(II) alone (low picomolar) and that for binding supported by Mg(II) alone (10–30 nM) (0.8 nM). This value was found to be quite reliable across all fits and simulations (data not shown). These values are summarized in Table 1.

In determining which model best describes the data, we considered a number of factors:
  1. 1.

    Errors in both an individual parameter and in the overall standard deviation relative to another model, and the ability of the model to reproduce the data. This helps in determining confidence in the parameters and models.

     
  2. 2.

    The reasonableness of the value of a parameter. For example, metal ions do not bind the enzyme with picomolar binding constants, and DNA does not bind the enzyme with millimolar binding constants.

     
  3. 3.

    In addition, interpretations are limited to experimental error: that is, if a parameter is changed within the experimental error of its value (either as a fixed parameter or as an initial guess), the effect of this change on other fit parameter(s) was/were small and not interpreted.

     
Finally, with multiple unknowns, the mathematical solutions are often not unique. However, imposed on any solution are the above-mentioned factors that make the concluded best model the most reasonable one within the framework of the analysis. Thus, we are confident some conservative and informative distinctions among models can be made.

Model I: which site (A or B) is the high-affinity Ca(II) site?

Before the cleavage activity of mixed metal enzyme complexes can be assessed, it is first necessary to assign strong and weak Ca(II) binding constants (60 μM and 2 mM) to sites A and B. Since the experimentally determined Ca(II) binding constants cannot specify individual metal ion sites, fits with model I require comparison of two global fit trials: one in which site A binds Ca(II) more strongly (trial 1), and another in which B site binds Ca(II) more strongly (trial 2). These trials are two fits of model I, where we assume that any enzyme species in which site A does not contain Mg(II) is not capable of cleavage (EM2BS and EC2AM2BS shown in gray in Fig. 4). This means that there are three enzyme species capable of cleavage: EM2AM2BS, EM2AS, and EM2AC2BS. Although this assumption will be tested with subsequent models, it is consistent with previous studies [4, 5, 17] and is utilized here to reduce the number of floating parameters.

In addition, it is clear from performing various fits and simulations that the stronger Ca(II) binding constant is closer to 60 μM than to 120 μM. The suitability of this parameter was subsequently confirmed by fixing other determined values and performing a series of simulations to establish the sensitivity of the global fit to the values of this parameter (see Fig. S1). Since this value is within experimental error of the measured value (120 ± 80 μM [18]), this value adjustment is reasonable. The weaker Ca(II) binding constant is 2 mM [18]. There are only two parameters floated in these trials: the first is K8, the binding constant for the formation of EC2AC2BS, with an initial guess of 56 pM. In our experience with multiple fits and simulations, this constant is very diagnostic. The second is the cleavage rate constant for EM2AC2BS (k13), with an initial guess of 0.01 s−1, the rate constant established previously for EM2AS.

The results of these trial fits of model I are summarized in Fig. 5 and Table 2. Sample raw data are poorly represented by model I trial 1 (Fig. 5, panel A), and the fit parameters are unreasonable (Table 2): 50 μM is far weaker than any DNA binding constant measured for this system under any condition, and the cleavage rate constant for the active mixed species exceeds that of EM2AM2BS (3 vs. 1.1 s−1). On the other hand, model I trial 2 fits the raw data much better, and the parameters are much more reasonable. They suggest that the formation of EC2AC2BS (K8) is a bit stronger than the initial guess, but certainly much closer to 56 pM than the 50 μM obtained for trial 1. We observed this to be true throughout the study, and found by trial simulations that a value of 5 pM best represents the data (data not shown).
Fig. 5

Summary of fits and simulations for model I [assigning Ca(II) sites, one mixed species active]. In model I, there are three active species, one of which is a mixed metal enzyme complex. See text and Fig. 4 for other details. ad are for trial 1, where it is assumed that site A holds Ca(II) with a Kd of 60 μM, and site B holds Ca(II) with a Kd of 2 mM; eh are for trial 2, where it is assumed that site A holds Ca(II) with a Kd of 2 mM, and site B holds Ca(II) with a Kd of 60 μM. a and e are sample progress curves: circles data points for 10 mM Mg(II), solid line prediction of experimental curve using parameters determined from the fit. Squares data points for 5 mM Mg(II)/250 μM Ca(II), dashed line prediction of experimental curve using parameters determined from the fit. Triangles data points for 5 mM Mg(II)/1 mM Ca(II), dotted line prediction of experimental curve using parameters determined from the fit. bd and fh feature a comparison of experimental kobs (closed squares) and predicted kobs (open circles) for the indicated conditions. When an open circle is not visible, it is coincident with a closed square

Table 2

Fitted values and percentage errors for parameters in model I

Parameter (species formed)

Trial 1

Trial 2

KC2A

60 μM

2 mM

KC2B

2 mM

60 μM

k8 (EC2AC2BS)

50 μM (41,580%)

3.5 pM (9.9%)

k13 (EM2AC2BS + P)

3.1 s−1 (5,680%)

0.0097 s−1 (8.7%)

Standard deviation 10−8

9.74

3.65

Three species active, only one mixed species active. The errors are for the floated association rate constant values. Off-rate constants for metal ion and DNA binding are fixed at 1,000 s−1 and 1 × 10−3 s−1, respectively, as established previously [11] and are used to convert between equilibrium constants (K) and rate constants (k). See Fig. 4 and Table 1 for clarification of the mechanistic steps and known parameters. Initial guesses for K8 and k13 were 56 pM and 0.01 s−1, respectively

In using the fits to simulate the metal ion dependence of kobs, we find that the data obtained for the trials at fixed Mg(II) concentrations are at first glance similar (Fig. 5, panels B, C and F, G). However, closer inspection reveals that model I trial 1 does not predict the rates well at very low Ca(II) concentrations (circles are not close to their corresponding black squares). The data obtained at 50 μM Ca(II) are most diagnostic (Fig. 5, panels D, H): model I trial 2 is clearly superior in representing the data. On the basis of all the data, it is clear that site B is the higher-affinity Ca(II) site (Kd 60 μM). In all subsequent models (I and II), this feature will be fixed.

Model II: which mixed species is active?

With the Ca(II) binding constants for sites A and B established, we next determine which mixed species is active. This is accomplished by fixing the constants for Ca(II) binding (the result of model I analysis) and then introducing the possibility that EM2BS (k11) and EC2AM2BS are active (k14), in addition to EM2AS (k10), EM2AM2BS (k12), and EM2AC2BS (k13). The condition of model 1 trial 2, in which site B binds Ca(II) with a Kd of 60 μM and the Ca(II) Kd for site A is 2 mM, is applied.

As summarized in Fig. 6, this model represents the data as well as model I trial 2. Table 3 summarizes the cleavage constants that emerge from the fit. Fitted values for k11 and k14 are essentially zero (with the expected high error), confirming the assumption that EM2BS and EC2AM2BS were not active in model I was appropriate. The cleavage constant for EM2AC2BS (k13) is very similar to that obtained from model 1 trial 2 (0.0084 s−1). This is basically the same value for EM2AS (k10), and thus the presence of Ca(II) in site B of PvuII endonuclease provides neither an advantage nor a disadvantage when Mg(II) is bound in site A relative to EM2AS (see “Discussion”).
Fig. 6

Summary of fits and simulations for model II [both mixed species active, site B is the strong Ca(II) site]. See the text and Fig. 4 for other details about the model. a Sample progress curves: circles data points for 10 mM Mg(II), solid line prediction of experimental curve using parameters determined from the fit. Squares data points for 5 mM Mg(II)/250 μM Ca(II), dashed line prediction of experimental curve using parameters determined from the fit. Triangles data points for 5 mM Mg(II)/1 mM Ca(II), dotted line prediction of experimental curve using parameters determined from the fit. bd Comparison of experimental kobs (closed squares) and predicted kobs (open circles) for the indicated conditions. When an open circle is not visible, it is coincident with a closed square

Table 3

Fitted values and percentage errors for parameters in model II

Parameter (species formed)

Fitted value (s−1)

Percentage error

k11 (EM2AS + P)

2 × 10−6

3,424

k13 (EM2AC2BS + P)

0.0084

8

k14 (EC2AM2BS + P)

1 × 10−8

2,923

Both mixed metal species active, site B is the tight Ca(II) site. Fixed parameters: KC2A 2 mM, KC2B 60 μM, K9 0.8 nM, K8 5 pM. Off-rate constants for metal ion and DNA binding are fixed at 1,000 s−1 and 1 × 10−3 s−1, respectively, as established previously [11] and are used to convert between equilibrium constants (K) and rate constants (k). See Fig. 4 and Table 1 for clarification of the mechanistic steps and known parameters. The standard deviation is 3.44 × 10−8. The initial guess for all parameters floated was 0.01 s−1

Model III: mixed species formed but are not active

The cleavage rate constant for the active mixed species is slow relative to EM2AM2BS (130-fold smaller), which prompts the question of whether or not the data can be satisfactorily represented by a model in which mixed species do not contribute to cleavage. To that end, we compared the data with a simulation using model III, which includes all steps except k13, k14, and k11, again with site B as the stronger Ca(II) site (60 μM). Figure 7 illustrates the result when all of the parameters are fixed to those established earlier. It is clear that the amount of product is underestimated when Ca(II) is present. If a few parameters are floated in an attempt to improve the fit, the observation is the same (data not shown). Thus, the formation of active mixed species is indeed necessary to account for the kinetic traces under these experimental conditions for PvuII endonuclease.
Fig. 7

Summary of fits and simulations for model III [both mixed species inactive, site B is the strong Ca(II) site]. See the text and Fig. 4 for other details about the model. a Sample progress curves: circles data points for 10 mM Mg(II), solid line prediction of experimental curve using parameters determined from the fit. Squares data points for 5 mM Mg(II)/250 μM Ca(II), dashed line prediction of experimental curve using parameters determined from the fit. Triangles data points for 5 mM Mg(II)/1 mM Ca(II), dotted line prediction of experimental curve using parameters determined from the fit. bd Comparison of experimental kobs (closed squares) and predicted kobs (open circles) for the indicated conditions. When an open circle is not visible, it is coincident with a closed square

Distribution and contribution of species under mixed metal conditions

Global analysis of kinetic data provides an unprecedented level of information about the reaction mixture over a wide range of conditions. Of the various models tested, the experimental data are best represented by a model in which site B is the strong Ca(II) site and in which the enzyme is not active when Ca(II) is in site A (model I trial 2). Using the parameters determined earlier, one can use this model to examine the distribution of species at any point during the reaction, as well as to determine how each active species contributes to product formation, providing unprecedented information about the reaction mixture.

Briefly, the concentrations of all species at all time points can be obtained from the output of the global fit. These data were extracted and were plotted as a function of Ca(II) concentration at 10 and 50 s (Fig. 8, panels A, B). The former is a snapshot of conditions very early in the reaction; the latter reflects the reaction near completion at high Mg(II) concentrations, beyond which there are only very small changes in species distribution. Owing to the conditions and the relevant binding constants, EM2AM2BS, the most active species (k13 1.1 s−1), exists in only very small concentrations relative to the other species, and is only visible on this scale very early in the reaction (10 s; Fig. 8, panel A, black bars) and only when Mg(II) is in large excess over Ca(II). EM2AS (green bars) exists at comparable concentrations. EC2AC2BS, which is a dead-end complex, dominates at high Ca(II) concentrations (red bars). Owing to the stronger binding of Ca(II) in the B site, EC2AM2BS does not form to an appreciable extent; the remaining species (EM2BS, EC2BS, and EC2AS) also exist at low concentrations not easily visible on this scale. At 50 s into the reaction, the EM2AC2BS concentration is decreased slightly owing to conversion to product but otherwise there is very little change in the species distribution. Interestingly, at high Ca(II) concentrations, EC2AC2BS serves as a formidable substrate “sink,” tying up substrate and preventing it from becoming available for product formation. Indeed, we observed this effect in many progress curves that plateaued well below 100% product formation (data not shown).
Fig. 8

Distribution of species and contributions to the product. The plots represent data simulated at 5 mM Mg(II) as a function of Ca(II) concentration based on parameters obtained from applying model I trial 2 to the data [one mixed species active, site B is the strong Ca(II) site]. a enzyme–metal–substrate species distribution at 10 s. b enzyme–metal–substrate species distribution at 50 s. c percent contribution to the product at 10 s. d percent contribution to the product at 50 s. Red EC2AC2BS, green EM2AS, blue EM2AC2BS, black EM2AM2BS. The remaining species (EC2AS, EC2BS, EC2AC2BS, and EM2BS) are plotted but are not appreciably populated and therefore are not visible on this scale

Panels C and D in Fig. 8 feature the contributions to the product at the same time points. These are obtained by multiplying the species concentration by its rate constant and then dividing by the total product concentration. Although it is not very abundant, the fastest species, EM2AM2BS, contributes the most to the product early in the reaction (Fig. 8, panel C); under single-turnover conditions, this species does not exist after product formation and thus is not represented later in the reaction. However, the slower EM2AC2BS continues to exist at later time points and thus contributes to the product. At 50 s, the slower EM2AS contributes appreciably at low Ca(II) concentrations (Fig. 8, panel D).

Discussion

Conditions for observing Ca(II)-stimulated cleavage

As stated earlier, an apparent increase in either Mn(II)- or Mg(II)-supported cleavage activity in metallonucleases upon the addition of Ca(II) is generally taken as evidence for a two metal ion mechanism in which the role of one metal ion is regulatory in nature. That is, merely the concentration of charge represented by a divalent cation is sufficient for the reaction to proceed, as opposed to a requirement for a second equivalent of the native cofactor.

Although Ca(II) is clearly not stimulatory in mixed metal complexes of PvuII endonuclease, this is not necessarily the case for other metallonucleases, and it is of considerable interest to understand how a stimulation of activity by Ca(II) in a Mg(II)-dependent metallonuclease could occur. With the matrix of parameters in hand from the global analysis, it is straightforward to use simulations to establish which parameter(s) could be responsible for an apparent stimulation of cleavage activity reported for other metallonucleases.

To investigate this, we used the parameters obtained from the fitting of single-turnover data to model I trial 2 [site B binds Ca(II) more strongly] and varied a few key parameters in turn in simulations. At the outset, it would be reasonable to suspect that an increase in k13, the cleavage rate constant for the mixed metal species EM2AC2BS, would be critical. As shown in Fig. 9a, as this value approaches the cleavage constant for EM2AM2BS (1.1 s−1), a stimulation at low Ca(II) concentrations can indeed be observed. If the conditions are changed to multiple turnover (10 nM enzyme, 100 nM substrate), the simulated rates are of course slower, and the lagging side of the curve rises above the x-axis (Fig. 9b). This indicates that the trend (of stimulation) is not affected by inverting the ratio of enzyme to substrate concentration.
Fig. 9

Simulations showing the effects of various parameters on kobs versus Ca(II) concentration. Model I trial 2 [one mixed species active, site B is the strong Ca(II) site] is used with all parameters fixed to those determined earlier in the study except where indicated. a Varying k13 (the cleavage constant of EM2AC2BS) under the single-turnover conditions used in this study. Circles, solid line k13 is 1.5 s−1, squares, dashed line k13 is 0.5 s−1, triangles, dotted line k13 is 0.01 s−1. b Comparing single-turnover (closed squares) and multiple-turnover (closed circles) conditions (10 nM enzyme, 100 nM substrate). k13 is set to 1.5 s−1. c Comparing KC2B set to 6 µM (triangles), 60 µM (circles), and 600 µM (squares). k13 is set to 1.5 s−1 and the conditions are single turnover

Other factors that could affect the shape and position of this dependence are binding constants. As shown in Fig. 9c, if k13 is set to 1.5 s−1 and the Ca(II) binding constant for EC2AC2B (KC2B) is decreased tenfold from 60 to 6 μM, the simulated profile changes very little; however, increasing this constant tenfold (to 600 μM) blunts the effect of the 1.5 s−1 cleavage constant. This suggests that there is a concentration threshold below which Ca(II) is held strongly enough to lead to a critical population of EM2AC2BS. If Ca(II) affinity is sufficiently weak [relative to Mg(II) affinity], a stimulation of kobs is not observed, even if the cleavage rate constant for the mixed species is high. Although other scenarios could be easily explored, for this model and parameters at least, it is the cleavage rate constant of the active mixed metal enzyme–substrate complex which dominates the observed stimulated cleavage behavior; however, equilibria can clearly affect the observation.

Potential for means of modulating endonuclease activity

The activity of a mixed metal enzyme species begs the question of whether or not such species exist in a cell, and what role they might play in modulating metallonuclease activity. Metal ion analyses indicate that Mg(II) exists in Escherichia coli at low millimolar concentrations; Ca(II) concentrations vary somewhat but are generally about an order of magnitude lower [24]. If the environment in Proteus vulgaris is similar, Ca(II) would be bound to PvuII endonuclease to some extent in vivo, since this metal ion is held with Kd values in the high micromolar range. EM2AM2BS, the most active enzyme–metal complex, would represent a very small percentage of enzyme species in the cell; owing to the higher affinity of site B for Ca(II), EM2AC2BS would be somewhat more abundant and EC2AM2BS considerably less so. As long as site B is either unoccupied or occupied by Ca(II), the activity of the enzyme will be low. In this scenario, Ca(II) serves as a placeholder, keeping Mg(II) out of site B and the cleavage rate low. This could represent a subtle means of controlling metallonuclease activity in a cell, although a connection between Ca(II) concentration and the imperative of restriction-modification systems to protect the cell [25] is not immediately clear. Finally, the lack of stimulation by Ca(II) ions may make PvuII endonuclease an exception. Determining if this is the case would require a similar analysis of at least one other well-characterized metallonuclease.

Conclusion

We have provided the first detailed analysis of the behavior of a mixture of metalloenzyme species that results from the introduction of a second metal ion into the reaction. Global analysis permits not only the determination of parameters not accessible by direct experiment, but also by simulation provides a means of understanding the contributions of the multitude of processes that govern observed cleavage rates. This makes global analysis a uniquely powerful tool in the study of two metal ion mechanism reactions. Using the well-characterized PvuII endonuclease system, we used this approach to dissect the contribution of various enzyme–metal complexes to cleavage activity. The global analysis is consistent with only one mixed metal species being active. Although the kinetics alone does not permit unequivocal assignment of metal ion binding sites to specific structural locations, earlier mechanistic proposals [3, 4, 5] allow us to attribute the active species to EM2AC2BS [i.e., occupancy of the A site by Mg(II) and the B site by Ca(II)]. Owing to the differing affinities of the two sites for Ca(II) in PvuII endonuclease, this species is more abundant than EC2AM2BS; however, it is no more active than enzyme species with only one Mg(II) bound per active site (EM2AS). Thus, in this system, Ca(II) in the active site serves to slow down cleavage activity whether Mg(II) is also bound or not. Finally, we showed by simulation that when stimulation of activity by Ca(II) is observed, it is most likely due to high cleavage activity for a mixed metal enzyme species. However, since this observation can be blunted by a weak affinity for Ca(II), the efficient activities of mixed metal enzyme species of other metallonucleases could be obscured. This underscores the importance of understanding the behavior of the complex mixtures that result from doping a Mg(II)-dependent metallonuclease reaction with another metal ion.

Supplementary material

775_2010_621_MOESM1_ESM.pdf (190 kb)
Supplementary material (PDF 191 kb)

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Copyright information

© SBIC 2010

Authors and Affiliations

  • Charulata B. Prasannan
    • 1
  • Fuqian Xie
    • 1
  • Cynthia M. Dupureur
    • 1
  1. 1.Department of Chemistry and Biochemistry, Center for NanoscienceUniversity of Missouri St. LouisSt. LouisUSA

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