# MD Simulations to Calculate NMR Relaxation Parameters of Vanadium(IV) Complexes: A Promising Diagnostic Tool for Cancer and Alzheimer’s Disease

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

_{2}]·H

_{2}O (VC1) and [VO(bpy)

_{2}Cl]

^{+}(VC2), being metformin and bipyridine ligands of the respective complexes, with the biological targets AMPK and ULK1. These biomolecules are involved in the progression of Alzheimer’s disease and triple-negative breast cancer, respectively, and may act as promising spectroscopic probes for detection of these diseases. To initially evaluate the behavior of the studied ligands within the aforementioned protein active sites and aqueous environment, four classical molecular dynamics (MD) simulations including VC1 + H

_{2}O (1), VC2 + H

_{2}O (2), VC1 + AMPK + H

_{2}O (3), and VC2 + ULK1 + H

_{2}O (4) were performed. From this, it was obtained that for both systems containing VCs and water only, the theoretical calculations implied a higher efficiency when compared with DOTAREM, a famous commercially available contrast agent for MRI. This result is maintained when evaluating the system containing VC1 + AMPK + H

_{2}O. Nevertheless, for the system VC2 + ULK1 + H

_{2}O, there was observed a decrease in the vanadium complex efficiency due to the presence of a relevant steric hindrance. Despite that, due to the nature of the interaction between VC2 and ULK1, and the nature of its ligands, the study gives an insight that some modifications on VC2 structure might improve its efficiency as an MRI probe.

## 1. Introduction

_{2}]·H

_{2}O (VC1) and [VO(bpy)

_{2}Cl]

^{+}(VC2), where metf is metformin and bpy is bipyridine, have shown great potential regarding their application to AD and autophagy associated with triple-negative breast cancer, respectively [38,39].

## 2. Results and Discussion

#### 2.1. Calculating T_{i} and R_{i} from MD Simulation Data

_{i}and R

_{i}values for VC1 and VC2, MD simulation data were used to perform the calculations. As proposed by Chen, P. et al. and Villa, A. and Stock, G. [43,44], the NMR spin relaxation parameters can be obtained from MD simulation data. To perform such calculations, the work published by Gonçalves, M. A. et al. [45] shed some light on the procedure. First, the distances V⋯

^{1}H were measured in MD trajectory for each conformation selected by the OWSCA methodology, then the autocorrelations of the measured set of distances were computed and fitted. If it is assumed that the overall internal motion of molecules is independent, then the total correlation function C(t), expressed in Equation (1), can be divided into two different equations, the overall motion correlation function C

_{O}(t) and the internal motion correlation function C

_{I}(t), expressed by Equations (2) and (3), respectively.

_{c}is the rotational correlation time, S

^{2}is the order parameter, and τ

_{e}is the effective correlation time. The three mentioned terms are estimated from the above equations, and once this is done, the spectral density J(ω) can be given by the Fourier transform of C(t), resulting in Equation (4).

^{−1}= τ

_{c}

^{−1}+ τ

_{e}

^{−1}. This equation can be used to determine the longitudinal and transverse relaxation rates and times, according to Equations (5) and (6), respectively.

_{0}= γ·B

_{0}, which represents the rate of precession of the magnetic moment of the proton with an external magnetic field B

_{0}and gyromagnetic radius of hydrogen γ.

_{0}being the vacuum permeability, h being the Planck constant, I being spin quantum number, ϕ being average V⋯

^{1}H distance, as shown in Figure 1, and γ being the gyromagnetic radius of hydrogen. In this work, B

_{0}was considered equal to 1.5 T and γ equal to 42.58 MHz/T. This choice was made because when discussing contrast agents for clinical applications, it is customary to reference R

_{i}and T

_{i}values at 1.5 T and a standard body temperature of 37 °C. [46].

#### 2.2. Validation of the T_{i} and R_{i} Calculations from MD Simulation Data

_{i}and R

_{i}from MD simulation showed to be reliable when reproducing experimental data. Both published works of Gonçalves et al. [45] and Lino et al. [47] used the algorithm explained in the previous section to compute NMR spin relaxation parameters from MD simulation data. Table 1 summarizes the results obtained for validation.

_{1}value of 35.72 s

^{−1}, which was just 4.47 s

^{−1}different from the experimental one, with an R

_{1}value of 31.25 s

^{−1}. For R

_{2}, the obtained value was 55.55 s

^{−1}, only 5.05 s

^{−1}different from the experimentally measured one, which was 50.50 s

^{−1}. In addition, R

_{1}/R

_{2}ratios were very similar, being that the theoretically calculated equals 0.643 and the experimental one is equivalent to 0.619. In addition, from the work published by Lino et al. [47], trichloroethylene (TCE) and iodotrifluoroethylene (TFE) were also used to validate the algorithm. For the theoretical calculations for TCE, C-C distance was used, and for TFE, F-1-F-2 and F-2-F-3 distances were used. For TCE(C-C), the calculated T

_{1}value was 8.98 s, very close to the experimental data value, which was 8.90 s. For TFE(3F-4F) and TFE(5F-3F) the T

_{1}values were 5.35 and 5.52 s, respectively, also very close to the experimental data values, which were 5.37 and 5.56 s, respectively. The same is valid for T

_{2}, which is also shown to be very similar.

#### 2.3. MD Simulation of VC1 and VC2 in Water Only and in the Presence of the Respective Protein Targets

#### 2.4. OWSCA Conformational Selecting and Calculated T_{i} and R_{i} Values

_{i}and R

_{i}calculations. Figure 3 shows the selected conformations for all systems. Therefore, the OWSCA methodology was able to reduce MD simulation data of 2000 conformations for each system in about 100 conformations, varying between 96 and 119 conformations. It is also possible to see that the use of the db1 (haar) wavelet was able to capture the MD simulation data behavior, implying that the important information is contained in the compressed dataset.

_{i}) and their respective relaxation rates (R

_{i}) were calculated using Equations (1)–(7) and presented in Table 2. It is important to notice that all values resided very close to each other, except the one corresponding to the system VC2 + ULK1 + WAT, which was considerably higher than others. In addition, Table 2 presents the R

_{1}/R

_{2}ratio for all formulations. It is possible to see the similarity between them, including the magnetite system used for validation of the R

_{1}/R

_{2}ratio, provided in Table 1, indicating the consistency of the calculation.

^{1}H and V(IV). The MD simulation of the built models containing only VC + WAT showed an average distance V⋯

^{1}H for VC1 of 3.19 Å, and for VC2, 3.66 Å.

^{1}H average distance in VC2 + WAT, as mentioned before. Therefore, the two characteristics mentioned imply considerable interaction differences between the VCs and the chemical medium.

^{1}H distance observed for the system VC1 + AMPK + WAT was 3.29 Å, only 0.10 Å higher than for the system VC1 + WAT.

^{1}H distance observed for the system VC2 + ULK1 + WAT was 5.55 Å, 1.89 Å higher than for the system VC2 + WAT.

^{1}H distance by a considerable amount. In addition to the fact that VC1 also interacts with AMPK by the V=O group, this site of interaction does not become completely unavailable, allowing the water molecules to approach the vanadium atom, which leads to a very small increase in the average V⋯

^{1}H distance.

_{1}and T

_{2}calculations. An increase in the average distance also increases the relaxation time, decreasing the relaxation rate. Due to the high order power of ϕ, a small increase in its value has a considerable impact on T

_{i}and R

_{i}values.

_{i}can be interpreted based on relaxation concepts. Both longitudinal and transversal relaxation times are a measurement of how quickly a molecule can return to its equilibrium state after the removal of a radio pulse in the presence of a magnetic field B

_{0}. This way, the return to its equilibrium state is possible due to the energy distribution with the surroundings [56,57]. Hence, when evaluating the influence of VCs in

^{1}H relaxation time, it is assumed that the VCs are important agents for receiving this dissipated energy, contributing to a faster returning of

^{1}H to its equilibrium state. For that distribution to be more effective, it is important that the distance V⋯

^{1}H should be as close as possible. Therefore, in a situation where the distance between the vanadium atom and

^{1}H is larger, it is expected to have a higher relaxation time.

^{1}H distance. This increase resulted in a considerably higher T

_{i}value when compared with the other systems.

_{1}and T

_{2}have a value of 0.032 and 0.025 s, respectively [52,53]. For Gd-DTPA, also one of the most common contrast agents, the T

_{2}value is 0.020 s [46,50,55]. Then, the VC1 showed to be a potential longitudinal and transversal MRI probe, being more effective than Gd-DOTA and Gd-DTPA, with superior relaxation times. In fact, its T

_{1}and T

_{2}values were 0.084 and 0.056 s, respectively, considering interactions in a chemical medium with only water, and 0.074 and 0.050 considering the presence of AMPK. Although VC2 presented a T

_{1}and T

_{2}of 0.086 and 0.058 s, respectively, when considering the system only with water, its effectiveness did not hold for a system considering interactions with ULK1, in which T

_{1}and T

_{2}were 1.046 and 0.702 s.

_{i}and R

_{i}suggest that modifications in the structure of VC2 might lead to a more effective potential contrast agent. The foundation for this proposal remains in the fact that since the unavailability of the V=O group increases T

_{i}value, an addition or substitution of a ligand, capable of interacting in the same ULK1 site as V=O, might make it more available for hydrogen bonding interactions, allowing the water molecules to approach the vanadium atom and dissipate energy faster.

## 3. Materials and Methods

#### 3.1. Systems Descriptions and Docking Studies

_{2}]·H

_{2}O (VC1) in a solvation box (VC1 + WAT), VC1 and its biological target AMPK with water molecules (VC1 + AMPK + WAT), [VO(bpy)

_{2}Cl]

^{+}(VC2) with only water molecules (VC2 + WAT), and VC2 with its target protein in aqueous medium (VC2 + ULK1 + WAT). The chemical structures of the vanadium complexes are shown in Figure 6.

#### 3.2. Molecular Dynamics Simulations

#### 3.3. Conformational Selections of V(IV) Complexes Using the Optimal Wavelet Signal Compression Algorithm and MD Data for T1 and R1 Estimation

_{j,k}is the wavelet coefficient, t is the time normalized between 0 and 1, j represents the scaling parameter responsible to determine the time and frequency resolutions of the scaled wavelet function ψ, and k represents the shifting parameter, which translates the scaled wavelet along the time axis [45]. The wavelet ψ has oscillating wave-like characteristics and has it concentrated in time or space. Consequently, there are several types and families of wavelets, whose properties differ along convergence speeds when time tends to 0, symmetry, compression potential, and smoothness [45]. Thus, when using OWSCA for reducing the original dataset and maintaining the principal characteristics of the system, the choice of the appropriate wavelet is an important step to consider.

_{i}and R

_{i}, where i = 1 indicates longitudinal and i = 2 indicates transverse, were estimated from the computed V⋯

^{1}H distances, obtained for each conformation selected by the OWSCA procedure. The flowchart shown in Figure 7 summarizes the needed steps for the work purposes. The OWSCA procedure is implemented in a homemade software [67,68,69].

## 4. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

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**Figure 1.**Representation of the measured V⋯

^{1}H distances. The central gray sphere represents the vanadium atom, and the blue sphere represents the

^{1}H proton of the closest water molecule, being both connected by a black dashed line, representing the measured distance.

**Figure 2.**RMSD analyses of each system under investigation. The results are as follows: VC1 in the presence of WAT (depicted in blue), VC1 in the presence of AMPK and WAT (depicted in orange), VC2 in WAT (depicted in yellow), and VC2 in the presence of ULK1 and WAT molecules (depicted in purple).

**Figure 3.**OWSCA conformational selection for (

**a**) VC1 + WAT, (

**b**) VC2 + WAT, (

**c**) VC1 + AMPK + WAT, and (

**d**) VC2 + ULK1 + WAT.

**Figure 4.**Structures of the V(IV) complexes in study, where the red region denotes the double bond between V and O.

**Figure 7.**Flowchart of the steps followed for the estimation of T

_{1}and T

_{2}from MD simulation data.

System | Theoretical | Experimental | ||||||
---|---|---|---|---|---|---|---|---|

T_{1} | R_{1} | T_{2} | R_{2} | T_{1} | R_{1} | T_{2} | R_{2} | |

Magnetite | 0.028 | 35.72 | 0.018 | 55.55 | 0.032 | 31.25 [48] | 0.020 | 50.50 [49,50] |

TCE(C-C) | 8.98 | 0.11 | 1.17 | 0.85 | 8.90 [51] | 0.11 | 1.18 [51] | 0.85 |

TFE(3F-4F) | 5.35 | 0.18 | 0.12 | 8.33 | 5.37 [51] | 0.19 | 0.14 [51] | 7.14 |

TFE(5F-3F) | 5.52 | 0.10 | 0.10 | 10.00 | 5.56 [51] | 0.18 | 0.12 [51] | 8.33 |

**Table 2.**R

_{i}and T

_{i}values for all V(IV) complex systems in s

^{−1}and s, respectively. In addition, R

_{1}/R

_{2}values were calculated for all the formulations.

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**MDPI and ACS Style**

Santos, R.M.; Tavares, C.A.; Santos, T.M.R.; Rasouli, H.; Ramalho, T.C.
MD Simulations to Calculate NMR Relaxation Parameters of Vanadium(IV) Complexes: A Promising Diagnostic Tool for Cancer and Alzheimer’s Disease. *Pharmaceuticals* **2023**, *16*, 1653.
https://doi.org/10.3390/ph16121653

**AMA Style**

Santos RM, Tavares CA, Santos TMR, Rasouli H, Ramalho TC.
MD Simulations to Calculate NMR Relaxation Parameters of Vanadium(IV) Complexes: A Promising Diagnostic Tool for Cancer and Alzheimer’s Disease. *Pharmaceuticals*. 2023; 16(12):1653.
https://doi.org/10.3390/ph16121653

**Chicago/Turabian Style**

Santos, Rodrigo Mancini, Camila Assis Tavares, Taináh Martins Resende Santos, Hassan Rasouli, and Teodorico Castro Ramalho.
2023. "MD Simulations to Calculate NMR Relaxation Parameters of Vanadium(IV) Complexes: A Promising Diagnostic Tool for Cancer and Alzheimer’s Disease" *Pharmaceuticals* 16, no. 12: 1653.
https://doi.org/10.3390/ph16121653