D2: Multi-Substrate Ping-Pong Mechanisms - Biology

In this mechanism, one substrate binds first to the enzyme followed by product (P) release. Typically, product (P) is a fragment of the original substrate (A). The rest of the substrate is covalently attached to the enzyme (E), which is designated as (E'). Now the second reactant, (B), binds and reacts with the E' and forms a covalent bond to the fragment of (A) still attached to the enzyme, forming product (Q). This is now released and the enzyme is restored to its initial form, (E). This represents a ping-pong mechanism An abbreviated notation scheme is shown below for ping-pong mechanisms. For this mechanism, Lineweaver-Burk plots at varying (A) and different fixed values of (B) give a series of parallel lines.

One example of a ping-pong enzyme is low molecular weight protein tyrosine phosphatase. It reacts with the small substrate p-initrophenylphosphate (A) which binds to the enzyme covalently with the expulsion of the product P, the p-nitrophenol leaving group. Water (B) then comes in and covalently attacks the enzyme, forming an adduct with the covalently bound phosphate releasing it as inorganic phosphate. In this particular example, however, you can't vary the water concentration and it would be impossible to generate the parallel Lineweaver-Burk plots characteristic of ping-pong kinetics.

What are the meanings of the kinetic parameters, (K_m) and (V_m), for multisubstrate/multiproduct mechanisms? Consider a random sequential bi-bi reaction for a "simple" case in which the rapid equilibrium assumption defines the binding of substrates (A) and (B).

By inspection, there would appear to be two types of "effective" dissociation constants for reactant (A). One describes the binding of (A) to E ((K_{ia})) and the other the binding of (A) to (EB) ((K_a)). Using mass balance for (E) and relationship that


the following initial rate equation can be derived.

Note that Kib does not appear in the final equation. How can that be? The answer lies in the fact that the final concentration of (EAB) can be derived from the path (E) to (EA) to (EAB) or from the path (E) to (EB) to (EAB). Assuming rapid equilibrium,


The following equation can be derived from ping-pong bi-bi mechanism.

[ v =dfrac{V_M AB}{K_bA + K_aB + AB}]

For simplicity, all of the enzyme kinetic equations have been derived assuming no products are present.

10.4: Multisubstrate Systems

The Michaelis &ndashMenten model of enzyme kinetics was derived for single substrate reactions. Enzymatic reactions requiring multiple substrates and yielding multiple products are more common and yielding multiple products are more common than single-substrate reaction. In these types of reactions, the all the substrates involved are bound to the enzyme before catalysis of the reaction takes place to release the products. Sequential reactions can be either ordered or random. In contrast to the Michealis-Menton kinetics where a binary Enzyme-Substrate complex is generated in the mechanism (([ES]), in bisubstrate enzyme reactions, a ternary complex of the enzyme and two substrates is generated:

Bisubstrate reactions account for

60% of the known enzymatic reactions. Multi-substrate reactions follow complex rate equations that describe how the substrates bind and in what sequence. The analysis of these reactions is much simpler if the concentration of substrate (A) is kept constant and substrate (B) varied. Under these conditions, the enzyme behaves just like a single-substrate enzyme and a plot of (v) by ([S]) gives apparent (K_M) and (V_) constants for substrate B. If a set of these measurements is performed at different fixed concentrations of A, these data can be used to work out what the mechanism of the reaction is. For an enzyme that takes two substrates A and B and turns them into two products P and Q, there are two types of mechanism: ternary complex and ping&ndashpong.

How do you resolve the enzymes kinetics of these more complicated systems? The answer is fairly straightforward. You keep one of the substrates (B, for example) fixed, and vary the other substrate (A) and obtain a series of hyperbolic plots of (v_o) vs (A) at different fixed (B) concentrations. This would give a series of linear (1/v) vs. (1/A) double-reciprocal plots (Lineweaver-Burk plots) as well. The pattern of Lineweaver-Burk plots depends on how the reactants and products interact with the enzyme.

DNA Repair Enzymes: Structure, Biophysics, and Mechanism

Nadine L. Samara , . Wei Yang , in Methods in Enzymology , 2017


Structures of enzyme–substrate/product complexes have been studied for over four decades but have been limited to either before or after a chemical reaction. Recently using in crystallo catalysis combined with X-ray diffraction, we have discovered that many enzymatic reactions in nucleic acid metabolism require additional metal ion cofactors that are not present in the substrate or product state. By controlling metal ions essential for catalysis, the in crystallo approach has revealed unprecedented details of reaction intermediates. Here we present protocols used for successful studies of Mg 2 + -dependent DNA polymerases and ribonucleases that are applicable to analyses of a variety of metal ion-dependent reactions.

Parameter-less approaches for interpreting dynamic cellular response

Cellular response such as cell signaling is an integral part of information processing in biology. Upon receptor stimulation, numerous intracellular molecules are invoked to trigger the transcription of genes for specific biological purposes, such as growth, differentiation, apoptosis or immune response. How complex are such specialized and sophisticated machinery? Computational modeling is an important tool for investigating dynamic cellular behaviors. Here, I focus on certain types of key signaling pathways that can be interpreted well using simple physical rules based on Boolean logic and linear superposition of response terms. From the examples shown, it is conceivable that for small-scale network modeling, reaction topology, rather than parameter values, is crucial for understanding population-wide cellular behaviors. For large-scale response, non-parametric statistical approaches have proven valuable for revealing emergent properties.

The interpretation of dynamic cellular processes is indispensable for biological research. Especially in the last two decades, there have been tremendous efforts that were aimed at understanding complex biological networks in different cell types to various kinds of stimulations or perturbations, and in disease conditions using systems biology approaches. What sort of models do we need to conceptualize biological networks for interpreting or predicting dynamic responses?

In the early 1900s Victor Henri, Leonor Michaelis and Maud Menten thoroughly investigated enzymatic reactions in vitro, and developed the hyperbolic rate equation that we now popularly call the Michaelis-Menten enzyme kinetics. This is a more sophisticated form of mass-action type reaction, considering the saturation of kinetics at higher substrate concentrations instead of ever increasing profile for the latter. Subsequent work on this basic principle led to the extension of the kinetics to represent more complex scenarios, such as multi-substrate ping-pong and ternary-complex mechanisms [1].

As the development of computing power progressed significantly in the 1960s, there have been numerous efforts to model complete biological pathway modules, such as the glycolysis, using enzyme kinetic equations with the aim of estimating parameter values by fitting to steady-state concentration levels of metabolites. However, the more truthful abstraction of enzymatic complexity resulted in a dilemma where increased accuracy required increased knowledge of many parameters that were too difficult to obtain precisely. If parameter values are not accurately determined, the enzymatic reaction models will not be able to recapitulate experimental outcome reasonably well.

Most, if not all, studies adopting in vitro experiments determine the parameter values of reaction species for computational modeling from an artificial environment where the species are deliberately purified from its physiologic neighbors. This is because, until today, the in vivo kinetic parameters cannot be reliably measured using the current experimental technologies. Notably, there have been various reports that claim the kinetic parameters determined through in vitro and in vivo experiments can differ by several orders of magnitudes [2]. As a result, when combining these errors into the model, the final predictions could differ by several orders of magnitude. For example, the steady-state concentration of the glycolytic metabolite 3-phosphoglycerate in Trypanosoma brucei was under-predicted by an order of 7 [3].

The difficulty of accurately determining parameter values led to the development of non-parametric approaches such as the flux-balance analysis (FBA) [4]. Here, only the reaction topologies or stoichiometry of the network and steady-state levels are required to be known. Constraints are introduced by the stoichiometric coefficients in the system for the optimization of certain biological function, such as growth or production of certain compounds. Although, the FBA requires the assumption that metabolite concentrations remain at steady-states for analysis, it has been successfully used to interpret important physiological functions of a living cell. For example, Palsson and colleagues experimentally verified their prediction for the primary carbon source and oxygen uptake rates for maximal cellular growth in E. coli[5]. So, why is such simple steady-state method relying on stoichiometry of reactions make useful predictions? (Note that FBA requires the network topology to be largely known, as is the case for metabolic networks. For signaling pathways, where the detailed role of numerous molecules are still incomplete, FBA has limited application).

In a pioneering work on understanding the complex dynamics of bacterial chemotaxis, Leibler and colleagues created a highly simplified two-state mass-action model of E. coli chemotactic network [6]. Using the model, and subsequently with experiments [7], they showed that the adaptation precision of bacterial chemotaxis was insensitive to the large variation of its network parameter values. This mechanism, therefore, allows E. coli to display robust behavior to a wide range of attractant and repellent concentrations. However, at the same time, other properties, such as adaptation time and steady-state tumbling frequency, were variable to the stimulant concentration. Overall, their work demonstrated that bacterial adaptation property is a consequence of network’s connectivity and does not require the precision of parameter values. This work is a milestone paper that indicates complex biological phenomena can be understood using simple models that are not sensitive to parameter values.

The observation of simplicity in what appears to be highly dynamic and complex can have profound benefits in understanding and controlling disease conditions. Our research has focused on cell signaling dynamics of innate immune response and cancer cell survival. Over the last decade, we adopted systems biology approaches to study toll-like receptor (TLR) signaling [8-10], tumor necrosis factor (TNF) signaling [11] and TNF-related apoptosis-inducing ligand (TRAIL) signaling [12], from receptor stimulation through downstream gene expressions, via transcription factor activations.

The strategy was to first create a dynamic computational model based on current known pathways of a signaling process. Next, first-order response (mass-action) equation was used to represent each signaling reaction or process (protein binding, complex formation, ubiquitination, etc.). Subsequently, the model parameters were chosen to fit wildtype experimental dynamics, and compared with mutant cells for reliability of the models and their parameters [13]. When a single model is unable to simulate multiple experimental conditions, the model’s topology was allowed to be modified, using response rules, in accordance with the law of signaling flux conservation [9-13]. This is simply because we do not yet possess complete knowledge of all signaling reactions or molecules involved.

Notably, for all the complex signaling processes that we have investigated so far, we were successful to predict novel signaling features, such as missing intermediates, crosstalk mechanisms, feedback loops [8,11,12], and identify novel targets for controlling proinflammatory response [11] and cancer apoptosis [12]. All the predictions have been experimentally validated [9,11,14,15]. So why do simple models utilizing first-order response equations sufficient to produce insightful results of a complex system?

Firstly, the main reason for us to utilize first-order terms is due to the experimental observation of deterministic response waves of signal transduction within the period of investigations, usually up to 1-2 h after stimulation. That is, stimulating cell population in a dish with respective ligands resulted, in general, to dynamic activation response of intracellular proteins that followed gradual increase from their initial state to reach peak activation levels and, subsequently, decay to their original state (Figure  1 A). Such responses are observed for the first round of response waves of myriad signaling species (Figure  1 B). Although the kinetics could vary slightly from sample to sample, the general average response profiles are very well reproducible. In other words, regardless of how complex a signaling topology might be, the species’ average dynamic responses followed deterministic formation and depletion waves [13,17,18].

The observation of linear response waves. A) Schematic of activated signaling species, such as protein binding and gene expressions, with respect to time following formation and decay waves. Top panel represents a simple linear cascade with single wave. Bottom panel illustrates two linear waves superposed, as a consequence of an additional time-delay formation term. This may arise from feedback or crosstalk mechanisms. B) Quantitative dynamics of key molecules in insulin signaling pathway, showing similar dynamics to schematic in A). Figures adapted from [16]. C) Schematic of linear and switch-like relationship between transcription factor concentration and gene expressions.

Secondly, it can be shown, theoretically, that no matter how complex or non-linear the signaling system is, the dynamic response can be approximated using first-order terms if the perturbation levels are small. Consider the general form of a complex kinetic equation: ∂ X ∂ t = F X . F can be any non-linear function constituting of reaction and diffusion terms of species X. In engineering, for relative changes and when insufficient information is available, such systems are often carefully linearized using power or Talyor series ( ∂ δ X ∂ t = ∂ F X ∂ X X a δ X + ∂ F 2 X 2 ! ∂ X 2 X a δ X 2 + … , where X = X a is the point for linearization). Given a small perturbation, the higher order terms become less significant, leaving only the first-order term as the dominant factor. Note that the linearization techniques are approximate methods to understand general behaviors and, in many cases, cannot be used to interpret detailed mechanisms of response.

In light of this linear response hypothesis, it is noteworthy to quote the recent findings of two relevant works, that studied the relationships between the transcription factors and gene expressions in TNF-induced [19] and Msn2 overexpressed [20] stress response. Collectively, they found that increasing transcription factor concentration resulted in graded gene expressions that approximately followed a linear relationship (Figure  1 C). Although it is known that many transcription factors produce switch-like or digital relationship due to cooperativity in DNA binding, the stress response transcription factors have shown simple graded behavior. This finding may justify that certain key cellular processes, such as the immune response, may be guided by linear response through the signaling cascades. Taken together, it appears that linear response, as a governing principle, is key to invoke precise and optimal response when living cells are faced with immediate threats.

In other studies, even without the need to know graded response, binary (ON/OFF) state approaches have yielded fascinating results in understanding cell signaling. One notable study developed discrete Boolean network modeling to investigate the survival mechanism of cytotoxic T lymphocytes (CTL) in T cell large granular lymphoctye (T-LGL) leukemia [21]. Loughran and colleagues created a T-LGL survival signaling model with 58 nodes, representing molecular species, and 123 edges, representing causal interactions between the species. Using the model, they identified the most significant interactions for activating CTL in disease state compared to normal. Subsequent experiments confirmed their model predictions.

It is conceivable that the arrival to parameter-less approaches may be unrealistic in the realm of complex systems, where non-linear factors and stochastic effects can cause even small variation in perturbations to produce diverse multistable outcomes or oscillatory patterns. Such is the case observed for cell fate decisions where a single fertilized egg can diversify into distinct cell lineages or a bacteria being able to change fate under nutrient-deficient condition [22]. To model such complexity, dynamical systems theory adopting non-linear equations may possibly be used [23]. Also, for understanding self-organizing behaviors such as biological clocks/rhythms, spatial patterns, Hopf bifurcation or other non-linear dynamics, Goodwin, Brusselator, and Lotka–Volterra equations have been widely adopted [24-26]. However, these models require the precision of parameter values and most often reproduce only the general behavior of complex biological responses in one (wildtype) condition.

Another issue to consider is the scale of networks. So far, biological modules or network modeling that have been successfully used consist of molecular species that are relatively small, in the order of tens or a few hundreds. However, the living system invokes response of thousands of species and such large-scale studies probably require different approaches. One common strategy used to tackle large-scale effects is to use statistical techniques that investigate regression or correlation between species and samples, or apply clustering techniques to identify groups of genes with similar temporal or functional behaviors [27,28]. These methods have been instrumental in revealing emergent behaviors, for example, the observation of collective oscillations of numerous cell cycle independent specific metabolic cycle genes in Saccharomyces cerevisiae[29,30], and the collective genome-wide expression dynamics, including lowly expressed genes, for innate immune response [31,32] and neutrophil cell differentiation [33,34]. For classifying distinct cancer types for targeted therapy, self-organizing maps on high-dimensional gene expression data have been highly useful [35]. Thus, non-parametric statistical works on high throughput gene expression datasets have been crucial in showing emergent self-organized behaviors in cell populations.

In the future, non-parametric autonomous Boolean circuits, that have been recently shown to generate chaos, with multiple attractor states through time-delayed feedback loops in physical signal propagation [36,37], may also be investigated for biological systems. These could, especially, be valuable for the application of cell signaling related to non-linear cell fate decisions or disease formation.


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d -2-Hydroxyglutarate dehydrogenase from Pseudomonas aeruginosa PAO1 (PaD2HGDH) catalyzes the oxidation of d -2-hydroxyglutarate to 2-ketoglutarate, which is a necessary step in the serine biosynthetic pathway. The dependence of P. aeruginosa on PaD2HGDH makes the enzyme a potential therapeutic target against P. aeruginosa. In this study, recombinant His-tagged PaD2HGDH was expressed and purified to high levels from gene PA0317, which was previously annotated as an FAD-binding PCMH-type domain-containing protein. The enzyme cofactor was identified as FAD with fluorescence emission after phosphodiesterase treatment and with mass spectrometry analysis. PaD2HGDH had a kcat value of 11 s –1 and a Km value of 60 μM with d -2-hydroxyglutarate at pH 7.4 and 25 °C. The enzyme was also active with d -malate but did not react with molecular oxygen. Steady-state kinetics with d -malate and phenazine methosulfate as an electron acceptor established a mechanism that was consistent with ping-pong bi-bi steady-state kinetics at pH 7.4. A comparison of the kcat/Km values with d -2-hydroxyglutarate and d -malate suggested that the C5 carboxylate of d -2-hydroxyglutarate is important for the substrate specificity of the enzyme. Other homologues of the enzyme have been previously grouped in the VAO/PMCH family of flavoproteins. PaD2HGDH shares fully conserved residues with other α-hydroxy acid oxidizing enzymes, and these conserved residues are found in the active site of the PaD2HDGH homology model. An Enzyme Function Initiative-Enzyme Similarity Tool Sequence Similarity Network analysis suggests a functional difference between PaD2HGDH and human D2HGDH, and no relationship with VAO. A phylogenetic tree analysis of PaD2HGDH, VAO, and human D2HGDH establishes genetic diversity among these enzymes.

1 Answer 1

The issue with Michaelis menten curves, is that they presume only one pathway the enzyme can act by. Therefore if an enzyme has multiple pathways the presumptions fail. An example of this is monoamine oxidase, (Ramsay, R. R., Olivieri, A. & Holt, A. An improved approach to steady-state analysis of monoamine oxidases. J. Neural Transm. 118, 1003–1019 (2011).) This paper has the enzyme specific kinetics for monoamine oxidase - the development of the models is incredibly complicated but if you look at the equations you can see how there are multiple pathways.

They also presume only one substrate, so multi-susbtrate reactions need to have the kinetics modified as such. For that the mechanism are: Ping-pong, ternary- ordered and random, all of which impact on the kinetics.If the concentration of the intermediate complex is presumed not to change with time, then another model is the Briggs-Haldane model, known as quasi-steady state kinetics.

Then there are the kinetic models for inhibition. Of which the michaelis menten, where the kinetics vary according to how the inhibitors binds. But as is seen with the above MAO paper, can vary depending on the pathways and binding affinities. If an enzyme is irreversible then the kinetics also differ (Mcdonald, A. G. & Dublin, T. C. Enzymes : Irreversible Inhibition. 1–17 (2012). doi:10.1002/9780470015902.a0000601.pub2).

It is also worth noting, it is better to use non-linear regression to analyze kinetics as linearizing the data can lead to calculation errors (despite admittedly being the easier and clearer option).

Need for Different Kinetic Mechanisms

Enzymatic reactions proceed through a series of steps. These steps can shed light on the enzyme’s properties. Some enzymes have single-substrate molecules, such as hammerhead ribozymes (Murray et al. 2002) or proteases (Vitte 2015) According to the RNA world hypothesis, the early evolution of life depended on some RNA sequences catalysing the type of polymerisation needed for RNA replication (Benner 1989). Simple kinetic mechanisms are thought to have evolved first in ribozymes or protease enzymes (Murray et al. 2002 Vitte 2015). Single-substrate kinetic mechanisms are thought to represent the first steps in evolutionary processes (Johnston et al. 2001). In reality, most enzymes have complex active centres and have more than one substrate and more than one product. The complex biological activity of enzymes requires extraordinarily complex machinery, and the activity proceeds via very complex reactions. Enzymes that can catalyse complex reactions have multiple substrates and complex enzyme kinetic mechanisms. For enzymes with two substrates, the binding of these substrates can occur through two mechanisms: a sequential mechanism and a non-sequential mechanism. If the substrate forms an enzyme–substrate complex before a reaction takes place, the products that are released are called ‘sequential’. Sequential mechanisms have displacement reaction both substrates bind to the enzyme and then reaction begins and proceeds to form products which are then released from the enzyme. Sequential mechanisms consist of three subgroups: random, ordered and Theorell–Chance types. In random mechanisms, any substrate can bind first to the enzyme, and any product can be produced. Theorell–Chance mechanism in which there is an obligatory order of substrate association and product release without the accumulation of the ternary complex. In ordered mechanisms, substrates are added and products are produced in a specific order. Non-sequential mechanism is also known as the “ping-pong” mechanism is characterised by the change of the enzyme into an intermediate form. The reaction proceeds with the release of one or more products between the additions of two substrates. This mechanism is also called the double placement reaction and common in group transfer. One key character of this reaction is the existence of a substituted enzyme intermediate, in which the enzyme is temporarily modified. The possible evolutionary order of these kinetic mechanisms is given in Fig. 1 (Murray et al. 2002 Vitte 2015 Benner 1989 Wang and Wu 2007 Zuccotti et al. 2001 McClard et al. 2006 Yu et al. 2014 Freist and Sternbach 1984 Celeste et al. 2012 Kim and Kang 1994 Menefee and Zeczycki 2014 Vergnolle et al. 2013).

Possible evolutionary order of kinetic mechanisms. The figure schematically shows the going from top to bottom represents an evolutionary advance of kinetic mechanisms both of complexity and time

Two or more enzymes (or multiple forms of the same enzyme) catalyse the same reaction. The substrate concentration determines the velocity of the enzyme reaction (Nagao et al. 2014 Wolfe 2005). In random-reaction mechanisms, the order in which the substrates bind does not matter. In ordered reactions, one substrate must bind the enzyme before the second substrate is able to bind (Segel 1975). The Theorell–Chance catalytic mechanism, also known as ‘hit-and-run’, is a specific type of ordered mechanism. The main difference between the Theorell–Chance mechanism and the ordered bi–bi mechanism is that the concentration of EAB and EPQ complexes is essentially zero (A and B are the substrates and P and Q the products and EAB is enzyme–substrate complex and EPQ is the enzyme product complex) (Segel 1975 Zhang et al. 2014). Sequential kinetics can be distinguished from ping-pong kinetic mechanisms by the formation and release of one product before the binding of the second substrate.

In random mechanism, there is no obligatory binding sequence and this makes the reaction mechanism much more complex. Therefore, we may predict/explain that ordered bi–bi evolve into random bi–bi catalytic mechanisms (Segel 1975). It has been suggested that promiscuous activities are common because the evolution of a perfectly specific active site is both difficult and unnecessary (Copley 2015). The non-sequential mechanism, also known as the ping-pong mechanism, does not require both substrates to bind before releasing the first product. The name refers to the way in which the enzyme bounces back and forth from an intermediate state to its standard state (Segel 1975). For example, in the aminoacylation of tRNAIle, there are four different orders of substrate addition and product release that take place via sequential ordered ter–ter, rapid equilibrium sequential random ter–ter, random bi–uni uni–bi ping-pong and bi–bi uni–uni ping-pong, with a rapid equilibrium segment, mechanisms. tRNAVal is aminoacylated in rapid equilibrium random ter–ter order via a bi–bi uni–uni ping-pong mechanism with a rapid equilibrium segment and via two bi–uni uni–bi ping-pong mechanisms. It is assumed that assay conditions can be regarded as a stepwise approximation of physiological conditions and that considerable changes in error rates, up to one order of magnitude, may be possible in vivo (Freist and Sternbach 1984). Numerous steady-state kinetic studies have examined the complex catalytic reaction mechanism of multifunctional enzymes, such as pyruvate carboxylase. This enzyme catalyses reactions through a non-classical sequential bi–bi uni–uni reaction mechanism (Menefee and Zeczycki 2014). However, in experiments of another multifunctional enzyme, enzyme fatty acyl-AMP ligase FadD33, the researchers clearly demonstrated that catalysis proceeded via a bi uni–uni bi ping-pong kinetic mechanism (Vergnolle et al. 2013). N10-formyltetrahydrofolate synthetase is a folate enzyme that catalyses the formylation of tetrahydrofolate in an ATP-dependent manner, specifically, via a random bi uni–uni bi ping-pong ter–ter mechanism (Celeste et al. 2012). Malonyl-CoA synthetase catalyses the formation of malonyl-CoA directly from malonate and CoA, with hydrolysis of ATP into AMP and pyrophosphate (PPi). The catalytic mechanism of malonyl-CoA synthetase was investigated in steady-state kinetics and initial-velocity and product inhibition studies with AMP and PPi. The results strongly pointed to an ordered bi uni–uni bi ping-pong ter–ter system as the most probable steady-state kinetic mechanism of malonyl-CoA synthetase (Kim and Kang 1994).

Enzyme kinetic mechanisms are specific to their substrates because of their functional specificity. Determining enzyme functions is essential for a thorough understanding of cellular processes. The functional specificity of an enzyme can change dramatically following the mutation of a small number of residues. Information about these critical residues can potentially help discriminate enzyme functions (Nagao et al. 2014). In a previous study, researchers added glycerol to their activity assay buffer, and this molecule ‘glycerol’ caused a decrease in both K m and K i values with respect to the enzyme’s substrate. They attributed this finding to glycerol causing a conformational change in the enzyme, resulting in tighter binding of the enzyme’s substrate and its product (Kulaksiz-Erkmen et al. 2012).

Multienzyme complexes and multifunctional proteins may confer a kinetic advantage by channelling reaction intermediates between consecutive enzymes and reducing the transient time for the establishment of steady states (Easterby 1989). Therefore, various enzymes with different catalytic functions may come together and make big complex machines or complex enzymatic reaction fabrics. One such enzyme is fungal fatty acid synthase, which has played a key role in the evolution of complex multi-enzymes. It has 48 functional domains, which are embedded in a matrix of scaffolding elements (Bukhari et al. 2014). Mechanism pathways for multi-substrate multi-product enzyme-catalysed reactions can become very complex and lead to kinetic models comprising several terms (Bornadel et al. 2013) or quite simple terms, such as random, sequential binding mechanisms (Burke et al. 2013). The most important thing is more than one enzyme come together to improve the productivity and reduce the cost of various processes. The most important point to remember is that more than one enzyme is required to produce any product.

Reaction mechanisms are diverse substrate specificity is achieved by a diversity of not only substrate recognition, but also hydrolysis mechanisms (Arimori et al. 2011). However, it is difficult to predict which bi–bi substrate enzyme kinetic mechanisms emerged first. From an evolutionary perspective, the random mechanism may be much more evolved than the ordered bi–bi mechanisms. In the ordered mechanism, the binding of the first substrate to the enzyme’s active site causes a conformational change, which is required for binding the second substrate. Alternatively, the second substrate binds directly to the first substrate. If the active site of the enzyme contains various catalytic functional groups, then the substrate selectivity of this enzyme will decrease, enabling it to interact easily with various substrates, such as GST enzymes. Cytochrome p450 and GST enzymes have broad substrate specificity. They are responsible for the metabolism of non-physiological substances, such as xenobiotics. Cytochrome P450 enzymes catalyse the metabolism of a wide variety of naturally occurring and foreign compounds, via a ping-pong bi–bi mechanism. GST enzymes from humans and other sources display a random mechanism in which the combination of the enzyme with one substrate does not influence its affinity for the other (Hollenberg 1992 Breton et al. 2000 Caccuri et al. 2001 Bowman et al. 2007 Wang et al. 2011 Kolawole et al. 2011). Enzymes with promiscuous activities are also likely to have a long evolutionary history (Copley 2015).

1 Introduction

Chemical synthesis of complex organic molecules for drug development has benefited immensely from recent developments in flow chemistry and automation. 1 In this respect, the use of microfluidic devices is highly advantageous as it simplifies the precise adjustment and control of essential reaction parameters, such as temperature and diffusion-based mixing efficacy, and it also allows the separation of incompatible reaction steps. 2 In this area of research, the spatial compartmentalization and cascading of reaction steps are increasingly exploited for chemical transformations in microfluidic reactors. 3 Here the synthesis of drugs with multiple stereocenters is a prime example of how cascaded biocatalytic 4 or chemoenzymatic 5 reaction sequences can be used for efficient, scalable production processes. 6

For effective implementation of continuous flow processes, however, the integration of biocatalysts into microfluidic devices is still a major challenge. 7 The immobilization of whole cells or isolated enzymes can be achieved by a plethora of methods, ranging from non-specific physisorption to the use of sophisticated chemical methods, which are often based on genetically-encoded tag systems, such as the (His6)-tag. 8 Likewise, tag systems used for purification, e. g., streptavidin-binding peptide (SBP), 9 or cell biology research (e. g., SpyTag/SpyCatcher, 10 SNAP-Tag, 11 HaloTag 12 ) are being exploited for flow-through biocatalysis. Indeed, the use of fusion proteins decorated with such tag systems has led to the establishment of ‘self-immobilizing biocatalysts’ that can be used in continuous microfluidic processes with high efficiency and specificity. 13 The self-assembled immobilization of such fusion proteins can, for example, be achieved on magnetic beads with a high level of control over stoichiometry and geometric alignment by single-point immobilization. 14 The further integration of such enzyme-functionalized magnetic nano- and microparticles into flow-through reactors enables a variety of applications, ranging from sensors 15 and lab-on-a-chip systems 16 to continuous flow-through reactors for biocatalysis. 13a, 13b, 17

The use of immobilized enzymes in flow-through systems allows the biocatalysis process to be carried out in a heterogeneous catalysis regime, often in a packed-bed reactor format. For an optimization of such systems, it would be desirable to model the process in silico, in order to gain a better understanding of the biotechnological process and to enable its economic optimization with reduced experiments and resources. However, it is still difficult to describe and simulate coupled enzyme reactions that occur in a microfluidic setup with an overflown, porous, catalytically active bed due to the high complexity of such systems.

The detailed simulation of the reactor performance in such a system requires mathematical models for the enzymatic processes, which depend on kinetic models for the distinctive chemical conversions. Mathematical descriptions of enzyme kinetics, in particular Michaelis and Menten kinetics, 18 have led to the range of today's methodologies, such as canonical, approximate and mechanistic rate formalisms. 19 However, Michaelis-Menten kinetics assumes constant, excess concentrations of co-substrates, and these conditions are usually not present inside microfluidic packed-bed reactors. For instance, Lilly et al. found decreased Michaelis-Menten Km values for increased flow rates and therefore made estimations on enzyme kinetic parameters in continuous-flow systems. 20 In addition, for enzymes using two substrates, multi-substrate laws such as bi-bi mechanisms must be considered, which are divided into sequential mechanisms (ordered or random binding) and the ping-pong mechanism. 21

In order to implement such mechanistic reaction kinetics into packed-bed reactors containing porous particles, several mathematical models have been developed in earlier works. 22 However, these works focused on investigations of packed bed reactors with particle diameters larger than 300 μm operated by perfusion through the packed bed. To expand this methodological repertoire to complex, multi-substrate enzymatic reactions, we here describe a new model for a plug flow reactor consisting of a porous bed of compact, uniform particles functionalized with an immobilized reductase which is overflowed with an aqueous mobile phase containing an enzymatic NADPH cofactor regeneration system. We show that through the synergy of experiment and mathematical modeling, the behavior of the reaction system can be predicted, thereby reducing the number of experiments as well as the material consumption for optimizing the catalytic performance of the system.


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Watch the video: Ping pong catalysis of enzymes (January 2022).