saturation-recovery epr with nitroxyl radical–dy(iii) spin pairs: distances and orientations

Saturation-Recovery EPR with Nitroxyl Radical−Dy(III) Spin Pairs:Distances and OrientationsDonald J. Hirsh,* Joselle McCracken, Ryan Biczo, and Kelly-Ann Gesuelli

Department of Chemistry, The College of New Jersey, Ewing, New Jersey 08628, United States

ABSTRACT: We describe a method for measuring the distance between a radical and aDy(III) ion using saturation-recovery electron paramagnetic resonance (EPR) anddemonstrate its application using four chemically modified DNA duplexes. The four DNAduplexes contain a terminal nitroxide spin-label and a midsequence, EDTA-bound Dy(III)ion but differ in the nitroxyl radical (NO)−Dy(III) distance. Distances can be determinedwith high precision because of their sixth-root dependence on the experimentallydetermined dipolar rate constant. Furthermore, the orientation of the NO−Dy(III)interspin vector in the Dy(III) g-tensor reference frame can be determined for two of theDNA duplexes. The shortest mean NO−Dy(III) distance, 18.3 ± 0.3 Å, and the longest,50.3 ± 2.4 Å, are near the lower and upper distance limits of what can be measured withthe NO−EDTA(Dy(III)) pair at X-band. These methods are applicable to structuralstudies of nucleic acids, proteins, and their complexes.

1. INTRODUCTION

1.1. Distance Measurements by EPR. The past decadehas seen the development of elegant electron paramagneticresonance (EPR) methods to measure distances betweenparamagnetic sites in macromolecules.1−3 The long-rangedistances derived from these measurements can supply essentialstructural information. For a pair of nitroxide spin labels, thepulsed EPR methods of double quantum coherence and doubleelectron−electron resonance (DEER) are typically used.4,5

DEER can also be used to measure the distance between aradical and a spin 1/2 metal ion provided the metal ion has verylittle g-anisotropy.6,7 For spin 1/2 metal ions of greater g-anisotropy, radical−metal ion distances can be measured usingthe relaxation-induced dipolar modulation EPR (RIDME)experiment.8 While these methods vary somewhat in theirpulse sequences and constraints, they all work by measuring themetal ion’s dipolar field generated at the radical.During this same period there has been relatively little

development of an older method for measuring radical−metalion distances and interactions known as saturation-recoveryEPR.9−14 This seems unfortunate, since it complements thedipolar field methods nicely. Rather than measure the dipolarfield at the radical, the saturation-recovery EPR methodmeasures the dipole-induced, spin−lattice relaxation enhance-ment at the radical. This makes it possible to measure radical−metal ion distances when the metal ion has spin greater than1/2, indeed, when the metal ion itself is invisible to EPR.11,15

Furthermore, saturation-recovery EPR can also be used toprobe other paramagnetic interactions, for example, the strongexchange coupling within a dinuclear metal complex, or theweak exchange coupling between a metal complex and theradical.16 However, the apparent necessity of having a referencesystem of known structure containing an identical metal center,has limited its application in measuring distances.17

If the paramagnetic properties of the metal ion wereinsensitive to the precise nature of the coordinating ligands,the requirement of a reference system would become lessburdensome because the same reference could be used for avariety of macromolecular systems of unknown structure. Inthis regard the lanthanide ions appear most promising, sincetheir unpaired electron spins reside in shielded f-orbitals andtheir crystal field splittings are modest in comparison to thoseof the transition metal ions.18 Of the lanthanide ions,dysprosium is an obvious choice, since it has long been usedin EPR experiments to enhance the spin−lattice relaxation ofradicals.19−23

The lanthanide ions all have a stable 3+ oxidation state andsimilar ionic radii and ligand affinities.24 While they have noknown biological role, they can substitute for calcium ions,Ca(II), and magnesium ions, Mg(II), in proteins and nucleicacids. Lanthanide ions can substitute for Ca(II) in a widevariety of proteins, in many cases providing full enzymaticactivity and in others inhibiting the enzyme.25 The substitutionof erbium ion, Er(III), for Mg(II) inhibits Dicer, a specializedribonuclease, while the substitution of lanthanum ions, La(III),for Mg(II) improves the processivity of reverse transcriptase, aDNA polymerase.26 The terbium ion selectively displaces amagnesium ion in the hammerhead ribozyme, inhibiting itsfunction.27

We are not the only group to notice the potential oflanthanide ions for measuring pairwise distances by EPR. Jageret al.9 have already reported a distance measurement bysaturation-recovery EPR in a model system containing anitroxide spin-label and the Dy(III) ion. Also, it is possible to

Received: June 21, 2013Revised: August 26, 2013Published: August 27, 2013

Article

pubs.acs.org/JPCB

© 2013 American Chemical Society 11960 dx.doi.org/10.1021/jp406159m | J. Phys. Chem. B 2013, 117, 11960−11977

pubs.acs.org/JPCB

use another lanthanide ion, Gd(III), in the DEER experi-ment.28−30 The central transition of this S-state ion can be usedas a pseudo-spin-1/2 system, paired with either another Gd(III)ion or with a nitroxyl radical.In this work, we apply similar experimental methods as Jager

et al.9 and we make many of the same assumptions. However,whereas Jager et al. analyze their data in terms of a generalizedrelaxation parameter and multiple spin−spin interactions, weanalyze ours in terms of the original dipolar Hamiltonian andpurely pairwise interactions. This approach allows us toexplicitly evaluate the underlying assumptions of our modelsand confirm their validity. It also allows for greater precision indistance measurements.Still, if the same distance measurement can be made with

Gd(III) using DEER spectroscopy, is there any reason toconsider the saturation-recovery methodology? We note that athigher frequencies, the application of DEER to Gd(III)-labeledmacromolecules appears to be very promising. A distance of 60Å between Gd(III) ions has been measured by Song et al.31 atKa-band (30 GHz) and by Yagi et al.28 at W-band using theprotein dimer ERp29. The same protein dimer has been usedto demonstrate the ability to measure nitroxyl radical (NO)−Gd(III) distances of 60 Å at W-band using DEER.32 However,at X-band, the Gd(III) spin-label may be less useful for distancemeasurements.33 The maximum distance measured so farbetween a nitroxide spin-label and Gd(III) ion at X-band is∼25 Å.34 The maximum NO−Dy(III) distance that we reporthere at X-band, ∼50 Å, is comparable to what has beenmeasured at Ka- and W-bands with Gd(III). Since pulsed X-band spectrometers are more common than pulsed K- and W-band spectrometers, this may be a significant practicaladvantage. Furthermore, the sensitivity of the saturation-recovery experiment is comparable to that of the DEERexperiment. A potential advantage for the saturation-recoverymethodology is precision. Since distances determined by spin−lattice relaxation enhancement have a sixth-root dependence onthe measured rate constant, an error of 6% in the rate constantcontributes only 1% to the distance error. Finally, thesaturation-recovery methodology makes the entire series oflanthanide ions available as spin probes, including phosphor-escent lanthanide ions like Tb(III) and Eu(III) that can reporton their ligand environment or be used for Forster resonanceenergy transfer experiments (FRET).25,35

In this paper, we describe a family of DNA duplexes used toinvestigate the electron spin−spin interactions of a nitroxidespin-label and a Dy(III) ion. Well-established equations used todescribe the spin−spin interactions of two spin-1/2 species areintroduced. We assume that they are applicable to Dy(III)because only the lowest lying spin states of the Dy(III) ion, theKramer’s doublet, contribute to the spin−lattice relaxation ofthe nitroxyl radical (NO). We then develop models using theseequations to simulate the saturation-recovery transients arisingfrom the nitroxyl radical when the NO−Dy(III) interspinvector has a random distribution of orientations and a normal(Gaussian) distribution of lengths. The models are fit to theexperimental saturation-recovery transients of the nitroxylradical in the DNA duplexes in order to extract the dipolarrate constants. The temperature dependence of these dipolarrate constants allows us to calculate the average NO−Dy(III)distance in each DNA duplex. With this distance information,the temperature dependence, T, of the Dy(III) ion’s spin−lattice relaxation time, T1, can be determined from thesaturation-recovery transients. A plot of log(1/T1) versus 1/T

for the Dy(III) ion is consistent with the Kramer’s doubletrelaxing via an Orbach mechanism. The slope of this plotreveals that the energy separating the Kramer’s doublet fromthe lowest lying pair of excited spin states is large compared tokT, where k is the Boltzmann constant and T is the temperatureat which the distance is measured. This supports our originalhypothesis that the Kramer’s doublet is the source of relaxationenhancement. Finally, knowing the secondary structure of theDNA duplex and the potential locations of the Dy(III) ions,possible locations for the nitroxyl radical are determined bytrilateration.

1.2. DNA Model System. The electron spin−spininteractions between a nitroxide spin-label and a chelateddysprosium ion, Dy(III), were examined in the four DNAduplexes shown in Figure 1. The duplexes are 19 base pairs in

length and essentially identical in sequence. They differ only inthe location of the modified base, E, in the left-hand strand,which substitutes for deoxythymidine, T. E is a chemicallymodified form of deoxythymidine with the chelator EDTAcovalently linked to the thymidine ring (Figure 2a). Thenitroxide spin-label, SL, is attached to the 5′-end of thecomplementary strand in the manner shown in Figure 2b. TheEDTA group of modified base E complexes the Dy(III) ion inthese duplexes, so that changing the location of E changes thespin label−Dy(III) distance (Figure 1).The chemical modifications of the DNA duplexes are used to

name them. As a group, the four DNA duplexes with Dy(III)are referred to the as the SE#Dy DNA duplexes. For example,the SE15Dy DNA duplex has a spin-label (S) at the 5′-terminusof the right-hand strand, the base E is at position 15 withrespect to the 5′-end of the left-hand strand, and the Dy(III)ion binds to the EDTA group of base E. The control DNAduplex, SE15Ca, is identical to the SE15Dy DNA duplex,except that the diamagnetic Ca(II) ion is bound to the EDTAmoiety.

Figure 1. Four DNA duplexes containing both EDTA-bound Dy(III)ions and a nitroxide spin-label (SL). The base sequences are identicalexcept for the position of E, the chemically modified base dT-EDTA.The name of the duplex indicates the position of E in the left-handDNA strand. Not shown is the SE15Ca DNA duplex, identical to theSE15Dy DNA duplex except that diamagnetic Ca(II) replacesparamagnetic Dy(III).

The Journal of Physical Chemistry B Article

dx.doi.org/10.1021/jp406159m | J. Phys. Chem. B 2013, 117, 11960−1197711961

The structure of these DNA duplexes has been extensivelycharacterized by ultraviolet (UV) absorption spectroscopy,circular dichroism (CD), and thermodynamic studies.36,37

Circular dichroism (CD) spectroscopy was used to show thatthese duplexes adopt a B-form conformation in cryoprotectantsolution. CW EPR was used to establish that the EDTA(Dy-(III)) moiety reduces the mobility of the nitroxide spin-label.The data are consistent with the formation of a metal−ligandbond between EDTA-bound Dy(III) ion and the phospho-diester backbone of the complementary strand. We call thisinteraction “secondary binding”, and molecular mechanicscalculations predict that it is thermodynamically favorable atthe 5′-3 or 5′-4 phosphate (Figure 1). Microwave progressivepower saturation experiments were used to probe theparamagnetic dipole−dipole interactions between the Dy(III)ion and the nitroxyl radical. These experiments show that thestrength of the interaction is inversely proportional to distanceand that even in the SE3Dy DNA duplex, the relaxationenhancement produced by the Dy(III) ion can be detected.

2. THEORY2.1. Treatment of Dy(III) as an S = 1/2 Ion. We assume

that only the Kramer’s doublet of the Dy(III) ion contributessignificantly to the spin−lattice relaxation enhancement of theradical. The J states of the rare earth ions are subject to largezero-field splittings and may differ in energy by a 1000 cm−1 ormore.18 These spin manifolds, in turn, are further split intopairs of MJ states by more modest crystal field splittings on theorder of 10−100 cm−1.38 If the separation between theKramer’s doublet of Dy(III) and the next highest pair of MJstates is on the order of 100 cm−1, then the spin state of thegreat majority of Dy(III) ions will be that of the Kramer’sdoublet at cryogenic temperatures. In this case, S = |MJ| =

1/2.2.2. Spin−Lattice Relaxation Enhancement with

Isotropic g-Values. The overall spin−lattice relaxation rate,k1(r, θd), of a radical in proximity to a paramagnetic metalcenter can be considered to be the sum of two rate constants.11

θ θ= +k r k k r( , ) ( , )1 d 1i 1ss d (1)

The rate constant k1i is the intrinsic spin−lattice relaxation rate,that is, the relaxation rate of the radical when not in proximityto other paramagnetic species. It is assumed to be independentof the orientation of the radical in the static magnetic field. Therate constant k1ss(r, θd) represents the relaxation rate enhance-

ment provided by electron spin−spin interactions. As shown inFigure 3, the interspin vector r connects the radical (s) and the

metal center (f). It represents the distance, r, between them andthe angle, θd, formed with the static magnetic field, H0. Thegeneral equation for k1ss(r, θd) when both the radical and themetal ion are spin 1/2 species has been presentedpreviously.11,12,14,39−42 The rate constant k1ss(r, θd) is expressedas the sum of three terms arising from the dipolar Hamiltoniandesignated B, C, and E.If only the B term contributes significantly to the spin−lattice

relaxation enhancement of the radical, we identify k1ss(r, θd) ask1ssB (r, θd) and write11

θ θ= −k r k( , )16

(1 3 cos )B B1ss d 1d

2d

2(2)

where

βτ

τω

= +ℏ

=+ −

k S Sg g

rT

g g T

( 1) and

1 ( / 1)

BB

B

1ds

2f

2 4

2 6

2f

f s2

s2

2f2

(3)

We identify the term k1dB as the dipolar rate constant for the B

term. The constant β is the Bohr magneton and the constant ℏis Planck’s constant divided by 2π. The symbols gf and gsrepresent the isotropic g-values of the metal ion and radical,respectively. The subscript f denotes the paramagnetic metalion since its spin−spin (1/T2f) and spin−lattice (1/T1f)relaxation rates are typically much faster than those of theslowly relaxing radical, subscript s. The term ωs represents theresonant frequency of the radical at the experimental field value.We have assumed that the distance between the radical and themetal ion is sufficiently large that the scalar exchange couplingis negligible, that is, Jex = 0.It is possible for the B term to dominate the spin−lattice

relaxation enhancement at temperatures below 77 K at X-band(∼9 GHz). At these low temperatures, T1f and T2f may besufficiently long that the terms ωs

2T2f2 and ωs

2T1f2 are much

greater than 1. If, in addition, the metal ion’s g-value is close tothat of the radical (g ≈ 2), such that (gf/gs − 1)2ωs

2T2f2 ≪

ωs2T1f

2, the B term will dominate.If instead the metal ion’s g-value is far from that of the

radical, such that ωs2T1f

2 ≪ (gf/gs − 1)2ωs2T2f

2, the C term willdominate the spin−lattice relaxation enhancement. Since k1ss(r,θd) would then effectively be a function of the C term only, weidentify it as k1ss

C (r, θd) and write

θ θ θ=k r k( , ) 3 sin cosC C1ss d 1d

2d

2d (4)

where

Figure 2. (a) dT-EDTA (E). The structure within brackets ispredicted to be nearly planar on the basis of UV absorption andcircular dichroism measurements. (b) The nitroxide spin-label, 1-oxyl-2,2,5,5,-tetramethylpyrroline-3-carboxylate, is linked to the 5′-terminalphosphate of the right-hand DNA strand via a three-carbon linker andamide bond.

Figure 3. The interspin vector r forms an angle θd with the staticmagnetic field H0.



βτ τ

ω= +

ℏ=

+k S S

g g

rT

T( 1) and

1C

C C1ds

2f

2 4

2 61f

s2

1f2

(5)

We identify the term k1dC as the dipolar rate constant for the C

term.2.3. Spin−Lattice Relaxation Enhancement with an

Axial gf-Tensor. A general solution for the case of a radicalwith an isotropic g-value and a metal ion with an anisotropic g-tensor has been derived by Deligiannakis.43 We describe hereequations for the special case of a radical with an isotropic g-value, gs, and a metal ion with an axially symmetric g-tensor(Figure 4). In the figure, θg is the fixed angle between g∥ and

the interspin vector, γd is the angle of rotation about theinterspin vector, and θH is the angle between g∥ and staticmagnetic field, H0. The angle θH can be calculated from θd, θg,and γd using rotation matrices.44 The value of gf can becalculated from the following equation.

θ θ θ= + ⊥g g g( ) cos sinH H Hf2 2 2 2 2

(6)

The anisotropy of the metal ion’s g-tensor means that the B,C, and E terms of k1ss(r, θd) can all make significantcontributions to the spin−lattice relaxation enhancement atthe same temperature. However, it is still possible to expressk1ss(r, θd) as the product of two terms, a rate constant and anorientation dependent term, by assuming T1f = T2f = Tf. Thisassumption will be true if the spin−lattice relaxation time of themetal ion is so short that it limits the transverse (spin−spin)relaxation time. If one also makes the substitution a = 1/(ωsTf),k1ss(r, θd) can be written as

θ θ θ

θθ

θ θ

θθ

=

−+ −

++

++ +

⎡

⎣⎢⎢⎢

⎧⎨⎪⎩⎪

⎛⎝⎜

⎞⎠⎟

⎛

⎝⎜⎜

⎞

⎠⎟⎟⎫⎬⎪⎭⎪

⎤

⎦⎥⎥⎥

k r k g

g g a

a

g g a

( , , ) ( )

(1 3 cos )1 ( ( )/ 1) (1/ )

18sin cos

1 (1/ )

9sin

1 ( ( )/ 1) (1/ )

H H

H

f H

1ss d 1d f2

2d

2

f s2 2

2d

2d

2

4d

s2 2

(7)

where

β

ω= +

ℏk S S

g

r a( 1)

61ds

2 4

6 2s (8)

The three terms inside curly brackets in eq 7 correspond to theB, C, and E terms of dipole−dipole induced spin−latticerelaxation enhancement.11

2.4. Saturation Recovery Transients Produced by aFrozen Solution. The equations in the previous sectiondescribe the relaxation enhancement expected for a pairwiseinteraction between a radical and fast relaxing paramagneticmetal ion at a single orientation and distance. However, whatwe measure by saturation-recovery EPR is the bulk recovery ofthe radicals’ z-magnetization in a frozen solution. Therefore, amathematical representation of the saturation-recovery tran-sients must include the expected distribution of orientationsand distances found in the frozen solution.First consider the case of a radical and metal center in the

same macromolecule, where both paramagnetic moieties haveisotropic g-values. For any single orientation of the interspinvector in the static magnetic field, θd1, with length r1, therecovery of the radical’s magnetization along the static magneticfield axis, Mz(r1, θ1, t) after a saturating pulse is described by thefollowing equation

θ θ θ

θ

θ

= ∞ − −

= ∞

− − +

M r t M r k r t

M r

k k r t

( , , ) ( , , ){1 exp[ ( , ) ]}

( , , )

{1 exp[ [ ( , )] ]}

z z

z

1 d1 1 d1 1 1 d1

1 d1

1i 1ss 1 d1 (9)

where Mz(r1, θd1, ∞) is the equilibrium magnetization. For asingle value of r and θd, that is, r1 and θd1, the recovery will besingle exponential.In a frozen solution, however, the recovery of the spin−

lattice relaxation will not be single-exponential. In this case, theangle θ can take on all values between 0 and π, causing thesquare of sine or cosine to vary between 0 and 1. For a fixeddistance r1, the recovery of the z-magnetization will be given by

∫ θ θ

θ

= ∞

−

− +

π{}

M r t M r

N

k k r t

( , ) ( , )

1 sin d

exp[ [ ( , )] ]

z z1 1

0d d

1i 1ss 1 d (10)

The term sin θ gives the appropriate weighting to the numberof interspin vectors r with angle θ.45 The normalizationconstant N insures that at time t = 0, after a series of saturatingpulses, the magnetization will be zero. The observed recoverywill be a weighted sum of single-exponential recoveries, but thissum is not itself single-exponential.There is another potential source of variability in the spin−

lattice relaxation rates. Given the 1/r6 distance dependence ofthe rate constant, even a modest variation in the pairwisedistance between radical and metal center can producesignificant changes in spin−lattice relaxation enhancement.For example, if the distance distribution of r falls within ±6% ofthe average distance, those radical−metal center pairs at +6%and −6% will differ by a factor of 2 in their spin−latticerelaxation rate enhancement for the same θd. Given theinherent conformational flexibility in the linkage between thespin-label and DNA helix (Figure 2b), it is prudent to modelthe recovery of the z-magnetization with an equation that

Figure 4. Schematic diagram of the interspin vector r and the axial g-tensor. The vector g∥ and H0 form the angle θH.



accounts for the variation in both the direction of the interspinvector and the distribution of radical−metal center distances.

∫ ∫σ πθ θ

σ θ

= ∞ −

− − − +

π⎧⎨⎩⎫⎬⎭

M t MN

r

r r k k r t

( ) ( ) 12

d sin d

exp[ ( ) /2 ] exp[ [ ( , )] ]

z z

r

0

2

0d d

02 2

1i 1ss 1 d

0

(11)

In eq 11, σ is the standard deviation in the distance distributionalong the interspin vector, assumed to be normal (Gaussian),and r0 is the mean interspin distance. We assume that σ < r0.We refer to the combination of eqs 2, 3, and 11 or eqs 2, 3, and14 (see below) as a “model”, specifically, the B_NDr model.This stands for B term with a normal distribution (ND) of rvalues. Similarly, we refer to the combination of eqs 4, 5, and 11or eqs 4, 5, and 14 as the C_NDr model.In the case where the paramagnetic metal ion’s g-tensor is

axially symmetric, eqs 6 and 7, one must also account for thevariation in the value of gf(θH) with γd. Equation 11 becomes

∫ ∫

∫σ π

θ θ

γ σ

θ θ

= ∞ −

− −

− +

π

π

⎧⎨⎩

⎫⎬⎭

M t MN

r

r r

k k r t

( ) ( ) 12

d sin d

d exp[ ( ) /2 ]

exp[ [ ( , , )] ]

z z

r

H

0

2

0d d

0

2

d 02 2

1i 1ss d

0

(12)

where it is understood that gf(θH) is a function of a fixed θg, andvariable θd and γd. We refer to the combination of eqs 6, 7, 8,and 12 or eqs 6, 7, 8, and 15 (see below) as the BCE_NDrmodel because eq 7 contains contributions from all three termsarising from the dipolar Hamiltonian.2.5. Measurement of Distance Ratios. Less information

is required to calculate distance ratios than absolute distances.No information about τB, τC, or Tf, is required. Saturationrecovery transients are recorded at the same temperature for aradical in two samples with different radical−metal iondistances. Dipolar rate constants can then be determined byfitting the saturation-recovery transients with eq 10, 11, or 12,as appropriate. The dipolar rate constants are used to calculatethe distance ratio using eq 13 below.46

= _

_

⎛⎝⎜⎜

⎞⎠⎟⎟

rr

k

kx

y

1d y

1d x

1/6

(13)

The rate constants k1d_y and k1d_x represent the dipolar rateconstant, k1d

B , k1dC , or k1d. In eq 13, x indicates one sample and y

the other. Equation 13 can be applied in any case where twomacromolecules share the same paramagnetic metal ion ormetal complex. If one of the two distances in eq 13 is known,the other can be calculated.15

3. MATERIALS AND METHODS3.1. Sample Preparation. The DNA duplexes were

prepared at a concentration of 56 μM in PIB-cryoprotectantas previously described.36,37 PIB-cryoprotectant is composed ofpH 7.0 buffer [50 mM piperazine-N,N′-bis(2-ethanesulfonicacid) (PIPES)], 85 mM NaCl, polyethylene glycol, andethylene glycol in a w/w/w ratio of 55/30/15. The DNAsolutions were degassed by cyclic heating to 70 °C and coolingto 10 °C, performed four or more times during thermodynamic

measurements. The EPR samples were 100 μL aliquots of DNAduplex solution in 4 mm OD thick-walled quartz EPR tubes(Wilmad). Solutions of 2 mM EDTA(Dy(III)) and 2 mMEDTA(Ca(II)) were prepared in PIB-cryoprotectant andtransferred to EPR tubes in 200 μL aliquots. These EPRsamples were degassed by three cycles of heating to ∼80 C for3−5 min and then cooling to room temperature.

3.2. EPR Experiments. Continuous-wave (CW) andsaturation-recovery (SR) EPR experiments were performedwith a Bruker ELEXSYS 580 X-band spectrometer and a Brukerdielectric MD5 resonator at a resonant frequency of 9.68 GHz.An Oxford Instruments CF935 cryostat provided temperaturecontrol. First derivative absorption spectra were collected with10 G field modulation. Saturation-transfer spectra werecollected at the second harmonic and 90° out-of-phase withrespect to the 1 G field modulation, using the method firstdescribed by Weger.47

SR-EPR experiments were performed using a 1 kW travelingwave tube (TWT) amplifier.46 Pulse power was adjusted toproduce a 16 ns π/2-pulse. The magnetic field was placed at themaximum (center) of the spin label’s signal as determined froma field-swept spin−echo spectrum. In the SR-EPR experiments,local saturation of the nitroxide signal was achieved by a seriesof 8−20 π/2-pulses spaced 3−40 μs apart, and the recovery wassampled at evenly spaced time points using a simple Hahn-echosequence48 with two-step phase cycling. Saturation-recoverytransients were signal averaged over a 20−40 min time period.

3.3. Numerical Evaluation of Equations 11 and 12.There is no analytical solution to the integrals found in eqs 11and 12. They must be solved numerically. This was done usingprograms written in MatLab. In this section we describe howwe approached these calculations.

3.3.1. Distribution of r Values. Equations 11 and 12 containintegrals that are not separable, as k1ss(r, θd) and k1ss(r, θd, θH)are functions of both r and θd. Our approach was to start with acentral value of the rate constant k1d

B , k1dC , or k1d and then

determine the distribution of rate constant values that wouldresult from a normal distribution of r values. These r valuesshould be distributed about r0, the mean distance value, suchthat each represents an equal increment of area under thenormal curve. Equal increments of area under the normal curveare represented by equal increments of the error function,erf(z). We divided the error function into 11 equally spacedvalues centered on the mean, r0, that covered 95% of the areaunder the normal curve, that is, ±2σ, where σ is one standarddeviation. The 11 equally spaced values of the error functionprovided 11 corresponding values of z. From these elevenvalues of z, the corresponding ratios of r/r0 can be calculatedusing the equation r/r0 = 1−(z(2)1/2 × RSD) where RSD is therelative standard deviation in the distribution of distances, thatis, RSD = σ/r0. The RSD represents the breadth of theDy(III)−NO distance distribution along the interspin axis in asample and was either optimized by the fitting subroutine orfixed by the user. From these 11 values of r/r0 and the centralvalue of the rate constant, the corresponding 11 values of k1d

B ,k1dC , or k1d values were found using eq 13.3.3.2. Distribution of θd Values (eq 11). The second integral

in eq 11 can be approximated by a summation over evenlyspaced values of θd with each term weighted by sin θd.However, it is more efficient to simply increment over evenlyspaced values of cos θd.

49 At each 0.01 increment of cos θd from0 to 1, single-exponential saturation-recovery transients weregenerated for each of the 11 rate constants modeling the



distance distribution (see above). These saturation-recoverytransients were then averaged to produce a saturation-recoverytransient that reflected both a distribution of interspindistances, r, and angles, θd.3.3.3. Calculation of gf

2(θH) (eq 12). Since calculation ofgf2(θH) requires cos2 θH and sin2 θH (eq 6), these were

calculated directly. The term gf(θH) was taken to be the squareroot of gf

2(θH). The user selected the g-tensor’s two principalcomponents, g∥ and g⊥, and the angle, θg. These threeparameters were held fixed. As was done for eq 11, the secondintegral was approximated by a summation over evenincrements of cos θd, although in this case it was divided into30 increments from 0 to 1. The third integral, rotation aboutthe interspin axis, γd, was approximated by a summation over 45increments of 8° each. Rotation matrices were used to calculatecos2 θH for each increment of γd at each increment of cos θd.These values of cos 2θH were used to generate a 30 × 45 arrayof values for gf

2(θH). For each value of gf2(θH), single-

exponential saturation-recovery transients were generated foreach of the 11 rate constants modeling the distance distribution(see above). These 14 850 transients (30 × 45 × 11) wereaveraged to generate the final saturation-recovery transientrepresented by eq 12.3.4. Fitting the Saturation-Recovery Transients. The

purity of the EDTA-bearing strand was not 100%. We describehere how we modeled the saturation-recovery transients for ouractual samples. We also describe which parameters were set bythe user, which parameters were optimized (fit) to provide thebest match between the simulated and experimental saturation-recovery transients, and how we compared the quality of the fitsfrom two or more simulations.3.4.1. Modeling the Saturation-Recovery Transients of

Actual Samples. In previous work, the purity of the strandsbearing the dT-EDTA moiety was determined by reverse-phasehigh-performance liquid chromatography (RP HPLC).37 Shortfailure sequences had been removed postsynthesis by anion-exchange HPLC, and the impurities observed eluted atretention times close to those of the primary peak. It is likelythat the impurities are primarily (n − 1) failure sequenceswhere dT-EDTA failed to couple to the growing oligonucleo-tide strand. The coupling efficiency of the phosphoramidateform of dT-EDTA is much lower than that of the standardnucleotides. These (n − 1) failure sequences would beincapable of specifically binding Dy(III) ions. Since thecomplementary strands were combined 1:1 (mol:mol), thepercentage of spin-labeled strands duplexed to a dT-EDTAbearing complementary strand is equal to the RP HPLC purity.For example, the purity of the (dT-EDTA)-bearing strand inthe SE15Dy DNA duplex is 88%. This means that 88% of thespin label bearing strands are duplexed to strands with anEDTA(Dy(III)) moiety and 12% of the spin-label bearingstrands are duplexed to strands with no EDTA(Dy(III))moiety. Therefore, 88% of the spin-labels will obey eq 11 or 12and 12% will recover as isolated spin labels with relaxation ratek1i. This expectation was supported by the examination ofsaturation-recovery traces of the SE15Dy DNA duplex samplesat different time scales. The saturation-recovery tracesrecovered rapidly to a large fraction of Mz(∞) by t = 100 μsand then continued to recover on a time scale that was >100times slower.Equation 14 below is eq 11 modified to account for the fact

that a fraction of the nitroxide spin-labels in the SE3Dy, SE9Dy,SE13Dy, and SE15Dy DNA duplexes are paired with a

complementary strand that does not contain an EDTA(Dy-(III)) moiety. FDy is the fraction of DNA duplexes in which theEDTA(Dy(III)) moiety is present, and FNo_Dy, (1 − FDy), is thefraction of DNA duplexes in which the EDTA(Dy(III)) moietyis absent.

∫ ∫σ πθ θ

σ θ

= ∞

−

− − − +

+ −

π

_

⎧⎨⎩⎡⎣⎢

⎛⎝⎜

⎞⎠⎟

⎤⎦⎥⎫⎬⎭

M t M

FN

r

r r k k r t

F k t

( ) ( )

12

d sin d

exp[ ( ) /2 ] exp[ [ ( , )] ]

exp( )

z z

r

Dy0

2

0d d

02 2

1i 1ss 1 d

No Dy 1i

0

(14)

When the same modification is made to eq 12 the result is eq15 below.

∫ ∫

∫σ π

θ θ

γ σ

θ θ

= ∞

−

− −

− + +

−

π

π

_

⎧⎨⎩⎡⎣⎢

⎛⎝⎜

⎞⎠⎟

⎤⎦⎥⎫⎬⎭

M t M

FN

r

r r

k k r t F

k t

( ) ( )

12

d sin d

d exp[ ( ) /2 ]

exp[ [ ( , , )] ]

exp( )

z z

r

H

Dy0

2

0d d

0

2

02 2

1i 1ss d No Dy

1i

0

(15)

3.4.2. Parameters and Fitting of the Saturation-RecoveryTransients. The fitting routines written in MatLab for eqs 14and 15 required the user to supply values for FDy and k1i andinitial estimates of the dipolar rate constant (k1d

B , k1dC , or k1d) and

relative standard deviation (RSD) in r0. Equation 15 alsorequired the user to specify values for g∥ and g⊥ and the angleθg. The user-supplied values of FDy, k1i, g∥, g⊥, and θg were keptfixed while the dipolar rate constant (k1d

B , k1dC , or k1d) and

Mz(∞) were adjusted to optimize the fit of the simulation tothe experimental saturation-recovery transient. The RSD couldbe adjusted or held fixed, depending on the user’s preference.Simulations of the experimental saturation-recovery transientswere optimized (fit) using the MatLab function fminsearch.This function uses the simplex search method to find theminimum of an unconstrained multivariable function.50

The value of FDy was determined by the HPLC purity of theEDTA-bearing DNA strand (see above). The value of k1i wasdetermined at each temperature from single-exponential fits tothe saturation-recovery transients of the spin-label in thecontrol, that is, the SE15Ca DNA duplex. User-suppliedestimates of the dipolar rate constants were based on the timescale of the saturation-recovery transient.

3.4.3. Comparing the Quality of the Fits. Prior to fitting,the saturation-recovery transients were normalized by dividingevery point in the curve by the average of the last five points inthe saturation-recovery transient. The saturation-recoverytransient was fit using the B_NDr, C_NDr, or BCE_NDrmodel, and the norm of the residual vector was calculated.These norms were used to compare the quality of two fits thatused different fitting functions or that used the same fitting



function but different fixed parameters.The smaller normindicated the better fit.3.5. Calculation of the SE#Dy/SE15Dy Distance Ratios,

Mean Distances (r0), and Errors. Distance ratios werecalculated using eq 13 and either the k1d

B or k1d rate constants at35, 42, and 50 K. The distance ratios reported are the averageof these three values with the error (uncertainty) equal to halfthe range. The mean NO−Dy(III) distances, r0, were calculatedby applying the BCE_NDr model to saturation-recoverytransients collected at 42 and 50 K, the peak in the rateconstant versus temperature curve.The r0 values reported for the SE15Dy and SE13Dy DNA

duplexes are the average of values calculated for θg equal to 0°and 15° (SE15Dy) and 0°, 15°, and 30° (SE13Dy). The r0values reported for the SE9Dy and SE3Dy DNA duplexes areaverages based on all values of θg (0−90°). Since there were fivesaturation-recovery transients recorded at 42 or 50 K for theSE15Dy DNA duplex, the error reported for its r0 is thestandard deviation in the r0 values used to calculate the average.The reported errors in the r0 values for the SE13Dy, SE9Dy,and SE3Dy DNA duplexes are equal to half the range.

4. RESULTS4.1. CW EPR of EDTA(Dy(III). Selecting the correct

equation to employ in calculating the NO−Dy(III) distancesrequires knowledge of the Dy(III) ion’s g-tensor. CW EPRspectra were collected at 1.9 K of “free” EDTA(Dy(III)) at 2mM concentration in the same cryoprotectant solution used forour SE#Dy DNA samples (Figure 5, blue spectra). At this

temperature, we observed an apparent turning point at g = 14reported earlier by Blum and co-workers.20 However, we alsoobserved a very broad signal that extended from approximately1000 to 8000 G. This signal was more easily distinguished fromthe g = 14 feature at higher power (lower attenuation) becauseit is not as easily saturated. This broad resonance was moreeasily seen at temperatures near or slightly above 4 K bymaking use of a passage effect described by Hyde as “saturationtransfer”47,51 (Figure 5, black spectrum, thick line). Observed inthis manner, there is an apparent maximum near g = 2.3.Neither the g = 14 turning point nor the broad resonance isobserved in the diamagnetic control, EDTA(Ca(II)), although

signals from the resonator itself are still present (Figure 5, blackspectrum, thin line).The large range of g-values (g-anisotropy) observed in the

CW EPR spectrum of EDTA(Dy(III)) indicates that we willneed to use the BCE_NDr model to solve for r0, the meanNO−Dy(III) distance in the SE#Dy DNA duplexes. As a firststep, we assign g∥ a value of 14 and g⊥ a value of 2.3 based onthe low field turning point and midfield maximum of thespectra in Figure 5. These values will be used in eq 9 tocalculate gf

2(θH).4.2. Fitting the Saturation Recovery Transients Using

the B_NDR and C_NDr Models. Examples of saturation-recovery transients from the SE15Dy, SE3Dy, and SE15CaDNA duplex at 35 K are shown in Figure 6. As expected, the

nitroxyl radicals in the SE15Dy DNA duplex experience thegreatest spin−lattice relaxation enhancement, since they havethe shortest Dy(III)−NO distance (Figure 6a). This results inthe fastest (shortest) recoveries. The recovery of the z-magnetization is nearly complete after 100 μs.In contrast, complete recovery of the z-magnetization of the

nitroxyl radical in the SE3Dy DNA duplex takes approximately20 000 μs (20 ms) (Figure 6b). The relatively slow recovery ofthe nitroxyl radical in the SE3Dy DNA duplex was notsurprising, since we estimated that its Dy(III)−NO distancewould be 30−40 Å greater than that of the SE15Dy DNAduplex. Comparison of the SE3Dy DNA duplex radical’srecovery with that of the control, the SE15Ca DNA duplex,confirms that the nitroxyl radical in the SE3Dy DNA duplexstill experiences spin−lattice relaxation enhancement from the

Figure 5. X-band CW EPR spectra of 2 mM EDTA(Dy(III)) andEDTA(Ca(II)), a control. The sharp features at 1800 G, Cr(III), and3300 G, Cu(II), arise from the dielectric resonator.

Figure 6. (a) A saturation-recovery transient from the SE15Dy DNAduplex (black) and residual error from fitting it to eqs 10 and 4, blue;eqs 10 and 2, red; eq 11 and 4, orange; and eqs 11 and 2, green. (b)Comparison of the saturation-recovery transients of the SE3Dy andSE15Ca (control) DNA duplexes. The residual errors from fitting thesaturation-recovery transient of the SE3Dy DNA duplex to eqs 11 and4, orange; and eqs 11 and 2, green are shown.



Dy(III) ion (Figure 6b). Note that the recovery of z-magnetization for the SE15Ca DNA duplex’s nitroxide (gray)does not catch up with that of the SE3Dy DNA duplex (black)until ∼18 000 μs (∼18 ms) have passed.The large g-anisotropy observed in the CW EPR spectra of

EDTA(Dy(III)) (Figure 5) makes it clear that the BCE_NDrmodel will be required to calculate the actual NO−Dy(III)distances in the four SE#Dy DNA duplexes. However, theB_NDr and C_NDr models are easier to implement and fasterto run because there is no need to specify the additionalparameter θg or integrate over γd. One cannot determine theactual NO−Dy(III) distances with these equations, but if thefits are good, the calculated rate constants will reflect thetemperature dependence of the Dy(III)-induced relaxationenhancement. This will allow one to determine the “peak” inthe spin−lattice relaxation enhancement. As will be seen, oncethe peak in the relaxation enhancement has been found, theNO−Dy(III) distance can be determined using the BCE_NDrmodel.The residual errors for different fits are plotted in Figure 6a,b.

These give a visual sense of how well the different equations forspin−lattice relaxation enhancement fit the experimentalsaturation-recovery transients. The difference between thebest fit achieved by a particular model (set of equations) forthe spin−lattice relaxation enhancement and the experimentalsaturation-recovery transient are shown in color as residualerrors. For clarity, the Mz(t) values of the residual errors havebeen multiplied by a factor of 5.The blue and red curves in Figure 6a show the residual error

when the saturation-recovery transient is fit to a model thatassumes that the NO−Dy(III) distance is identical for all DNAduplexes in the sample (eq 10) and that the spin−latticerelaxation enhancement arises from either the C term (eq 4,blue curve) or the B term (eq 2, red curve). The residual errorswhen the saturation-recovery transients are fit to the C_NDrmodel (orange curves) or B_NDr model (green curves) arealso shown in Figure 6.Determining which model best simulated the observed spin−

lattice relaxation enhancement requires a means to objectivelycompare the fits of different model equations to the saturation-recovery transients. For example, it is clear from Figure 6a thatassuming a normal distribution of Dy(III)−NO distances (eq11) in the SE15Dy DNA sample results in a better fit to thedata than assuming a single Dy(III)−NO distance (eq 10).However, it is not clear whether it is the C_NDr or B_NDrmodel that provides the best fit.How well the model equation fits the saturation-recovery

transient can be quantified by calculating the norm of theresidual error. A smaller norm indicates a better fit of theequations simulating the saturation-recovery transient. Sincethe nitroxyl radical of the SE15Dy DNA duplex experiences thestrongest electron spin−spin interactions with Dy(III), wechose saturation-recovery transients of this sample forcomparison of the fits.Saturation-recovery transients of the SE15Dy DNA duplex at

35, 42, and 50 K that had the best signal-to-noise were used forthe comparison shown in Figure 7. The norm of the residualerror was then calculated for each model and compared to thenorm of the noise, Figure 7. The norm of the noise representsthe error expected from a perfect fit given the presence ofrandom noise in the experimental data. The norm of the noisein the entire spectrum was estimated from the norm of the

noise found by fitting the last portion of the recovery to astraight line.Starting from the top in Figure 7, the first two data sets, C

and B, represent a pairing of eqs 4 and 2, respectively, with eq10. Equation 10 assumes that the Dy(III)−NO distance isidentical for all DNA duplexes in the sample. The data setslabeled C_NDr and B_NDr in Figure 7 represent a pairing ofeqs 4 and 2, respectively, with eq 11. It is clear from Figure 7that C_NDr and B_NDr provide a much better fit to the datathan C and B, that is, allowing for a distribution of Dy(III)−NO distances in the sample greatly improves the fit to theexperimental data. Furthermore, the quality of the fits forC_NDr and B_NDr approach that of the perfect fit,represented by Noise. These results are consistent with whatis observed qualitatively in Figure 6a. One can also see fromFigure 7 that the fits of B_NDr are slightly, but consistently,better than those of C_NDr for all three saturation-recoverytransients. This was true for the saturation-recovery transientsof the other three SE#Dy DNA duplexes also. Furthermore, inthe case of the saturation-recovery transients of the SE3DyDNA duplex, the fitted values of k1d

C were either zero ornegative, which are not physically reasonable. Therefore, furtheranalysis was performed using the B_NDr model.

4.3. Calculation of Dipolar Rate Constants andDistance Ratios. Figure 8 shows the dipolar rate constants,k1dB , from the B_NDr model plotted as a function oftemperature for each of the four SE#Dy DNA duplexes. Thedipolar rate constants are represented by open symbols, with adifferent symbol for each of the four SE#Dy DNA duplexes. Asexpected, the dipolar rate constants are inversely proportionalto distance. The SE15Dy DNA duplex, with the shortestDy(III)−NO distance, has the largest dipolar rate constants,k1dB , for a given temperature. The SE3Dy DNA duplex, with thelongest Dy(III)−NO distance, has the smallest. Saturation-recovery transients were collected from 10 to 105 K for theSE15Dy DNA duplex. Over this temperature range, the fittedvalue of k1d

B increased by 3 orders of magnitude between 10 and20 K, gently peaked between 42 and 50 K, and then slowlydecreased between 50 and 105 K.Figure 8 also shows the intrinsic spin−lattice relaxation rate

constants, k1i, plotted as a function of temperature. The k1i rateconstants were determined by fitting the saturation-recoverytransients of the control, the SE15Ca DNA duplex, to a single-

Figure 7. Quantitative comparison of how well the model equations fitthe experimental saturation-recovery transients for the SE15Dy DNAduplex.



exponential rate equation and are plotted as “+” signs over the10−105 K temperature range.Distance ratios can be calculated using k1d

B values and eq 13.However, the most reliable values of k1d

B will come from thetemperature range where k1d

B /k1i is large, so that these twocontributions to the spin−lattice relaxation are easily separable,and where the temperature dependence of k1d

B is weak, so thatsmall errors in temperature measurement produce small errorsin k1d

B . Since the greatest spin−lattice relaxation enhancement,k1dB /k1i, and weakest temperature dependence were seenbetween 35 and 50 K for the SE15Dy DNA duplex, wecollected saturation-recovery transients of the SE13Dy, SE9Dy,and SE3Dy DNA duplexes in this temperature range. The k1d

B

values for the SE13Dy and SE9Dy DNA duplexes show thesame weak temperature dependence as the k1d

B values of theSE15Dy duplex. The k1d

B values of the SE3Dy also show thisbehavior at 35 and 42 K, but there is an apparent drop in k1d

B at50 K.The apparent drop in k1d

B for the SE3Dy DNA duplex at 50 Kis an artifact of the fit. It results because the value of k1i isapproaching that of k1d

B for the SE3Dy DNA duplex at thistemperature (Figure 8). While the saturation-recovery tran-sients of the nitroxyl radical in the SE15Ca DNA duplex werefit to a single exponential, k1i, the spin−lattice relaxation rates ofnitroxyl radicals have a modest orientation dependence of theirown.52 When the dipolar rate constant, k1d

B , is more than anorder of magnitude larger than k1i, as it is for the SE15Dy,SE13Dy, and SE9Dy DNA duplexes, the orientation depend-ence of the intrinsic spin−lattice relaxation of the nitroxylradical does not have a significant impact on the determination

of k1dB because the time scales for k1d

B and k1i are very different.However, as k1d

B and k1i become comparable, the orientationdependence of the intrinsic spin−lattice relaxation of thenitroxyl radical has an impact on the fitted value of k1d

B .It appears that the orientation dependence of k1i also

influences the value of the relative standard deviation (RSD) ofr0 for the SE3Dy DNA duplex. (See “ave RSD of r0” in Table1.) Overall, the size of the average RSD of r0 values for the fourSE#Dy DNA duplexes appear to be reasonable. Since RSD = σ/r0, the values listed in Table 1 indicate that the standarddeviation is small compared to the actual distance, σ < r0, yetlarge enough to have a significant impact on k1d

B . However, it isalso expected that the relative standard deviation (RSD) shouldbecome smaller as r0 increases, since the standard deviation willbe constant if the distribution of nitroxyl radical locations isisotropic. This general trend in RSD is observed for theSE15Dy, SE13Dy, and SE9Dy DNA duplexes (Table 1).However, the fitted RSD for the SE3Dy DNA duplex has thelargest value, 0.23.Having a more accurate value for the RSD in r0 should

produce a more accurate value for the dipolar rate constants,k1dB , of the SE3Dy DNA duplex. Determining a more accuratevalue for the RSD of r0 requires some knowledge of how RSD iscorrelated with distance in the other three DNA duplexes. Theratio of NO−Dy(III) distances in two different SE#Dy DNAduplexes can be calculated using the k1d

B values shown in Figure8 and eq 13. In Table 1, the distance ratios are referenced to theshortest NO−Dy(III) distance, that found in the SE15Dy DNAduplex. A plot of average RSD of r0 versus (r0(SE#Dy)/r0(SE15Dy))

−1 was created and fit to a straight line passingthrough the origin. [The average RSD of r0 should approachzero as (r0(SE#Dy)/r0(SE15Dy))

−1 approaches zero, that is, asr0(SE#Dy) approaches infinity.] The equation of this line andthe value of r0(SE3Dy)/r0(SE15Dy) were used to determinethe expected value of the RSD of r0 for the SE3Dy DNAduplex, that is, 0.07. The saturation-recovery transients of theSE3Dy DNA duplex were once again fit with the B_NDRmodel, but this time with the RSD held fixed at 0.07 (Table 1).The gray diamonds in Figure 7 indicate the values of these“corrected” k1d

B rate constants. These corrected k1dB rate

constants were then used to calculate the corrected value ofthe distance ratio, r0(SE3Dy)/r0(SE15Dy) = 2.71 ± 0.06(Table 1).

4.4. Calculating r0 for the SE#Dy DNA Duplexes Usingthe BCE_NDr Model. We can see from Figure 8 that thedipolar rate constant, k1d

B , for the SE15Dy DNA duplex reachesits maximum value or “peaks” between 42 and 50 K. Weassume that k1d

B peaks at the same temperature for the otherthree SE#Dy DNA duplexes since the source of relaxationenhancement is the same. The data in Figure 8, although

Figure 8. Geometric shapes indicate the dipolar rate constants, k1dB , of

the SE#Dy DNA duplexes. Crosses (+) represent the intrinsic spin−lattice relaxation rate, k1i, of the control, the SE15Ca DNA duplex. Thecurves are included to guide the eye.

Table 1. Distance Ratios and Mean Distances Based on B_NDr (k1dB ) and BCE_NDr (kld)

B_NDr BCE_NDr

DNA duplex ave RSD of r0 ave distance ratio r0(SE#Dy)/r0(SE15Dy) ave RSD of r0 ave distance ratio r0(SE#Dy)/r0(SE15Dy) distance (r0)

SE15Dy 0.17 1.00 0.14 1.00 18.3 ± 0.3SE13Dy 0.15 1.35 ± 0.01 0.15 1.36 ± 0.01 24.9 ± 0.5SE9Dy 0.11 1.84 ± 0.01 0.11 1.84 ± 0.01 33.4 ± 1.0SE3Dy 0.23a 2.76 ± 0.03a 0.21a 2.84 ± 0.03a 50.3 ± 2.4c

SE3Dy 0.07b 2.71 ± 0.06 0.07b 2.73 ± 0.05

aBased on saturation-recovery transients from 35 and 42 K only. bRSD held fixed at this corrected value when fitting saturation-recovery transients at35, 42, and 50 K. cDistance and error reflect values from fits using both fixed and optimized values of the RSD.



limited, are consistent with this hypothesis. Furthermore, weassume that when the BCE_NDr model is fit to the saturation-recovery transients, the average value of k1ss(r, θd, θH) will alsopeak at this temperature. Here, the average value of k1ss(r, θd,θH) is understood to mean the value of k1ss(r, θd, θH) averagedover equal increments of cos θd (from 0 to 1) and γd (from 0 to2π). We call this average k1ss(ave).The peak value in k1ss(ave) is important because it holds the

key to finding r0, the mean NO−Dy(III) distance, for each ofthe SE#Dy DNA duplexes. In general, both r0 and a in eq 7 areunknown. However, at the peak value of k1ss(ave), a has aunique value that can be found through simulation if g∥, g⊥, andθg are known. As it turns out, we know only two of these threeparameters, g∥ and g⊥. However, as we will show in a moment,ignorance of θg when calculating a introduces only a smalluncertainty in a and a negligible uncertainty in r0.For example, if only the C term in eq 7, 18((sin2 θd cos

2 θd)/(1 + (1/a)2)), contributed to k1ss(r, θd, θH), then the equationwould peak at a = 1.0, which corresponds to 1/Tf = ωs. Figure 9

shows how k1ss(ave) varies with 1/Tf for g∥ = 14 and g⊥ = 2.3.Each of the three curves represents a different value of θg.Changes in θg change the shape of the curve slightly and have amodest effect on the location of (1/Tf)max. For example, at θg =0°, a = 1.10 and (1/Tf)max = 1.10ωs, while at θg = 90°, a = 1.18and (1/Tf)max = 1.18ωs. We find that changes in either g∥ or g⊥of ±2 resulted in similarly modest changes in a.We first simulated the saturation-recovery transients of the

SE15Dy DNA duplex using the BCE_NDr model and theparameters a = 1.0, g∥ = 14, and g⊥ = 2.3. The quality of thesefits is shown in Figure 7 as the bars labeled BCE_NDr. [Thesaturation-recovery transient at 35 K was fit with this value of a,even though it is not technically at the peak of k1ss(ave).]Table 2 illustrates how changes in a, θg, and g⊥ affect the fittedvalue of r0 for a single saturation-recovery transient of theSE15Dy DNA duplex at 42 K. As shown in Table 2, r0 is thesame for a = 1.1 and a = 1.2. (Compare lines 4 and 5 inTable 2.) Therefore, ignorance of θg is has little impact on r0through the parameter a. Indeed, a change in the parameter afrom 0.8 to 1.2 changes the calculated distance by less than 2%.(Compare lines 1−6.) This also means that finding the precise

location of the peak in k1ss(r, θd, θH) is not necessary to obtainan accurate value of r0. The value of r0 is more sensitive to thedirect effect of errors/changes in θg and errors/changes in g⊥.(Compare lines 3 and 7−12 to see how r0 changes with θg andline 3 with lines 13−16 to see how r0 changes with g⊥.) Even so,all of the values for r0 fall within ±4%.The value of r0 was calculated for each of the SE#Dy DNA

duplexes using the saturation-recovery transients at 42 and 50K, the two values at the peak. We found that there is an angulardependence to the norm of the residual error for both theSE15Dy DNA duplex and the SE13Dy DNA duplex. Figure 10

indicates that the value of θg is close to 0° for the SE15Dy DNAduplex and close to 15° for the SE13Dy DNA duplex. This isthe angle between the interspin vector and g∥ (Figure 4). As canbe seen in Figure 10, the norm of the residual error for theSE9Dy DNA duplex also varies with θg. However, since there isno clear minimum in the curve, in this case it is not possible toassign a single value to θg with confidence. The norm of the

Figure 9. Finding the value of 1/Tf that produces a maximum ink1ss(ave).

Table 2. Sensitivity of r0 to θg, g⊥, and a

line θg g∥ g⊥ a [1/(ωsTf)] r0 (Å) norm of error

1 0 14 2.3 0.8 18.4 0.0242 0.9 18.5 0.0253 1.0 18.6 0.0274 1.1 18.7 0.0275 1.2 18.7 0.0306 1.4 18.7 0.0297 15 14 2.3 1.0 18.4 0.0278 30 18.0 0.0369 45 17.7 0.04810 60 17.7 0.05911 75 17.9 0.06912 90 17.9 0.06713 0 14 3.3 1.0 18.8 0.03514 4.3 19.1 0.04715 1.3 18.5 0.02916 0.3 18.5 0.030

Figure 10. The effect of θg on the quality of the fits for each of the fourSE#Dy DNA duplexes is shown. Each symbol represents the averageof the norm of the error for saturation-recovery transients collected at42 and 50 K, except in the case of the SE3Dy DNA duplex. In thiscase, only the norm of the error from the 42 K saturation-recoverytransient was used.



residual error for the SE3Dy DNA duplex does not changesignificantly with θg.The dependence of the norm of the error on θg was used to

select which fits would be included in determining r0 and itserror for the SE15Dy and SE13Dy DNA duplexes (Table 1).The same fits were used in calculating the SE#Dy/SE15Dydistance ratios and their errors using eq 13 and k1d. However,no selection based on θg and the norm of the error wasperformed when calculating r0, the distance ratios, or theirerrors for the SE9Dy and SE3Dy DNA duplexes.The B_NDr and BCE_NDr models produced similar

observations when fitting the saturation-recovery transients ofthe SE3Dy DNA duplex. As before, there was an apparent dropin the value of the dipolar rate constant going from 42 to 50 K.The optimized value of the RSD in r0 was also greater than thatof the other three SE#Dy DNA duplexes. (See Table 1.)Corrected values of the RSD in r0, k1d, and distance ratios werecalculated in the same manner as described earlier for theB_NDr fit. These corrected values of average RSD of r0 andr0(SE#Dy)/r0(SE15Dy) are listed on the last line in Table 1under BCE_NDr. The distance r0 reported in Table 1 for theSE3Dy DNA duplex is based on the 42 K saturation-recoverytransient, both with the RSD in r0 optimized and with it fixed at0.07, and on the 50 K saturation-recovery transient with theRSD in r0 fixed at 0.07. The calculation of errors in the distanceratios and distances is detailed in the Materials and Methodssection. Note that the B_NDr and BCE_NDr models producedsimilar average RSD of r0 values and r0(SE#Dy)/r0(SE15Dy)average distance ratios (Table 1).4.5. Mechanism for Spin−Lattice Relaxation in the

Kramer’s Doublet of Dy(III). One of the key assumptions inusing eq 7 is that only the Kramer’s doublet of the Dy(III) ioncontributes significantly to the spin−lattice relaxation enhance-ment of the radical. If the Kramer’s doublet spin states of theDy(III) ion are the source of relaxation enhancement for thenitroxyl radical, the magnitude and temperature dependence ofk1dB and k1d must reflect relaxation processes occurring withinthis pair of lowest-lying spin states. Between 10 and 20 K, k1d

B

increases by 3 orders of magnitude. This steep temperaturedependence in k1d

B could be explained by the presence of eitheran Orbach or Raman relaxation process for the Dy(III) ion’sKramer’s doublet.38,53 In a survey of the literature, there were10 reports of the Dy(III) ion relaxing via an Orbach relaxationprocess in a variety of compounds.54−63 We found only onereport of a compound in which the Dy(III) ion relaxed via aRaman process.64

In the Orbach relaxation process, the ground state is excitedby lattice phonons to a spin state with an energy, Δ, above theground state energy level(s) and below kBθD, where kB is theBoltzmann constant and θD is the Debye temperature. Emissionof a second phonon returns the system to the ground state. ForDy(III), Δ represents the crystal field splitting between theKramer’s doublet and the second lowest pair of MJ levels. Forrare earth ions, the crystal field splittings are typically10−100 cm−1.38 The general form of the Orbach equation is

= Δ −Δ −T A1/ (e 1)T1f

3 / 1(16)

where the term A satisfies the expression 103 < A < 105 for therare earth ions38 and Δ is expressed in units of temperature (K)rather than energy.In order to determine if the Kramer’s doublet of the Dy(III)

ion in the SE#Dy DNA duplexes relaxes via an Orbach process,it was first necessary to determine the temperature dependence

of its spin−lattice relaxation rate, that is, 1/T1f. We obtainedthese values from the saturation-recovery transients of theSE15Dy nitroxyl radical using the BCE_NDr model and itsNO−Dy(III) distance, r0. With the distance known, thesaturation-recovery transients over the entire 10−105 Ktemperature range were fit by allowing the a parameter tovary. The value of 1/T1f was calculated from the fitted value ofa and the experimental value of ωs using the relationshipsa = 1/(ωsTf) and 1/Tf = 1/T1f = 1/T2f.Figure 11 shows a plot of log(1/Tf) versus 1/T for the

SE15Dy DNA duplex (circles). The data were fit to eq 16 using

MatLab and a nonlinear least-squares fitting routine (solidline). The data are well fit by eq 16, supporting the hypothesisthat an Orbach mechanism is the dominant mode of spin−lattice relaxation for the Kramer’s doublet over this temperaturerange. The fitting process yielded Δ = 124 ± 2 K (86 ± 2cm−1) and A = 5.7 ± 0.7 × 105 K−3 s−1. These values of Δ andA are within the range of expected values for the rare earth ions,that is, 10 < Δ < 100 cm−1 and 103 < A < 105 K−3 s−1.38

Furthermore, the crystal field splitting value of Δ = 124 Kindicates that for the temperatures at which the distances weredetermined, 42 and 50 K, approximately 95−92% of theDy(III) ion spins were in the Kramer’s doublet state.

4.6. Locating the Nitroxide Spin-Label Using Trilater-ation. Trilateration is the process by which the position of apoint in three-dimensional space can be narrowed to twolocations by its distance from three other points with knowncoordinates.65 Its unique location can then be determined byother constraints or by its distance from a fourth point withknown coordinates. Trilateration has been used with ENDORdata (electron-nuclear double resonance) to determine theeffective location of the point dipole due to an unpairedelectron in a nitroxyl group.66 Trilateration is also the processby which your car’s GPS receiver locates its position on earth.65

The receiver determines its distance from three satellites ofknown location, narrowing its position to one of two points.Only one of these lies on the surface of the earth.In the case of the four chemically modified DNA duplexes

shown in Figure 1, one can think of the Dy(III) ions as the“satellites” and the spin-label as the “GPS receiver” (Figure 12).Since the underlying DNA structure is the B-form, the locationsof the bases and the phosphodiester backbone are known. Thelocation of the Dy(III) ions can then be determined by

Figure 11. Determining A and the crystal field splitting energy, Δ, foran Orbach spin−lattice relaxation mechanism.



molecular mechanics calculations that simulate either 5′-3 or 5′-4 secondary binding of the EDTA(Dy(III)) complex.37

In principle, because there are four Dy(III)−NO distances,we should be able to specify the location of the nitroxide groupuniquely. However, each Dy(III) ion has two potentialsecondary binding sites, 5′-3 and 5′-4, in each DNA duplex(Figure 1).37 Since three distances are required for trilateration,this means that there are 23 = 8 combinations of Dy(III)(satellite) locations and therefore 16 possible locations for thenitroxide spin-label. (Trilateration will yield two solutions foreach combination of three Dy(III) locations.) However, at leasthalf of these locations can be eliminated by use of the fourthNO−Dy(III) distance constraint. Even if we cannot determinea unique location for the nitroxyl radical by trilateration, wemay be able to say something about its approximate location inspace.Each combination of Dy(III) locations can be represented by

a secondary binding sequence, that is, a sequence of fournumbers that represent the secondary binding positions of theEDTA(Dy(III)) moiety in the four SE#Dy DNA duplexes. Thefirst number in the sequence represents the secondary binding

position in the first DNA duplex in Figure 1, SE15Dy, and thesecond number in the sequence represents the secondarybinding position of the second DNA duplex in Figure 1,SE13Dy, etc. Thus, the sequence “3434” represents 5′-3secondary binding for the SE15Dy and SE9Dy DNA duplexesand 5′-4 secondary binding for the SE13Dy and SE3Dy DNAduplexes.We can now ask the question, which of these secondary

binding sequences produce a trilateration location that isconsistent with the fourth distance constraint? The answer for aparticular secondary binding sequence is not necessarily binary(yes/no). Each of the distances used for trilateration has anuncertainty associated with it, as does the fourth distanceconstraint. The result is that a trilateration location is betterdescribed as a localized surface, dA, rather than a point in space.Thus, while one secondary binding sequence might produce atrilateration location, dA1, which lies completely within therange of the fourth distance constraint, another trilaterationlocation, dA2, might lie only partly within the range of thefourth distance constraint.In order to determine approximately what fraction of the

trilateration location, dA, lies within the range of the fourthdistance constraint, the uncertainties in the NO−Dy(III)distances used for trilateration were represented as a distancearray.

=distance array18.0 24.4 32.418.3 24.9 33.418.6 25.4 34.4

Column one corresponds to the SE15Dy DNA distances,column two to the SE13Dy DNA distances, and column threeto the SE9Dy DNA distances. Each column includes, from topto bottom, the mean distance value minus the error(uncertainty), the mean distance value, and the mean distancevalue plus the error. (See Table 1.) For each distance value incolumn one, there are nine possible combinations of distancevalues in columns two and three. Therefore, each trilaterationlocation, dA, is represented by 27 points, each generated bytrilateration with a slightly different set of distances. Each ofthese 27 points was evaluated to see which, if any, lie within theSE3Dy NO−Dy(III) distance range of 50.3 ± 2.4 Å (Table 1).

Figure 12. Schematic showing the four Dy(III)−NO distances.

Figure 13. Two perpendicular views of the spin-labeled terminus of the SE15Dy DNA duplex with 5′-3 secondary binding of the EDTA(Dy(III))moiety. For clarity, waters bound to the Dy(III) ion (green ball) are omitted. The red and yellow balls indicate potential average locations for thenitroxyl radical (NO) based on trilateration. The highest probability locations (red balls) are labeled with the corresponding secondary bindingsequence.



Of the 16 possible trilateration locations, six fell at leastpartially within the SE3Dy NO−Dy(III) distance range. Thelocations of the central points of these six trilateration locationsare shown in Figure 13 as red and yellow balls (spheres). Redballs represent trilateration locations where all 27 points (all ofdA) fell within the SE3Dy NO−Dy(III) distance range and areconsidered “high probability” locations. These are labeled withthe corresponding secondary binding sequence. The yellowballs represent trilateration locations where some fraction of the27 points (some fraction of dA) fell within the SE3Dy NO−Dy(III) distance range. This fraction ranged from 0.37 to 0.74.While we cannot locate the nitroxyl radical’s average position

uniquely, we can say that it is localized near and below theterminal base pair, on the major groove side (Figure 13). All sixsecondary binding sequences satisfying the SE3Dy NO−Dy(III) distance constraint had 5′-4 secondary binding in theSE3Dy DNA duplex. Both high probability trilaterationlocations (red balls) have 5′-3 secondary binding for theSE15Dy and SE9Dy DNA duplexes (Figure 13). The two highprobability trilateration locations have different secondarybinding locations for the SE13Dy DNA duplex, so we areunable to determine the likely secondary binding position forthis DNA duplex based on trilateration alone. Theseobservations and the NO−Dy(III) distances are reflected inFigure 1.Another approach to eliminating incorrect trilateration

locations is to calculate the conformational energy associatedwith each location. If the conformational energy associated of aparticular location is very high, that location is unlikely to becorrect. We used this approach to see if it was possible toeliminate any of the six trilateration locations based on theconformational energy of the spin-label and its tether. We firstcalculated the energy of the unconstrained spin-label and itstether using molecular mechanics calculations. The calculationswere performed within HyperChem using the amber99parameter set.67 The DNA helix, including the 4′-carbon ofterminal ribose covalently linked to the spin-label, was heldfixed while the atoms of the spin-label and its tether were freeto move in an AMBER force field.67,68 We then constrained theoxygen of the nitroxyl radical to lie at the center of atrilateration location and repeated the molecular mechanicscalculations. The differences in energy between these con-strained and unconstrained conformations were then calculated.The differences in energy were all small, between 20 and 27 kJ/mol, indicating that all six trilateration locations wereenergetically accessible. Therefore, we were unable to eliminateany of the six trilateration locations by this method.We note that the red and yellow balls in Figure 13 do not

represent possible unique locations for the nitroxyl radical, butrather possible unique average locations for the nitroxyl radical.Our model is that, for individual DNA duplexes, the nitroxylradicals will occupy positions around the actual averagelocation, with the probability for occupation falling off in aGaussian fashion for positions further away from the averagelocation.

5. DISCUSSION5.1. Assumptions. 5.1.1. Setting Jex = 0. There are several

reasons to assume that there is no exchange coupling betweenthe nitroxyl radical and the Dy(III) ion. First, the shortestdistance is 18.3 Å. We are unaware of the exchange couplingsbeing observed at this distance without an intervening andhighly conjugated “bridge” molecule of some type. Second, the

through (covalent) bond distance is even larger. While long-range exchange couplings in DNA have been inferred fromelectron-transfer experiments,69 these two paramagnetic speciesare not optimally located for such an interaction. Third, thespin−lattice relaxation behavior of the SE#Dy DNA duplexescan be modeled without including exchange coupling (Figure7).

5.1.2. Representing the g-Anisotropy of Dy(III) Ion with anAxial g-Tensor. Blum and co-workers reported that the CWEPR spectrum of EDTA(Dy(III)) at 4 K had one turning pointat g = 14 and another at g = 4.2, although they acknowledgedthat the latter feature might be due to contamination fromferric iron impurities.20 Our CW EPR spectra of EDTA(Dy-(III)) display a turning point at g = 14 but not the g = 4.2feature reported by Blum et al. Rather, we observe a broad,essentially featureless absorption extending from the g = 14turning point down to g ≈ 0.9, and possibly lower. Although wehave modeled the g-tensor of the Dy(III) ion as axiallysymmetric, the absence of a distinct second turning pointsuggests that it is actually rhombic, with it is lowest principal g-tensor value being g ≤ 0.9. If we are going to approximate theg-tensor of Dy(III) as being axial, it is reasonable to assign g∥ =14 since we have a clear turning point at the lowest fieldposition. The question then is, how much error do weintroduce in the distance r0 by approximating the other (two)principal value(s) of the g-tensor as g⊥ = 2.3?Table 2 suggests that the answer to this question is, not very

much. When g⊥ was decreased from 2.3 to 1.3 or 0.3, thecalculated distance decreased from 18.6 to 18.5 Å, a change ofless than 1% in r0. (Compare lines 3, 15, and 16 in Table 2.) Itis true that increasing g⊥ from 2.3 to 3.3 or 4.3 had a moresignificant effect. (Compare lines 3, 13, and 14 in Table 2.)However, this also increased the norm of the error, more sothan decreasing g⊥, indicating that the data were not fit as wellwith g⊥ at these values. (One could argue that the norm of theerror increases because we have not made compensatorychanges in a. However, a only varies by ∼0.1 for changes in g⊥of this magnitude, and lines 1−6 in Table 2 indicate that thenorm of the error is not very sensitive to changes in a of thismagnitude.) One could replace eq 6 with the equation for arhombic g-tensor. However, since one of the three principle g-values would logically still be 14 and the other two of would beclose together in value, say 2.3 and 0.9, the effect on thecalculated values of gf(θH) would be modest. We conclude,therefore, that approximating the g-tensor of the Dy(III) ion asaxial with g∥ = 14 and g⊥ = 2.3 introduces little error in r0.

5.1.3. T1f = T2f = Tf. Looking at Figure 11, the assumptionthat T1f = T2f = Tf appears reasonable. The spin−latticerelaxation of the Dy(III) ion is fast, 106 s−1 < 1/T1f < 1012 s−1,over the 10 −105 K temperature range. One would expect T2fto be limited by these small values of T1f. The quality of theOrbach fit over the entire 10−105 K temperature rangesuggests that the T1f = T2f = Tf condition holds throughout.One would not expect T2f to be shortened by spin−spininteractions between Dy(III) ions at a concentration of 56 μM.This corresponds to an average Dy(III)−Dy(III) distance ofmore than 300 Å.

5.1.4. Description of Distance as a Normal Distribution.The B_NDr and BCE_NDr models assume that each frozenSE#Dy DNA duplex sample has a normal distribution of NO−Dy(III) distances with the standard deviation less than themean distance, r0. The fitted values of the RSD in r0 reported inTable 1 are consistent with this latter assumption, since RSD =



σ/r0 and all of the RSD values are much less than 1. Now thattrilateration has provided us with potential average locations forthe nitroxyl radical, as illustrated in Figure 13, we can askwhether the standard deviations corresponding to these RSDvalues are physically reasonable. For example, one can askwhether the spin-label and its tether have sufficient length andflexibility to reach positions located at ±σ from the locationsshown in Figure 13.Our model equations yield a relative standard deviation of

0.14−0.17 along the interspin vector for the SE15Dy DNAduplex (Table 1). Given that the NO−Dy(III) distance in theSE15Dy DNA duplex is 18.3 Å, this corresponds to a standarddeviation of 2.6−3.1 Å. For a normal distribution, this meansthat 68% of the nitroxyl radicals will lie within a distance rangeof 18.3 ± 3.1 Å of the Dy(III) ion in the SE15Dy DNA duplex.Similarly, 68% of the nitroxyl radials will lie within a distancerange of 24.9 ± 3.7 Å of the Dy(III) ion in the SE13Dy DNAduplex for a normal distribution. The conformational energyassociated with the spin-label and tether was calculated whenthe nitroxyl radical’s oxygen was constrained to these locations,that is, ±σ along the interspin vector for the SE15Dy andSE13Dy DNA duplexes. This was done for the two highprobability nitroxyl radical locations found by trilateration,those corresponding to the 3334 and 3434 secondary bindingsequences (Figure 13). The energy of these constrainedconformations was compared to the energy of the uncon-strained spin-label and tether, using the computational methodsdescribed earlier. The constrained conformations at ±σ for the3334 trilateration location were 20 to 40 kJ/mol higher thanthe unconstrained conformation, while the constrainedconformations at ±σ for the 3434 trilateration location were40−50 kJ/mol higher. These energy differences are low enoughthat one can consider these distances/positions accessible tothe spin-label.In a normal distribution, 95% of the nitroxyl radicals will lie

within a distance range of r0 ± 2σ. This corresponds to adistance range of 18.3 ± 6.2 Å for the SE15Dy DNA duplexand a distance range of 24.9 ± 7.4 Å for the SE13Dy DNAduplex. When the nitroxyl radical was constrained to distancesthat were ±2σ along the interspin vector, the energies of theconstrained conformations became significantly higher. Theconstrained conformations at ±2σ for the 3334 trilaterationlocation were 60−130 kJ/mol higher than the unconstrainedconformation, while the constrained conformations at ±2σ forthe 3434 trilateration location were 30−260 kJ/mol higher. Wenoted that the highest energy conformations were the ones atr0 + 2σ, which required the spin-label and its tether be fullyextended.These observations at r0 ± 2σ might indicate that the

distribution of distances is not completely centrosymmetric andtherefore not Gaussian. However, they should be treated withsome caution. In calculating the energy of the spin-label andtether, the DNA duplex itself was kept fixed in a canonical B-form conformation. In the actual sample, it is reasonable toassume that the DNA duplex will also assume a distribution ofstructures about some average conformation. Some of thesestructures will allow for a greater NO−Dy(III) distance, quitepossibly as large or larger than r0 ± 2σ in the SE15Dy andSE3Dy DNA duplexes. Therefore, modeling the distribution ofdistances as Gaussian is still reasonable, although we cannotrule out the possibility that the distribution is slightly skewed.5.1.5. Representing θg by a Single Value. In the BCE_NDr

model, the angle θg is the angle formed by the interspin vector

and the principle tensor axis g∥ (Figure 4). It is assumed to be asingle value for the purposes of calculating the k1ss(r, θd, θH)and r0. However, since the nitroxyl radical will occupy locationsaround the average nitroxyl locations shown in Figure 13, it isclear that while θg will be fixed for each DNA duplex, it will notbe exactly the same value for all the DNA duplexes. Thequestion then is, how broad is the distribution of θg values in asample and do they need to be accounted for in fitting thesaturation-recovery transients?We can estimate the range of values for θg using

trigonometry. If we consider the length of the NO−Dy(III)interspin vector and the Dy(III) ion’s position to be fixed, thenmovement of the nitroxyl radical will trace an arc. On the basisof our assumption of a normal, isotropic distribution of nitroxylradical locations about the average position, approximately 68%of the nitroxyl radicals will lie within an arc of length of ±σ.This corresponds to an angle of θ = sin−1(σ/r0) = sin−1(RSD).For the SE15Dy DNA duplex, 68% of the nitroxyl radicals willlie within ±10° of the average value for θg, and 95% will liewithin ±20° of the average value. For the SE9Dy DNA duplex,68% of the nitroxyl radicals will lie within ±6° of the averagevalue for θg, and 95% will lie within ±13° of the average value.Looking at Table 2, lines 3 and 7−12, one can see that

changing θg by as little as 15° can change the fitted distance, r0,by a few percent. However, the effect on r0 of having adistribution of values for θg cannot be directly discerned fromTable 2. Given that the BCE_NDr fits to the saturation-recovery transients are quite good (Figure 7), it seems unlikelythat omitting the distribution of θg values is creating significanterror. However, we cannot rule out the possibility that the truemean distance, r0, for the SE15Dy DNA duplex differs by 1 or2% from that listed in Table 1. We note, however, that anyerror introduced by not accounting for a distribution of θgvalues becomes smaller as r0 becomes larger.

5.1.6. A Representative Sampling of All Orientations ofthe Interspin Vector Contribute to the Saturation-RecoveryTransient. We assume that the orientations of the N−O bondaxis and the interspin vector are uncorrelated. There are twoobservations that make this approximation reasonable. First,free rotation occurs about seven of the bonds that separate thenitroxyl radical from the terminal base of the DNA helix(Figure 2b). Second, on the basis of our calculations in section5.1.4, the nitroxyl radical can be found anywhere in a roughlyspherical area ∼12 Å in diameter. These two observationssuggest that the NO bond is free to point in many differentdirections and is not correlated with the interspin vector or theDy(III) ion’s g-tensor. Therefore, it is not necessary that theentire line width of the nitroxyl radical be sampled by thesaturation-recovery experiment in order for eqs 10 − 12 toapply.

5.2. Comparison with Previously Published CW EPRExperiments. 5.2.1. Microwave Power Progressive Satu-ration Results, Saturation-Recovery Transients, and DipolarRate Constants. Figures 6 and 8 show the effect of the NO−Dy(III) distance on the saturation-recovery transients of thenitroxyl radical. As expected, as the NO−Dy(III) distanceincreases, the rate constant k1d

B decreases, indicating that thespin−lattice relaxation enhancement experienced by thenitroxyl radical is less when the Dy(III) ion is further away.This behavior is in qualitative agreement with microwaveprogressive power saturation experiments performed on thesame DNA duplexes at 77 K.37 As the NO−Dy(III) distanceincreased, the nitroxyl radical became progressively easier to



saturate. This indicated that as the NO−Dy(III) distanceincreased, the relaxation enhancement experienced by thenitroxyl radical decreased.In principle, the relaxation enhancement produced by the

Dy(III) ion could have arisen from a reduction in either T1 orT2 of the nitroxyl radical.70 However, the proximity of theDy(III) had no affect on the line shape of the nitroxyl radical,suggesting that its effect was primarily, if not exclusively, toincrease the spin−lattice relaxation rate of the nitroxyl radical.This was confirmed by the saturation-recovery experimentsperformed here.At the highest microwave powers, saturation of the nitroxyl

radical’s EPR signal in the SE3Dy DNA duplex was onlyslightly, although distinctly, less than that of the control, theSE15Ca DNA duplex.37 This is consistent with what we see inFigure 6b, where the saturation-recovery transients of thenitroxyl radical in the SE3Dy DNA duplex and the control arecomparable, but the recovery is still distinctly faster for theSE3Dy DNA duplex.5.2.2. Location and Correlation Times of the Spin-Label.

In previous work, the correlation time of the spin-label wasindirectly measured36,37 using the line shape of the nitroxylradical’s signal in the CW EPR spectrum.71 It was observed thatthe correlation time of the nitroxyl radical was longer in all ofthe SE#Dy DNA duplexes than the same duplex without adivalent or trivalent cation or without an EDTA moiety. Ourexplanation for this is that the EDTA-bound metal ion alsobinds to a phosphate in the phosphodiester backbone of thecomplementary strand.37 This secondary binding of the metalion may attenuate the torsional oscillations of the DNA helix.The effect was a reduction in mobility of the spin-label on thenanosecond time scale.The average locations for the nitroxyl radical determined by

trilateration in this work (Figure 13) are consistent with ourprediction that the spin-label would be localized near theterminal base pair because of hydrophobic effects.37 Thislocation may also explain why the spin-label’s correlation timeis sensitive to secondary binding, even when this occurs 13 basepairs away, as it does in the SE3Dy DNA duplex (Figure 1).Consider, for example, the spin-label and its tether, as shown inFigure 13, at the trilateration location predicted by the 3334secondary binding sequence. One can see that the spin-labeland tether are in a compact, folded conformation, such thatmovements of the helix would result in movements of the spin-label also, making the spin-label sensitive to helix winding/unwinding motions. If secondary binding reduced theamplitude of the helix winding/unwinding motions, then onecould reasonably expect this to be reflected in the correlationtime of the spin-label. While this trilateration location is only anaverage location for the nitroxyl radical, a normal distributionwould place many of the spin-labels and tethers in similarcompact conformations.5.3. Structural Information from θg. The possibility of

getting additional structural information from the angularrelationship between the interspin vector and the g-tensor ofthe Dy(III) ion via the BCE_NDr model is intriguing (Figure10). A previous experimental study has shown an angulardependence in the transverse relaxation, 1/T2s, of the CuAcenter of cytochrome c oxidase in the presence of positivelycharged cytochrome c.72 It has also been shown that the relativeorientations of two nitroxide spin-labels that are rigidly fixedwith respect to each other can be determined by PELDOR atX-band.73 However, to our knowledge, this is the first time that

angular information has been extracted from spin−latticerelaxation enhancement, although this possibility was predictedearlier.43 The ability to extract both distance and angularinformation could be quite useful in exploring changes in thestructure of a nucleic acid or a protein in response to changes inthe environment or the presence or absence of a ligand.In the case of these SE#Dy DNA duplexes, this orientation

information could be used to further narrow the selection ofpossible secondary binding sequences. For example, Figure 10suggests that g∥ lies nearly parallel to the NO−Dy(III) interspinvector in the SE15Dy DNA duplex and that this angle changesonly by ∼15° in the SE13Dy DNA duplex. If the situation weresuch that the EDTA(Dy(III)) metal complex occupied thesame location in the two DNA duplexes and the position of thespin-labels were different, one could reasonably propose thatthe angle between the two interspin vectors is ∼15°. This mightallow one to determine whether the 3334 trilateration locationor the 3434 trilateration location is the correct one.Unfortunately for us, since it is the EDTA(Dy(III)) complexthat is in two different locations, this hypothesis is moretenuous. The structure of the EDTA(Dy(III)) complex maydiffer in the two DNA duplexes and, therefore, so too may thedirection of g∥ with respect to the donor atoms of the complex.

5.4. Radical−Dy(III) Distance Limits. The saturation-recovery transients of the SE15Dy and SE3Dy DNA duplexes(Figure 6) indicate that the corresponding mean NO−Dy(III)distances are near the minimum and maximum that can bemeasured at X band. The first time point in the SE15Dysaturation-recovery transient has a delay of 1 μs and it appearsthat the recovery of the bulk z-magnetization is already roughly15% complete. The reason for the 1 μs delay is the use of aprotection pulse to isolate the microwave bridge from thereceiver’s electronics. While it might be possible to shorten thisdelay slightly, some delay will be necessary in order to protectthe receiver’s electronics from saturation due to resonator “ringdown”. Thus, it is unlikely that Dy(III)−radical distancesshorter than 16 or 17 Å can be measured accurately since therecoveries will be substantially complete before data collectioncan begin. Lower temperatures would slow the dipolar rateconstant, but the extreme temperature sensitivity of the dipolarrate constant between 10 and 35 K may make accuratecomparisons challenging (Figure 8).In the case of the SE3Dy, we are approaching the limit where

the intrinsic relaxation rate, k1i, is approaching the dipolarrelaxation rate (Figure 8), and it becomes difficult todiscriminate between the two contributions to the overallspin−lattice relaxation rate. Thus, it will be challenging tomeasure distances much greater than ∼50 Å with the nitroxylradical. This is primarily because of the orientation-dependenceof the nitroxyl radical’s intrinsic spin−lattice relaxation.52 It maybe possible to measure somewhat greater distances withporphyrin-based radicals. Previous work indicates that theirk1i values will be similar to that of the nitroxyl radical,15 but theorientation dependence should be weaker, making it easier toseparate the two contributions to the radical’s spin−latticerelaxation.

5.5. Why Does the B_NDr Model Predict the CorrectDistance Ratios? On the basis of our findings, the BCE_NDrmodel represents the most physically accurate representation ofthe spin−lattice relaxation enhancement produced by theDy(III) ion. The analysis presented in section 4.4 predicts thata = 1.10−1.18. This indicates that of the three terms in theBCE_NDr model, the C term is the dominant source of



relaxation enhancement. Why then does the B_NDr modelshow a better fit to the saturation-recovery data (Figure 7) andprovide an accurate estimate of the distance ratios? One’s“physical intuition” is that because the C term is dominant, theC_NDr model should be the better approximation to the actualorientation dependence of the spin−lattice relaxation enhance-ment.We do not have a definitive answer to this question currently.

As noted earlier, at the center of all three models is anexpression for k1ss(r, θd) (eq 1) that consists of the product oftwo terms: a dipolar rate constant that is a function of distance,r, and an orientation dependent term that is a function of θd.Table 1 indicates that the average distance ratio and the averageRSD of r0 predicted by the B_NDR and BCE_NDr models areessentially the same, to within the uncertainty. This suggeststhat the orientation-dependent terms for these two modelsmight produce statistically similar distributions of orientation-dependent values. However, when histograms of the mean-normalized distribution of orientation-dependent values for thethree models are plotted (data not shown), it is found that thethree distributions are distinctly different. We observe that thedistributions of the B_NDr and BCE_NDr models are bothbroader than that of the C_NDr model.When the saturation-recovery transients were fit with the

C_NDr model, the fitted values of average RSD of r0 for theSE#Dy DNA duplexes were consistently greater than those ofthe B_NDr and BCE_NDr models. One hypothesis for thebetter fit of the B_NDr model is that the greater breadth of itsdistribution of orientation-dependent values may allow it tobetter fit the full range of spin−lattice relaxation rates thatcomprise the saturation-recovery transient. Because the C_NDrmodel cannot replicate the full range of spin−lattice relaxationrates, the fitting equation increases the average RSD of r0 tocompensate. A second hypothesis is that despite designing ourpulse sequence to suppress spectral diffusion, it still makes asmall contribution to the saturation-recovery transients.13,17,46

Spectral diffusion would contribute “fast” components to thesaturation-recovery transients. Because the B_NDr model hasthe broadest distribution of orientation-dependent values, itmay be able to fit these fast components without skewing thedipolar rate constant. The C_NDr model may not be able to fitboth the spectral diffusion components of the recovery and theslower components due to actual spin−lattice relaxationprocesses, giving a poorer fit and less accurate distance ratios.

6. CONCLUSION

We note that if one calculated the NO−Dy(III) distances in theSE13Dy, SE9Dy, and SE3Dy DNA duplexes by simplymultiplying the appropriate B_NDr distance ratio by theSE15Dy distance of 18.3 A, the calculated distances would bethe same as those listed under BCE_NDr, to within the error.This suggests an easy way to measure Dy(III)−radical distancesin any system with a similar dispersion of principle gf-values.The experimentalist simply needs to record saturation-recoverytransients over a range of cryogenic temperatures to find thetemperature(s) of maximum relaxation enhancement. On thebasis of eq 13, the distance in the unknown system can then becalculated using the equation

= ± ± × −⎛⎝⎜

⎞⎠⎟r

k(18.3 0.3 Å)

(1.18 0.05) 10 s(max)B

6 1

1d

1/6

(17)

where 18.3 ± 0.3 Å is the NO−Dy(III) distance for theSE15Dy DNA duplex, (1.18 ± 0.05) × 106 s−1 is the averagevalue of k1d

B for the SE15Dy DNA duplex at the peak in its curvein Figure 8, and k1d

B (max) is the maximum value of k1dB in the

unknown system. Since the percent error in the NO−Dy(III)distance for the SE15Dy DNA duplex is small, ∼1.6%, distanceerrors arising from eq 17 should also be small. For example, ifthe principle values of the gf-tensor are the same as those ofEDTA(Dy(III)), an uncertainty of ±10% in the experimentalmeasurement of k1d

B (max) will result in a total uncertainty in rof approximately ±2.5%. This is a result of r’s sixth-rootdependence on k1d

B (max).

■ AUTHOR INFORMATION

Corresponding Author*E-mail: [email protected].

NotesThe authors declare no competing financial interest.

■ ACKNOWLEDGMENTS

We thank Alexei Tyryshkin for his technical support, expertise,and helpful criticism. We thank Charles Dismukes, StephenLyon, and Princeton University for generously sharing theirBruker ELEXSYS 580 X-band spectrometer. We also thankMichael Bowman for his helpful correspondence regarding theCW EPR “saturation-transfer” method. The College of NewJersey and the American Chemical Society Petroleum ResearchFund, Grant 41380-GB4, provided financial support for thisresearch.

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■ NOTE ADDED AFTER ASAP PUBLICATIONThis paper was published ASAP on September 17, 2013. Figure6 caption and the Table of Contents/Abstract graphic wereupdated. The revised paper was reposted on September 26,2013.



http://en.wikipedia.org/wiki/Trilateration

saturation-recovery epr with nitroxyl radical–dy(iii) spin pairs: distances and orientations

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