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Spin symmetry transitions make DNA strands separate. New insight into the mechanism of transcription

This content has been downloaded from IOPscience. Please scroll down to see the full text. 2015 Phys. Biol. 12 066017 (http://iopscience.iop.org/1478-3975/12/6/066017) View the table of contents for this issue, or go to the journal homepage for more

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Phys. Biol. 12 (2015) 066017

doi:10.1088/1478-3975/12/6/066017

PAPER

RECEIVED

12 June 2015

Spin symmetry transitions make DNA strands separate. New insight into the mechanism of transcription

REVISED

8 November 2015 ACCEPTED FOR PUBLICATION

12 November 2015 PUBLISHED

8 December 2015

Alexander A Tulub and Vassily E Stefanov Centre for Interdisciplinary Computational and Dynamical Analysis, University of Manchester, Oxford Road, Manchester M13 9PL, UK Saint-Petersberg State University, University Embankment, 7/9 Saint-Petersberg, 199034, RF E-mail: [email protected] Keywords: singlet-triplet conversions, DNA transcription, molecular spintronics

Abstract The DFT:B3LYP (6–31G** basis set) method, including the hyperfine and spin–orbit couplings (HFC and SOC, respectively), is used to study the separation of two complementary trinucleotide sequences, (dC–dG–dA)–(dG–dC–dT), upon the action of two Mg(2+) cofactors (a simplified model). The computations reveal a crossing of the singlet (S) potential energy surface by the triplet (T) surface at two distinct points. Within the crossing region the T curve lies below the S curve. Adhering to the concept of the minimal energy path, one can assume that the T path is more favorable compared to that of the S path. The T path is not simple; it consists of two, T+ and T−, curves initially separated by the HFC and SOC. On reaching the second crossing point, both curves merge into the T0 state, which facilitates the T→S transfer. Totally, the process of the two trinucleotide separation (the first step of transcription) appears as the S→T→S symmetry conversion.

1. Introduction Symmetry is a core nature concept making a physical quantity conserved [1] (the Noether theorem [2], 1918). Symmetry breaking signals that the conservation law is no longer valid [3]. Most chemical and biochemical processes/reactions deal with the total spin conservation [4]. Hopping from one branch of the reaction to another often assumes the change of spin [5]. Mostly these changes are low energy singlet (S)—triplet (T) conversions, which occur at some critical points (crossing points) of equal energy where two or more potential energy surfaces (PESs) meet [6]. In living cells the external magnetic fields, except that of the Earth (∼5G), do not exist [7]. The fact does not exclude local magnetic fields which locally affect this or that process directing it toward the desired path. The origin of local magnetic fields in any material, living and nonliving, is the spin–orbit coupling (SOC) [8] and hyperfine coupling (HFC) [9]. In living cells the effect of both couplings is small, but not negligible [7]. Nevertheless, the main load on the formation and change of spin orientation falls on the cations (cofactors) whose presence modifies the object’s behavior. One of these cations is magnesium (2+), © 2015 IOP Publishing Ltd

an integrable part of initiating ATP/GTP cleavage, DNA/RNA synthesis, recognition, and cell signaling [10]. The major property, distinguishing Mg(2+) from other cations, is in its ability to serve as a redox cofactor. Mg(2+) easily gains electrons, becoming a Mg(+) and even Mg(0), and then gives them up to the object to which it interacts. Redistribution of the electron density between the magnesium and the object might result in production of unpaired electrons changing the path of the reaction. The current paper aims to show that three DNA nucleotides, paired to their three DNA nucleotide counterparts according to the famous Watson–Crick pairing rule [11], fall apart upon the action of two Mg (2+) cations in the T state. In living cells the separation of DNA strands (the first step of transcription) occurs upon the action of DNA polymerase [12], which complex structure does not allow revealing the nature of this separation. Our system simulates the real process. The results rest on the DFT:B3LYP computations (6–31G** basis set) [13], including the SOC and HFC, which facilitate spin transitions in the vicinity of the crossing points.

Phys. Biol. 12 (2015) 066017

A A Tulub and V E Stefanov

Figure 1. The initial optimized structure of the {(dC–dG– dA)–(dG–dC–dT)+2Mg(2+)} fragment in the S state. Numbers 1, 2, 3, 4 indicate the oxygens to which the Mg cations are bound in the fragment.

2. Model and computations The complementary trinucleotide pair, (dC–dG–dA)– (dG–dC–dT), is selected as a model structure (the larger fragment is practically unavailable because of the computer and time resource limits). The initial atomic positions are obtained from the Neuroscience Research Institute (NRI), National Institute of Advanced Industrial Science and Technology (AIST) databank. The two magnesium cations (+2) were added to the structure on both sides of the structure backbone; they found their optimal positions during the optimization, the S curve at ΔR=0,00 Å, figures 1, 2, table 1. The nucleotide bases from both sides are held by hydrogen bonding according to the Watson–Crick pairing rule. The distances between the bases are those in [12, 14]. The computations are carried out (separately for the S and T states; the T state is ‘prepared’ by the Franck–Condon excitation from the ‘min’, ΔR=0,00 Å, of the S curve) with the Blue Gene/P computer cluster (the Argonne National Laboratory, USA).

3. Results and discussion Thanks to hydrogen bonding between the nucleotide bases, the initial state of the (dC–dG–dA)–(dG–dC– dT) fragment (hereinafter ‘the fragment’) is stable, the S state, ΔE=0,00 kcal mol−1 (‘min’, the reference point), figure 2. The Mg(2+) cations are located close to the center of the trinucleotide backbone—the optimal structure obtained with the B3LYP(6–31G**) computational method, the S state, figure 1. The effective charges (the Lowdin population analysis [15]) on both magnesiums are +0,55 (left) and +0.57 (right), table 1. These values indicate that the initially added Mg(2+) cations act as effective oxidants accepting the electron density from the fragment. Figure 2 reveals the crossing of the S (the S PES) and T (the T PES) curves at two points differing in the distance of 0,25 Å [18, 19]. In this region, the T curve lies below the S curve. The S curve has the global minimum, ΔR=0,00. The minimum corresponds to the Watson–Crick (W–C) pairing distance [14]. The 2

Figure 2. Two-dimensional cuts of the S and T PESs.; the ‘min’ is taken as a reference point, ΔR=0, 00, and corresponds to the initial Watson–Crick (W–C) distances between the bases. The positive values of ΔR mean the separation between the nucleotides, the negative—their repulsion. The vertical line, starting from the ΔR=0, 00, shows the Franck–Condon excitation (ΔE=22,47 kcal mol−1). The T+, T−, T0 and S are shown separately in figure 4.

distances Mg(left)-O1(O2) and Mg(right)-O3(O4), figure 1, are 2,14; 2,16; 2,17; 2,19 Å, table. At the distances below the ‘min’, ΔR0, 42 Å (see the text).

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S ‘min’ and S at ΔR>0, 42 Å (in parentheses) q

Crossing 1

d

Mg (left)

Mg (right)

0,55

0,57

Crossing 2

q

d

q

d

MgO1 MgO2

MgO3 MgO4

Mg (left)

Mg (right)

MgO1 MgO2

MgO3 MgO4

Mg (left)

Mg (right)

MgO1 MgO2

MgO3 MgO4

2,14 (2,16) 2,16 (2,17)

2,17 (2,18) 2,19 (2,18)

1,02

1,03

2,29 2,31

2,32 2,34

0,99

0,98

2,27 2,29

2,30 2,29

A A Tulub and V E Stefanov

Phys. Biol. 12 (2015) 066017

A A Tulub and V E Stefanov

Figure 3. The spin density on the separated trinucleotide strands (ΔR=0, 40 Å). Arrows indicate the direction of spins (Sz), small on the Mg atoms, large on the trinucleotides.

On distances are little shorter. Totally, the fragment between the 0,17–0,42 Å is composed of two spinseparated subfragments—Mg–(dC–dG–dA) and (dG– dC–dT)–Mg. The spins on the Mg atoms are parallel, the spins on the (dC–dG–dA) and (dG–dC–dT) subfragments are also parallel, but their signs are opposite to those on the Mg. The effect is highly intriguing. The details are given below. The region, ΔR=0,17–0,42 Å, leaves the fragment on the T path in the total singlet state (do not confuse it with the S curve; the two named states have nothing in common!). This state arises thanks to four electrons—the two unpaired electrons on the Mg atoms produce the triplet state, T+ (↑↑); the two unpaired electrons on the trinucleotide subfragments produce the triplet state, T− (↓↓), figure 3. The T+ and T− states are the product of the HFC (0.7×10−5 (Mg) and 10−5 (subfragment) kcal mol−1) and SOC (2×10−5 (Mg) and 4×10−5 (subfragment) kcal mol−1); [17] the data correspond to the first crossing point. Different energies (they are highly small compared to the energy of excitation and thus not seen in figure 2) show that the electron on the Mg atom experiences a smaller field effect than that on the subfragment. The T+ and T− curves show the tendency to merge within the range 0,17–0,42 Å, figure 4. The asymptotic point is T0. The T0 curve (it is unoccupied except the asymptotic point at ΔR=0,42 Å) is equidistant from the T+ and T− curves and facilitates the transfer T0→S at ΔR=0,42 Å (the T0 is somewhat identical to the S, for details see [17]). When back onto the S curve, the Mg-On distances are restored: MgO1=2,16; Mg-O2=2,17; Mg-O3=2,18; Mg-O4= 2,18 Å, table 1. The merger of the T+ and T− curves into the T0 curve automatically changes the system symmetry from the T to S, figure 2. The further separation of nucleotide strands proceeds according to the S mechanism, figure 2. As a result, we have two separated trinucleotide strands of S symmetry. Principally, each strand is able to participate in further DNA–RNA interaction (the second step of transcription). 4

Figure 4. The region 0, 17–0, 42 Å shows the merge of the T+ and T− curves. The asymptotic point is T0 which facilitates the T0→S transfer at ΔR=0, 42 Å.

4. Concluding remarks (i) Change of symmetry, as we see, plays a crucial role in DNA strands separation. The S→T transfer (in our case this is the excitation) makes the process irreversible. The key role in a choice of the path, T or S symmetry, plays the minimum energy principle. The nature always selects the optimal energy path (in our case, this is the T path, 18,12, kcal mol−1; the S paths lies higher, ΔE=25,37 kcal mol−1). (ii) The study reveals the crossing of the S curve by the T curve at two distinct points. The crossing region (ΔR=0,17–0,42 Å) is highly essential. Within it we might observe a highly interesting physics. Initially separated (this means that the Mg atoms and the trinucleotides experience different local fields), the T+ and T− curves merge producing the T0 state. The T0 state is somewhat identical to the S state [17]. The transfer to the S state (ΔR=0,42 Å) signals that the produced trinucleotides has no excess spin density and might be quite inert until some external impact is switched on.

Phys. Biol. 12 (2015) 066017

A A Tulub and V E Stefanov

(iii) We really do understand that our model system (only Mg atoms instead of the DNA polymerase [21, 22]) is highly simplified. The nature has developed a more sophisticated tool [21]. Unfortunately, the DNA polymerase, which functioning is unable without Mg cations [22], is a too complicated system to be studied in detail from the spin point of view, theoretically and experimentally. However, the singlet-triplet transitions might be very helpful in understanding the nature of DNA transcription (in our case, this is the first step of transcription). The external factor here is the spin, which primarily affects the magnesium atoms and then trinucleotides (redox reactions). (iv) The simultaneous presence of the equally occupied T+ and T− states produces the singlet state. Despite the fact that the whole system remains in this ‘inert’ state, the spins on the inner surface of trinucleotides, figure 3, promote the divergence of trinucleotides—a direct proof of the Inverse Spin Hall Effect [20] accompanying by the charge current within the Mg-trinucleotide sequences. The Mg atoms undergo the reduction, the trinucleotide subfragments—the oxidation. The internucleotide charge current does not exceed 1,2% of the total charge redistribution (this is the evidence of the charge imbalance within the subfragments during their separation). (v) Some incompleteness might arise in considering the only one fragment (the rest fragments automatically occur from the initial under the nucleotide transpositions). However, this is not a fact. Why? We deal with DNA complementary (W–C) trinucleotides. Each DNA complementary pair is isoelectronic to any other pair (two complementary bases in sum give 134 electrons; the rest core, including the sugar, is identical to every nucleotide). This property is surely valid for trimers. So, nucleotide transpositions in the complementary trinucleotide dimers give us no more than ‘isomers’, which energy difference does not exceed (at most) 0,5–2,5 kcal mol−1, a common computational fact, including the H-bonded systems (the W–C distances are stored; this prevents dramatic geometry changes between ‘isomers’). To prove this we can compare the initial energy (ΔR=0,00 Å) of the {dC–dG– dA}–{dG–dC–dT} fragment (our case) with the energy of the {dG–dC–dA}–{dC–dG–dT} fragment. The obtained data (our own computations with the same B3LYP:6–31G**method [23]) reveal that the first fragment lies higher in energy than the second fragment by 1,35 kcal mol−1. The result proves that the energy shift rather comes from the different stacking environment [23] than the origin of the nucleotide

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transposition (the core is still rigid!). Now let’s remember that the first crossing point occurs at 18,12 kcal mol−1 and the second at 13,05 kcal mol−1. So, the energy corrections, arising from the transpositions, are inevitable, but the energy shifts caused by them are unable to cancel the observed effect—the T PES crosses the S PES. The shifts are negligible when one purine base replaces the other purine base (our fragment). In general, when we speak about all possible trinucleotide pairs (there are 32 different trimers, 8 made of identical monomers and 24 made of different monomers [24]), the energy shifts might reach bigger, but not crucial values. This problem stands separately and needs further computations. With this publication we want to attract the reader’s attention to the (S-T)/(T-S) crossing effect which seems to be of importance to understanding the mechanism of DNA separation.

Acknowledgments The author thanks Dr JF Cooper (the Argonne National Laboratory, USA) for helpful discussions during the computations. The study is sponsored by the NASA Ecology grant 05789(A)-2015.

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[15] Brunh G, Davidson E R, Mayer I and Clark A E 2006 Löwdin population analysis with and without rotational invariance Int. J. Quant. Chem. 106 2065–72 [16] Quapp W and Heidrich S 1984 Analysis of the concept of minimum energy path on the potential energy surface of chemically reacting systems Theoret. Chim. Acta. 66 245 [17] Turro N J 1983 Influence of nuclear spin on chemical reactions: magnetic isotope and magnetic field effects Proc. Natl Acad. Sci. 80 609 [18] Jockush S and Turro N J 1998 Phosphinoyl radicals: structure and reactivity. A laser flash photolysis and time-resolved ESR investigation J. Am. Chem. Soc. 120 11773 [19] Turro N J, Ramamurthy V and Scaiano J C 2009 Principles of Molecular Photochemistry (USA: University Science Books)

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[20] Averkiev N S and Dyakonov M I 1983 Possibility of orienting electron spins with current Sov. Phys. Semicond. 17 393 [21] Ochoa S 1959 The Nobel Prize Lecture [22] Yang L, Arora K, Beard K, Wilson S H and Schlick T 2004 The critical role of magnesium ions in DNA polymerase cloning and active site assembly J. Am. Chem. Soc. 126 8441–53 [23] Dabkowska I, Gonzalez H V, Jurecka P and Hobza P 2005 Stabilization energies of the hydrogen-bonded and stacked structures of nucleic acid base pairs J. Phys. Chem. A 109 1131–6 [24] Lambropoulos K, Kaklamanis K, Georgiadis G and Simserides C 2014 THz and above THz electron or hole oscillations in DNA dimers and trimers Ann. Phys. 526 249–58

Spin symmetry transitions make DNA strands separate. New insight into the mechanism of transcription.

The DFT:B3LYP (6-31G** basis set) method, including the hyperfine and spin-orbit couplings (HFC and SOC, respectively), is used to study the separatio...
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