Therortical Studies and Investagting of Selected Potnet CDK2 Inhibitors as Anticancer Agents

In this study eight selected of the most potent cyclin dependent kinase 2 inhibitors in which targeting adenosine triphosphate -pocket site theoretically investigated to support literature information of frontier molecular orbitals, molecular electrostatic maps, and global chemical reactivity descriptors such as chemical hardness, chemical softness, chemical potential, electronegativity and electrophilicity of cyclin dependent kinase 2 inhibitors. Calculation and three-dimensional plotting were achieved thr ough Gaussian 09W and Gausview 6 software’s utilizing density functional theory quantum modeling applying both hybrids extended and not extended basis set. Crystal structure of CDK2 with inhibitors was obtained from protein data bank and visualized through PyMol Schrödinger software to assign polar and non-polar interactions of inhibitors with enzyme. A promising conclusion trend obtained in this research regarding to molecules that could have an inhibition activity toward the cyclin dependent kinase 2 enzymes. Our theoretical investigation emphasizes that, the anti-cancer activity has directly relationship with value of chemical hardness and chemical softness, where the most potent compounds was the pyrazolopyrimidine and imidazole pyrimidine and they have higher chemical hardness value and at the same time lower value of chemical softness compared with the rest of compounds.


Introduction
Cyclin dependent kinases are class of serine / threonine protein kinase enzymes, which are in combination with their partners cyclin are key regulatory of cell division cycle, the primary function of such kinase enzymes is control process through cell cycle (CDK1 to CDK6) while CDK7-CDK17) implicated in transcription regulation [1].
As CDK's binds to the cyclins the partial active complexes formed then go further phosphorylation leading to active complexes which it regulates the cell development by means of passing cell through check points of cell cycle phases [2] as explained in figure 1 [3].
When mutation in check points through phases take place or deregulation by overexpression of CDK's in cell cycle, cells become abnormally and uncontrolled growth to from different type of tumors leading to cancer [4], CDK2 has an important role in cell division as shown in figure 1, when it binds to its partner cyclin E and the complex then phosphorylated, it driving the cell into the S-phase where DNA being synthesized, turn to late S-phase and it activated by phosphorylation CDK-cyclin A complex where the cell is preparing to become in G2 phase [5]. therefore CDK's become potent target in drug development and discovery over the last years [6], New generation of CDK-2 inhibitors targeting ATP binding site where it overcome the disadvantage of the first generation inhibitors such as low selectivity and potency [7], here we mention the most potent and selective CDK-2 ATP inhibitors ( Table 1) [8].   [9] NU2058 Purine / guanine 17µM [10] NU6102 Purine / guanine 0.006 µM [11] CYP51 Indole Indirubin-5-sulphonate CDK 2-A 0.035 µM [12] R547 Aminopyrimidine 0.003 µM [7] Pyrazolopyrimidine CDK 2-A 0.001 µM [13] Imidazole pyrimidine 0.001 µM [14] PHA-793887 Pyrrazole 0.008 µM [15] Fig 2 A CDK2 secondary structure (PDB ID: 4EK3), B CDK2 primary structure CDK2 has three sites in which binds to inhibitors, site I represent ATP binding pocket as shown in figure 2, precisely β1, β2, β3, β6, β8, β9 while site II and site III are noncompetitive binding sites, in this study we focus on ATP competitive bind site for their conservation after bind to small molecule inhibitors such as inhibitors in table 1 [16].
Density functional theory it's a quantum mechanical modeling method where it's applications has a great significance in targeting drug discovery studies especially invention of new anti-cancer agents [17], [18], [19]. Interrupting of DFT calculations aid in create a comprehensive picture about physical and chemical properties such as stability and reactivity toward electrophiles or nucleophiles as well as build a molecular electrostatic map that represents the electropositive and electronegative sites over the chemical structure, polarity, reactivity descriptors etc.
There are different theoretical studies such as electronegativity equalization principle (EEP), maximum hardness principle, minimum polarizability principle (MPP) that utilize DFT calculations specifically using energy values of frontier molecular orbitals; highest occupied molecular orbital HOMO and lowest unoccupied molecular orbital LUMO, to specify global and local reactivity descriptors such as chemical hardness, softness, chemical potential, electrophilicity, electronegativity, Fukui function and local softness [20].
In 1934 Koopman's assign the values of ionization potential I and electron affinity A as the negative value of HOMO and LUMO energy respectively in his theorem (equation 1 and 2) [21] I = -EHOMO eq 1 A = -ELUMO eq 2 The stability and reactivity of the chemical molecules are usually could be assigned from the values of chemical hardness and softness regarding to the Pearson theorem "maximum hardness principle" [22], where chemical hardness η measure resistance of the molecule to charge transfer intramolecularly and it could be obtained mathematically by subtraction of ionization potential from electron affinity equation 3, in contrast the chemical softness S is ability of the molecule system to react and mathematically obtained from the reciprocal of the chemical hardness equation 4 [23].
Chemical potential μ is used to measure the propensity of the electrons to escape from the system in an equilibrium state, equation 5. Electronegativity χ it's an important physical description of the atoms in molecules, where it defined as "the power of an atom in a molecule to attract electrons to itself" and it's the negative value of the chemical potential equation 5.
Another important chemical reactivity descriptors is the electrophilicity ω in which measures how much energy of the system need to become stable after accepting an additional electrons, it determined by dividing the square of chemical potential μ by 2 fold chemical hardness equation 6 [24]. Due to lake in information and the relation between strong binding of CDK2 inhibitors previously mentioned and the reactivity descriptors in this study 8 selected of the most potent CDK2 inhibitors will be theoretically investigated by global chemical reactivity descriptors, molecular electrostatic potential maps and HOMO-LUMO plotting and energy orbitals anticipating and make a relationship between the reactivity parameters and physio-chemical properties and the selectivity, potency of the inhibitors toward CDK2 kinase enzyme. The aim of this study is to support the theoretical literature with chemical reactivity descriptors of the most potent CDK2 inhibitors under clinical studies further to build a good visualization about design new CDK2 targeting anti-cancer agent that would have drug like characteristic, selectivity, and potency.

Methods
All DFT calculation of 10 potent CDK2 inhibitors was performed using Gaussian 09W and Gausview 6 full software packages [26,27], energy mode at gas phase ground state Becke, three parameters, Lee-Yang-Parr "B3LYP" hybrid basis set [28] at 6-31G and 6-311++ G (d,p) level of theory to study the effect of extended basis set on the calculations [29]. Gaussian output CHK point file of each basis set was analyzed by Gausview 6 to obtain HOMO, LUMO orbitals and energies with restricted wave function, transparent molecular electrostatic potential maps were performed by applying total density cube with SCF density matrix, ESP mapping surface. Crystal structure of CDK2 with each inhibitor was downloaded as pse extension file type and visualized using Schrödinger software PyMol 2.5 python license windows version.

CDK2-ATP competitive inhibitor interactions
Purine / Adenine analogues purvalanol B show good inhibition activity against CDK2, in fact table 2 A represent interactions whether polar or non-polar, where the two nitrogen atoms on purine ring made H-bonding with carbonyl and amino groups of Leu-83 residue. While amino acids with hydrophobic side chain like Leu-134, Ile-10, Val-18, Ala-31, Phe-82 make a hydrophobic interaction with purvalanol [9]. Second purine derivative is NU2058, where the amino group at position 2 and nitrogen atom of purine ring making two hydrogen bonding with carbonyl and amino group of Leu-83 residue while Leu-134, Phe-82, Phe-80, Ala-31, Val-18, Ile-10 making hydrophobic interactions as they close to inhibitor (Table 2 B) [10]. Addition of benzene sulfonamide on amino group at position 2 of purine ring allowing the ligand to make another 2 hydrogen bonds additionally on that Leu-83 at oxygen atom of sulfonate group with amino group of Asp-86 and amino group of sulfonamide with carbonyl of the same backbone residue [11]. Indirubin-5-sulphonate is indole-based structure show potent inhibition activity with IC50 0.035 µM against CDK2-cyclin A complex, by studying it's interactions with CDK2 it turned out that indirubin-5-sulphonate create at sulfonate group, 3 hydrogen bonding with amino groups of Lys-33 and Asp-145, and at NH-CO-N of indirubin a network hydrogen bonding interaction with carbonyl and amino groups of Leu-83 and with carbonyl group of Glu-81 backbone residues respectively, Ile-10, Leu-134, Phe-82, Phe-80, Ala-31 non-polar side chain backbone residues get closer to indirubin inhibitor and making hydrophobic interactions as presented in table 3-D [12]. Next CDK2 ATP-pocket inhibitor is R547, aminopyrimidine is the chemical structure and it is forming 5 hydrogen bonding, two at sulfonyl group with amino groups of Lys-89 and Asp-86, at nitrogen atom of piperidine ring with hydroxyl group on His-84, at amine groups 6 and 2-positions substituted on pyrimidine ring with carbonyl Leu-83 and Glu-81 respectively, non-polar interactions of R547 could be concluded with Ile-10, Val-18, Phe-80, Ala-31 at hydrophobic side chain of most closer residues table 2 E [7]. Pyrazolopyrimidine inhibitor with IC50 value around 0.001 µM against CDK2-cyclin A which is great inhibition activity, polar interactions of this agent indeed at different nitrogen atoms at 1, 7, positions and substituted position 4 of pyrimidine ring with amino group of Lys-33, Leu-83 and carbonyl group of Leu-83 respectively, however the hydrophobic interactions included non-polar side chain of Leu-134, Ile-10, Ala-31, Phe-82 amino acid residues at ATPbinding pocket on CDK2 table 2 F [13]. Imidazole pyrimidine inhibitor invented by AstraZenca pharmaceuticals-research team exhibit a great activity against CDK2 with IC50 0.001 µM and after analyzing complex co-structure of ligand and CDK2 using PyMol software it deduced that the hydrogen bonds could be formed at two places in the structure, the first place is on nitrogen atom of pyrimidine ring and amino group at position 2 with amino and carbonyl groups of Leu-83 respectively, the second place is sulfonyl and amino group para-substituted on phenyl ring with amino and carbonyl of Asp-86 backbone residue. Hydrophobic attractions as previously inhibitors on the same site ATP-pocket the competitive inhibitor site with non-polar side chain of the following amino acid residues, Val-18, Ile-10, Ala-31, Phe-82 table 2 G [14]. Considerable activity exhibited by PHA-793887 against CDK2 and the interactions presented in table 2 H, polar interaction (hydrogen bonding) of this inhibitor after analyzing the complex co-structure of CDK2 with PHA-793887 appear at 3 sites, nitrogen atoms at pyrazole ring on positions 1,2 and 9 with carbonyl of Glu-81, amino and carbonyl of Leu-83 respectively, on the other hand a set of amino acids residues making hydrophobic attraction toward carbon atom skeleton of PHA-793887 such as Phe-82, Ala-31, Leu-134, Phe-80, Tyr-15 [15]. The molecular visualization interaction of inhibitor-enzyme interaction could be concluded as follows, molecules have functional group contain N,O atoms can make a hydrogen boding interaction especially with Leu-83, and molecules which have hydrophobic carbon residue it could making hydrophobic attraction with non-polar side chain residues at ATP-pocket site on CDK2 enzyme, consequently molecule with this features that expected to have inhibition activity against CDK2 allowing it to be anti-cancer agent.

FMO HOMO-LUMO
Frontier molecular orbital of the inhibitors was obtained by means B3LYP method using 6-311G++(d,p) extended basis set including the polarization of d and p orbitals and double diffused on triple zeta function as to get more reliable results the orbitals 3D-diagrams illustrated in table 3. Red color represents the positive phase while the negative phase in green color. As quantum explanation of ligand-binding site (inhibitor-ATP competitive site) mechanism [30] HOMO orbital diagrams expressing the ability to donate electrons from the inhibitor to the binding site of CDK2 in our case ATP-competitive pocket site oppositely, the LUMO orbitals express the ability of the inhibitor to accept electrons from the binding site of the CDK2. Purvalanol B, CYP51 and PHA-793887 HOMO and LUMO orbitals appear similarly means that sites that trend to donate electron from HOMO to the enzyme binding site approximately the same sites on the molecules that trend to accept an electron from the binding site of the enzyme on LUMO orbitals of inhibitors table 3 A, D and H. The HOMO orbitals of NU2058 locate from 6-subtitution position on pyrimidine ring to cyclohexanol ring, while the LUMO orbitals extends from 6-position of pyrimidine ring to the whole chemical structure table 3 B. Regarding to NU6102 inhibitor HOMO orbitals distributed over the all chemical structure accept cyclohexyl group but the LUMO orbitals confined at purine ring, amino group at position 2 oxygen atom at position 6 table 3 C. R547 HOMO-LUMO orbitals divided the structure equally where HOMO orbitals distributed from position to of pyrimidine to sulfonyl group whereas LUMO orbitals located from pyrimidine to substituted phenyl ring table 3 E. HOMO orbital surfaces of pyrazolopyrimidine inhibitor locate at the main scaffold with little at phenyl ring position 5 while LUMO locate at phenyl ring substituted with nitro group table 3 F. Lastly HOMO orbitals of imidazole pyrimidine inhibitor locate over structure from sulfonyl group to pyrimidine ring but the LUMO orbitals locate from pyrimidine to imidazole ring except its alkyl substituted table 3 G.

Molecular electrostatic potential maps
The molecular electrostatic maps of the inhibitors were done utilizing the extended basis set 6-311G++(d,p) consequently to recognize the distribution of the charge over the chemical structure to assign theoretically electrophilic and nucleophilic sites that will involve in the chemical reactions. The maps have different color range start from red, orange yellow, green to blue where the red color show electronegative potential (nucleophilic site reactive toward the electrophiles) and the blue color show electropositive potential (electrophilic site that reactive toward the nucleophiles). Table 4 show the MEP maps and electrophilic, nucleophilic sites of the selected inhibitors.

Global chemical reactivity descriptors
The global chemical reactivity descriptors were obtained using 6-31G and 6-311++G(p,d) basis set in eV unit as shown in table 5, the descriptors values show no difference between the basis set except increasing in electrophilicity ω, electron donating ωand electron accepting powers ω + except that the difference not observable consequently we will analyze result with extended basis set as it's more reliable. The values are arranged ascending in table 6. First parameter in GCRD is the chemical hardness from table 6 pyrazolopyrimidine inhibitor have maximum resistance to charge transfer intramolecularly unlike purvalanol B, chemical softness counter to hardness maximum ability for reaction and charge transfer among inhibitors is purvalanol B it's expected that due to its chemical structure show diversity of functional groups, another GCRD is the electronegativity and the chemical potential, as we mentioned previously they have the same value but different in mathematically sign where indirubin shows maximum ability to attract electrons to the molecule itself but minimum ability for PHA-793887 inhibitor. Electrophilicity parameters describes the reactivity by propensity the molecule to accept electrons (ω -) or donating electrons (ω + ) and the net electrophilicity (Δω±), Indirubin-5-sulphonate have maximum ability to donating an electron to binding site, theoretically which agrees with HOMO orbitals diagram by distributing over the chemical structure means that there are more than one cites could donate an electron. Also, MEP show for Indirubin-5-sulphonate molecule 4 electronegative sites with red color, it's interestingly that the same inhibitor shows the highest value which represent the propensity to accept an electron means that its chemical structure has a wide range of the electronic behavior in different chemical systems.
We can summarize the relation between inhibition activity against CDK2 enzyme and the GCRD which is the main idea to perform the study. All inhibitors have a convergent value of chemical softness, chemical hardness, and electronegativity descriptors with standard deviation 0.31, 0.57, 0.8 respectively. The electrophilicity, electron donating accepting powers, and net electrophilicity have far apart values with standard deviation 6.58, 6.78, 6.61 and 12.39 respectively and this is promising trend result that will help research groups in design an anti-cancer agent, however we can conclude that the chemical agent have a chemical softness value around 0.51 eV, chemical hardness value around 1.27 eV and 3.94 eV value for electronegativity it's theoretically expected that to have inhibition activity against CDK2 enzyme.

Conclusion
In this study 8 of potent CDK2 inhibitors was theoretically investigating through visualization the interaction with the CDK2 enzyme by ligand interaction PyMol software resulted in hydrogen bonding associated mainly with Leu-83, Glu 81 and Lys-33 while non-polar residues on CDK2 at ATP binding pocket site such as Leu-134, Ala-31, Phe-82, Val-18, Ile-10 and others make a hydrophobic interaction with the inhibitors. FMO diagrams results in purvalanol B, CYP51 and PHA-793887 show approximately same diagrams for HOMO and LUMO orbitals while other inhibitors show differences in the HOMO LUMO orbital diagrams, also the chemical compound have HOMO LUMO distribution over the chemical structure possess a relatively high value of electrophilicity descriptors. Molecular electrostatic maps show the nucleophilic and electrophilic sites in the chemical structure of the inhibitors presented in table 4. In analyzing and investigating the GCRD of the inhibitors we have reached a promising conclusion that the most important factors on the inhibition activity against CDK2 was chemical softness, hardness and electronegativity and we expected that any chemical molecule can make a hydrogen bonding and hydrophobic interactions along with possessing a 0.51 eV, 1.27 eV and 3.94 eV approximately values for chemical softness, chemical hardness and electronegativity it will have promising inhibition activity against the CDK2 enzyme which means that this is the start point in new strategy of develop a new potent anti-cancer agents by implement the theoretically expectation.