The conformational analysis of adenosine triphosphate by classical potential energy calculations

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  • BIOPOLY MERS VOL. 14, 2159-2179 (1975)

    The Conformational Analysis of Adenosine Triphosphate by Classical Potential Energy


    0. E. MILLNER, JR. and JON A. ANDERSEN, Research and Development Department, Norwich Pharmacal Company, Norwich,

    New York 13815


    The conformational analysis of adenosine triphosphate was conducted by using classical potential energy calculations. All rotatable bonds were examined, i.e., no dihedral angles were fixed a t predetermined conformations except for the ribofuranose ring, which was held in the C(3)-endo conformation-the conformation observed for adenosine in the crystal state.

    The energy terms included in the total energy expression consist of nonbonded pairwise interaction, electrostatic pairwise interaction, free energy of solvation, and torsional bond potentials.

    Two separate approaches were used in the conformational analyses. The first consisted of a sequential fragment approach where four bonds were rotated simultaneously at 30 increments. Each fragment overlapped the preceding one by a t least one bond. All ro- tors were then simultaneously examined a t their minima and a t f15O. The second ap- proach consisted of a coarse grid search where all rotors were examined simultaneously, but only a t staggered positions. The low-energy conformations thus obtained were then used as starting conformations for a minimization routine based on the method of conju- gate directions. The first approach required about 40 hr of central processing unit (CPU) computer time, while the coarse grid/minimization approach required about 4 hr of CPU time.

    Both the sequential fragment approach and the minimization approach yielded lowest- energy conformations which are remarkably similar to the solid-state conformation of C(3)-endo ATP.


    The ubiquity of adenosine triphosphate (ATP) in biological systems has stimulated investigations of the conformation of the ATP molecule by X-ray spectroscopy,1,2 nuclear magnetic resonance s p e c t r o s ~ o p y , ~ ~ molecular orbital calculation^,^ and immunochemical studies.* In addi- tion, specific structural aspects of ATP have been examined by using ul- traviolet spectroscopy? and optical rotatory dispersion.lOJ1

    Although several molecular orbital calculation^^^-^^ and classical po- tential energy (CPE) c a l c ~ l a t i o n s ~ ~ J ~ have been performed on nucleo- sides and nucleoside analogs, few calculations on nucleoside triphos- phates have been reported. The authors are aware of one molecular or-


    0 1975 by John Wiley & Sons, Inc.


    bital investigation of ATP7 and of no CPE calculations on nucleoside triphosphates. Furthermore, the molecular orbital investigation of the conformation of ATP by Perahia et al.7 consisted of a reduced treat- ment where only certain rotors were rotated, the remainder being fixed at the crystallographic values. Thus, it seems that a more complete ex- amination of the conformational degrees of freedom for ATP via CPE calculations is warranted. Classical potential energy calculations in the manner of Scheragal* have been used with noticeable success in the con- formational analysis of a variety of molecular type^.'^-^^ While the conformational analysis of large molecules by molecular orbital methods is restricted to the examination of a relatively few conformations, con- formational analysis by CPE calculations allows one to examine a large number of conformations. For example, the conformational analysis of a molecule with four rotors could be performed by allowing all four ro- tors to be rotated simultaneously at 30" increments. While an exami- nation of the total permutations (20,736) by molecular orbital methods would require far too much computer time, the computational time re- quired to evaluate all 20,736 conformations by CPE calculations is feasi- ble.


    The theoretical method employed has been described in detail by Scheraga.18 Briefly, the approach taken here entails the determination

    TABLE I Variables Used in Calculating dji and eji

    Atom rvdw ,a ai x 1024,

    A cm3 Npff

    H 1.20 0.42b 0.9e 0 (hydroxyl) 1.52 0.59b 7 .Oe 0 (carbonyl) 1.52 0.846 1.0e 0 (ether or phosphate 1.52 0.64b 7.0e

    0 (pendant phosphate 1.52 1.ooc 7.0e

    C (aliphatic) 1.70 0.93b 5.2e C (aromatic) 1.70 1.22d 5.2e N (primary) 1.55 0.87b 6.le N (aromatic) 1.55 1.03b 6.le

    1.80 3.00d 14.3f P

    chain oxygen)

    0 XY gen )

    ~ _ _ _ _ _ _______ a Van der Waals'radii taken from Bondi, A. (1964) J. Phys. Chem. 68, 441-456. b Taken from Ketelaar, J. A. A. (1958) Chemical Constitution, Elsevier Pub-

    lishing Company, New York, p. 91. c Estimated on the basis of electron density on the pendant phosphate oxygens.

    The effect of varying the value from 1.0 to 2.0 was found to be negligible. d From Ref. 27. e From Ref. 18. f From Scott, R. A. & Scheraga, H. A. (1965) J. Chem. Phys. 42,2209-2215.


    of the molecular conformation which gives a minimum value for Etot in


    E,b represents the nonbonded pairwise interaction energy, U j , which consists of a van der Waals repulsive energy contribution and a London attractive energy contribution. These are represented by the first and second terms, respectively, in the Lennard-Jones 6-12 equation (Eq. (2)).

    Eq. (1).

    Etot = Enb -I- Eel i- Esolv i- Etors

    u.. 1J = d.. /r!a- IJ V e../rG. 1J Y (2) The coefficient eij of the attractive term is obtained from the Slater- Kirkwood equation (Eq. (3))

    TABLE I1 Constants for Nonbonded Potential Energy Equationa9b

    CaI 370 car 546 874 H 128 202 47 OOH 278 404 89 217 Oc=o 372 552 124 283 369 0.0. 297 443 99 231 300 246 N-NH, 365 553 135 278 356 29 125 Nar 525 640 143 315 414 33 412 456 OPO 422 514 144 321 421 339 418 474 480 P 1150 1410 401 860 1138 917 1134 1291 1303 3567

    a Key: C,I = aliphatic carbon;C, = aromatic carbon; OOH = hydroxyl oxygen; Cc=o = carbonyl oxygen; 00- = ether oxygen or phosphate chain oxygen; N-NH, = primary amine nitrogen; Nar = aromatic nitrogen; O p a = pendant phos- phate oxygen.

    b The values given are for the interaction of the two atoms found in the column and row corresponding to those values.

    where e is the electronic charge; h is Plancks constant divided by 27r; m is the electronic mass; ai and aj are the atomic polarizabilities of atoms i and j ; and Ni and Nj are the effective numbers of valence shell elec- trons of atoms i and j . The coefficient dij of the repulsion term is ob- tained by minimizing U , in Eq. ( 2 ) when rij is equal to the sum of the van der Waals radii (rvdw) of atoms i and j . The values used for a,, Ni, and rvdw are given in Table I. The values obtained for eij and dij are given in Tables I1 and 111.


    TABLE I11 Constants for Nonbonded Potential Energy Equationa?b

    dij x kcal a'*/mole

    ca1 Car H OOH OC=O 0.0. N-NH, N, 0p.0- P

    Ca1 286 car 477 740 H 38 7 1 45 OOH 149 245 17 80 OC=O 209 470 25 108 145 00- 146 224 15 78 100 9 4 N-NH, 203 285 32 110 145 122 27 Nar 352 311 28 117 173 135 166 181 OPQ 225 280 28 125 165 130 173 196 181 P 1015 1280 139 562 750 559 785 900 825 3660

    a Key: Gal= aliphatic carbon; Car = aromatic carbon; OOH = hydroxyl oxygen; CC=O = carbonyl oxygen; 0.0. = ether oxygen or phosphate chain oxygen; N-NH = primary amine nitrogen; N, = aromatic nitrogen; 0p.0 = pendant phos- phati oxygen.

    b The values given are for the interaction of the two atoms corresponding to the column and row of the respective numerical values.

    Eel represents the electrostatic component of the total energy and is calculated with the coulombic potential function (Eq. (4)).

    Here, qi and qj are the net atomic charges of the respective atoms and rij is their interatomic distance. D is the apparent local dielectric constant and has been assigned the value of 3.5 in this study-a value within the range of dielectric constants examined by Brant and F l ~ r y , ~ ~ who took the experimental dielectric constants of polymers into consideration. The net atomic charges were obtained from Alving and Laki's CNDO/2 results25 on ADP-3 and ribose phosphate and extrapolated to ATPW3. The phosphate atoms, pendant oxygen, and intrachain oxygens were as- signed atomic charges of 0.32, -0.49, and -0.36, respectively. Values of -0.31 and 0.21 were assigned to the oxygen and hydrogen atoms of the y-phosphate hydroxyl. Remaining atomic charge assignments are list- ed in Ref. 24. The numerical factor is included in Eq. (4) to yield ener- gies in units of kcal/mole.

    Esolv, representing the contribution to the total energy made by the free energy of solvation, is found by summing the free-energy change for each atom that arises as the result of other approaching atoms (Eq. (5)).

    Gi represents the free-energy contribution arising from the removal of solvent from atom i and is calculated according to Eq. (6)


    where GP represents the free-energy change resulting from the removal of one water molecule from the first hydration shell of atom i. 4(Wi,AJ represents the function shown in Eq. (7)

    where Wi is the amount of water removed from atom i by the approach of all other atoms, and Ai is the number of water molecules belonging to the first shell of atom i.

    This function was designed to give a value of zero when Wi = 0 and a maximum value of Ai.26 Wi is calculated bywmming the amount of water, q i j removed from atom i by approach of atom j for all approach- ing atoms,

    Wi = C qij (8) j # i

    and qi; is described by Eq. (9), where Vj is proportional to the volume of the approaching atom j .

    (9) g(rij) is a continuous function (Eq. (10)) designed to give qi, a value of zero when the interatomic distance ri, is equal to ro, the sum of the van der Waals radii of atoms i and j plus 2.2 A.

    4. . i j = V . ,g( r i j )

    g(r;j) was designed26 to be a very steep function which would reflect the assumption that when ri; becomes less than ro an amount of water is displaced which is proportional to atom j and that further decreases in rij down to the sum of the van der Waals radii should not profoundly affect the solvation. When r > ro, g(rij) is assigned a value of zero.

    The values for GP, A;, and V; used in the calculation of the free-ener- gy change due to solvation effects are listed in Table IV.

    Etors represents the torsional energy component and is represented by Eq. (11)


    where U$ is the barrier height of rotation about the respective bond, X is the periodicity of the barrier, and 4 is the angular rotational incre- ment. The P-0 bonds were assigned a barrier height of 1.0 kcal/mole while the C(5)-0 and C(4)-C(5) bonds were assigned barrier heights of 3.0 and 3.5 kcal/mole, re~pectively.~~ The barrier height of the glyco- sidic bond was considered to be negligible in accordance with Lakshmi- narayanan and Sasisekharan.16 Each bond was considered to have threefold periodicity.

    Etors = (U4/2) (1 + cos X 4)


    TABLE IV Parameters Employed in the Calculation of Esob

    Atom or group

    H (amino) H (hydroxyl) 0 (ether, carbonyl,

    phosphate ) 0 (hydroxyl) C (aromatic) CH (aromatic) CH (aliphatic) CH, (aliphatic) N (aromatic, amide) P

    G: ,a A fa kcal/mole (solvation number)

    0.31 0.31 0.94

    0.84 0.11 0.11

    -0.13 -0.13


    2 2 4

    5 2 3 2 3 2 O*

    0.102 0.096 0.225c

    0.172 0.158 0.269 0.226 0.342 0.110 -

    a Taken from Ref. 26. b Calculated by dividing by 30 the volume of the atom or group (in A3) given C Vi calculated by using an average value for the volume of an oxygen atom from

    d The solvation of the phosphorus atoms was assumed to be negligible based

    by Bondi (J. Phys. Chem. 68,441-456 (1964)).

    those given by Bondi (J . Phys. Chem. 68, 441-456 (1964)).

    upon space-filling models.


    First Method

    The nomenclature of the rotatable bonds is presented in Figure 1. The immensity of the number of possible conformations if one examines all rotors simultaneously at 30' increments of rotation (1211, or almost 9 trillion for ATP-3) makes it apparent that a fragment approach must be taken.

    1-Methyltriphosphate. Bond angles and distances required for the coordinates program2* were obtained from refinements by Cruick- shank29 on the X-ray crystallographic data of sodium triphosphate de- termined by Davies and C ~ r b r i d g e . ~ ~ In the conformational analysis of the trivalent anion of l-methyltriphosphate, w3!, w3, and w2t were rotated simultaneously at 30' increments from 0' to 360'. This was followed by simultaneous rotation of 0 2 ' , wg, wl', and ax', 01, 6 respectively. The calculated minimum for each rotor was incorporated in the succeeding calculations. All local secondary minima within 1.5 kcal of the calculat- ed lowest-energy conformation were carried through successive calcula- tions also.

    ATP. The geometry of the adenine-ribose moiety (C(3')-endo) was taken from Lai and Marsh.31 The rotors x, $, 4, and w1 were rotated si- multaneously at 30' increments from 0' to 360' starting from eclipsed positions. Rotors w1' through w3' were fixed at their predetermined minima. This was followed by simultaneous rotation of $, 4, w1, and w1' with x examined at positions found in all conformations within approxi-


    Fig. 1. Nomenclature of the rotatable bonds examined in the conformational analyses.

    mately 2 kcal of the calculated lowest-energy conformation ( O O , 300, 330O). Next, rotations about a and p were examined simultaneously along with x and II/ to determine the effect of the ribose hydroxyls on the preferred conformations at x and II/.

    The results of the fragment approach were further examined by si- multaneous rotations around all rotors, excluding a and p. To do this, each rotor was examined at its predetermined minimum energy confor- mation and at f30. The results were then refined by repeating the procedure at f 1 5 O increments.

    Second Method

    A second approach to the conformational analysis of ATP was per- formed in the following manner. Simultaneous rotations were made at all bonds from x through w3, excluding bonds a and p (Fig. 1). In order to keep the computer time at a practical level, only the energies (Eq. (1)) of the staggered conformations (60, 180, 300, where the starting, eclipsed conformation is Oo) were determined. The results from the grid search were then used in a Powell minimization s u b r o ~ t i n e ~ ~ , ~ ~ based on the method of conjugate directions. Starting conformations for the minimization subroutine were selected from the low-energy con- formations of the grid search in the following manner. Conformations corresponding to various values of x through w3 were considered if, for all three positions of w y , the total conformational energy was within 14 kcal/mole of the grid minimum. This yielded 3 X 36 conformations-36 different permutations of x through w3 and three staggered positions of w3. From th...


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