Without any exaggeration adenosinetriphosphate (ATP), Fig. 1, can be considered as the most important and fascinating molecule in living nature thanks to its ability to maintain the energy balance in living cells and initiate numerous biochemical reactions by releasing an imposing amount of energy, 7.3 ÷ 10.9 kcal/mol, which is then regained via recycling, a repeated process that occurs 2000 – 3000 times a day 123456. The energy is stored in the ATP triphosphate tail (TT), Fig. 1, and its release, as widely accepted, results from the ATP hydrolysis, partial (ΔE = -7.3 kcal/mol) or total (ΔE = -10.9 kcal/mol) 1, accompanied by the production of adenosinediphosphate (ADP) or adenosinemonophosphate (AMP), respectively 157. The same is true for other known in nature nucleosidetriphosphates NTPs, N = A (adenosine), C (cytidine), G (guanosine), T (thymidine), U (uridine).

In water containing environment, like living cells, ATP, and NTP in general, is quite stable, and its cleavage proceeds through overcoming a significant energy barrier of 25 kcal/mol 8910. The cleavage rate is highly sensitive to presence of Mg²⁺ (Mg cofactor) acting on the TT as a specific catalyst 78. Basically, Mg²⁺ can bind to each oxygen of the TT, but generally it prefers making a chelate with O1 and O2, Fig. 1, and highly rare with O2 and O3 123456. The O1-O2 chelate lowers the energy barrier by 5 kcal/mol 910, and the cleavage proceeds through a typical hydrolytic mechanism.

What we have just outlined is a conventional view on the NTP cleavage 12345678910. The reaction path, from its initial stage and up to final, includes only ionic forms, and diphosphate NDP and monophosphate NMP products are also ionic. The ionic forms, in turn, have paired spins (singlet states) and hardly thought to be involved in rapid reactions based on the NTP cleavage. At the same time there are numerous very rapid reactions using Mg-induced NTP cleavage. Among them are tubulin assembly into microtubules (NTP = GTP) 1112 and DNA/RNA single chain polymerization 13141516. These reactions can be understood only through producing short-living radical forms carrying on the unpaired spins 17. Additionally, the ionic (hydrolytic) mechanism is unable to explain why polymerization reactions demand the presence of Mg²⁺ and not other possible cations, like Ca²⁺ or Zn²⁺. These cations (cofactors) can easily bind the TT fragment with no serious distortions in its structure and provide similar electron density redistribution within a cluster of its atoms 123. The unique role of Mg in NTP cleavage was repeatedly discussed by different groups of biologists and chemists, see 181920 e.g., and found no appropriate answer up to present. To make the problem more puzzled, one should recall that Mg contains 10% of the active nuclear spin, ²⁵Mg, and this spin (5/2), through a hyperfine interaction, can activate unusual reaction paths 1721.

The paper aims to answer the following questions:

i) why Mg cation, and not other one, is essential for initiating NTP cleavage.

ii) why Mg shows different affinity to the O1-O2 and O2-O3 fragments.

iii) why chelation is a typical way of binding and why formation of a single Mg-O bond is rather atypical.

iv) why NTP cleavage is governed mostly by ionic and rarely by a free radical mechanism.

v) why Mg isotope, ²⁵Mg, with an active nuclear spin is highly important in NTP cleavage.

To answer the above questions we have modeled the interaction between ATP (it reproduces the common features of NTP) and Mg cofactor in its singlet (S) and triplet (T) states (see the following sections). The modeling is based on the Schlegel-Frisch ab initio molecular dynamics (ADMP) method 2223 with atom-centered functions 24, which logically develops the computational ideas earlier forwarded by Car and Parrinello 25.

Cellular media mostly consists of water, in which Mg²⁺ exists in a water coat of octahedral configuration, Fig. 1, the most stable among other ones 262728. With this in mind, in our computations we consider as a realistic Mg cofactor Mg [(H₂O)₆]²⁺ (Mg subsystem) interacting with ATP (ATP subsystem), Fig. 1. The geometries of both subsystems, Mg and ATP, were primarily optimized with the DFT:B3LYP (6–31G** basis set) method. The obtained geometry parameters (interatomic distances and angles) for S states are in perfect agreement with the previously obtained ones 910. T states deserve separate consideration.

Our previous computations (the computations are carried out in a cubic water box (the side length is 15.3 Å) of 132 water molecules with the full geometry optimization; DFT:B3LYP, 6–31G** basis set) show that ATP in T and S states reveal practically the same value of the total energy E^tot 16:ΔE^tot(T-S) = E^tot(T) - E^tot(S) = -0.57 kcal/mol (T = 0⁰ K). The difference in the E^tot is of a kT level, and at T = 310⁰ K (ADMP DFT:B3LYP, see below) the barrier between the T and S states is easily overcome, and both states are entangled over time. This finding implies that the T state of Mg-ATP system comes up only thanks to excitation of Mg in its water coat; the ensemble of water molecules (water pool) is always in S state.

Earlier it was shown that an isolated Mg [(H₂O)₆]²⁺ (gas phase) in its T state is unstable 262728: the gap in the total energy between the T and S states is remarkable, ΔE^tot(T-S) = 8.3 eV, and the complex shows the tendency to eliminate one hydrogen. Finally, it appears in the form of [Mg(H₂O)₅OH]⁺ with the distorted geometry compared to that of the original state 29. This is evidently not good for our purposes if we want to "prepare" the Mg [(H₂O)₆]²⁺ in its T state. Fortunately, the situation is not as sad as it might seem. Our earlier computations 16 show that the Franck-Condon (F-C) S → T excitation of the Mg [(H₂O)₆]²⁺ in the presence of ATP and 78 water molecules gives a much smaller gap, 0.40 eV, between the T and S states, which leaves the water molecules in the Mg shell undestroyed (the computations were carried out at T = 0 K with the DFT:B3LYP method, 6–31G** basis set, and a full geometry optimization procedure at a frozen distance between the ATP and Mg atom of 8 Å; the system is fully identical to that we started off in the ADMP computations). The finding allows us to deal with triplet runs in the ADMP computations by starting from the singlet Mg [(H₂O)₆]²⁺ geometry, which then, after reaching a thermodynamical equilibrium with the environment at T = 310 K (see below), is converted into the triplet state through the F-C S → T excitation.

In the current molecular dynamics ADMP computations (details see below), the Mg [(H₂O)₆]²⁺ and ATP (S or T state, see above) are placed in a cubic water box (the side length is 17.5 Å) of 78 water molecules, allowing each subsystem having at least three-shell water environment around them. Within the box the water molecules can change their initial positions when the Mg and ATP subsystems begin to approach. The rearrangements in the water environment during the computations, according to previous results 1530, meet the following limits: R_OO ≤ 3.60 Å; R_OH ≤ 2.45 Å; φ_OHO ≤ 45⁰ (R_OO is the distance between oxygens, R_OH is the distance between the oxygen and hydrogen, and φ_OHO is the angle between two bonds, formed by a hydrogen atom and two oxygen atoms). With these parameters the water molecules can form hydrogen bonds with the ATP on its periphery (up to 12 molecules) and between themselves in the rest water bulk, but the molecules are not allowed to approach each other close. Interatomic distances and angles within each subsystem are varied at each point of computations along the reaction coordinate. This coordinate coincides with the vector r [Mg→(O1-O2-O3)] of a length 8 ÷ 0 Å, which starts at the Mg atom (the center of the Mg complex) and goes perpendicular to the imaginary line, connecting the O1, O2, and O3 atoms, where it ends. The line has a length of ± 4.0 Å with a zero point located on the O2 atom. The named oxygens and Mg are not in the same plane. To span all the space formed by these atoms the vector r was increased in regular intervals of 0.05 Å along the imaginary line followed by its shift along the other vector n (± 1 Å) directed perpendicular to the Mg atom. Near the PES (PES = Potential Energy Surface) crossings the interval was reduced from 0.05 to 0.01 Å. In total, the ADMP DFT:B3LYP computations included 7500 independent runs.

The computations are carried out separately for S and T states with the ab initio molecular dynamics (ADMP) code by Schlegel and Frisch 222324, introduced now into the NwChem software package (non-distributed version 5.3 plus) 31. The method is based on the extended Lagrangian (EL) molecular dynamics approach with the wave function propagating along with the classical nuclear degrees of freedom. Unlike the widely known Car-Parrinello (CP) method 25, using EL approach and employing plane-wave basis sets (introduced into the distributed version of NwChem), the current method uses the atom-centered basis functions, Gaussian orbitals 6–31G** built in DFT:B3LYP 323322. Computations are carried out on a Compaq Alpha Workstation cluster, at a constant human body temperature, T = 310 K. Heating to the final temperature, the initial one is 0 K, used a step-by-step procedure, each step of 10 K per 1 ps. Subsequent cooling to 0 K occurred in the reverse sequence with the same step. Such a procedure at each step provides reaching thermodynamic equilibrium between the Mg and ATP subsystems and the water pool.

Additionally, around the T-T crossing we used the same computations with a switched on hyperfine spin-coupling Hamiltonian, S_N(²⁵Mg = 5/2) - S_e. Charges on atoms are computed according to the Löwdin population analysis 34.

Initially separated by 8.0 Å (see section 2), the Mg and ATP subsystems in the pool of 78 water molecules immediately begin to interact by approaching each other and moving along the S or T PESs, depending on a spin state of the system. Fig. 2a displays the S and T PES projection profiles on the imaginary line, connecting the O1, O2, and O3 atoms; Fig. 2b is the 3D topside view of these PESs in the configuration space, restricted by r [Mg-(O1-O2-O3)] and O1-O2-O3 coordinates. At r [Mg-O2] = 8.0 Å the energy gap between the T₂ and S₁ states is 9.8 kcal/mol and between the T₁ and S₁ is 7.4 kcal/mol. Within all the space the T PESs go above the S ones; in addition, T and S states are remarkably separated in space. The S₁ PES reveals the global minimum (in our computations it is taken as a zero point, ΔE^tot = 0.0 kcal/mol), corresponding to the formation of a stable chelate, [Mg(H₂O)₄-(O1-O2)ATP]^2-. The distances Mg-O1 and Mg-O2 are identical, r [Mg-O1] = r [Mg-O2] = 2.05 Å, Table 1. The S₂ has a local minimum, which is by 21.2 kcal/mol higher than that of the global one. The S₂ and S₁ states are separated by a low energy barrier of 1.8 kcal/mol that allows us to consider the S₂ minimum as a metastable, easily surmountable in real cellular environment. The T₁ and T₂ PESs, initially separated by a long-range barrier of 2.7 ÷ 2.4 kcal/mol, perpendicular to the O1-O2-O3 line and strictly positioned against the O2 atom (r [Mg-O2] = 8.0 ÷ 1.90 Å), exhibit the crossing at r [Mg-O2] = 1.90 Å, ΔE^tot = 39.6 kcal/mol. This crossing is responsible for producing S₂ and S₃ states and a spin-separated state, see below. The S₃ state reveals a local minimum at ΔE^tot = 37.8 kcal/mol, which then transforms into a more stable S₄ state, ΔE^tot = 34.2 kcal/mol, the [Mg(H₂O)₂-O2(O3)ATP]^2- ⇒ [Mg(H₂O)₄-O2(O3)ATP]^2- transition. The spin-separated state, unstable and corresponding to the electron redistribution between the Mg and ATP subsystems, arises as a small reverse cone (r [Mg-O2] = 1.87 Å) of 2.8 kcal/mol height above the T₁-T₂ crossing, Table 1.

The paper gives a new insight into the nature of NTP energetics depending on the spin activity of Mg cofactor. Up to present, Mg-induced ATP cleavage has been viewed only in the light of the hydrolytic (ionic) mechanism 12345678910. The computations show that this mechanism is not unique. Other hidden mechanisms come from the T state of Mg cofactor. When in this state, Mg cofactor directs itself to the O2-O3 fragment of NTP. This way of complexation rarely occurs, one case out of ten, but leads to significant rate enhancement in ATP cleavage, recently observed by Williams 37.

The most surprising finding is in the ability of the triplet Mg to form an unstable single-bonded state with the O2 oxygen. The state shows immediate decomposition into radical fragments – reaction (*), which starts in the femtosecond time interval 15 and finds the experimental confirmation in the Chemically Induced Dynamic Nuclear Polarization (CIDNP) studies 1516. This Mg-O2 single-bonded state is highly sensitive to the Mg nuclear spin. If Mg is in the triplet state with a switched on nuclear spin (²⁵Mg), this ensures that ATP cleavage will proceed via a radical cleavage mechanism. This finding is absolutely new for molecular biology and unveils the mystery why the nature has chosen Mg, and not other cation, as an ATP/NTP catalyst. In living nature there is only 10% of Mg with an active nuclear spin (²⁵Mg) and 90% with inactive one. And now recall that in nine cases out of ten Mg binds to NTP through the O1-O2 atoms and only in one case through the O2-O3 atoms 123456! With the unchanged ratio of active to inactive spin (R) throughout cellular medium, a living cell, according to its program, chooses either active or inactive sort of Mg thus directing ATP cleavage through a radical or ionic path. Natural Zn has a lower content of active spin – 4.1%, and Ca is absolutely inert with its 0.15% of active spin 17. The fact prevents these cations from entering the competition with Mg.

One might be puzzled by the fact that a relatively weak hyperfine interaction 17 can affect the way of reaction, specifically with regard to overcoming energy barriers, which normally exceed the thermal ones. If we speak about low-energy reaction paths, the effect of hyperfine coupling on overcoming chemical barriers is very unlikely. But if we are in the vicinity of conical intersections 38, where T and S states are mixed up (our case), the effect seems not surprising. The reason is that hyperfine coupling makes T and S states non-orthogonal. The nonorthogonality, in turn, produces a phase (angle) ϕ between the states. In our case the T and S PESs get a rotation relative to each other by ϕ = 15⁰. This allows the cone, Fig. 2, 3, to drop down in energy (disappear) and make the spin-separated state energetically preferable. A similar situation is observed in Watson-Crick pairing, where T and S states experience crossings 39.

The effect of hyperfine coupling on a reaction path waits for its experimental confirmation. Recently published data by Buchachenko 21 and then repeated by him in the American journals 4041 show that replacement of nuclear inactive ²⁴Mg and ²⁶Mg by nuclear active ²⁵Mg gives two-threefold enhancement in the rate of ATP synthesis. This is surely an uncommon finding, but we are not very optimistic about it. If the effect works, it should at least give tenfold rate enhancement (R > 10)! Moreover, with the lack of theoretical and experimental proof, confirming the existence of ²⁵Mg⁺ and other radical forms in the reaction, the results seem highly speculative. However, we strongly believe that our computational results will find someday reliable experimental proof.

Besides nuclear specifics, distinguishing it from other cations, Mg is a unique redox center, which first accepts an electron from ATP and then gives it back to products. Ca²⁺ shows the lack of this electron-based specificity and Zn²⁺ is always a poor redox center. Historically, the latter was experimentally proved by Grignard 42, when he replaced Zn by Mg and thus discovered his famous reaction, which a hundred years later found a surprisingly simple explanation in S-T level conversions of Mg 43.

In summary, Mg uniquely combines redox and nuclear spin properties, and they make the cation act as a unique biological catalyst, assisting NTP to release its energy slowly (hydrolytic mechanism) or rapidly (free radical mechanism) and then gain it back via NTP synthesis. By manipulating with triplet and singlet states of Mg we can direct NTP cleavage in a desired way, and these studies are in the full swing.