Bridging Disciplines in Enzyme Kinetics: Understanding Steady-State, Transient-State and Performance Parameters

Abstract

Enzyme kinetics is fundamental across diverse fields—from enzymology and medicine to biocatalysis and metabolic engineering. Analyses of enzyme kinetics provide insights into catalytic rates, substrate affinities, inhibition patterns, productivities and mechanistic pathways, which are critical for areas such as drug development, industrial biocatalysis and mechanistic enzymology. However, each research field emphasizes different types of kinetic parameters, leading to challenges in establishing a common ground for understanding and interpreting enzyme properties. This review covers interpretation of enzyme kinetic parameters under three main categories—steady-state, transient-state and performance metrics—in a descriptive way and discusses their relevance with respect to different scientific and applied fields that investigate and utilize enzymes. By comparatively defining key kinetic and thermodynamic parameters, the review aims to help researchers interpret and report enzyme behavior more effectively, bridging gaps across interdisciplinary fields.

1. Introduction

Enzymes are biological macromolecules, primarily proteins, that speed up biochemical reactions to sustain life through their catalytic effect. Kinetic analysis of enzymes is crucial for all researchers and practitioners of enzymes in various fields, from basic enzymology, biocatalysis and metabolic engineering to medicine, pharmacology and bioremediation. The main characteristics of enzymes, like their enhancement of catalytic rate and their substrate specificity, can be evaluated using various parameters of enzyme kinetics [1,2,3].

Measurement of the catalytic rates and binding affinities for substrates and inhibitors is of utmost importance for basic characterization as well as for comparative assessment of enzymes for various purposes, such as inhibitor drug development, biocatalytic synthesis of high-value chemicals, characterizing elimination of drugs in the body and revealing a full mechanistic picture of an enzyme reaction. However, various fields dealing with different aspects of enzymes often use different sets of kinetic parameters, which overlap only to a certain extent. In this regard, we can consider kinetic analyses of enzymes, and thus the set of kinetic parameters, to fall into three categories: (1) steady-state kinetics, (2) transient-state (pre-steady-state) kinetics and (3) performance (productivity) metrics. Steady-state kinetics is apparently the most utilized type of analyses for almost all researchers working on enzymes, from basic enzymology and biocatalysis to the medical field [1,2,4,5]. Transient-state kinetics, which mainly investigate the reaction rate patterns at the first (or first few) turnovers, is mainly used by enzymologists, together with steady-state kinetic data, to reveal information towards mechanistic understanding of enzyme reaction cycles. On the other hand, performance (productivity) metrics are indispensable for biocatalysis and enzyme technology researchers and practitioners, since they provide valuable information on the feasibility of the enzyme for application purposes, like enzymatic synthesis and bioremediation, often on larger and industrially relevant scales.

The different set of kinetic parameters or the different strengths of emphasis put on common kinetic parameters in separate enzyme-related fields lead to difficulties in forming a common language between researchers working with different aspects of enzymes. This might present a particular challenge for young researchers working in interdisciplinary areas in terms of interpreting these parameters and reporting the most meaningful parameters from their research results. Thus, in this review, we will introduce and comparatively discuss each of the enzyme kinetics categories and briefly explain many of the widely used kinetic parameters, as well as some important thermodynamic parameters. We will highlight the usefulness of the most important parameters through different aspects of enzyme function and utility. Our aim is to guide researchers and practitioners of enzymes on the definitions and interpretations of kinetic parameters, without going into mathematical detail but by comparatively illustrating their meaning and use.

2. Steady-State Kinetics

The development of steady-state kinetics for enzymes goes back to more than a century ago. In particular, the studies of Victor Henri published at the start of 20th century [6], followed by the seminal work of Leonor Michaelis and Maud Leonora Menten published in 1913 [7], led to the very well-known Michaelis–Menten equation, which formed the basis of steady-state kinetic analysis of enzymes, followed by many other studies deriving equations for more complicated enzyme reaction systems, e.g., for multi-substrate kinetics and for various types of inhibition kinetics [2,3,8,9,10]. Most enzymes exhibit a steady-state kinetics pattern that fits well to a Michaelis–Menten model. This model considers the reversible formation of an enzyme–substrate complex (ES) that collapses into product with a certain rate constant (k₂, chemical step) and explains how the reaction rate depends on the concentration of enzyme (E) and substrate (S) (Scheme 1) [3,8,9]. Over a century since its formulation, Michaelis–Menten kinetics is still the most widely used method in enzyme kinetics, representing a fundamental analysis in the characterization of a newly discovered enzyme or a mutant variant, as well as being one of the main teaching lab experiments of many enzyme course curriculums [11,12,13,14].

Scheme 1. General enzyme reaction scheme in its minimal form.

Steady-state kinetics analysis is based on a set of initial rate (initial velocity; v₀) measurements performed with a constant enzyme concentration and varying substrate concentrations (with at least an order of magnitude higher substrate concentration over enzyme). During this initial stage of the reaction under multiple-turnover conditions, the rate for the appearance of ES complex (Michaelis complex) is almost equal to rate of its breakdown (steady-state period). This is ensured by the practical approach that aims to only use a small fraction of the substrate (in general about 10% or less) during the initial velocity measurement period, where the change in substrate concentration is negligible, so that the substrate concentration can be considered almost constant, resulting in pseudo-first-order kinetics for the first step in Scheme 1 (the derivation of the Michaelis–Menten equation based on this steady-state approximation was shown by Briggs and Haldane in 1925 [15]). For many enzymes, it is relatively simple to perform steady-state analysis through the Michaelis–Menten kinetics model; the slope for the change in concentration of substrate or product per time (initial velocity) is measured at different concentrations of the substrate—the resulting data is then plotted as substrate concentration (independent variable) vs. initial velocity (dependent variable) and fit to the Michaelis–Menten equation (Scheme 2, left equation) by non-linear regression using computer programs, giving a hyperbolic curve (Figure 1). Results from such a fit give us the steady-state kinetic parameters of: V_max, K_m and V_max/K_m. If the enzyme concentration is known, k_cat and k_cat/K_m can also be calculated (Scheme 2, right equation). These are the main kinetic parameters that are extracted from a steady-state kinetic analysis. V_max and k_cat both indicate the highest rate that the enzyme can approach at infinite (saturating) substrate concentration under given conditions (temperature, pressure, buffer conditions). Since V_max is dependent on the amount of enzyme, if possible, it should always be reported together with the enzyme concentration used in the initial velocity assays, otherwise it would not be very meaningful. In this respect, k_cat has the edge over V_max, since it is not dependent on concentration and has the unit of reciprocal time. In other words, k_cat, (also known as turnover number) is the maximum number of product molecules produced per enzyme molecule per unit of time. k_cat (and k_cat/K_m) can be directly compared for different enzymes assayed under the same or similar conditions. k_cat is also equivalent to k₂ (in Scheme 1) in most cases (when k₋₁ >> k₂). K_m (Michaelis constant) can be defined as the substrate concentration at which the rate of the enzymatic reaction (initial velocity) is half of V_max (Figure 1). In other words, K_m indicates the affinity of an enzyme for its substrate—the lower the K_m, the stronger the interaction between E and S. In general, K_m is given as (k₋₁ + k₂)/k₁ according to the rate constants in Scheme 1, although the expression for K_m can indeed become much more complicated in a complex mechanistic scheme with multiple reaction steps and rate constants for intermediates [16,17]. In the case where k₋₁ >> k₂, K_m will be almost equal to dissociation constant K_d, which is given by (k₋₁/k₁).

Scheme 2. Michaelis–Menten equation (left) and relation between V_max and k_cat (right).

Figure 1. A typical Michaelis–Menten plot showing the graphical meaning of kinetic parameters from a steady-state kinetic analysis and the regions of first-order and zero-order kinetics with respect to substrate concentration [S].

V_max/K_m (or k_cat/K_m) is most commonly known as “specificity constant” or “catalytic efficiency” (other terms have also been suggested [18]) and encompasses two parameters in a single term. It is a measure of the preference of an enzyme towards its substrate, thus useful in comparing different enzymes (e.g., mutant variants) for the same substrate or the same enzyme for different substrates, although care must be taken in the former case, as has been discussed in reference [19]. It has been argued in the literature that k_cat and k_cat/K_m should be regarded as the main kinetic parameters that can be obtained from a steady-state analysis, and K_m should be considered as just a ratio of k_cat and k_cat/K_m [16,17,18]. k_cat/K_m represents the apparent second-order rate constant for (productive) binding of the substrate to the enzyme to form an ES complex (it approaches a true second-order rate constant if collapse of the ES complex to P is much faster than its reverse reaction to E and S) [17]. Calculation of k_cat/K_m (or V_max/K_m) can be performed in different ways. One can simply derive k_cat and K_m from non-linear regression of the initial velocity data using Michaelis–Menten equation and take the ratio of the two parameters. That will require error propagation to report the error estimates on k_cat/K_m, which can lead to large standard errors (since both parameters, k_cat and K_m, are calculated from extrapolations to an infinite substrate concentration that is never reached). However, the Michaelis–Menten equation can also be rearranged to directly involve the term k_cat/K_m (Scheme 3) so that non-linear regression directly gives this term, often with lower error estimates, as has been demonstrated by Johnson [17]. Overall, whether k_cat/K_m or k_cat or K_m is a better parameter for comparing enzymes depends on the purpose and application. Since most biocatalytic application areas of enzymes require saturating high concentrations of the substrates (for a feasible synthesis), k_cat can be a better term to use in comparing enzymes for their application potential. However, in the study of enzyme mechanisms and for in vivo studies, k_cat/K_m can be a better parameter. Since k_cat/K_m is affected by all the initial steps up to and including the first irreversible step of the enzymatic reaction, evaluating the effect of different substrates, isotope exchange and medium viscosity on k_cat/K_m gives valuable mechanistic information on these initial steps [20,21,22,23].

Scheme 3. Rearranged form of Michaelis–Menten equation that enables us to calculate k_cat/K_m and k_cat directly from non-linear regression analysis.

The Michaelis–Menten equation was transformed into linearized forms by rearranging the original equation (Scheme 2, left equation) such that the equation takes the form of y = mx + n, which can be easily fit by linear regression. The most common among these linear forms is the Lineweaver–Burk plot (also called the double-reciprocal plot), where the reciprocal of initial velocity (1/v) is plotted versus 1/[S] [24]. The slope of the line from linear regression is equal to K_m/V_max and the y-axis intercept to 1/V_max. Two other common linearized forms of the Michaelis–Menten equation are Eadie–Hofstee (v vs. v/[S]) and Hanes–Woolf ([S]/v vs. [S]) plots [1,3].

With easy access to computer programs for non-linear regression, these linearized forms are no longer popular for the fitting of initial velocity data to calculate steady-state kinetic parameters. Indeed, small variations in certain data points can translate into big errors in calculating the parameters using linear equations, so several data points and great precision in measurements are needed for accurate parameter determination [3]. On the other hand, fitting the initial velocity data directly to the Michaelis–Menten equation gives more reliable results even with less data points and enables easier error evaluation. However, the linearized plots are still very useful for more complex forms of the Michaelis–Menten equation that involve inhibitors and multiple substrates [1,25,26,27]. As described below, inhibition patterns and substrate/product binding/release order are commonly deduced using linearized plots.

The reaction in Scheme 1 points to a simplified minimal kinetic mechanism for an enzyme, which is sufficient to derive the steady-state kinetic parameters according to the Michaelis–Menten equation. However, in many cases, the real reaction scheme is more complex due to many intermediate steps. Moreover, multiple substrates, the presence of inhibitors, allosteric properties and substrate and product inhibition can make steady-state analysis quite complicated. Even in those cases it is possible to derive equations and calculate kinetic parameters, as has been shown in many studies from the literature for various enzymes [2,28,29,30]. Especially, the graphical method of King–Altman [31,32] and the systematic methods developed by Cleland make it possible to derive rate expressions and calculate kinetic parameters for complex multi-substrate enzymatic reactions [8,33,34,35,36]. One simplifying approach with multiple substrates is to vary only one substrate at a time and fix the other substrates at their saturating concentration, to calculate K_m values for each substrate [28]. The method of net rate constants introduced by Cleland further simplifies the derivation of steady-state parameters in terms of intrinsic rate constants [37].

There are several considerations for designing a successful steady-state experiment. In particular, the choice of substrate concentrations, enzyme concentration and assay time are very important. For a newly studied enzyme, initial activity assessment at different conditions is required to determine the optimum conditions for a subsequent steady-state kinetic analysis. One should always keep in mind that different pH and temperatures will affect steady-state parameters, so a consistent set of reaction conditions should be decided from the very beginning in order to avoid uneven comparisons. For more details on the design of steady-state kinetic experiments, we refer the reader to some methodology articles [25,38,39].

Steady-state kinetic analysis can also be used to determine the type of inhibition and inhibition constant (Ki; dissociation constant for the inhibitor, I). Such information is especially valuable in designing enzyme-inhibitor drugs, which make up a significant portion of clinical drugs in use today [5]. Where reversible inhibition is concerned, there are three types of inhibition: competitive, non-competitive and uncompetitive (there is some discrepancy in the naming of “non-competitive inhibition”—in some sources from the literature, the term “mixed-inhibition” is used to indicate the case in which the inhibitor could bind both the free enzyme (E) and the ES complex with varying affinities, and (pure) non-competitive inhibition is only used to refer to the special case of mixed-inhibition when these affinities are equivalent; however, in other sources, non-competitive inhibition is used as the single term describing all possibilities as long as the inhibitor binds both E and ES). The Michaelis–Menten equation can be modified to integrate K_i into the equation (considering the new equilibria for the enzyme, the ES complex and inhibitor interactions). The most common method to determine the type of inhibition is to use double-reciprocal or another type of linearized plots [1,26,40]. Here, initial velocities at varying substrate concentrations are measured in the absence of an inhibitor and in the presence of an inhibitor at a constant concentration. The experiment is then repeated at a set of different inhibitor concentrations. The resulting data is plotted as 1/v vs. 1[S] for each inhibitor concentration and fitted to the linearized form of the modified Michaelis–Menten equation that also includes the terms K_i and [I]. The pattern of the lines indicates the type of inhibition; lines intersect for competitive inhibition at the y-axis (1/V_max), for (pure) non-competitive inhibition at the x-axis (−1/K_m) and for uncompetitive inhibition, the lines are parallel [1]. K_i can also be calculated from these plots. The Dixon plot is another form of a linearized Michaelis–Menten equation involving K_i and [I] and plotted as 1/v vs. [I] at constant [S] [41]. This makes it possible to directly obtain the Ki value from the plot, which is the x-axis value of the intersection point of the lines. Substrate inhibition can also be integrated into a steady-state model through a modified Michaelis–Menten equation. Generally, non-linear regression is the most convenient way to calculate the K_i value for substrate inhibition. Many basic graphing and curve-fitting software include the pre-set equation for substrate inhibition (Scheme 4).

Scheme 4. Modified version of the Michaelis–Menten equation to include substrate inhibition.

Moreover, the order of substrate binding and product release steps in multi-substrate enzymatic reactions can be deduced from steady-state kinetic analysis, as has been shown by the work of Cleland in the 1960s [2,33,34,35]. In a two-substrate enzymatic reaction (with S₁ and S₂ as the two substrates) a sequential (random or ordered) vs. a ping-pong mechanism can easily be distinguished by a double-reciprocal plot (1/v vs. 1[S₁]) obtained at multiple fixed concentrations of S₂; a series of parallel lines indicates a ping-pong mechanism, whereas intersecting lines point to a sequential mechanism (Scheme 5 and Scheme 6).

Scheme 5. Random sequential mechanism.

Scheme 6. Ping-pong bi-bi mechanism.

Steady-state kinetic analyses through initial velocity measurements are convenient for most enzymes. The requirement for a low enzyme concentration and sufficiency of simple apparatus, like a basic spectrophotometer, are some of the main advantages of steady-state analysis. Moreover, since the analysis is performed at the initial period of enzyme activity, complications due to enzyme denaturation and product inhibition are avoided [42]. Steady-state parameters enable one to easily compare enzymes when using different substrates. Comparison of these parameters for mutant enzymes can also provide a lot of useful information on changes in substrate binding and on the chemistry steps (Table 1).

Table 1. Most common parameters obtained from steady-state kinetic analysis, their definitions and interpretation.

Parameter (Unit)	Definition	What Does It Reveal?	What Does It Not Reveal?
kcat (1/time)	Rate of product formation after initial substrate binding, turnover number	-Maximum rate that an enzyme can reach at saturating substrate(s) concentration -Rate-limiting step of the enzyme reaction	-No insight into stability -No information about individual reaction steps -No information on substrate binding
Vmax (conc./time)	Similar to kcat, but dependent on enzyme concentration	-Maximum rate that an enzyme can reach at saturating substrate(s) concentration -Rate-limiting step of the enzyme reaction	-No insight into stability -No information about individual reaction steps -No information on turnover number, unless the enzyme conc. is known -No information on substrate binding
Km (conc.)	Michaelis constant or substrate concentration at half the value of kcat (or Vmax)	The affinity of an enzyme towards its substrate	-No direct information about catalytic performance -Only under certain conditions equivalent to Kd
kcat/Km (1/time·conc.)	Specificity constant or catalytic efficiency	-Apparent second-order rate constant for the reaction between E and S -Reflects steps up to and including the first irreversible step	-No insight into stability -No information about individual steps following substrate binding
Ki (conc.)	Inhibition constant	How strongly the inhibitor binds to the enzyme	-No information on the type of inhibition

There can be challenges in analyzing steady-state kinetics with some enzymes, for which it may not be technically possible to reach saturating substrate concentrations due to the availability or low solubility of the substrate. In this case, although a hyperbolic curve indicating substrate saturation may not be obtained (thus V_max, k_cat or K_m cannot be determined), k_cat/K_m (or V_max/K_m) can still be accurately calculated from the slope of the initial linear portion of the Michaelis–Menten curve (first-order region where the rate is linearly proportional to S) by linear regression (Figure 1) [16,17]. Under the conditions of [S] < <K_m, the Michaelis–Menten equation will simplify into v = (V_max/K_m)·[S] and the slope of the linear curve will give V_max/K_m.

Besides using initial velocities, it is also possible to use full time-courses obtained at different substrate concentrations (i.e., progress curves where the reaction is monitored over long time periods beyond the linear phase or to completion) in order to derive steady-state kinetic parameters [17,43,44,45]. Here, a certain enzymatic mechanism (such as in Scheme 1 or Figure 2) is simulated computationally using numerical integration of rate equations to fit progress curves globally to estimate intrinsic or net rate constants for each step. These rate constants can then be used to obtain estimates of, e.g., k_cat/K_m or K_m [17]. This means of obtaining steady-state kinetics can have some advantages, such as higher signal amplitudes or the sufficiency of fewer substrate concentration data points, but requires more advanced data fitting compared to conventional Michaelis–Menten curve fitting. It has been demonstrated that global fitting of the progress curves provides less uncertainties in kinetic parameter estimation (lower errors or standard deviations) compared to conventional non-linear regression of initial velocity vs. [S] data [17,43]. Progress curves can also be fitted using integrated forms of the Michaelis–Menten equation, although this is rare in practice [45,46].

Figure 2. Progress curves of a simulated hypothetical enzymatic reaction, according to the mechanism given above the graph. The simulation was carried out using the following input parameters: k₁ = 0.1 µM⁻¹s⁻¹, k₋₁ = 10 s⁻¹, k₂ = 45 s⁻¹, k₋₂ = 1 s⁻¹, k₃ = 30 s⁻¹, k₋₃ = 4 s⁻¹, k₄ = 5 s⁻¹; [E] = 50 µM; [S] = 200 µM. The response factors of each species have been assumed to be equal. In a real case, signals can be measured for each species separately using a different technique and can be converted to concentrations using response factors (e.g., extinction coefficients). The simulation has been performed with the program DynaFit [47].

Although very convenient to obtain and analyze, steady-state kinetics have limitations in two main areas: (1) With regard to mechanistic enzymology, steady-state kinetic analysis does not provide sufficient insight into individual reaction steps and does not provide information on the kinetics of intermediates and conformational changes. The slowest step in the reaction pathway is measured as the k_cat, but faster steps are not resolved. To complement steady-state kinetics, transient-state kinetics (pre-steady-state) by rapid reaction techniques are needed to investigate individual reaction steps and to obtain a complete kinetic mechanism of the enzyme reaction pathway, as described in Section 3. (2) With regard to the practical use of enzymes in biocatalysis, steady-state kinetics do not contain any information on the stability or long-term performance of the enzyme. The rates are only measured for very short time periods, which are mostly irrelevant to an industrial biocatalytic process. Moreover, steady-state kinetics are generally carried out under low substrate conditions (highest in the mM range). On the other hand, biocatalytic processes often need molar range concentrations, which are almost never tested in steady-state assays (although insights into substrate and product inhibition can be obtained via steady-state analysis). Thus, performance metrics are needed, together with steady-state analysis, for the evaluation of biocatalytic processes, as discussed in Section 4.

3. Transient-State Kinetics

After the initiation of an enzymatic reaction, the short time window before reaching steady-state conditions is called the pre-steady-state period [48,49]. Steady-state analysis simplifies the enzymatic reaction as the ES complex being converted into the product (E + P) in a unified single step, thus does not reveal information on the steps at the active site that take place after substrate binding and before product release. Transient-state kinetics (also called pre-steady-state kinetics or rapid-reaction kinetics) explores the pre-steady-state period and provides useful information on the mechanism of an enzyme. Transient-state methods enable the direct observation of individual events along a reaction pathway on very short time scales, such that the formation of intermediates and conformational changes that take place within a single turnover can be monitored, allowing for the kinetics of the elementary steps of the reaction pathway to be determined [3,50,51]. Since the ES complex will likely go through different intermediates and transient complexes during the catalytic cycle for most enzymes, transient-state kinetics aims to resolve all these individual steps taking place between ES and E + P (Figure 2). Those steps are mostly invisible in a steady-state analysis. Moreover, unlike steady-state kinetics, which measure kinetics after the reaction reaches the steady-state (generally after a few seconds), transient-state kinetics observe and measure discrete physical and chemical events taking place at the active site on a short time scale of milliseconds, enabling one to deduce intrinsic rate and equilibrium constants of the enzymatic reaction, including substrate binding, chemical steps, conformational changes and product release steps (Figure 2). Such resolution of individual steps of the enzyme reaction brings important insights into the identity and kinetics of the reactive intermediates, nature of transition states, conformational changes following substrate binding and rate-limiting steps of the catalytic pathway. While steady-state kinetics can be used to determine the order of binding and release of substrates and products, it is insufficient in precisely identifying the elementary steps of these individual events [50,51]. However, steady-state kinetics still serve as a crucial guide in designing the conditions for transient-state experiments such as concentrations and time scales. Moreover, when coupled with steady-state analysis, transient-state kinetic analysis can reveal which of the individual chemical or physical steps is (partially) rate-limiting. k_cat will often be equivalent to the slowest rate of the catalytic cycle following substrate binding—either one of the chemical steps leading to the product or the release of the product from the enzyme active site. This information is valuable from multiple aspects. For example, one can engineer the enzyme specifically towards increasing the rate for the rate-limiting step. Otherwise, affecting the rate of the other, faster steps would not make a difference.

Transient-state kinetics also enable researchers to use substrate analogs, inhibitors, isotopically labeled substrates or pH variation to obtain direct information on the nature and rate of the physical and chemical changes taking place at the active site [3,48,52]. Overall, when combined and supported with steady-state analysis, transient-kinetics provide a more complete mechanistic picture of enzyme catalysis on a kinetic and thermodynamic foundation [48], making it possible to compare the effect of reaction conditions, altered substrates and active-site mutations on the individual chemical and physical events taking place during an enzyme reaction sequence. Many enzymatic reaction mechanisms have been explored using transient-state kinetics in combination with steady-state kinetics [20,53,54,55,56].

In general, transient-state experiments can be carried out using two main approaches. In the first and more common approach, the substrate is used in excess of the enzyme (slight excess to multiple-fold excess), but the observation of the reaction is performed for such a short time—transiently—that only a few turnovers are observed. This approach may have difficulties in deconvoluting spectroscopic signals (like absorbance and fluorescence) that overlap due to multiple turnovers taking place. However, in the second approach, namely single turnover kinetics, the enzyme is used in excess over the substrate so that only one turnover is observed. This makes it possible to resolve the reaction steps better without interference from the subsequent turnovers. Such flexibility to use excess enzyme over substrate or excess substrate over enzyme is also advantageous in distinguishing the saturation kinetics pattern (formation of a prior non-covalent complex) vs. second-order kinetics for the interaction of the enzyme with its substrate, as used for analyzing reactions of oxygenases with O₂ [57].

In experimental terms, transient-state kinetics often require rapid-mixing techniques involving instruments that enable monitoring of the reaction a few milliseconds after its initiation and often require high concentrations of enzyme to ensure enough signal intensity. The two most common techniques are (1) stopped-flow, which monitors the progress of the reaction by recording changes in signals such as absorbance, fluorescence, fluorescence anisotropy or circular dichroism; and (2) rapid-quench-flow, which enables quenching of the enzymatic reaction after short time periods via a quenching solution or via freezing, enabling further analysis with any analytical method of choice, such as HPLC, LC-MS and EPR, to quantify the substrate, product and stable intermediates [50]. Each technique has its own advantages and can be used based on the properties of the product and intermediates to be analyzed. Lower temperatures are often used to slow down the reaction steps to better observe the intermediates and products. More information on the practical aspects of various types of stopped-flow and rapid-quench-flow experiments can be found in the following references [58,59,60,61,62,63,64,65]. Some less common but highly powerful techniques in enzymology, like flash photolysis and relaxation methods (temperature-, pH- or pressure-jump) are not limited by mixing hydrodynamics and enable monitoring down to picosecond and microsecond ranges, respectively [49,61]. Light-dependent enzymes are highly suited to transient-state kinetic analyses using rapid-reaction techniques, since all reaction components can be mixed before the catalysis is initiated with a short pulse of light (flash photolysis), enabling reaction monitoring on extremely fast time scales using various techniques [66]. For example, DNA photolyases were investigated this way in many studies over decades, including with ultrafast absorption and fluorescence spectroscopies that enabled femtosecond resolution [67,68,69]. More recently, the kinetic dissection of the reaction steps in a novel light-dependent fatty acid photodecarboxylase has been demonstrated, using a combination of advanced flash photolysis techniques including ultrafast fluorescence and transient absorption spectroscopies and time-resolved serial femtosecond crystallography, enabling the resolution of intermediates down to a range of a few hundred picoseconds and providing important insights into the reaction mechanism [70].

While transient-state kinetics has little direct relevance to the application of enzymes in the fields of biocatalysis and enzyme technology, the investigation of enzyme reaction pathways via rapid-reaction techniques is essential to deduce the mechanism and working principles of a given enzyme, which can help efforts in enzyme optimization by protein or reaction engineering, as well as helping to understand possible challenges that may be faced in different enzyme applications. Moreover, kinetic characterization of an intermediate will guide the conditions required for its isolation and further characterization. Taken together with static and dynamic structural information, the mechanistic details of an enzymatic pathway are especially important for rational design engineering and de novo enzyme design to mimic native reactions. Without mechanistic information of an enzymatic pathway, transition states and intermediates, it is not possible to design enzymes for a particular reaction [71,72].

Fitting data from transient-state kinetic experiments requires the integration of rate equations for each step; in most cases it is not possible to fit the time-course data (concentration change vs. time; Figure 2) to analytical solutions without significant approximations and simplifications (such as fitting to single and double exponential equations), due to the complexity of the rate equations involved [3,48,51]. Instead, numerical integration of the rate equations based on a proposed mechanism will provide a much better kinetic resolution, with good estimates of the rate and equilibrium constants, as long as sufficient data is obtained to account for the degree of the complexity of the mechanism [48,51]. Precise information on the starting state (active enzyme and substrate concentrations) and response factors (extinction coefficients, concentrations of intermediates), as well as initial estimates of some of the rate constants, are important for a successful least-squares fitting of the data to a kinetic model. Moreover, if one has time-course data from multiple transient-state experiments monitoring different signals (belonging to the same intermediates/products or different intermediates/products) and under different conditions (varying concentrations of enzyme and substrate), all these data can be fitted globally to a single unified mechanism by numerical integration to deduce a single set of rate constants that best account for all the data. Besides data fitting, the data can be simulated in the same way to a certain mechanism to predict rate constants. The difference between fitting and simulations is that all input parameters (rate constants and concentrations) in a simulation are kept constant, whereas at least some of the input parameters are allowed to vary in data fitting. Parameters in a simulation are modified by the user until the simulated time-course traces best match the data. There are various free and commercially available computer programs for enzyme kinetic data fitting and simulations [51,73,74]. Moreover, data from steady-state kinetics can also be integrated into this analysis, e.g., to account for the slowest step as the k_cat or using K_m as an estimate of K_d [20,48]. Recently other type of numerical solutions have been proposed for enzyme kinetic data analysis [45].

Overall, although steady-state and transient-state kinetic experiments require different types of experimental techniques and different analysis methods, they can be complementary as well. A comparison of both techniques is given in Table 2.

Table 2. Comparison of steady-state and transient-state kinetics.

	Steady-State	Transient-State
Time scale	Several seconds to minutes	(Sub)millisecond to second range
Instrumentation	Simple instrumentation like a UV-Vis spectrometer or HPLC	Requires high-tech rapid-reaction equipment
Enzyme quantity needed	nM to few µM range	Varies significantly—from a few µM up to mM range
Relative concentrations of substrate and enzyme	Orders of magnitude higher substrate over enzyme	Substrate excess over enzyme or enzyme excess over substrate
Extracted parameters	kcat, Vmax, Km, Vmax/Km, kcat/Km, Ki, Kd	k1, k−1, k2, k−2, k3, k−3 etc. (as in Scheme 3)
Data analysis	Simple non-linear regression or linear regression	Analytical solutions for simple mechanisms, but mainly numerical integration to fit/simulate data to a single unified mechanism
Nature of rate-limiting step	No direct information (unless experiments like viscosity effect are performed [20])	Direct information possible if all/most intrinsic rate constant are obtained

4. Performance (Productivity) Metrics

While steady-state and transient-state kinetic parameters give information on the intrinsic catalytic properties and kinetic mechanisms of enzymes under conditions that are generally close to the enzyme’s physiological conditions (low concentrations, physiological temperature/pressure and short time scales), they do not provide much insight into the performance of an enzyme under industrially relevant conditions, e.g., high enzyme and substrate concentrations, high temperatures, presence of organic solvents, harsh agitation and long reaction times. This information is generally obtained through a set of parameters, often called performance or productivity metrics. Precise and consistent reporting of enzyme catalytic performance metrics is essential for the clear communication and reliable interpretation of experimental results in the application-oriented fields of biocatalysis and enzyme technology, where economic and environmental feasibility of using an enzyme in a catalytic process is crucial. Besides steady-state kinetic parameters, terms such as conversion, yield, selectivity, productivity, space-time yields, total turnover numbers and stability parameters are widely used in biocatalysis. However, unlike transient-state and steady-state parameters (which report well-defined rate and binding constants), the reporting and interpretations of performance parameters often vary largely between publications and research groups. As a result, even experienced practitioners may encounter ambiguity or confusion when comparing data sets across studies. These challenges are not merely semantic: differences in how key metrics are calculated or reported can lead to misunderstandings about enzyme performance, hamper reproducibility and obscure the impact of experimental variables. This is particularly relevant as enzyme technology continues to advance, with increasing attention to enzyme stability, process intensification and the integration of kinetic and thermodynamic data to characterize biocatalysts comprehensively.

The standardization of enzyme performance metrics is crucial for biocatalysis. Although several guidelines have been proposed to standardize the reporting of enzymatic data [4,75,76], inconsistencies remain common in the literature. In many cases, basic questions—such as whether a reported “yield” refers to substrate conversion or isolated product, or whether “turnover frequency” has been determined under initial velocity conditions—are left unanswered. For many researchers and practitioners of enzyme technology, this lack of clarity can be a significant obstacle to designing robust experiments and presenting data transparently.

A common confusion lies in distinguishing between conversion and yield, which are some of the most widely used performance metrics for enzymes, especially in preliminary studies, and generally measured after the reaction is allowed to proceed for a certain time before being quenched (few minutes to hours and days—depending on enzyme inactivation or degree of completion). Conversion refers specifically to the depletion of the substrate at the end of a reaction period, regardless of what products are formed, and is typically expressed as a percentage (%) or decimal. Therefore, determining conversion requires accurate knowledge of the substrate’s initial and residual concentration at the end of the reaction. Yield, by contrast, quantifies the formation of a desired product relative to the initial amount of substrate after quantification, either by direct analytical measurement of the reaction content or by measuring isolated product (analytical yield vs. isolated yield). The common mistake here would be reporting “yield” based on substrate disappearance without isolating or quantifying the actual product. When side reactions or incomplete transformations occur, the discrepancy between conversion and yield can be substantial. A reaction with 90% substrate conversion may only yield 50% of the desired product if byproducts are formed (either enzymatically or non-enzymatically). In such cases, selectivity becomes a crucial parameter, reflecting the distribution of products and the enzyme’s preference for a specific transformation.

Beyond conversion and yield, which are not based on reaction duration, a range of time-dependent parameters are used to describe catalytic performance in biocatalysis. Specific activity, steady-state parameters (like k_cat, k_cat/K_m) and TOF each capture different aspects of enzymatic behavior. Specific activity, reported in units (U; μmol·min⁻¹) per milligram of protein (U·mg⁻¹), provides a quick and practical measure of overall enzyme performance under defined assay conditions. However, it reflects only the apparent rate of catalysis in a given preparation and does not reveal mechanistic information such as substrate affinity, catalytic turnover (k_cat) or the nature of the rate-limiting step. In addition, reporting only volumetric activity (U mL⁻¹) is less informative, as it depends on enzyme concentration and cannot be compared across studies. Thus, to enable consistent comparison between studies reporting enzyme activity as specific activity (U·mg⁻¹) or volumetric activity (U·mL⁻¹), it is essential to normalize activities based on the actual amount of enzyme present in the reaction. Determining the protein (or active-site) concentration or the mass of the catalytically active enzyme allows for conversion between these units, ensuring that reported activities accurately reflect intrinsic catalytic performance rather than differences in enzyme loading or assay volume. On the other hand, as described in Section 2, k_cat is a fundamental kinetic constant that measures the number of catalytic cycles per active site per time under saturating substrate conditions, and k_cat/K_m offers a measure of catalytic efficiency that incorporates both binding affinity and catalytic turnover [19]. The term “turnover frequency” (TOF), often used in the broader catalysis literature, describes the rate of product formation per mole of catalyst but is sometimes used in enzymology without clear reference to saturating conditions or initial rates [76]. The inconsistent use of TOF and k_cat (both have the same unit of reciprocal time), particularly in the absence of full kinetic characterization, can lead to misinterpretation and overestimation of enzyme efficiency. Quantitatively, these parameters are related but represent different levels of observation. k_cat is the maximum turnover number per active site under saturating, steady-state conditions. TOF describes the observed turnover number under the actual experimental setup and may be lower than k_cat if the substrate is not saturating or if deactivation occurs. TTN (total turnover number) indicates the total moles of product per mole of catalyst over the enzyme’s lifetime and is especially valuable for describing biocatalyst efficiency and long-term usability [77]. When combined with enzyme stability metrics (see below), TTN can help to assess the overall performance and economic viability of a biocatalytic process [76,77]. Turnover number (TON) is also frequently reported in various studies, but with some ambiguity; TON is sometimes used to mean the same as TOF or k_cat, whereas in some cases, it is used to represent TTN. This should be clearly defined in reporting; units will reveal the distinction between some of these different terms (TTN will be unitless and TOF will have reciprocal time units); however, if TOF is reported based on the TTN per total reaction time, it would not reflect a very meaningful parameter since the rate of the enzyme may decrease significantly during long reaction times due to enzyme inactivation. An accompanying time-course will give higher confidence in reporting TOF, TON and TTN, revealing more insight into the enzyme’s long-term performance, since enzyme inactivation will eventually occur due to various factors such as enzyme denaturation or product inhibition.

Other performance metrics take into account reactor volume and are more relevant to preparative and semi-industrial scale applications. Volumetric productivity, defined as the mass of product formed per unit reactor volume per hour (g·L⁻¹·h⁻¹), is a key measure of process efficiency and scale-up potential. Space–time yield (STY), which measures the efficiency of a reactor system by quantifying the amount of product generated per unit of reactor volume over a specific time period, often used interchangeably with volumetric productivity, is widely adopted in chemical engineering and provides a standardized measure for comparing different reactor configurations or enzyme formulations. Biocatalyst yield, calculated as the amount of product formed per mass of enzyme used, reflects the economic efficiency of a catalyst, particularly in large-scale or cost-sensitive applications [78].

As the field of biocatalysis increasingly intersects with green chemistry, environmental metrics such as the E-factor and process mass intensity (PMI) have gained as much importance as the performance metrics. The E-factor measures the mass of waste generated per unit mass of product [79], while PMI accounts for the total mass of input materials per mass of product [80]. These parameters, though not measures of catalytic efficiency per se, provide valuable insight into the environmental footprint of biocatalytic processes. However, they should be interpreted with caution, especially in academic settings where solvent recovery, downstream purification and energy use are often not fully accounted for. Nonetheless, reporting E-factor and PMI can help contextualize enzyme performance within broader sustainability goals and may guide decisions about process optimization or enzyme reuse [81,82].

Enzyme performance over time can be captured using (thermo)stability metrics. The most widely reported stability metric is the enzyme’s half-life (t_1/2), defined as the time required for a 50% loss of catalytic activity under specified conditions. It is particularly valuable when evaluating an enzyme’s durability during extended reactions or under continuous processing. However, this measure alone does not provide information about the structural integrity of the protein, since the activity can also be lowered by other effects such as product inhibition. Thermostability is frequently assessed through thermal denaturation experiments, which yield parameters like the $T_{50}^{10}$ value (determined by the temperature where the enzyme has lost 50% of its activity after 10 min), inflection point (IP) from unfolding curves and the melting temperature (Tₘ). These terms are often used to indicate stability, but important distinctions exist between them. Tₘ refers to the midpoint temperature at which half the protein population is unfolded. It is a thermodynamic parameter, ideally derived from equilibrium unfolding experiments. In contrast, the inflection point (IP) is calculated directly from the derivative of the unfolding curve, representing the point of maximal slope during unfolding. While both values are often numerically similar, they are not identical in principle, especially in well-behaved unfolding curves—Tₘ requires more stringent data quality and assumptions, such as defined baselines and reversible unfolding. IPs, while more approximate, are more practical when dealing with noisy data or irreversible aggregation [83]. Heating rates also influence these values; slower rates approximate equilibrium conditions better, whereas fast ramps (e.g., 1 °C/min) may deviate significantly from true thermodynamic behavior [84]. In practice, both metrics are often used in publications, but it is essential to report how they are derived and under what conditions, as this choice can significantly affect the interpretation of enzyme stability.

Ambiguous terminology of catalytic parameters and performance metrics remains one of the most persistent challenges in the field of biocatalysis. Terms such as yield, conversion, activity and stability are often used without clear definition, leading to confusion and misinterpretation. Each metric should therefore be explicitly defined in reporting and clearly linked to the corresponding method of determination. A list of important performance metrics with their definition, key data required for their determination and their typical reporting formats are given in Table 3.

Table 3. Important biocatalytic metrics, required experimental data for their calculation and preferred reporting formats *.

Category	Metric	Brief Definition/Purpose	Key Data Required	Typical Reporting Format
Substrate and Product Quantification	Conversion (X)	Fraction of substrate consumed	Initial and residual substrate	%; specify analytical method
	Yield (Y)	Desired product formed vs. substrate	Product or isolated amount	%; clarify isolated/ calculated
	Selectivity (S)	Ratio of target to total products	Product distribution	%; specify detection method
Catalytic performance	Specific activity	Rate normalized by enzyme mass	Reaction rate, protein conc.	U·mg−1; report conditions
	kcat	Catalytic cycles per active site per time	Vmax, active-site conc.	s−1; specify assay temp.
	kcat/Km	Catalytic efficiency (turnover + affinity).	Initial rates at varying [S].	M−1·s−1; include fit/error
	TOF	Moles of product per mole catalyst per time	Product formation rate, catalyst amount	h−1 or s−1; note if initial/overall
Stability	t½	Time for 50% activity loss	Residual activity vs. time	min or h; include temp./medium
	$T_{50}^{10}$	Temp. giving 50% activity after 10 min.	Activity after heat challenge	°C; state assay time
	Tm/IP	Midpoint or inflection of unfolding.	Thermal-denaturation curve	°C; note method/heating rate
Process and Productivity	TON/TTN	Moles of product per mole of enzyme (defined time or lifetime)	Product and enzyme amount	mol product; mol−1 enzyme.
	Volumetric productivity/STY	Product formed per reactor volume per hour	Product conc., reaction time	g·L−1·h−1; specify reactor type
	Biocatalyst yield	Product mass per enzyme mass	Product mass and enzyme mass	g product; g−1 enzyme.
Environmental	E-factor	Waste mass/product mass	Waste and product quantities	kg waste; kg−1 product.
	PMI	Total input mass/product mass	Total input and product quantities	kg input; kg−1 product.

* All metrics should be reported together with reaction conditions (temperature, pH, solvent, concentrations, time and enzyme purity). When reporting kinetic parameters, include number of replicates, fitting model and error estimates. For clarity, distinguish between initial rate and overall (or long-time) conversion data and indicate whether values are apparent (k_cat,_app, K_m,_app) or derived under steady-state conditions.

5. Homogeneous vs. Heterogeneous Enzyme Catalysis

Most kinetic analyses assume homogeneous conditions (where enzymes and substrates are uniformly distributed in solution), which is largely true with soluble enzymes and soluble substrates. However, many practical biocatalytic systems are carried out under heterogeneous conditions. This includes immobilized enzymes, enzyme–nanoparticle hybrids, whole cell biocatalysis and interfacial catalysis involving insoluble or partially soluble substrates (e.g., lipases). In addition, enzymes in biological systems are also subject to heterogeneity in their physiological environment [85]. In such systems, the observed kinetic behavior is influenced not only by intrinsic enzyme properties but also by mass-transfer and diffusion phenomena, which can obscure the true kinetic parameters [86,87,88].

Heterogeneous conditions introduce an additional layer of complexity because substrate diffusion [89], boundary-layer effects [90] and local concentration gradients [91] determine the rate of substrate access to the active site. As a result, the experimentally measured kinetic constants often represent apparent parameters (k_cat,_app, K_m,_app) rather than the conventional kinetic parameters observed under conditions free of mass-transfer limitations.

To accurately interpret kinetic data in heterogeneous systems, it is critical to (i) evaluate external and internal diffusion limitations (e.g., using effectiveness factors or Thiele modulus) [92], (ii) report experimental details such as particle size, agitation speed and substrate solubility and (iii) apply models that separate chemical reaction steps from mass-transport steps. Ignoring these factors can lead to inaccurate estimation of kinetic parameters such as k_cat and K_m, resulting in misleading comparisons with homogeneous systems. A comparative overview of the main differences between homogeneous and heterogeneous enzymatic systems is presented in Table 4.

Table 4. Comparison of kinetic characteristics between homogeneous and heterogeneous enzymatic systems.

Feature	Homogeneous Enzymatic System	Heterogeneous Enzymatic System
Phase behavior	Single phase (enzyme and substrate both soluble)	Multiple phases; substrates may be insoluble (oil, polymer, etc.), requiring an interface for reaction
Mass transfer	Negligible; uniform distribution of enzyme and substrate(s)	Can limit observed rate due to diffusion and boundary-layer effects
Kinetic parameters	kcat, Km describe true enzyme performance	kcat,app, Km,app depend on diffusion efficiency and immobilization support properties
Normalization basis	Enzyme concentration	Immobilized enzyme mass or reactor volume
Experimental control	Homogeneous mixing; substrate fully accessible	Sensitive to agitation, particle size and support porosity
Rate limitation	Reaction-controlled (intrinsic rates of chemical steps)	Often diffusion-controlled at high substrate loadings
Interpretation of kinetic constants	Reflect enzyme–substrate chemistry	Reflect combined effects of catalysis and mass transfer

Overall, homogeneous enzyme catalysis offers the simplicity of direct kinetic interpretation without mass-transfer complications, whereas heterogeneous enzyme catalysis requires careful analysis of apparent kinetics. The kinetic parameters in heterogeneous systems must be viewed as composite values influenced by both the intrinsic catalytic properties of the enzyme and the physical transport processes of substrates. By understanding the distinction between intrinsic and apparent parameters and accounting for diffusion effects, one can properly evaluate and compare the performance of heterogeneous biocatalysts to their homogeneous counterparts. This comprehensive perspective ensures that steady-state kinetic parameters, intrinsic rate constants and performance metrics are correctly interpreted for enzyme applications ranging from soluble enzyme reactions to immobilized enzyme reactors.

6. Future Trends and Outlook

Structured and transparent reporting frameworks will play an increasingly vital role in enzymology and biocatalysis. Following the FAIR principles (Findable, Accessible, Interoperable and Reusable) ensures that kinetic data can be effectively integrated, compared and reused [93]. The STRENDA guidelines (https://www.beilstein-institut.de/en/projects/strenda/guidelines/) (accessed on 8 November 2025) provide a general robust checklist for reporting enzymology data [94,95,96,97], while the harmonized terminology proposed by Gardossi et al. promotes the consistent use of catalytic metrics in biocatalysis [75]. To facilitate the implementation of STRENDA guidelines, EnzymeML (https://enzymeml.org/) (accessed on 8 November 2025) was recently developed as a convenient data exchange format to document enzymology information like reaction conditions, time-course data and kinetic parameters, in line with FAIR principles [98,99]. Adopting such frameworks strengthens data transparency, reproducibility and interoperability, building a foundation for large-scale comparative and computational analyses.

Emerging computational technologies are reshaping how enzyme kinetics are studied. The integration of artificial intelligence (AI) and machine learning (ML) allows for the rapid exploration of complex kinetic landscapes and the prediction of catalytic constants directly from sequence or structural data. These tools can also optimize kinetic models by identifying hidden correlations among parameters, conditions and conformational dynamics. Some examples of recent advances include DLKcat, a deep-learning approach that predicts k_cat values from substrate structures and protein sequences [100], and CatPred, a framework for predicting k_cat, K_m and K_i values with built-in uncertainty estimation [101]. Such data-driven models highlight a paradigm shift toward predictive and standardized enzymology, where AI-assisted workflows can accelerate both enzyme discovery and rational design.

7. Conclusions

Using the right kinetic parameters in the right place is of utmost importance in correctly evaluating an enzymatic system for a given purpose. Lack of reporting of the necessary kinetic and thermodynamic parameters, insufficient explanation of the parameters and incomplete experimental descriptions represent the biggest challenges in the standardized reporting of enzyme characterization data. Without essential details such as substrate and enzyme concentrations, buffer composition, pH, temperature, reaction time, stirring conditions, etc., results cannot be reproduced or accurately compared. Kinetic parameters like k_cat and K_m must be derived under steady-state conditions; when these assumptions are not satisfied, the resulting values should be reported as apparent constants (k_cat,_app and K_m,_app). Likewise, reporting volumetric activities (U·mL⁻¹) without normalization to enzyme mass or active-site concentration prevents meaningful cross-study comparison.

The omission of error estimates further reduces data reliability. Reporting single-point values without replicates or standard deviations gives a false impression of precision. Including even approximate uncertainty ranges communicates the robustness of kinetic fits and experimental reproducibility. Researchers should also clarify the basis for any “relative activity” data in their reporting, explicitly defining what condition represents 100% reference activity. Through precise reporting and adherence to standardized frameworks, researchers can ensure that enzymology and biocatalysis progress toward greater transparency, reproducibility and shared understanding.