Measuring specificity in multi-substrate/product systems as a simple tool to investigate selectivity in vivo

Abstract

Multiple substrate enzymes present a particular challenge when it comes to understanding their activity in a complex system. Although a single target may be easy to model, it does not always present an accurate representation of what that enzyme will do in the presence of multiple substrates simultaneously. Therefore, there is a need to find better ways to both study these enzymes in complicated systems, as well as accurately describe the interactions through kinetic parameters. This review looks at different methods for studying multiple substrate enzymes, as well as explores options on how to most accurately describe an enzyme’s activity within these multi-substrate systems. Identifying and defining this enzymatic activity should clear the way ro use in vitro systems to accurately predict the behavior of multi-substrate enzymes in vivo.

1. Introduction

It is common for one enzyme to be able to catalyze multiple substrates or interact with multiple sites, as has been found from various in vitro enzymatic studies (for example, cytochrome P450 enzymes [1, 2], lysine acetyltransferases [3], and kinases [4]). In in vivo systems, as a consequence, all these potential substrates/sites also have the potential to act as competitors. Enzyme preference is usually revealed by different rates or affinities for substrates. The preference of an enzyme for one specific substrate is defined as the specificity, and the preference for one substrate over another is its selectivity. Given these facts, single target substrates matched with a single enzyme is the most direct and simplest system for investigating enzyme specificity in vitro (i.e., classical steady-state approach). From the kinetic parameters obtained via this straightforward approach, one can determine the specificity (i.e., specificity constant, k_cat/K_m) of a substrate [5, 6]. The ratio of specificity constants from two different substrates with the same enzyme may then be used to interpret the preference of that enzyme for one substrate over the other: the selectivity [7]. These enzymatic kinetic parameters seem adequate for applications for in vitro systems, but it has been shown that some predictions of these parameters fail to match up with corresponding observations from in vivo assays [8–10]. The complexity of in vivo assays may lead to the following potential factors being overlooked: protein-protein interactions [11–14], enzymatic structural/conformational changes [15–18], and internal inhibition [19–22]. Thus, recent research has utilized the method of internal competition (multiple substrates to one enzyme) to study the selectivity of an enzyme between substrates [23–26]. This experimental design can/may more closely simulate the in vivo environment. However, such assays also create difficulties in producing accurate detections for multiple targets, as signals from one target have to be independent of the others. Fortunately, advances in current technologies allow for the measurement of multi-substrates/products in a less labor-intensive and time-consuming manner.

In this review, we examine multiplexed, high throughput, and potentially even real-time methodologies applied on different enzymatic selectivity assays and we provide an overview of how to use the kinetic parameters from internal competition to interpret the potential selectivity in vivo. Using this approach, we also highlight the possible constraints of each method, such as choices of substrate concentrations, time frame selections (steady-state condition), and/or available cofactors/inhibitors.

2. Techniques for multiplexed, high throughput measurements of multiple substrates/products

Internal competition is a method that has been used to investigate the differences of an enzyme for individual mixed substrates by measuring either the consumption rate of individual substrates or the generation rate of individual products. This method has also been extensively used in studying kinetic isotope effects [27–29]. Since the concentrations of multi-substrates and/or multi-products need to be monitored, a multiplexed analytical technique is required to measure all of the concentrations of each of these components for data analysis. This section will discuss the recent analytical techniques applied to study the kinetics of internal enzyme competition.

This simplest method for these approaches is liquid chromatography (LC), which relies on the separation of multiple substrates by hydrophobicity or cation/anion exchange, depending on what is being separated. This is often a reverse phase column with the accompanying detection as UV absorption, fluorescence, or radio chemical. An example of this approach is the analysis of multiple substances in the bioremediation of polycyclic aromatic hydrocarbons (PAHs) [30, 31]. In this case LC alone can separate various forms of PAHs; in other cases additional verification is needed, such as mass/charge.

Mass changes (either cleavage or addition/removal of functional groups) of a substrate are often the result of catalytic reactions. Thus, mass spectrometry (MS) is a common analytical technology that is utilized for these types of studies [32–35]. The coupling of LC or gas chromatography to MS provides separation of multiple substrates, and therefore more accurate quantification, for multiple target analysis [36, 37]. Furthermore, tandem MS (MS/MS) can be used to acquire more spatial or structural information of analytes. For example, LC-MS/MS has been used to quantitate the substrates and/or products from enzymatic kinetic assays [13, 38–40], and a detection resolution as small as a single amino acid residue can be reached [7, 41, 42]. Recently, this kind of site-specific study has even been utilized for the investigation of non-enzymatic protein modifications [7, 14, 43].

Another technique used for these internal competition assays, nuclear magnetic resonance spectrometry (NMR), is used to determine the kinetic isotope effects between stable isotope labeled substrates and unlabeled substrates [27–29]. As more innovative methodologies have been developed to utilize this advanced technology, a very high degree of precision and accuracy can be obtained for the measurement of low abundance, stably isotope-labeled substrates [44–47]. Additionally, with the proper sample and safety controls, a method of radioactive remote labeling can be utilized to study internal competition. A scintillation detector with a multi-channel analyzer can record different radiation energy from different radioactive sources. With this technique, a high sensitivity and high accuracy of measurements can be achieved for the detection of various radioactively labeled substrates [48–50]. The study of hydrogen tunneling by using radioactive remote labeling is one example of the application of this technique [51, 52].

Internal competition assay are not limited to proteins. Substrates can also include DNA and/or RNA. Current biochemical and labeling techniques have been developed to effectively and efficiently measure the DNA/RNA kinetics of enzymatic catalysis [53–56]. For example, Goodman (et al.) used kinetic assays to investigate DNA polymerase fidelity by comparing the competition of right and wrong nucleotide incorporations [56]. As another example, substrate competition of endoribonucleases can occur in vivo because endoribonucleases can cleave multiple RNA substrates [57]. Harris (et al.) examined the internal competition between different tRNA precursors for ribonuclease P by radiolabelling substrates and directly quantifying the substrate specificity [58, 59]. Furthermore, it has been found that RNA sequence is very specific for ribonucleases (for example, RNase H) [60–62]. To understand the substrate sequence specificity and site specificity, deep sequencing methods (for review see [63–65]) were used to investigate the frequency and locations of ribonuclease L cleavage sites of viral RNAs [66, 67]. Site-specific studies have also been carried out, using primer extension reactions to characterize ribonuclease L specific cleavage sites in hepatitis C virus RNA [68] and DNA damage sites [69]. Utilizing the aforementioned analytical technologies (i.e., MS) coupled with these types of assays can be useful for the detection of not only the DNA/RNA sequences [70–72] but also the modifications on the individual nucleosides [73–75]. Additionally, MS analysis has been used to investigate the substrate selectivity of artificial restriction enzymes [76], which can be applied to manipulating RNAs for biotechnology applications.

Finally, the concept of this internal competition method was also applied to developing quantitative competitive polymerase chain reaction techniques to quantitate target DNA [77]. By competing with internal DNA segment, Tompkins (et al.) demonstrated that the reverse transcription-quantitative competitive polymerase chain reaction technique can quantitate the expression of seven cytokine mRNAs in domestic mammals [78]. This approach can be extended to barcoded samples like those demonstrated by Nguyen (et al.) where they paired unique DNA sequences to specific histone modifications in nucleosomes [79]. While this would require a separation step, it would also allow simple quantitative PCR in place of expensive sequencing or other technology. Through these types of experiments, we have seen the progress in adapting the knowledge gained from internal competition assays into the utilization in practical applications. All aforementioned methods that can be utilized to measure multiple substrates/products are summarized in Table 1.

Table 1.

Summary of published techniques for multiplexed measurements of multiple substrates/products

Subjects studied	Techniques for measurements	Categories of studies	Reference (year)
Multiple PAH biodegradation	HPLC	Monod kinetics	[30] (1988); [31] (1999)
Glycogen synthase for adenine- and uridine-diphosphate glucose polymerization	MS	Double-reciprocal kinetic	[33] (2003)
Sugar nucleotidyltransferases for multiple substrates		Michaelis-Menten kinetics	[34] (2005)
NodST, a GlcNAc-6-O-sulfotransferase, for four chitoologosaccharides synthesis		Internal competition kinetics	[38] (2004)
Gcn5-mediated histone H3 lysine acetylation and nonenzymatic acetylation		Site specific internal competition kinetics	[7] (2013)
Comparison of Rtt109-Vps75 mediated histone acetylation on different histone complexes		Site specific internal competition kinetics	[14] (2015)
P300 and CBP for histone H3 and H4 acetylation		Site specific internal competition kinetics	[41] (2013)
DNA methylation		Quantification of nucleosides	[73] (2008)
tRNA modifications		Quantification of nucleosides	[74] (2010); [75] (2014)
Sialidase hydrolysis of Neu5Acα2, 6LacβSPh (12C/13C and 16O/18O)	NMR	Competitive kinetic isotope effects	[28] (2010)
Catalysis by thymidylate synthase		Kinetic isotope effects and hydrogen tunneling	[51] (2004)
Catalysis by dihydrofolate reductase		Kinetic isotope effects and hydrogen tunneling	[52] (2011)
Mechanism of mutant and wild type T4 DNA polymerases (3H and 14C)	Radiolabeling	Internal competition kinetics	[53] (1979)
Steady state and pre-steady state kinetics for studying DNA polymerase fidelity (32P)		Internal competition kinetics	[56] (2010)
Kinetics of ribonuclease P over 80 competing tRNA precursors (32P)		Internal competition kinetics	[58] (2013)
Modeling of ribonuclease P processing 3 competing tRNA precursors (32P)		Internal competition kinetics	[59] (2014)
Specificity study on ribozyme for variable substrate sequences (32P)		Individual kinetics	[60] (1988)
Ribonuclease L cleavage sites in viral RNAs (32P)		Cleavage site study	[68] (2004)
Serial analysis of mutation spectra (32P)		Identification of DNA damage sites	[69] (2008)
Proofreading efficiency of wild type T4 DNA polymerase	Fluorescence	Internal competition kinetics	[54] (1994)
Cleavage rate study on 8–17 deoxyribozyme		Internal competition kinetics	[55] (2010)
Ribonuclease L cleavage sites in host (HeLa cell) and viral RNAs	Deep sequencing method	Characterization of cleavage sites	[66] (2014)
Ribonuclease L cleavage sites in viral RNAs		Characterization of cleavage sites	[67] (2014)
Cytokine gene expression in domestic mammals	Quantitative competitive PCR	Internal competition	[78] (1996)

3. Analysis of enzyme kinetics for substrate selectivity

3.1 Steady-state analysis of specificity and selectivity for multiple substrates/sites in simple systems

The enzyme kinetics of one substrate under multiple turnover steady-state conditions can be described by the Michaelis-Menten equation (eq. 1). The Michaelis-Menten equation describes a hyperbolic relationship when plotting the initial rate (v) versus substrate concentrations, [S]. Where [E] is the concentration of enzyme, and k_cat and K_m are steady-state kinetic parameters, representing the catalytic constant and the Michaelis constant, respectively. Conceptually, k_cat represents the number of turnover events occurring per unit time, and K_m is a relative measure of substrate binding affinity.

$$\frac{\mathrm{v}}{[\mathrm{E}]}={\mathrm{k}}_{\text{cat}}\frac{[\mathrm{S}]}{([\mathrm{S}]+{\mathrm{K}}_{\mathrm{m}})}$$ eq. 1

Differences in substrate specificity by a single enzyme have been studied since the 1920s [80], but it wasn’t until the 1960s that a usable definition was articulated [81]. Specificity is “… defined as a higher rate of reaction with respect to some reference substrate or reaction … to measure the special contribution of the enzyme to the catalysis, we should compare the velocity of the enzymatic reaction to the velocity of a nonenzymatic reaction” [81]. From this point Brot and Bender use the term specificity constant to refer to k_cat/K_m [82], but it wasn’t until 1974 that Fersht linked specificity and selectivity together, by using (v/[E])₁/(v/[E])₂, to show that induced fit and non-productive complexes are not represented in the specificity of an enzyme (in a simple system) [83]. From this point we can see specificity is linked to it ability to choose one substrate over another, or selectivity, and that k_cat /K_m, is the best description of specificity for a substrate because it will predict selectivity in a mixture of substrates in a simple system (eq. 2).

$${\left(\frac{v}{[E]}\right)}_A/{\left(\frac{v}{[E]}\right)}_B=[\mathrm{A}]{\left(\frac{k_{\mathit{cat}}}{K_m}\right)}_A/[B]{\left(\frac{k_{\mathit{cat}}}{K_m}\right)}_B$$ eq. 2

We can apply this foundation to modern methods to understand selectivity between larger numbers of substrates. To do this we need to keep the standard steady-state assumptions, namely that total substrate concentration should remain close to the free substrate concentration, that enzyme should be much less than the substrate concentration and that less than 10% of total substrate should be consumed [6]. This gets more complicated when you have either one substrate that can produce multiple products like we have with histone acetyltransferases [7, 14, 41] or multiple different substrates. In this simple system one substrate will not impact the specificity or selectivity of another substrate or product (see the next section of complications). It is important to note that in this description we are assuming that all substrates are in equal concentrations or that we have one substrate and multiple products. We can solve for the steady-state rate (v/[E]) for one substrate in the presence of multiple substrates or products from one substrate, in eq. 3, here k_x and K_x is rate and binding constant for the substrate we are monitoring, A and D are given by equations 4 and 5. Two important features come from this: 1) solving for k_cat/K_m we get k_x/K_x [7]; and 2) this makes it obvious that if we divide the rate for any substrate in this system by any other we will return to eq. 2.

$${\left(\frac{v}{[E]}\right)}_x=k_x\frac{A[S]}{(K_1\ast \mathrm{....}{K}_n)+D[S]}$$ eq. 3

$$A=\frac{K_1\ast \dots K_n}{K_x}$$ eq. 4

$$D={\sum }_{i=1}^n\frac{K_1\ast \dots K_n}{K_i}$$ eq. 5

If your main concern in studying an enzyme is substrate preference then measuring substrate turnover in the presence of all possible substrates has an advantage over individual kinetic measurements because they are able to determine selectivity with fewer measurements. We have shown that while the apparent k_cat/K_m for any one substrate measured in a complex background is the same as measured independently the apparent k_cat is not. However, if we solve for the ratio of k_cat(s) to compare any two substrates (eq. 6) then we get the same value as we would for the ratio of k_cat/K_m(s).

$$\frac{k_{\mathit{cat}(x),\mathit{app}}}{k_{\mathit{cat}(y),\mathit{app}}}=\frac{k_x\frac{\frac{K_1\ast \dots Kn}{K_x}[S]}{D[S]}}{k_y\frac{\frac{K_1\ast \dots K_n}{K_y}[S]}{D[S]}}=\frac{{\left(\frac{k_{\mathit{cat}}}{K_m}\right)}_x}{{\left(\frac{k_{\mathit{cat}}}{K_m}\right)}_y}$$ eq. 6

This means that as long as we can be confident that substrate is at saturation then we can measure selectivity or substrate preference by comparing the ratios of the apparent k_cat(s). With advancing technologies (e.g., deep sequencing and mass spectrometry, Table 1), which allow us to monitor multiple substrates in complex mixtures, this approach has potential to greatly increase our understanding of how enzymes function in a cell.

3.2 Steady-state analysis of specificity and selectivity for multiple substrates/sites in complex systems

In the previous section we assumed that all substrates are consumed in a hyperbolic dependence and the presence of once substrate would have little to no influence on the steady-state rate of another substrate. However, there are circumstances where the substrate binding can either positively or negatively influence catalytic activities [84–86], which can result in apparent cooperativity. This causes a deviation from the hyperbolic kinetics described by eq. 1. For example, the appearance of a sigmoidal curve in the plot of initial reaction velocity vs. substrate concentration indicates a potential event of positive cooperativity [84]. Thus, the Hill coefficient (nH) is used in eq. 7 to describe the kinetics of cooperativity [87]. In this case, K_m is replaced by K_1/2, which shows the substrate concentration where the reaction reaches half-maximal velocity. Sigmoidal kinetics might also be indicative of a slow transient conformational change seen in a monomeric single-site enzyme [88] or it could be a case of a random ordered mechanism of a two-substrate enzyme [89].

$$\frac{\mathrm{v}}{[\mathrm{E}]}={\mathrm{k}}_{\text{cat}}\frac{{[\mathrm{S}]}^{\text{nH}}}{({[\mathrm{S}]}^{\text{nH}}+{\mathrm{K}}_{1/2}^{\text{nH}})}$$ eq. 7

When the competing alternative substrates are considered in the steady-state conditions for a specific enzyme, the kinetics of individual substrates has been illustrated by eq. 7. From this equation you can see that the only difference is a Hill coefficient for every substrate and equilibrium constant, and that if we rewrite eq. 2, we get eq. 8, where we have added the Hill coefficients for each substrate. In this case we can only use the ratio of the apparent k_cat(s) if we know the Hill coefficients, which prevent single rate measurements.

$${\left(\frac{v}{[E]}\right)}_A/{\left(\frac{v}{[E]}\right)}_B={[\mathrm{A}]}^{nH(A)}{\left(\frac{k_{\mathit{cat}}}{{K_{1/2}}^{nH(A)}}\right)}_A/{[B]}^{nH(B)}{\left(\frac{k_{\mathit{cat}}}{{K_{1/2}}^{nH(B)}}\right)}_B=\frac{{[A]}^{nH(A)}{k}_{\mathit{cat}(A),\mathit{app}}}{{[B]}^{nH(B)}{k}_{\mathit{cat}(B),\mathit{app}}}$$ eq. 8

However, if the Hill coefficients are the same for all sites the substrate concentration still cancels out. While Cornish-Bowden orginally only consider substrate concentrations where they were beyond the inflection point of the enzyme [90], or that selectivity would not change as you move from low to high concentrations, we have seen this effect in lysine acetyltransferases p300 and CBP [41, 91].

In cases where different substrates have different Hill coefficients, understanding selectivity can be difficult. This is because at low substrate concentrations an enzyme could prefer A and at high concentrations it could prefer B; consider a enzyme where the K_1/2 and k_cat are the same but one has a nH of 2 and the other is not cooperative. The substrate with a Hill coefficient of 1 will be preferred at low concentrations while the substrate with the Hill coefficient will be preferred as we move to the maximum rate (Figure 1). We have proposed to use the plot of catalytic proficiency as a function of substrate concentration to simplify the understanding the enzyme specificity and how it changes with concentration. Catalytic proficiency is the second order rate constant k_cat/K_m divided by the non-enzymatic rate of catalysis, and is consistent with the definition of specificity as set by Bender and Kizdy [81]. This value will not change as a function of substrate concentration unless there is a Hill coefficient that is not equal to one, in which case the value will respond up (nH>1) or down (nH<1) in response to substrate. When dealing with multiple possible products like we have with p300 and CBP, converting this to a ΔΔG can make this easier to understand. In this case the selectivity between any two sites is simply the difference between the ΔΔG.

Figure 1. Use of catalytic proficiency to describe substrate dependent changes in selectivity.

We simulated v/E vs. substrate for two substrates both with the same k_cat (100/sec) and K_m (25μM) values, but one with a nH of 2 and one with a nH of 1. Right: is the standard v/E vs substrate and Left: is the ΔΔG of catalytic proficiency, or −RTln([S]^nH-1(k/K_1/2nH)/(k_nE).

In cases where there are multiple substrates and one substrate can influence the activity of another it can be extremely difficult to describe the possible selectivity in a cell. Under these conditions it is best to try and limit the possible conditions using any information that can be obtained from cellular studies. It may also be possible to build initial models and refine these by comparing them measured differences in cells. In these cases chemical biology approaches [91] such as inhibitors/activators and/or isotopic labeling of substrates or products can aid in the refining of proposed models.

3.3 Progress curve assays

For practical reasons, the same concentrations for individual competing substrates may not always be achievable, especially when more than two substrates are being investigated. Thus, in eq. 4, the terms of substrate concentration cannot be canceled out, even when no cooperativity is observed. However, in the case of nH,1 = nH,2 = 1, a viable alternative is to estimate the ratio of specificity constants by eq. 9 via measuring either individual substrate concentrations ([S₁] and [S₂]) or individual product concentrations ([P₁] and [P₂]) at a specific time point [40, 59, 92]. [S_1,0] and [S_2,0] in eq. 9 represent the initial concentrations of S₁ and S₂, respectively, before the assay starts. Taken together, this approach has several advantages; for example, there is no need to provide identical concentrations for all competing substrates, and one set of progress curves from an internal competition assay can be used to estimate the ratios of the specificity constants. The parameters estimated from eq. 9 are also in accordance with the calculations from eq. 7 or 8, without requiring the substrate concentrations to be the same. However, note that this approach can only be applied to cases where no cooperativity is observed. In addition, to obtain optimal estimations while maintaining a comparably competitive system, none of any substrate should be consumed either less than 30% or more than 70%.

$$\frac{{\mathrm{k}}_{\text{cat},1}/{\mathrm{K}}_{\mathrm{m},1}}{{\mathrm{k}}_{\text{cat},2}/{\mathrm{K}}_{\mathrm{m},2}}=\frac{ln\left(\frac{[{\mathrm{S}}_1]}{[{\mathrm{S}}_{1,0}]}\right)}{ln\left(\frac{[{\mathrm{S}}_2]}{[{\mathrm{S}}_{2,0}]}\right)}=\frac{ln\left(\frac{[{\mathrm{S}}_{1,0}]-[{\mathrm{P}}_1]}{[{\mathrm{S}}_{1,0}]}\right)}{ln\left(\frac{[{\mathrm{S}}_{2,0}]-[{\mathrm{P}}_2]}{[{\mathrm{S}}_{2,0}]}\right)}$$ eq. 9

4. Case studies

4.1 Lysine acetyltransferases (KAT)

The majority of HATs can acetylate more than one residue on a single histone, and often multiple histones. Acetylation can have different biological outcomes depending on which residues are acetylated. This presents a unique problem in that every substrate could result in multiple products. Almost all substrates used in KAT assays contain more than one target residue, including even short peptide substrates [7].

For this reason our group has been interested in the challenge of finding meaningful ways to describe specificity through in vitro assays which have predictive power in cellular and in vivo models. Much of the mechanistic discussion covered above became clear to us during our studies with Gcn5 and Rtt109 [7, 14]. Gcn5 acetylates only H3K14 as an initial acetylation event but after H3K14 has been acetylated, Gcn5 can then acetylate multiple residues, while Rtt109-Vps75 will initially acetylate two residues. It is the ability to observe multiple products simultaneously that has allowed us to understand how these two enzymes function. Additionally, simultaneous detection of multiple histone residues enabled us to characterize the differences in selectivity between highly conserved KATs, p300 and CBP: these results included the observation that while both p300 and CBP target similar residues, CBP has a much stronger preference for H3K18 than p300, and that p300 is more efficient than CBP at targeting H3K9 [41].

After characterizing these two enzymes, our follow-up investigation [91] involved determining how the in vitro kinetics of p300 in response to drug treatment correlated with in vivo effects of that drug. p300 is a prolific KAT, which is able to acetylate multiple residues of the histone [41]. We had previously shown that some residues were acetylated by p300 with cooperative dependence on acetyl-CoA, where other residues were hyperbolically dependent on acetyl-CoA. We hypothesized that this cooperativity was monomeric and the result of a slow conformation change between two or more conformations. This was evident by the fact that, had it followed a classically cooperative model, the result would have been suppression of non-cooperative products, which was not observed. Modeling this type of kinetic mechanism based on the model for hexokinase (see below), we could show that competitive inhibitors are capable of actually stimulating activity by altering the distribution of enzyme conformations. We tested this hypothesis by looking at the kinetics of the p300 response to the drug C646, a small molecule that competes for binding to the acetyl-CoA binding pocket of p300 [93]. One of the novel findings from this study was that while C646 was originally classified as an inhibitor of p300, in vitro assays determined that there was actually a biphasic effect, with low concentrations of the drug able to stimulate p300 activity.

To test whether this effect could be seen in vivo, cells were treated with differing amounts of C646. The acetylation patterns of the cells were compared to the kinetic data obtained from the in vitro assays. It was found that the changes in histone acetylation at individual residues that were detected in vivo correlated well with the changes in k_cat(app) at those residues in vitro. Specifically, looking at the ratio of the k_cat(app) (eq. 8) of histone H3 lysine 18 (H3K18) compared to H3K23 (or K18/K23) matched the increase in acetylation of K18 compared to K23 in cells.

These results help to support the usage of a multi-substrate in vitro system for determining enzyme selectivity. In the case of p300, the histone itself presents multiple potential targets for p300 binding and acetylation. As the findings of this study apply to multi-substrate enzymes in general, it would suggest that in a complex system with a multi-target enzyme, determining the k_cat(app) of that enzyme using an assay which contains multiple potential substrates could serve as a strong indicator of that enzyme’s selectivity in vivo.

4.2 Hexokinase

Hexokinase, originally called glucokinase was the first enzyme in which monomeric cooperativity was described: a sigmoidal dependence in the absence of a multiple substrate model. Hexokinase was shown to have a sigmoidal dependence on glucose but not on 2-deoxyglucose [94, 95]. Early models for this type of cooperativity suggested that cooperativity is due to a slow conformational step between two enzyme conformations where only one state was active (Figure 2) [94, 95]. Decades later NMR confirmed an order-disorder transition is responsible for the observed monomeric cooperativity [18]. This type of mechanism can also lead to difficulties in understanding the enzyme’s selectivity in a complex background. The presence of one substrate can affect the rate of another substrate’s turnover, by altering the concentration of the active enzyme complex [96]. In this model, anything that can bind in the active site could influence the conformational change and result in stimulation of enzyme activity, as modeled in Figure 2. These types of considerations highlight the difficulty in predicting enzyme selectivity in vivo that can act on multiple substrates, as their concentrations can vary independently of each other In this case, in order to accurately describe the selectivity between substrates for an enzyme displaying monomeric cooperativity, it becomes necessary to either know the free concentrations of all substrates or to know that at least one substrate is saturating. Without this information, the description of specificity becomes dependent on multiple substrates concentrations. Such a situation is problematic for analysis as a small amount of one substrate could increase the other substrate’s specificity, resulting in a decrease in its own selectivity.

Figure 2. Simulations of monomeric cooperativity and the link between second substrate/inhibitor activation.

We used KinTek Explorer to simulate monomeric cooperativity based on hexokinase [97, 98]. We then added an inhibitor to the simulation that binds one state of the enzyme and facilitates the conversation of enzyme conformation. Parameters are in the figure (enzyme concentration was 0.06 E and 0.04 E*, and 100 S). This simulation was used to calculate steady-state rate under k_cat conditions as a function of inhibitor concentration [I]. This data demonstrated a biphasic profile with an activation and inhibition phase. Right panel was fit using v/E=((k_initial+(k_active*[I])/K_activenH)/(1+ [I]((K_activenH+K_inhibitnH)⁻¹)) using data generated form KinTek Explorer.

5. Conclusions and outlook

Advancing technologies have facilitated the detection and quantitation of multiple substrate/product systems. Mass spectrometry, chromatography, NMR, and even DNA/RNA sequencing methods have all aided the advancement of this type of investigation. Using these systems, and carefully considering the conditions of the reactions, it is possible to obtain meaningful data from in vitro assays that can predict the behavior of enzymes in vivo. By understanding the caveats, as well as the kinetic analysis behind concepts like specificity and selectivity, we can continue to tailor multiple substrate and product experiments to more accurately model protein behavior in cellular systems.

Abbreviation

KAT

lysine acetyltransferases

PAH

polycyclic aromatic hydrocarbons

LC

liquid chromatography

MS

mass spectrometry

MS/MS

tandem mass spectrometry

NMR

nuclear magnetic resonance spectrometry

Gcn5

general control nonderepressible 5

Rtt109

regulator of Ty1 transposition 109

Vps75

vacuolar protein sorting 75

CBP

CREB-binding protein