High-throughput and reliable acquisition of in vivo turnover number fuels precise metabolic engineering

Abstract

As synthetic biology enters the era of quantitative biology, mathematical information such as kinetic parameters of enzymes can offer us an accurate knowledge of metabolism and growth of cells, and further guidance on precision metabolic engineering. k_cat, termed the turnover number, is a basic parameter of enzymes that describes the maximum number of substrates converted to products each active site per unit time. It reflects enzyme activity and is essential for quantitative understanding of biosystems. Usually, the k_cat values are measured in vitro, thus may not be able to reflect the enzyme activity in vivo. In this case, Davidi et al. defined a surrogate $k_{max}^{vivo}$ (k_app) for k_cat and developed a high throughput method to acquire $k_{max}^{vivo}$ from omics data. Heckmann et al. and Chen et al. proved that the surrogate parameter can be a good embodiment of the physiological state of enzymes and exhibit superior performance for enzyme-constrained metabolic model to the default one. These breakthroughs will fuel the development of system and synthetic biology.

Traditional synthetic biology and metabolic engineering focus more on the trial-and error-based pathway engineering, which consumes lots of time and effort. With the development of big data and machine learning, synthetic biology has evolved to the era of quantitative biology, and it is possible to conduct precise metabolic engineering guided by rational design like multi-scale data processing and learning from microbial intelligence. For this purpose, mathematical parameters are crucial for a better knowledge of cell growth and metabolism [1], [2]. Among them, k_cat is considered as one of the most important parameters that illustrate the basic metabolic activities.

k_cat values, also called the turnover numbers, are parameters describe the maximum number of substrates converted to products per unit time per active site. It is a quantitative measurement of enzyme activity. The k_cat values are defined by equation (1),

$$k_{cat}=\frac{v_{max}}{E_0}$$ (1)

where v_max is the maximum reaction rate and E₀ is the concertation of the enzyme. In system and computational biology, the k_cat values are adopted for enzyme-constrained genome scale models, which offers a better understanding of metabolic activities of living cells [2]. Also, k_cat values can provide quantitative guidance for pathway engineering and metabolic reconstitution (Fig. 1). To this end, it is important to develop strategies for k_cat acquisition.

Fig. 1.

Stages of the development of k_cat extraction methods for higher throughput and better coverage.

k_cat values are normally obtained from protein expression assays by a low throughput way (Fig. 1), which is labor-intensive and time-consuming [3]. Indeed, the in vitro k_cat measurements differ among literatures and only 9% of k_cat values of the well-studied Escherichia coli are available [4]. Furthermore, the in vitro k_cat may not be a true reflection for in vivo scenarios since the conditions are significantly changed [5]. Actually, the k_cat value varies according to pH, buffer, temperature, and immobilization. For example, the in vitro k_cat of catalase varies from 11 s^-1 to 151 s^-1 due to changes in pH and buffer in E. coli [6]. Therefore, it is an urgent necessity for a universal method to estimate k_cat data that well matching the in vivo scenarios.

To address the aforementioned issues, Davidi et al. defined k_app, as a surrogate for in vitro k_cat [7]:

$$k_{app,ij}=\frac{v_{ij}}{E_{ij}}=\eta k_{cat,ij}$$ (2)

$$k_{app,maxi}=k_{cat,i}$$ (3)

where v_ij is the reaction rate of i-th enzymatic reaction under j-th cultivation conditions. E_ij is the enzyme concentration. η is a condition-dependent function, ranging between 0 and 1, which describes the decrease in the catalytic rate. The $k_{app,maxi}$ values represent the maximum turnover number under optimal state among varied cultivation conditions. It can be determined when the growth condition pools are large enough. Davidi et al. tested 31 different growth conditions and proteomic data Eij were extracted (Fig .1). For the reaction rate, flux balance analysis (FBA) was adopted for the calculation of v_ij. The $k_{app,maxi}$ values were then determined. Comparison of $k_{app,maxi}$ values with in vitro k_cat values for E. coli yielded a correlation factor of R² = 0.62, indicating a good agreement for in vivo and in vitro situations [7]. Chen et al. used the same method to obtain the k_app data of yeast and the correlation analysis results in a R² = 0.26, which suggested a high in vivo and in vitro discrepancy. The in vitro k_cat values of yeast were further analyzed by Chen et al. and the authors found that the weak correlation is caused by the heterologous expression of enzymes. Exclusion of these heterologous expressed enzymes led to a better R² = 0.41 but still not as good as for E. coli [8].

However, since the metabolic flux v_ij is calculated by FBA in the method, such estimation can be limited by poor FBA accuracy or incomplete genome-scale model, and the robustness of the k_app in response to various perturbations remains unclear [9]. Therefore, Heckmann et al. proposed a ¹³C metabolic flux analysis (MFA) based method for k_app predication [9] (Fig. 1). To obtain the v_ij data, E. coli cells with various knockouts of central metabolism were cultivated in minimum medium with glucose. The resulting cultures were then subjected to MFA to generate v_ij of 21 strains from adaptive laboratory evolution (ALE) [10], [11]. The MFA based $k_{app,maxi}$ showed good consistency with $k_{app,maxi}$ by FBA with R² = 0.9, indicating this method a good complementation for the systems lacking FBA data. Heckmann et al. [9] and Chen et al. [8] then applied k_app to the enzyme-constrained metabolic model and found that model with k_app showed better performance in compared with the original one. It is clear that flux data and proteome data from the well characterized species under the certain cultivation conditions are available and reliable. Although getting omics data under different cultivation conditions is still a tedious process for non-model organisms, the work flow and protocols, as described in this comment, are available to some extent.

The above summarized methods can effectively and unfailingly measure the k_app in a high-throughput way currently. However, the coverage is still limited. To address this issue, Chew et al. developed a 3D convolutional neural network to predict enzymatic catalysis rates based on experimental reaction data and corresponding molecular dynamics simulation data, which can be used to predict flux data [12]. It is worth mentioning that Heckman et al. [9] made use of machine learning to extrapolate the k_app to genome scale, which combined with the 3D structure and biochemical characteristics of enzymes in the database to further estimate the k_app for enzymes suffering from coverage issue of proteomic techniques [13]. This method offered another perspective for k_app calculation despite the availability of the structural information and biochemical property is limited for some enzymes of interest. Thus, Feiran Li et al have developed a deep learning based k_app data prediction, which exploited the most extensive and common information, like amino acid sequences and substrate structures to detect the k_cat values for better coverage of the enzymes in the system [14].

In summary, the development of k_cat data can be divided into three stages (Fig. 1). For the original k_cat measurement, in vitro assays were utilized, and the reaction data was fit to Michaelis-Menten equation [15], [16], [17]. Then methods integrating proteomics data together with FBA or MFA were introduced based on equation (1), (2) and (3) [7], [8], [9]. Currently, a more coverage method regarding the machine learning is being developed for generic k_app prediction. This shows that k_app data extraction methods are transitioning from a low-throughput, low-coverage approach to a high-throughput, high-coverage, high-accuracy approach.

In the outlook, the accurate and complete dataset of k_cat/k_app provides us another mathematical measurement in addition to transcriptome, proteome and metabolome and reveals the quantitative picture of genome scale metabolic network. On the one hand, k_app based enzyme-constrained metabolic model can presumably be improved for better depiction of intrinsic growth and metabolic activities of cells. On the other hand, kinetic features can effectively provide theoretical guidance for metabolic engineering modification and further realize the transformation from random trial-and-error to rational design. The development of k_cat values will support a revolutionary progress for synthetic biology and metabolic engineering.

Declaration of competing interest

The authors indicate that they have no conflict of interest.