# Multi-Target In Silico Prediction of Inhibitors for Mitogen-Activated Protein Kinase-Interacting Kinases

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Dataset and Calculation of Molecular Descriptors

_{j}). The latter are better expressed as an ontology [10,11,12,13] of the form c

_{j}→ (b

_{t}, m

_{e}, a

_{t}), that is, by defining them according to the following elements: b

_{t}—the ‘biological target’, accounting for the specific MNK enzyme isoform against which the compounds have been tested, m

_{e}—the kind of ‘measures of biological effects’ considered, namely, half-maximal inhibitory concentration (IC

_{50}), inhibition (K

_{i}) or dissociation (K

_{d}) constants, and a

_{t}—the ‘assay type’, focusing on either the binding affinity (B) or functional (F) responses. As such, each data-point of the input dataset pertains to one specific combination of the elements b

_{t}, m

_{e}, and a

_{t}or experimental condition c

_{j}, and then classified into two categories: positive (IAc

_{j}= +1; for high inhibitory potential) or negative (IAc

_{j}= −1; for low inhibitory potential). We selected a unique cut-off value for all measures of biological effects for classifying the data-points as positives (m

_{e}> 100 nM). The low sub-micromolar cut-off values ensured a more stringent search for potent hits using the mt-QSAR models.

_{j}value and experimental conditions (details of this input dataset are given in Table S1). Then, the SMILES structures of the compounds were first converted to 2D structures (.sdf format) using the MarvinView software (https://docs.chemaxon.com/display/docs/marvinview.md, accessed on 7 June 2021). Subsequently, these structures were standardized by resorting to the ChemAxon Standardizer tool using the following options: strip salts, aromatize, neutralize and add explicit hydrogen atoms [14]. The starting molecular descriptors were calculated with such standardized structures with the newly launched AlvaDesc.v.0.1 software [15] by employing the OCHEM webserver [16]. For the calculation of 3D descriptors, a geometry optimization of the compound structures was carried out using Corina [17].

_{i})c

_{j}) for both such sets using the simplest method— ‘Method1’ of QSAR-Co-X [18], that is represented as follows:

_{i}stands for the input starting descriptors and avg(D

_{i})c

_{j}for their averages—i.e., arithmetic means of active chemicals for a specific element of the ontology c

_{j}.

#### 2.2. Model Development and Evaluation

#### 2.2.1. Linear mt-QSAR Models

#### 2.2.2. Post-Selection Similarity Search-Based Modification

_{1}and D

_{2}) is simply calculated as follows:

#### 2.2.3. Non-Linear mt-QSAR Models

#### 2.2.4. Model Evaluation

_{c}-randomization test, which is a modification of the Y-randomization test [30]. In the Y

_{c}randomization test, both the dependent parameters and the experimental elements were scrambled 100 times to produce randomized Box–Jenkins modified descriptors for producing new randomized models. The average of the Wilks λ values (λ

_{r}) and that of the randomized accuracy (Accuracy

_{r}) were then compared to the corresponding parameters of the original model to check the uniqueness of the latter. Additionally, another parameter named random accuracy ($Ac{c}_{rnd}$) was proposed by Lučić et al. [31,32], and it is calculated using the following formulae:

_{r}, $Ac{c}_{rnd}$ is also compared to the original accuracy value of the model and a large difference of the latter with the original accuracy of the model clearly demonstrates that the classification model provides a significant level of useful information over the maximal level of random accuracy [31,32].

#### 2.3. Similarity Search Analysis

#### 2.4. Molecular Dynamics Simulations

^{−1}by keeping the complex fixed for 200 ps. This heating process was followed by equilibration for 2 ns in the NVT ensemble (T = 300 K), and then 50 ns MD simulations without any restrictions were run in the NpT ensemble at constant T = 300 K and p = 1 atm.

## 3. Results and Discussion

#### 3.1. Multi-Target QSAR Models

^{2}) between any two descriptors of the model was found to be 0.66. Furthermore, we performed a Y

_{c}-randomization test that, with 100 runs, provided λ

_{r}and Accuracy

_{r}values of 0.993 and 64.97%, respectively. Therefore, it can be assumed that the generated model is unique and not developed by chance, as the scrambled parameters destabilize the goodness-of-fit of the models and at the same time, the accuracy regarding the sub-training set is reduced to a considerable extent. Furthermore, comparatively small $Ac{c}_{rnd}$ values were obtained for each set of the final models, indicating that this model is capable of providing significant information at the maximal level of random accuracy [31,32]. The ROC plot of this final mt-QSAR model is shown in Figure 2, which clearly indicates a high predictive accuracy of the final model. More specifically, the AUROC scores obtained are 0.912, 0.923 and 0.878 for the sub-training, test and validation sets, respectively.

_{t}, m

_{e}and b

_{t}) contributed to the development of the final mt-QSAR model, clearly indicating their influence. The significance of the descriptors appearing in the final mt-QSAR model can be inferred from their absolute standardized coefficients that are depicted in Figure 2. Interestingly, two of the most significant descriptors of the model (i.e., $\mathsf{\Delta}(\mathrm{C}-012{)}_{{m}_{e}}$ and $\mathsf{\Delta}(\mathrm{C}-012{)}_{{a}_{t}}$) are derived from the same descriptor C—012, which simply represents a molecular fragment of the type CR2 × 2 (where R is alkyl group and X is any heteroatom). A positive contribution to higher inhibitory potential is found when the modified descriptor derived from this fragment relates to the experimental element m

_{e}(measures of biological effects). However, a negative influence is noted when it is related to the other experimental element, i.e., a

_{t}(assay type). It infers that the CR2 × 2 fragment is definitely a significant contributor in determining the higher inhibitory potential of the compounds, but its role may vary on the basis of experimental conditions. Descriptor $\mathsf{\Delta}(\mathrm{S}-109{)}_{{b}_{t}}$ emerges as the third most influential descriptor of the model, which is based on another atom-centered fragment S—109 (presence or absence of an R–SO–R fragment) and the experimental element b

_{t}(biological target). It shows a positive correlation with the response variable, indicating that the fragment R–SO–R may have a favorable influence on the higher inhibitory potential of the compounds against these enzymes. Chemically advanced template search (CATS) descriptors are a very useful category of descriptors that attempt to explain the structural requirements on the basis of various pharmacophore groups, along with the topological distances that separate these [50]. For example, $\mathsf{\Delta}(\mathrm{CATS}2\mathrm{D}\_09{\_\mathrm{DA})}_{{m}_{e}}$, which shows a positive relationship with biological activity, is based on hydrogen bond donor and acceptor features located at a topological distance of nine. The fifth most important descriptor of the model is $\mathsf{\Delta}\left(F08\right[\mathrm{C}-{\mathrm{O}\left]\right)}_{{m}_{e}}$, which is an atom-pair descriptor accounting for the frequency of C–O at a topological distance of eight. Both these two latter descriptors are dependent on the experimental element m

_{e}. However,$\mathsf{\Delta}\left(F08\right[\mathrm{C}-{\mathrm{O}\left]\right)}_{{m}_{e}}$ showed a negative relation with the higher inhibitory potential. The remaining five descriptors of the models are graph-based topological descriptors. Two of them, i.e., descriptors ${\mathsf{\Delta}(\mathrm{VE}2\_D/Dt)}_{{m}_{e}}$ and ${\mathsf{\Delta}(\mathrm{VE}1\mathrm{sign}\_D/Dt)}_{{b}_{t}}$, are 2D matrix-based descriptors derived from the distance/detour matrix, standing namely for the average coefficient of the last eigenvector (VE2_D/Dt) and for the coefficient sum of the last eigenvector (VE1sign_D/Dt). The presence of such descriptors in the model indicates that topological distributions of mass, charge and lipophilicity in the compounds contribute significantly to determining the inhibitory potential of the compounds [51]. The importance of topological distributions of polarizability and dipole moments is reflected by descriptors such as ${\mathsf{\Delta}\left(\mathrm{GATS}3p\right)}_{{a}_{t}}$ and ${\mathsf{\Delta}(\mathrm{SpMAD}\_\mathrm{AEA}(\mathrm{dm}\left)\right)}_{{b}_{t}}$. The former GATS3p is a 2D-autocorrelation descriptor that stands for the Geary autocorrelation of lag 3 weighted by polarizability. Similarly, SpMAD_AEA(dm) is a graph-based edge-adjacency index that stands for the spectral mean absolute deviation from the augmented edge adjacency matrix weighted by the dipole moment. Finally, the least significant descriptor ${\mathsf{\Delta}(\mathrm{HyWi}\_\mathrm{B}(\mathrm{s}\left)\right)}_{{b}_{t}}$ is also another 2D matrix-based descriptor that represents the hyper-Wiener-like index (log function) from the Burden matrix, weighted by the intrinsic state of the atoms [52].

_{e}: K

_{i}, a

_{t}: B, b

_{t}: MNK-2). Nevertheless, for this condition too an overall accuracy greater than 80% was achieved.

#### 3.2. Virtual Screening of Potential Hits

_{50}, K

_{d}, K

_{i}) of less than 5000 nM against these two drug targets. Such compounds (see Table S5) served as a target dataset whereas 20 virtual hits were used as a query dataset. The similarity searching was done with our in-house tool named SIMSEARCH, which first calculates the ECFP4 fingerprints of all queries as well as the target dataset compounds, and then, computes the Tanimoto similarity between each target and query dataset compound. We took a maximum cut-off value of 0.3 for the Tanimoto similarity to identify those query dataset compounds that show a high structural similarity with the target dataset compounds. Table 4 depicts the number of matches found in this similarity search process. It can be seen that only 14 virtual hits were found to match with at least one target dataset compound with a structural similarity greater than 0.3. In the current work however, we selected the top six query virtual hits that were found to match more than five reported MNK-1/2 inhibitors—these inhibitors are Asn1051, Asn0225, Asn1125, Asn2420, Asn0240 and Asn2447 (see Figure 3).

_{50}and 300 nM for K

_{i}and K

_{d}), this query compound or virtual hit may certainly have much improved the inhibitory potential towards these enzymes, as its structure is similar but not exactly the same as the query compounds.

_{bind}in kcal/mol). As can be seen, save for Asn1125 and Asn2447, all other virtual hits depict theoretical binding free energies less than −35 kcal/mol and, when compared to the positive control eFT508, display a satisfactory binding affinity towards the two enzyme isoforms. The maximum average binding affinity pertains to Asn0225, whereas Asn1051 shows the maximum consistency in the binding free energies against the two MNK isoforms. Overall, the MD results thus indicate that the most promising MNK-1/2 virtual hits are the following compounds: Asn0225, Asn0240, Asn1051 and Asn2420.

## 4. Conclusions

## Supplementary Materials

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 2.**ROC plot of the final mt-QSAR model (

**left**) and the absolute standardized coefficients of its descriptors (

**right**).

**Figure 4.**Six target dataset matches of Asn1051, with reported MNK-1/2 activity in the Binding Database, found by the similarity search analysis.

**Figure 5.**(

**A**) RMSD plot of MNK-2 protein complexes and (

**B**) their associated ligands. (

**C**) RMSD plot of MNK-1 protein complexes and (

**D**) their associated ligands.

**Table 1.**Statistical results of the mt-QSAR models generated with different model building strategies.

Parameters | Linear Model (Ten-Descriptor; FS-LDA) | Non-Linear Model (Ten-Descriptor; RF) | Non-Linear Model (All Descriptor; GB) | ||||||
---|---|---|---|---|---|---|---|---|---|

Sub-Train | Test | Validation | Sub-Train | Test | Validation | Sub-Train | Test | Validation | |

TP | 308 | 88 | 147 | 314 | 81 | 148 | 318 | 87 | 150 |

TN | 674 | 154 | 362 | 653 | 152 | 361 | 660 | 158 | 365 |

FP | 20 | 11 | 20 | 41 | 13 | 21 | 34 | 7 | 17 |

FN | 57 | 12 | 39 | 51 | 19 | 38 | 47 | 13 | 36 |

Sensitivity | 97.12 | 93.33 | 94.76 | 86.03 | 92.12 | 94.51 | 87.12 | 95.76 | 95.55 |

Specificity | 84.38 | 88.00 | 79.03 | 94.09 | 81.00 | 79.57 | 95.10 | 87.00 | 80.64 |

Accuracy | 92.73 | 91.32 | 89.61 | 91.31 | 87.92 | 89.61 | 92.35 | 92.45 | 90.67 |

F1-score | 88.89 | 88.44 | 83.29 | 87.22 | 83.50 | 83.38 | 88.70 | 89.69 | 84.98 |

MCC | 0.838 | 0.815 | 0.76 | na | 0.741 | 0.760 | na | 0.838 | 0.785 |

AUROC | 0.907 | 0.907 | 0.869 | na | 0.866 | 0.870 | na | 0.914 | 0.881 |

**Table 2.**Comparison between the original FS-LDA model and the final LDA model produced by PS3M refinement.

Model | Equation | Sub-Training | Test | Validation |
---|---|---|---|---|

Original (FS-LDA) | $\begin{array}{l}\mathrm{IA}{c}_{j}=+4.003+5.035\hspace{0.17em}\mathsf{\Delta}(\mathrm{N}-078{)}_{{b}_{t}}+1.633\hspace{0.17em}\mathsf{\Delta}(\mathrm{CATS}2\mathrm{D}\_09{\_\mathrm{DA})}_{{m}_{e}}\\ \hspace{1em}\hspace{1em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}+20.515\hspace{0.17em}\mathsf{\Delta}(\mathrm{C}-012{)}_{{m}_{e}}+6.210\hspace{0.17em}{\mathsf{\Delta}(\mathrm{VE}1\mathrm{sign}\_D/Dt)}_{{b}_{t}}+1.608\hspace{0.17em}\mathsf{\Delta}\left(\mathrm{B}03\right[\mathrm{N}-{\mathrm{O}\left]\right)}_{{b}_{t}}\\ \hspace{1em}\hspace{1em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}-0.600\hspace{0.17em}\mathsf{\Delta}\left(F08\right[\mathrm{C}-{\mathrm{O}\left]\right)}_{{m}_{e}}-17.842\hspace{0.17em}\mathsf{\Delta}(\mathrm{C}-012{)}_{{a}_{t}}-45.641\hspace{0.17em}\mathsf{\Delta}(\mathrm{VE}2\_D/Dt\hspace{0.17em}{)}_{{m}_{e}}\\ \hspace{1em}\hspace{1em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}-7.661\hspace{0.17em}{\mathsf{\Delta}\left(\mathrm{GATS}3p\right)}_{{m}_{e}}+16.232\hspace{0.17em}{\mathsf{\Delta}(\mathrm{SpMAD}\_\mathrm{AEA}(\mathrm{dm}\left)\right)}_{{b}_{t}}\end{array}$ Wilks λ = 0.319, F = 224.16, p < 10 ^{−16} | TP = 308 TN = 674 FP = 20 FN = 57 Sn = 97.12 Sp = 84.38 Acc = 92.73 F1 = 88.89 MCC = 0.838 $Ac{c}_{rnd}=55.91$ | TP = 88 TN = 154 FP = 11 FN = 12 Sn = 93.33 Sp = 88.00 Acc = 91.32 F1 = 88.44 MCC = 0.815 $Ac{c}_{rnd}=53.10$ | TP = 147 TN = 362 FP = 20 FN = 39 Sn = 94.76 Sp = 79.03 Acc = 89.61 F1 = 83.29 MCC = 0.760 $Ac{c}_{rnd}=57.11$ |

Final (PS3M) | $\begin{array}{l}\mathrm{IA}{c}_{j}=+4.000+1.532\hspace{0.17em}\mathsf{\Delta}(\mathrm{CATS}2\mathrm{D}\_09{\_\mathrm{DA})}_{{m}_{e}}+21.079\hspace{0.17em}\mathsf{\Delta}(\mathrm{C}-012{)}_{{m}_{e}}\\ \hspace{1em}\hspace{1em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}+6.037\hspace{0.17em}{\mathsf{\Delta}(\mathrm{VE}1\mathrm{sign}\_D/Dt)}_{{b}_{t}}-0.546\hspace{0.17em}\mathsf{\Delta}\left(F08\right[\mathrm{C}-{\mathrm{O}\left]\right)}_{{m}_{e}}-17.982\hspace{0.17em}\mathsf{\Delta}(\mathrm{C}-012{)}_{{a}_{t}}\\ \hspace{1em}\hspace{1em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}-52.531\hspace{0.17em}\mathsf{\Delta}(\mathrm{VE}2\_D/Dt\hspace{0.17em}{)}_{{m}_{e}}+16.415\hspace{0.17em}{\mathsf{\Delta}(\mathrm{SpMAD}\_\mathrm{AEA}(\mathrm{dm}\left)\right)}_{{b}_{t}}+5.531\hspace{0.17em}\mathsf{\Delta}(\mathrm{S}-109{)}_{{b}_{t}}\\ \hspace{1em}\hspace{1em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}-7.509\hspace{0.17em}{\mathsf{\Delta}\left(\mathrm{GATS}3p\right)}_{{a}_{t}}-0.050\hspace{0.17em}{\mathsf{\Delta}(\mathrm{HyWi}\_\mathrm{B}(\mathrm{s}\left)\right)}_{{b}_{t}}\end{array}$ Wilks λ = 0.329, F = 212.86, p < 10 ^{−16} | TP = 310 TN = 677 FP = 17 FN = 55 Sn = 97.55 Sp = 84.93 Acc = 93.20 F1 = 89.59 MCC = 0.848 $Ac{c}_{rnd}=55.94$ | TP = 89 TN = 158 FP = 7 FN = 11 Sn = 95.76 Sp = 89.00 Acc = 93.20 F1 = 90.82 MCC = 0.855 $Ac{c}_{rnd}=53.38$ | TP = 148 TN = 367 FP = 15 FN = 38 Sn = 96.07 Sp = 79.57 Acc = 90.67 F1 = 8 4.81 MCC = 0.785 $Ac{c}_{rnd}=57.35$ |

Condition | m_{e} | a_{t} | b_{t} | Test Set | External Validation Set | ||
---|---|---|---|---|---|---|---|

#Instances | %Accuracy | #Instances | %Accuracy | ||||

1 | IC_{50} | B | MNK-2 | 189 | 88.36 | 107 | 92.52 |

2 | IC_{50} | B | MNK-1 | 104 | 88.46 | 40 | 92.50 |

3 | K_{d} | B | MNK-2 | 20 | 95.00 | 11 | 90.91 |

4 | K_{d} | B | MNK-1 | 31 | 96.77 | 9 | 100.00 |

5 | K_{i} | B | MNK-2 | 19 | 84.21 | 1 | 0.00 |

6 | K_{i} | B | MNK-1 | 15 | 93.33 | 5 | 100.00 |

7 | K_{i} | F | MNK-2 | 190 | 93.16 | 92 | 94.57 |

Query Compounds | Number of Matches | Average MNK-1/2 Activity ^{b} | Average Similarity |
---|---|---|---|

Asn1051 | 45 | 1085.78 | 0.33 |

Asn0225 | 30 | 1218.10 | 0.32 |

Asn1125 | 14 | 646.57 | 0.32 |

Asn2420 | 14 | 36.36 | 0.32 |

Asn0240 | 12 | 608.00 | 0.32 |

Asn2447 | 6 | 22.50 | 0.32 |

Asn0252 | 4 | 2100.00 | 0.33 |

Asn2416 | 3 | 35.00 | 0.32 |

Asn2471 | 3 | 45.00 | 0.31 |

Asn2459 | 2 | 36.50 | 0.31 |

Asn2466 | 2 | 49.00 | 0.32 |

Asn4780 | 2 | 1032.00 | 0.33 |

Asn2422 | 1 | 46.00 | 0.31 |

Asn2458 | 1 | 46.00 | 0.32 |

**All matches in the target dataset show a Tanimoto similarity value greater than 0.3 with the query compound.**

^{a}**In this calculation, if the inhibitory potential of a compound is expressed as < 100 nM, it was considered equal to 100 nM.**

^{b}**Table 5.**ADME, drug-likeness and synthetic accessibility of the virtual hit compounds as predicted by the SwissADME webserver.

Compound | ESOL ^{a}Class | GI ^{b}Absorption | BBB ^{c}Permeant | p-gp ^{d} Substrate | Lipinski #Violations | Veber #Violations | Synthetic Accessibility |
---|---|---|---|---|---|---|---|

Asn0225 | Moderate | High | No | No | 0 | 0 | 3.06 |

Asn0240 | Moderate | High | No | No | 0 | 0 | 3.28 |

Asn1051 | Moderate | High | No | No | 0 | 0 | 2.77 |

Asn1125 | Moderate | High | No | No | 0 | 0 | 2.67 |

Asn2420 | Moderate | High | No | Yes | 0 | 0 | 4.18 |

Asn2447 | Moderate | High | No | Yes | 0 | 0 | 4.44 |

**Estimated aqueous solubility.**

^{a}**GI: Gastrointestinal.**

^{b}**BBB: Blood–Brain Barrier.**

^{c}**p-gp: p-glycoprotein.**

^{d}**Table 6.**Calculated binding free energies (ΔG

_{bind}in kcal/mol) for the MNK-1 and MNK-2 bound ligands.

Query Compounds | MNK-1 | MNK-2 |
---|---|---|

Asn1051 | −40.20 | −37.21 |

Asn0225 | −52.97 | −35.21 |

Asn1125 | −32.32 | −37.45 |

Asn2420 | −38.38 | −48.94 |

Asn0240 | −32.33 | −42.28 |

Asn2447 | −31.88 | −29.71 |

eFT508 | −36.41 | −44.82 |

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## Share and Cite

**MDPI and ACS Style**

Halder, A.K.; Cordeiro, M.N.D.S. Multi-Target In Silico Prediction of Inhibitors for Mitogen-Activated Protein Kinase-Interacting Kinases. *Biomolecules* **2021**, *11*, 1670.
https://doi.org/10.3390/biom11111670

**AMA Style**

Halder AK, Cordeiro MNDS. Multi-Target In Silico Prediction of Inhibitors for Mitogen-Activated Protein Kinase-Interacting Kinases. *Biomolecules*. 2021; 11(11):1670.
https://doi.org/10.3390/biom11111670

**Chicago/Turabian Style**

Halder, Amit Kumar, and M. Natália D. S. Cordeiro. 2021. "Multi-Target In Silico Prediction of Inhibitors for Mitogen-Activated Protein Kinase-Interacting Kinases" *Biomolecules* 11, no. 11: 1670.
https://doi.org/10.3390/biom11111670