Predictions of Enzymatic Parameters: A Mini-Review with Focus on Enzymes for Biofuel

Abstract

Enzymatic reactions are very basic processes in biological systems, and parameters related to enzymatic reactions always provide good indicators for understanding of mechanisms underlined in enzymatic reactions, for better controlling of enzymatic reactions, and for comparison of different enzymes. In this mini-review: first, parameters in enzymatic reactions were briefly reviewed from three different standpoints; second, predictions of parameters in enzymatic reactions without information on enzyme structure were shortly reviewed from viewpoints of geometric approach, graphic approach and compartmental approach; third, predictions of parameters in enzymatic reaction with information on enzyme structure were reviewed from the points of view of modeling, with 19 currently available databases, and 17 software packages and web servers; fourth, the current state of prediction on parameters in enzymatic reaction in biofuel industry with respect to cellulolytic enzymes were reviewed; fifth, the pros and cons for future development were discussed; and finally, a worked example was given in the Appendix to describe the whole procedures of prediction of enzymatic parameters in reactions.

Appendix—a worked example

In order to fully explain the prediction of parameters in enzymatic reaction, here we present a worked example to demonstrate the prediction of K _m in cellulases (EC 3.2.1.4) with all the procedures discussed in the “Current State of Predicting Parameters in Enzymatic Reactions in Biofuel Industry” section.

In BRENDA [38–40], there were four cellulases with their sequence information under the category of K _m as functional parameters, of which two cellulases were documented with their mutants [162]. There were three reduced-size mutants and 17 site-directed mutagenesis from the cellulose O58925 isolated from Pyrococcus horikoshii [163, 164]. Also, two K _m values were documented in each of the cellulose O58925, Q9REW0, and Q9X273. In total, BRENDA provided 29 matched sequences and K _m values of cellulases (Table 6), and their corresponding sequences were found in Universal Protein Resource [165]. The sequences of those 29 enzymes were coded each time with an amino acid property or the amino acid distribution probability, which is a property combining amino acid property and property of whole protein, and coded property served as predictors and their K _m as predicted value in neural network model.

Table 6 Grouped cellulases for training and validation with their recorded and predicted K _m values, where mean ± SD are based on 100 predictions

In this worked example, we used not only the 20-1 feedforward backpropagation neural network to model the relationship between coded enzyme sequences and their K _m values (Fig. 1), but also different combinations of layers and neurons of neural network model, including the models of 20-5-1, 20-10-1, 20-10-5-1, 20-30-10-5-1, and 20-30-20-12-5-1 (Fig. 2).

The issue of convergence can be seen in Fig. 3, which in fact plays a role to screen 25 predictors, that is, the predictors that do not converge should be eliminated from predictions as shown in Table 5 that summarized all our previous studies including this worked example.

As discussed in the “Current State of Predicting Parameters in Enzymatic Reactions in Biofuel Industry” section, linear regression was used to evaluate the predicted K _m with their recorded ones. The Chi-square test was used to compare the predicted K _m, which falls into different ranges of recorded K _m with respect to various predictors. Figure 2 summarizes the predictive performances of six different neural network models with eleven different predictors. This is a process to select the best predictive model among various models, which is important because the Akaike information criterion [166] suggested how to select a model statistically. In Figure 2, R and P values were used to evaluate the predictive performance. As can be seen from top to bottom, the more layers a neural network model has, the better the predictive performance is. However, this improvement is mainly related to the fitting. For the validation, the best performances were obtained from 20-10-1 model, beyond which the increase of neuron layers could not improve the predictions. On the other hand, the problem with multi-layer is that the model parameters increase unnecessarily, which compromise the model identification although the predictions are better. Thus, the 20-10-1 neural network model should be the best choice for predictions. With respect to predictors, the amino acid properties seem to work in a similar way because their predictions are similar while the prediction using the amino acid distribution probability, which combines the properties of both amino acids and whole protein, is better, except the R value for validation. Another characteristic is that amino acid distribution probability can get good predictive performance using 2-layer models, which can dramatically reduce model parameters compared to the use of multi-layer models.

Based on the predicted K _m of cellulases listed in Table 7, we need to furthermore look at the predictive performance in much greater details as showed in Table 6, where we stratified the predicted K _m according to its mean value of 100 predictions with respect to different ranges of recorded K _m. For example, the recorded K _m of cellulase O58925 H155A (row 3 Table 6) was 6.69, so the values less than or equal to ±10 % of 6.69 ranged from 6.021 to 7.359, and we can see that all the predicted K _m using various predictors did not fall into this range (row 3, Table 7). A similar manner was applied to all the ranges listed in Table 7 for all 29 cellulases. As seen in Table 7, the prediction using the amino acid distribution probability as predictor (last column) is statistically better than the predictions using other predictors. Figure 5 displays the results of training and validation groups using the predictor f(i + 1).

Table 7 Predicted K _m within different ranges of recorded K _m with respect to different predictors

Fig. 5

Linear regression between recorded K _m and predicted K _m of cellulases in training and validation groups using the predictor f(i + 1), respectively