A background-lying platform of this work derives from experimental data on magnetic isotope effects (MIE) towards both DNApolβ catalytic activity [1] [2] [3] and the viability of cancer cells [1] [2] . Thus, a sharp decrease of the survival ability patterns of ²⁵Mg²⁺-treated AML/HL-60 cells as compared to abundant spinless, non-magnetic, magnesium ions impact has been found [1] . Furthermore, a similar result was then obtained on the same leukemia cells treated with magnetic, nuclear spin possessing, ⁴³Ca²⁺ and ⁶⁷Zn²⁺ ions [1] [3] as well as on human retinoblastoma cells subjected to these metal isotopes [2] [3] .

It was also shown that a processivity of beta-like DNA polymerases isolated from the all above mentioned malignant cells depends on MIE, so the resulted DNA fragment sizes becomes shorter within a 40n - 250n range following the increase of magnetic isotope content in a total metal pool [2] [3] . For instance, an up to 58% elevation of ⁴³Ca²⁺ content leads to a monotonic decrease of sizes of polynucleotides processed from average 230n - 250n to an abnormal (DNA repair invalid) 36n - 40n as directed by beta-like DNA polymerases from Y-79 and WERI-1A retinoblastoma cells [1] .

This nuclear-magnetic control over the DNA synthesis, therefore, allows coming up with a firm statement that a replication mechanism involves some ion-radical steps consisting of the ion-radical pairs formation [1] . A key element of this mechanism deals with an electron transfer from the nascent DNA deoxyribose anion to a bivalent ion coordinated inside the DNA polymerase catalytic site [1] [4] (Figure 1).

However, from the chemical physics point of view, it is still obscure what makes the difference between molecular dynamics designs of these ion-radical DNA synthesis paths processed in healthy and malignant cells. Noteworthy, within the DNApolβ catalytic site nanotopology landscape which provides a

“compartment” for this reaction (10 - 15 nm or less), all physical parameters describing a molecular machinery in normal and cancer cells at proliferation rates observed are identical or pretty close to each other [5] - [10] .

Obviously, the DNA synthesis reaction [1] [2] [3] is unlikely a source for apoptosis of tumor cells as relates to dependence of their viability on MIE [1] . Nonetheless, this MIE-viability dependence might have a link to DNA repair activity expressed by beta-like DNA polymerases in neoplasma [2] [3] [11] .

According to our assumption, these enzymes are to produce the ultrashort PDRN sequences (≈40n) playing a role of DNApolβ inhibitors. Acting as the DNA repair limiting/damaging factors, these endogenous inhibitors may promote an essential anti-cancer effect. In case of ²⁵Mg/⁴³Ca/⁶⁷Zn-induced impacts on enzymatic activity in situ, these inhibitors might be originated as a direct response to MIE.

Moreover, due to a random mode of the cancer-specific repair-required local DNA damages, the DNA repair itself means a wide variability in primary structures of the repair-related PDRN species. This also means that the PDRN inhibitory function should be determined predominantly, if not exclusively, by the lengths of these sequences. These lengths alone might determine not only the molecular dynamics in DNApolβ-PDRN docking pairs but, simultaneously, they might make an impact on specific Coulomb and dispersion couplings and, hence, on the mean amounts of hydrogen bonds per one nucleotide of the DNA primer inside the enzyme catalytic site.

So if this assumotion is true, the DNApolβ activity must be “suppressible” by ≈ 40n-long polynucleotides regardless on their primary structures. This would make the MIE-promoting treatment a legitimate may to gain the in situ anti-cancer molecular events.

The aim of a present study is to test this hypothesis. For this purpose, several types of synthetic single-stranded polynucleotides (both DNA- and RNA-like ones) with molecular sizes ranged in 20n - 200n interval were investigated to reveal 1) their effects on catalytic activities of several beta-like DNA polymerases from HL-60, Y-79 and WERI-1A cancer cells, and 2) their enzyme-binding parameters. A selection of these peculiar cell models was determined solely by a sharp difference between the tumor proliferation rates, “aggressive” high (acute myeloid leukemia) and relatively low (retinoblastoma) [8] [9] [10] and, hence, by the difference in contributions made by the DNA repair key enzymes into the cancer cell survival capabilities.

A variable set of polynucleotide ligands (see Methods) was tested for both inhibitory effects and the ligand-enzyme binding properties using beta-like DNA polymerase species from acute myeloid leukemia (HL-60) and retinoblastoma (WERI-1A, Y-79) cells.

As seen from the data presented in Figure 2 and Figure 3, no matter what ligand concentration tested and whatever enzyme sample coupled, a molecular size of synthetic polynucleotide is the only, crucial, impact-making factor. It should be emphasized that a maximal inhibition effects were observed in cases of 50n - 100n-long polynucleotides (Figure 2(C) and Figure 2(D)), Figures 3(A)-(E)), while a post-denaturation misfolded tRNA test show no inhibition

effect at all (Figure 3(A) and Figure 3(B)). As per Aphidicolin and ddTTP controls,they just prove a true beta-specific nature of enzymes tested [2] [3] [11] (Figure 2(A)).

Unlike polydeoxyribonucleotides (PDRN), polyribonucleotides were found to be inert towards the DNApolβ processivity regardless on lengths of these ligand molecules (Figure 3(A) and Figure 3(B)).

The affinity isotherms clearly show an essential difference between the ligand-enzyme complex stability patterns, K_d and A_c (see Methods), estimated for numerous compositions of these couples (Figure 4 and Figure 5). Thus, dissociation constant K_d for Poly(dT)₅₀-DNApolβ was found by 2.5-fold smaller as compared to Poly(dT)₂₀₀-DNApolβ pair (Figure 5).

In all cases studied, except for the RNA-like Poly(A)₄₉-containing pairs (Figure 5), K_d and A_c values are minimal when the ligand length is close to 50n (Figure 6). For all RNA-like ligands, the high values of K_d and A_c were found practically equal to the ones estimated for Poly(dT)₂₀₀ (Figure 5).

The data presented in Figure 2 and Figure 3 leaves no doubt about a maximal inhibitory efficiency provided by ultrashort, 40n - 50n in length, cyano-polydeoxyribothymidyl derivatives. These agents are to show as high as nearly 6.5-fold extent of enzyme suppression. That does not mean, however, that

this particular type of “pseudoprimers” is the only one capable to play a role of a powerful DNApolβ inhibitor. A truly crucial parameter to reveal a potential pharmacophore signs have nothing to do with a structure of DNA fragments being entirely related to its molecular size (Figure 2 and Figure 3).

So the results observed looks worthy of not indicating to any particular and perfect pharmacophore found but, instead, of a detailed analysis as a new platform to upgrade a whole approach towards the DNA derivatives in a current

anti-cancer agenda. This a Discussion of our work is all about.

A wide diversity of investigated synthetic homopolynucleotides and their monotonic thio- and cyano-derivatives is itself a prove for universal, indiscriminate, mode of DNApolβ inhibition effect we described. This is in a favor with our assumption stated that the key role in this phenomenon belongs exclusively to molecular sizes of small DNA fragments regardless on their primary structure peculiarities.

The ligands diversity mentioned makes no way to explain a formation of the ligand-enzyme complexes just by a routine docking (“complimentary”) paradigm. This DNA-protein binding act may involve some random appearing hydrogen bonds, Coulomb hyperfine coupling along with dispersion interaction and, last not least, the hydrophobic connections, might also be a case in this scenario. A key point of this model derives from the homopolynucleotides related data and reveals that the mean energy of these “weak” interaction depends on the length of a ligand but not of its structure.

A similar event occurs in the DNA repair process as long as a randomly appeared local DNA damage comes first. In this case, a clearly indiscriminate mode of the ligand-enzyme coupling is a consequence of unpredictable variability in primary structures of DNA fragments suitable for the repair purposes.

Therefore, a polynucleotide length alone is an impact-making factor towards the DNApolβ catalytic function. This factor might determine a formation of the above listed “weak” non-covalent interactions and, hence, to control the mean amount of hydrogen bonds per one nucleotide of DNA-primer (ligand) inside the DNA polymerase catalytic site. That is indeed critical for the enzyme suppression in situ.

All the affinity isotherms presented and a variable ligand-enzyme binding data (Figures 4-6) reveals a maximal strength of this peculiar intermolecular interaction within the short interval of ligand sizes, 50n - 100n. This is to confirm that the enzyme inhibition we observed (Figures 2(B)-(E), Figure 3) is indeed a consequence of the stable ligand-enzyme pair formation which has nothing to do with either the solution properties changes or the enzyme surrounding disperse phase modulations.

A comparison between the ligand amounts bound with (a) DNApolβ and (b) HSA show that the ligand-enzyme complex includes two molecules of ligand per one molecule of enzyme, while the ligand-HSA (control) pair contains just one ligand per HSA molecule (Figure 4, Figure 7, Figure 8). This is in a favor to a mere fact of existance of two separate Mg²⁺-coordinating catalytic sites in β- and β-like DNA polymerases [8] [10] [20] [21] [22] .

Let’s evaluate the activation energy value for a ligand-enzyme complex dissociation following the data listed in Figure 4 and Figure 8. Obviously, a

dependence of K_d on temperature has a clear Ahrrenius mode:

K d = K 0 exp ( − E / R T ) (1)

where R—a universal gas constant and T-enzyme functioning temperature.

Taking into account a low level of the temperature interval tested as compared to an initial T₀ = 298K, we’ll use further a linear decay as T in (1). To estimate E, a linear reguliarity must be treated as:

ln K d ≅ ln K 0 − E / ( R T 0 ) + E Δ T / R T 0 2 (2)

where Δ T is a temperature change in experiment (Figure 7 and Figure 8).

The Equation (2) revealed activation energy value E was found 15 kJ for Poly(dT)₂₀₀ ligand within a whole range of temperatures tested, while the very same dependence for Poly(dT)₅₀ include two linear branches crossing each other nearby the 40˚C point where, most likely, a slight protein denaturation starts (Figure 7). Once the temperature is close to an enzyme function required optimal level (25˚C - 35˚C), the Equation (2) revealed E₅₀ = 70 kJ/mole whereas this value estimated at 40˚C is as low as 15 kJ/mole (Figure 7). The attention catching point here is that the E value measured at the enzyme denaturation launch-point (40˚C) is exactly the same as it has been found in case of the “inert”, non-inhibiting, polydeoxyribonucleotide ligands. This supports a statement on the enzyme inactivating protein structure dynamics initiated starting with a 40˚C heating point. A lack of two-compartment, “angle-breaking”, K d = f ( T ) dependence for long ligands and their E values low level are in a good accordance with a high probability of 3D-compactization of such sequences at our test conditions [7] [16] [17] [23] .

It’s easy to find out that the inhibition-promoting Poly(dNTP) species provide a pretty low value of activation energy for dissociation with DNApolβ-HL60, ε = 1.40 kJ/mole. That means, the complimentary hydrogen bonds do not contribute to formation of these particular Poly(dNTP)-enzyme complexes which is a prove for the absence of the affinity-specific, true docking links in these pairs. Most probably, this remarkable 1.40 kJ/mole value is determined by the U_d-dispersion related weak Van der Waals interactions along with a U_q Coulomb hyperfine coupling. These kinds of the ligand-enzyme complex stabilizing links are rather superficial ones due to both a U d ~ 1 / r 6 potential and the efficient screen-like separation of Coulomb forces in water occurred within a distance smaller than 0.4 nm [15] [17] [23] [24] . This certainly takes into account the superficial hydrophobic bounds as well which are nothing but the result of a cooperative (cumulative) act of all the above specified forces [23] [24] .

So the key role in formation of Poly(dNTP)/DNApolβ complexes belongs to Van der Waals bounds which energy corresponds directly to either 1) the efficient surface of ligand-enzyme pair or 2) a length of an enzyme-bound ligand.

Furthermore, since the mean value of the U_d dispersion patterns is hardly dependent on the element composition, and as long as the amounts of charged groups in U_q-determining Poly(dNTP) ligands tested are about the same, a very similar parameters of their inhibitory activity should be expected then. This explains well a lack of dependence of inhibitory capabilities of these ligands on their nucleotide composition (Figures 2(B)-(E), Figure 3).

Once ε ~ R T , we might suppose that the short ligands (50n - 100n, or shorter) are to get bound with the enzyme molecule throughout a whole linear chain, i.e. through nearly every nucleotide of Poly(dNTP) sequence.

Using the Ahrrenius equation, we may evaluate a ratio between the ligand- enzyme binding time values τ for Poly(dNTP)₂₀ and Poly(dNTP)₅₀, respectively:

τ 20 / τ 50 = exp ( − Δ n ε / R T ) ≅ 10 − 7 (3)

where Δ = 30 (difference in lengths between 50n and 20n). It shows that a short time of binding τ 20 does not allow n₂₀-ligand to promote a sharp suppression of the enzyme activity. A shorter time for the ligand “neighboring” around the enzyme catalytic site, the lesser inhibitory effect to be expressed.

On other hand, the longest ligands tested were found to be a rather poor inhibitors as well (Figure 2(E), Figure 4) due to their compactization-caused small square of the enzyme-ligand efficient interaction [23] [25] as also seen from Equation (3).

As per a zero inhibition affect shown by RNA-like ligands tested (Figure 3(A) and Figure 3(B)), their remarkable refolding capabilities [18] [25] and [– O-----Mg²⁺] coordination input [26] [27] are presumably beyond this phenomenon.

A clear pharmacological potential of oligo- and polydeoxyribinucleotides is a subject for numerous experimental and clinical studies performed since early 1990s [18] [27] [28] [29] [30] . Their applied medicinal significance, however, were treated predominantly by focusing on the aptomer properties, i.e. on capabilities to find the specific target molecules such as signaling proteins, membrane receptors, chromatin structure elements, etc [17] [26] [28] [30] [31] . Unlike our present work, therefore, these studies are all about the true docking participants. The inhibitory power of Poly(dNTP) species we found has nothing to do with their structures and composition being entirely dependent on molecular size (Figures 2(B)-(E), Figure 3(A), Figure 3(C), Figure 3(D), Figure 3(E)). This allows to “turn the page” in a long record of polynucleotide medicinal applications by just paying attention to the Poly(dNTP) motion on how to shut down a DNA repair in malignant cells. It makes sense for DNApolβ, key DNA repair enzymes, are found hyperexpressed in response to a high frequency of DNA damages followed by an increase of the cancer related cell proliferation rate [2] [3] [10] [11] [20] . With a respect to this statement, it has been already emphasized that the members of this enzyme family are the “legitimate targets” for cytostatic inhibitors like dNTP antimetabolites [8] [9] [10] [28] [32] and magnetic metal isotopes [1] [2] [3] [24] .

There is a good enough understanding on molecular mechanisms beyond the inhibition of the cancer-hyperexpressed DNApolβ species provided by magnetic isotopes of bivalent metals—²⁵Mg, ⁴³Ca and ⁶⁷Zn [1] [2] [3] [9] [24] . In particular, these mechanisms are dealing with the origin of “too short”, DNA repair insufficient, DNA fragments [1] [2] [3] . This effect leads to a massive release of the DNA repair related 40n - 100n DNA sequences with the unpredictable, unique structures [1] [2] , i.e. this provokes a magnetic isotope induced formation of the DNApolβ endogenous inhibitors. It looks like a good explanation for cytostatic activity shown by magnetic metal isotopes in several cancer cells [1] [24] .

Everything we know about pharmacokinetics of various DNA-based drugs and pharmacophores indicates to the fact that their bioavailability is far of being perfect mostly because of inevitable nucleases attack [18] [27] [28] [29] [30] . So this is the hardest task to manage a targeted delivery of Poly(dNTP) sequences to the DNApolβ-operating in situ compartments, for which some certain nanocarriers required [7] [18] [30] [33] . As for the magnetic metal ions, they can be delivered to the DNApolβ in situ targets with [1] [24] or even without [2] [3] nanocationite administration which would make the magnetic isotope effect a promising tool to gain the DNA repair machinery breakdown in neoplasma.

Knowing that the abundance of ²⁵Mg is relatively high (≈10%) and considering a remarkable role of magnesium in enzymatic phosphorylation processes [1] [24] [34] , it would be logical to suppose the existence of so called “hidden” effects of Magnesium-25 on numerous metabolic pathways. In this case, a high content of endogenous Fe²⁺ in cells and tissues of a living organism becomes a natural limiting factor to prohibit any expression of magnetic isotope effects in vivo. This is in accordance with the data on correlations between the ²⁵Mg²⁺-affected ATP synthesis levels in mitochondria and the Fe²⁺ contents in these mitochondria isolated from different rat tissues [34] as well as with the results stated an increase of Fe/Mg ratios in several types of cancer (ovarian cancer, renal adenocarcinoma, fibroblast lung cancer, hepatocellular cancer, osteosarcoma, thyroid follicular adenocarcinoma) compared to corresponding normal, non-malignant, tissues [9] [20] [26] [32] .

A variety of clinical case reports showing an appearance of short (100n - 300n) single-stranded DNA fragmets in a blood plasma of oncology patients [26] [35] may now also be treated under a point of view of the probable DNA repair related origin of these tumor-released Poly(dNTP) sequences.

Last not least, the infamous quorum sensing phenomena [36] could be engaged with an effort to uncover a biological meaning of what we’ve found testing the capabilities of different Poly(dNTP) species to affect some tumor-specific DNA repair key enzymes.

Ultrashort (40n - 100n) polydeoxyribonucleotides are found to be the efficient non-specific inhibitors of DNA polymerases β from chromatin of several cancer cells: HL-60, WERI-1A, Y-79.

Manifesting a positive correlation between these inhibitory capabilities and the strength of affinity in enzyme-ligand pairs, such poly(dNTP) species promote a sharp suppression of enzymatic catalysis regardless on their primary structures. Only molecular size matters.

The data presented show a clear regulatory potential of some short ssDNA entities once they are about to interact with the key DNA repair enzymes.

This may provide a promising platform for further research aiming to shut down the DNA repair machinery in malignancies.

This work was performed within the aims and scope of the Russian Federal Specialized Program on priorities in science and technologies trends for 2014-2020 supported by Russian Federal Ministry of Science and University Education. The RF Government budget beyond.

The authors declare no conflicts of interest regarding the publication of this paper.

Stovbun, S.V., Ermakov, K.V., Bukhvostov, A.A., Vedenkin, A.S. and Kuznetsov, D.A. (2019) Primer-Like Inhibitors for DNA Repair Enzymes of the AML-HL60 and WERI-1A/ Y79 Malignant Cells. Advances in Enzyme Research, 7, 27-44. https://doi.org/10.4236/aer.2019.73003

ssDNA, Single-Stranded DNA;

DNApolβ, DNA Polymerase Beta;

MIE, Magnetic Isotope Effects;

AML, Acute Myeloid Leukemia.