Thermal motion in the multi-subunit protein, apoferritin, as probed by high energy resolution neutron spectroscopy

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Thermal motion in the multi-subunit protein, apoferritin, as probed by highenergy resolution neutron spectroscopy

Mark. T. F. Telling,†*a Cameron Neylon,a Luke Clifton,a Spencer Howells,a Lambert van Eijckb

and Victoria Garc�ıa Sakaia

Received 6th April 2011, Accepted 31st May 2011

DOI: 10.1039/c1sm05603d

Insight into the dynamic landscape of the multi-subunit protein, apoferritin, using neutron

spectroscopy is presented in this paper. We combine elastic and quasi-elastic neutron scattering data,

collected using different neutron spectrometers, to probe length scales up to 10 �A and timescales up to

2 ns. We show, for the first time without ambiguity, and via a thorough and systematic approach, that

in its lyophilised form, apoferritin, above T z 100 K and in the pico- to nanosecond time regime,

exhibits a single dynamic response driven by methyl groups alone. No contribution is observed from

protons associated with non-methyl species. A distribution of CH3 activation energies is obtained in

line with the environmental heterogeneity that exists around the methyl species in this protein. In

addition, by performing a complete and detailed analysis of the neutron scattering data, we prove the

validity of the theoretical assumptions required by the methyl group activation model used to analyse

the observed spectral response.

1. Introduction

It is well established that protein dynamics play a pivotal role in

biological functions such as enzyme catalysis, ligand binding and

protein folding. As a result, detailed analysis of a biomaterials

dynamical landscape is required to fully appreciate the intricate

relationship between dynamics and biological function. Neutron

spectroscopy is an ideal tool with which to gain insight into the

dynamics of biomolecules1 since it is not only a non-destructive

and selective technique but also provides simultaneously spatial

and temporal information. In addition, the parameters extracted

from experimental neutron studies are directly akin to those

calculated in molecular dynamic (MD) simulations;2,3 such

interplay helping illuminate the dynamic complexity of biological

systems. The range of bio-macromolecular problems addressed

using neutron spectroscopy is considerable. For a comprehensive

overview see for example Fitter et al.4 and references therein.

However, in broad terms the neutron method has been success-

fully applied to problems that encompass proteins,5

membranes,6,7 lipids,8,9 nucleic acids10 and saccharides.11–13

aISIS Facility, STFC, Rutherford Appleton Laboratory, Chilton, OX11OQX, UK. E-mail: [email protected]; [email protected]; [email protected]; [email protected]; [email protected] of Applied Sciences, TU Delft, Mekelweg 15, 2629JB Delft,Netherlands. E-mail: [email protected]

† Position held: Academic Visitor at Department of Materials,University of Oxford, Parks Road, Oxford, OX1 3PH, UK. E-mail:[email protected]

6934 | Soft Matter, 2011, 7, 6934–6941

Previously, we used neutron scattering spectroscopy to char-

acterise the dynamic landscape in hydrated and lyophilised

apoferritin14 in the pico-second (ps) time regime and over length

scales of 3.5 to 9 �A. Apoferritin is an intracellular iron storage

protein found in almost all living organisms and represents

a model system for colloidal bio-systems due to its mono-

disperse spherical form factor. Considering the lyophilised

material, we observed a weak inflection in the mean squared

displacement (msd) parameter at z100 K, analogous to that

observed in other dry proteins, and the corresponding elastic

neutron scattering intensity was successfully modelled using

theory developed to describe methyl group activation processes

in glassy polymers.15 The role, contribution and importance of

methyl group motions to any measured bulk protein dynamic

response should not be understated, as stressed in ref. 16 and 17.

However, in this study it was unclear whether higher energy

resolution spectroscopy, which probed dynamical processes on

a nanosecond (ns) timescale, would reveal not only CH3

dynamics but also other dynamic processes at temperatures

between 100 and 300 K. In addition, certain theoretical

assumptions needed to be imposed when modelling the data,

including (i) that the relaxation rate followed an Arrhenius form

and (ii) that the elastic incoherent structure factor, Ao(Q) took

the form of the 3-fold jump rotation model.18

To truly understand the dynamic landscape in lyophilised

apoferritin, to investigate the presence of additional dynamic

processes on the nano-second timescale, and thus enhance the

experimental data available for future bio-molecular MD effort

on this protein system, we have now performed higher energy

This journal is ª The Royal Society of Chemistry 2011

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resolution quasi-elastic (QENS) and elastic window (EWS)

neutron scattering studies. We have done this by combining data

collected from the high energy resolution backscattering spec-

trometer, IN16 (DEfwhm¼ 0.9 meV, tmax�2000 ps), at the Institut

Laue Langevin, France, and the IRIS backscattering instrument

(DEfwhm ¼ 17 meV, tmax � 100ps) at the ISIS Facility, UK.

Furthermore, and of equal importance, our approach also allows

us to check the validity of the polymer model15 used to describe

dynamics above 100 K in this bio-material by testing the theo-

retical assumptions imposed. The results presented here are

likened to those reported for other lyophilised bio-materials.

2. Incoherent quasi-elastic neutron scattering

Since quasi-elastic neutron scattering is a well established tech-

nique, and described in detail elsewhere,18–20 only an overview of

those aspects pertinent to this work is given here.

2.1 Quasi-elastic neutron scattering and side group rotation

A neutron scattering experiment to investigate macromolecular

motion is essentially a measurement of the double differential

scattering cross-section, d2s/(dEdU) i.e. the probability that

a neutron is scattered with energy change, dE, into the solid angle

dU. The recorded scattered intensity is analysed as a function of

energy and momentum transfer, Q (¼4psin(q)/l where l is the

neutron wavelength). Both coherent and incoherent scattering

contributions are detected. For a discussion which considers the

effect of coherent scattering upon the measured spectra please see

our previous work.14 Suffice to say, unless a sample has been

selectively labelled using deuterium, the signal measured from

a majority of macromolecular materials is dominated by the high

incoherent scattering cross-section of the hydrogen atom

(sH, inc ¼ 80.27 � 10�28 m2). For comparison, the incoherent

scattering cross sections of other atoms found in proteins are

sC, inc ¼ 0.001� 10�28 m2, sN, inc ¼ 0.5� 10�28 m2, sS, inc ¼ 0.007

� 10�28 m2 and sO, inc ¼ 0.0008 � 10�28 m2. The incoherent

scattering cross section for deuterium is sD, inc ¼ 2.05� 10�28 m2.

For lyophilised, fully protonated apoferritin, we calculate that

incoherent scattering dominates a measured spectrum to a level

of 92%. This calculation is based upon the amino acid residue

composition reported by Bryce and Crichton.21 At this level the

coherent scattering contribution was deemed negligible.

For molecular motion within a fixed volume, the incoherent

scattering law describing rotational motion of side groups is

given by,

Srotinc(Q,u) ¼ Ao(Q)d(u) + Sqel

inc(Q,u) (1)

where Ao(Q), the Elastic Incoherent Structure Factor (EISF),

characterizes the geometryof themolecularmotionandSqelinc(Q,u)

describes any quasi-elastic scattering process. Srotinc has been

derived for side group motions in a variety of systems.18,22 In the

case of a methyl group rotation, in which the hydrogen nucleus is

considered to jump instantaneously between three equivalent sites

about a fixed axis,

SrotincðQ;uÞ ¼ AoðQÞdðuÞ þ 1

p½1� AoðQÞ�LðuÞ (2)

with,


AoðQÞ ¼ 1

31þ 2 joð

ffiffiffi3

pQaÞ

h i(3)

where jo is a zero-order Bessel function and a (¼1.032 �A23) is the

distance between moving protons. At its simplest, the quasi-

elastic component is described using a single Lorentzian

function,

LðuÞ ¼ G

ðG2 þ u2Þ (4)

whose width, G, is representative of the jump frequency between

sites. In practice, the heterogeneous environments in macromo-

lecular systems in the glassy state24,25 can result in a distribution

of methyl group jump frequencies. Similar heterogeneous envi-

ronments exist in lyophilised apoferritin as discussed in our

previous study.14 In such cases, the quasi-elastic component of

the scattering function is expressed as,

Sqelinc(Q,u) ¼ [1 � Ao(Q)]

PgiL(ui) (5)

where gi is the weight of each Lorentzian line determined from

a log-Gaussian distribution.

It should be mentioned that both the elastic and quasi-elastic

contributions to the scattered law will be reduced by a contribu-

tion from vibrational motions. In the harmonic limit, vibrational

motion can be expressed by the Debye–Waller factor,19

DWF ¼ exp(-Q2 < r2 > /3), such that,

SrotincðQ;uÞ ¼ exp

��Q2\r2.

3

�� ðAoðQÞdðuÞ

þ 1

p½1� AoðQÞ�LðuÞÞ

(6)

Here <r2 > is the temperature dependent mean squared atomic

displacement (msd) parameter. The msd value is representative

of all resolution limited, or elastic, processes within the material

be they vibrational, rotational or diffusive. The msd values pre-

sented in this paper were calculated by fitting elastic intensity,

Ielinc(Q,T), window scan data (see sections 2.3 and 4)26 to,

IelincðQ;TÞ ¼ Iel incðQ;T ¼ 5KÞexp��Q2\r2 .

3

�(7)

in the temperature range 5 < T < 100 K. In the above, Ielinc(Q,T)

is the Q and temperature dependent elastic incoherent neutron

scattering intensity.

2.2 Analysis of I(Q,t) data

Experimentally, the measured scattering function, Smeasinc(Q,u),

is a convolution of Sinc(Q,u) and the resolution function of the

neutron instrument, R(Q,u). For spectrometers operating in

Q-u space,

Smeasinc(Q,u) ¼ Sinc(Q,u)5R(Q,u) (8)

In its simplest form the instrument resolution approximates to

a Gaussian or Lorentzian function of finite width, Gres (usually

quoted as full width at half maximum). Using either a measured

or theoretical R(Q,u), least squares fitting or Bayesian analysis27

routines can be used to isolate the intensities and widths of the

spectral contributions to Sinc(Q,u). Here, however, we have

Soft Matter, 2011, 7, 6934–6941 | 6935


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chosen to adopt an analysis method which relies on the Fourier

transform of the scattering function. For polymeric materials,

the merits of fitting in the time regime are discussed in ref. 28 and

24. Using Fast Fourier Transform (FFT) methods, the measured

QENS and resolution spectra are converted to the time domain.

Deconvolution of R(Q,u) and Smeasinc(Q,u) is achieved by simply

dividing the Fourier response of the sample by that of the reso-

lution. The result is the time-dependent intermediate scattering

function, I(Q,t). In the simplest case, a single relaxation process

will manifest itself in the time domain as a simple exponential,

I(Q,t) ¼ Ao(Q) + [1 � Ao(Q)]exp(�(t/s)) (9)

Here, s is the relaxation time. A system that exhibits a distri-

bution of relaxation rates, however, may be better described

using the Kohlrausch–Williams–Watt (KWW) or stretched

exponential form i.e.

I(Q,t) ¼ Ao(Q) + [1 � Ao(Q)]exp(�(t/sKWW)b) (10)

It should be noted that here sKWW is an effective relaxation

time which is dependent upon both T and b, or more correctly

the temperature dependence of the spectral shape of the distri-

bution. As discussed by, for example, Arbe et al.29 and Tan-

chawanich et al.,30 a mean relaxation time, < s >, can be

extracted using the relationship,

\s. ¼ G

�1

b

�sKWW

b(11)

from which a mean quasi-elastic line width can be ascertained,

<G>. Note that in the equation above G() is the gamma function

and for b ¼ 1,s in eqn (9) is recovered. Non-exponential

behaviour in eqn (10) is immediately apparent should the

stretching parameter fall below unity and the EISF, Ao(Q), can

be extracted by considering the plateau reached in the long time

limit i.e. as I(Q,t / N).

2.3 Analysis of elastic window scan data, Ielinc(Q,T)

Information about the elastic scattering process alone can be

ascertained by recording only those neutrons scattered within

a narrow energy interval about the elastic line, DE z 0. The

resulting elastic incoherent neutron scattering intensity,

Ielinc(Q,T), is then monitored, and modelled, as a function of

temperature and scattering vector. In the absence of rotational or

translational motion, molecular vibrations give rise to a decrease

in the elastic scattering intensity with increasing temperature,

which is expressed by the DWF. For rotational motion, it has

been shown that the contribution of the quasi-elastic component

within the fixed energy window can be determined using,15

IelincðQ;TÞ ¼ DWF ��AoðQÞ þ 2

p½1� AoðQÞ�arctan

�Gres

G

��

(12)

where Gres is the width of the spectrometer resolution function

and G is the width of the Lorentzian line characterising the quasi-

elastic broadening. In this model, it is assumed that the width of

the quasi-elastic component broadens according to the Arrhe-

nius relationship,

6936 | Soft Matter, 2011, 7, 6934–6941

G ¼ Go exp

��Ea

RT

�(13)

where R (¼8.31 J K �1 mol �1) is the gas constant. The activation

energy, Ea, is related to the height of the potential barrier

hindering rotational motion while Go is the line width at infinite

temperature. For heterogeneous systems suspected of exhibiting

a distribution of jump frequencies,

IelincðQ;TÞ ¼ DWF ��AoðQÞ þ 2

p½1� AoðQÞ�

�X

gi arctan

�Gres

Gi

��(14)

Here gi gives the weight of each component according to

a Gaussian distribution of activation energies. It should be

mentioned that, like other macromolecular systems, it is possible

that not all protons contribute to the reduction or form of

Ielinc(Q,T) or the intermediate scattering function, I(Q,t). The

percentage of mobile species observed can depend upon the

temporal and spatial resolution of the spectrometer used.24 As

a result a reduced EISF parameter, A0o(Q), will be measured. A

true measure of the EISF value can be deduced from this reduced

parameter by noting that,

A0o(Q) ¼ pf + pm � Ao(Q); pf + pm ¼ 1 (15)

where pf and pm are the relative proportions of fixed (i.e. static on

the experimental time scale) and mobile atoms. As a result eqn

(14) becomes,

IelincðQ;TÞ ¼ DWF ��1� pm þ pmAoðQÞ þ 2

p½1� ½1� pm

þ pmAoðQÞ� �X

gi arctan

�Gres

Gi

��(16)

where the magnitude of Ao(Q) is given by eqn (3).

3. Experimental methods

3.1 Material

Apoferritin is the Fe depleted form of ferritin, the natural iron

storage protein found in all living things including plants,

bacteria and animals. The apoferritin molecule can be thought of

as a multi-subunit spherical shell of internal diameter z8 nm.

This shell, which is z2 nm thick, is composed of 24 polypeptide

chains which span the edges of a rhombic dodecahedron as anti-

parallel pairs.31–33 The amino acid residue composition of horse

spleen apoferritin was taken from Bryce and Crichton.21 Two

grams of equine spleen apoferritin (0.2 mm filtered material sus-

pended in 0.15 M sodium chloride) were purchased from Sigma

Aldrich (product number: A3641). The suspended material was

extensively dialyzed against 10 mM ammonium acetate to

remove non-volatile salts. The protein was then freeze dried. The

resulting tan-white powder was further dried over drying agents

(first silica gel and then potassium pentoxide). The subunit

molecular weights and protein integrity were confirmed using

sodium dodecyl sulphate (SDS) polyacrylamide gel electropho-

resis and were consistent with previously reported values.34 The

lyophilised sample was sealed in a flat plate aluminum sample



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can for the neutron measurements. Weighing the sample before

and after the experiment showed no change in mass. To minimize

the effects of multiple scattering, the thickness of the sample

(mass z 100 mg) was limited such that the total scattering from

the sample was no greater than 10%.

3.2 Neutron experiments

The quasi-elastic and elastic neutron scattering data presented

here was collected using the IN16 (Institut Laue Langevin,

France) and IRIS (ISIS, UK) backscattering spectrometers.

3.2.1 IN1635. The IN16 spectrometer was used to perform

elastic scattering (EWS) measurements, Ielinc(Q,T), the results of

which are shown andmodeled, according to eqn (16), in Fig. 1(a).

The instrument was configured to energy analyze the scattered

neutron beam using the (111) reflection of the silicon analyzer

crystals (referred to as Si111). The Si111 configuration affords

a full width half maximum (fwhm) energy resolution of 0.9 meV,

access to the nano-second time regime and a momentum transfer

range spanning 0.2 < Q < 1.9 �A�1. This momentum transfer

range provides access to length scales (d ¼ 2p/Q) 3.3 <

d < 31.4 �A. The Si111 reflection energy analyses only those

neutrons scattered by the sample with a wavelength of 6.27 �A

(Ef ¼ 2.08 meV). The sample was cooled using a standard orange

cryostat and data was collected upon warming at approximately

2 K intervals from 2 K to 300 K over a 10 h period.

3.2.2 IRIS36. The IRIS spectrometer was used to collect

quasi-elastic neutron scattering (QENS) data for line width

analysis. The instrument was configured to energy analyze the

scattered neutron beam using mainly the 002 graphite analyzer

reflection (PG002). The PG002 configuration affords a full width

half maximum (fwhm) energy resolution of 17.5 meV. An energy

transfer range of�0.5 < DE < 0.5 meV was used and the detector

array covered a momentum transfer range spanning 0.42 < Q <

1.85 �A�1 allowing access to length scales (d ¼ 2p/Q) 3.4 <

d < 15 �A. The PG002 reflection energy analyses only those

neutrons scattered by the sample with a wavelength of 6.6 �A

(Ef ¼ 1.845 meV). The instrument configuration used allowed

Fig. 1 (a) Elastic window scans from lyophilized apoferritin atQ¼ 0.78,

1.01, 1.24, 1.44, 1.61, 1.76 and 1.87 �A�1. The solid lines are the result of

simultaneously fitting eqn (16) to the data. (b) Temperature dependence

of the mean squared displacement parameter, <r2>. Solid line is a fit to

the data below T ¼ 100 K from which d < r2>/dT is determined.


access to an upper Fourier time limit of 100 ps; beyond which

artifacts of the FFT procedure became evident. High statistic

QENS data was collected at T ¼ 300 K for 6 h using the PG002

analyzer. Lower statistic QENS spectra were collected at 10 K

intervals (1 h data collection time per temperature) between 150

and 290 K. Spectra from an empty sample container, as well as

from a vanadium standard, were also collected for calibration

and data reduction purposes. The sample was cooled using

a standard orange cryostat. It was also possible to collect

exploratory data using the 004 muscovite mica analyser reflec-

tion (Mi004) at 300 K. Compared to the PG002 configuration,

the Mi004 configuration affords a full width half maximum

(fwhm) energy resolution of 4.0 meV, an energy transfer range of

�0.15 < DE < 0.15 meV, a momentum transfer range spanning

0.26 < Q < 1.2 �A�1 and a practicable upper Fourier time limit of

300 ps. This momentum transfer range allows access to length

scales (d ¼ 2p/Q) 5.2 < d < 24.2 �A. The Mi004 reflection energy

analyses only those neutrons scattered by the sample with

a wavelength of 10 �A (Ef ¼ 0.825 meV). Due to the greatly

reduced neutron flux on the IRIS instrument at 10 �A, the Mi004

data was signal limited. As a result, detailed interpretation of the

resulting QENS spectra was impaired by reduced statistics.

However, as Fig. 2(b) illustrates, the data collected using the

Mi004 configuration did allow us to consider the efficacy of our

model relaxation function up to 300 ps.

The data from both instruments was reduced using either ILL

and/or ISIS data reduction packages, LAMP (IN16), FORTE

(IN16) and MODES (IRIS), and analyzed using the suite of data

fitting tools in the DAVE package.37 Since the thickness of each

sample was limited so that neutron transmission was greater than

90%, multiple scattering effects were deemed negligible and no

such corrections were performed.

4. Results

4.1. Elastic window scan measurements

Elastic window scan measurements collected between 2 K and

300 K using IN16 are shown in Fig. 1(a).

Data collected in neighbouring detectors was collated to

improve statistics yet maintain sizable Q information. The

resulting elastic window scan data sets, covering distinct average

Qave values from 0.78 �A and 1.87 �A, were fitted using eqn (16).

Following the same methodology as in our previous study,14 the

following assumptions and constraints were imposed when

fitting the data to minimise the interdependency of the various

parameters required by the model:

(i) The EISF parameter above, Ao(Q), was fixed to a theoret-

ical value. This value was calculated by assuming the 3-fold jump

rotation model18 given by eqn (3).

(ii) The temperature dependence of the quasi-elastic line width

followed the Arrhenius form.

(iii) An average mean squared displacement (msd) rate

constant, d < r2>/dT, of 4.4 � 10�4 � 0.65 � 10�4 �A2 K�1 was

used to model the temperature and Q dependence of the DWF

(as required by eqn (16)). The rate constant was determined from

the low temperature response of the mean squared displacement

parameter, <r2>. The temperature dependence of the mean

squared atomic displacement (msd) parameter, as determined

Soft Matter, 2011, 7, 6934–6941 | 6937


Fig. 2 The results of modeling the intermediate scattering function, I(Q,t), T ¼ 300 K, using eqn (10). (a) IRIS PG002 (DEfwhm ¼ 17.5 meV) I(Q,t)

spectra and resulting fits. (b) Extension in time of I(Q,t) via superposition of experimental data collected using the IRIS Mi004 (DEfwhm ¼ 4 meV)

analyzing reflection. The solid lines are the result of extending the fits shown in Fig. 2(a) to 300ps. (c) The Q dependence of the mean relaxation time,

< s>. The stretching parameter was fixed at a mean value, bmean, of 0.64. Inset: the variation of b as a function of Q fromwhich bmean was determined. (d)

A0o(Q), the reduced elastic incoherent structure factor, as determined from the long time (i.e. t / N) limit of I(Q,t) and from the PG002 and Mi004

analyser types.

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using IN16, is illustrated in Fig. 1(b). The method of extracting

the msd value at each temperature is described in section 2.1. The

observed msd result is characteristic of lyophilised bio-materials.

A similar response, both in form and amplitude, has been

reported for dry bacteriorhodopsin,7 myoglobin,38 Ribonuclease

A39 and lysosyme.26 Only when the natural abundance of CH3

rich amino species is limited,40 or the CH3 molecules have been

selectively deuterated,17 is the inflexion at approximately 100 K

suppressed.

(iv) Using the amino acid residue composition reported by

Bryce and Crichton21 the number of H atoms associated with

CH3 species relative to the total number of H atoms in the

peptide chain (including carboxyl and amino groups) is z24%.

As a result, while pm was allowed to float during the fitting

procedure it was constrained to have a compositionally mean-

ingful upper limit of 0.24.

The fits to the data are shown in Fig. 1(a). It should be empha-

sized that all the data sets shown inFig. 1were fitted simultaneously

and modeled using the same parameterization of eqn (16). The

figure clearly shows that, despite IN16 accessing time scales in the

nano-second regime, the model is sufficient to describe the data

over the entire Q and T regime studied. As a result, and to address

our original hypothesis, no additional dynamic processes are

observed in lyophilised apoferritin over the temporal and spatial

6938 | Soft Matter, 2011, 7, 6934–6941

range studied. A mean activation energy of Ea,ave ¼ 17 kJ mol�1

with a width of the distribution of activation energies of 4 kJmol�1

was found. In addition, the relative proportion of mobile protons

contributing to the decrease in the elastic intensity tended to the

compositionally theoretical upper limit of pm ¼ 0.24

4.2. Modeling I(Q,t)

(a) Data at 300 K from IRIS. The results of modeling the

intermediate scattering function, I(Q,t), collected at 300 K using

eqn (10) are summarized in Fig. 2(a–d). The I(Q,t) spectra pre-

sented are the FFT of the experimentally determined frequency

dependent scattering function, S(Q,u).

Fig. 2(a) shows I(Q,t) spectra, and the resulting fits to the data,

at four distinct Q values. The data was deemed reliable up to

100ps beyond which artifacts of the FFT procedure became

apparent. During the fitting process, I(Q,t ¼ 0) tended to unity,

within error, at each Q value. Fig. 2(b) shows the extension in

time of I(Q,t) via superposition of experimental data collected

using the IRIS Mi004 (DEfwhm ¼ 4 meV) analyzing reflection.

Since the two analyser types access different momentum transfer

ranges (see Fig. 2(d)) I(Q,t) could only be extended at three

distinct Q values; only two are shown for clarity. The solid lines

are the result of extending the fits shown in Fig. 2(a) to 300 ps.



Fig. 3 The results of modeling the intermediate scattering function,

I(Qmean ¼ 1.49 �A�1,t) as a function of temperature using eqn (10). (a)

I(Q,t) spectra obtained from IRIS PG002 and resulting fits (solid lines) to

eqn (10). (b) Temperature dependence of the mean line width, <G>

(fwhm), as determined from <s> via eqn (11) and the effective relaxation

time, sKWW. The solid line is a fit to the Arrhenius form (eqn (13)). Inset

(b). The temperature dependence of the stretching parameter, b. The solid

line is a guide to the eye.

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Since the stretching parameter, b, was found to be Q-indepen-

dent over the length scales studied (Fig. 2(c), inset), its value was

fixed at a mean value, bmean, of 0.64 � 0.13 and the data refitted.

The Q independence of the mean relaxation time, <s> is high-

lighted in Fig. 2(c) from which an average <s> value of 46 � 8 ps

is determined. This average value equates to a quasi-elastic line

broadening (fwhm) of <G> ¼ 30 � 5 meV. <s> was determined

using eqn (11), a b value of 0.64 and sKWW parameters deter-

mined from fitting the I(Q,t) curves. It is interesting to note, as

pointed out in ref. 17 that NMR studies of the CH3 rich amino

groups (leucine, valine, analine and threonine) at room temper-

ature undergo 3-fold jump rotations with time constants of 30–80

ps.41,42 Such a Q-independent response is indicative of localized

diffusive behavior with a stretching factor less than unity sug-

gesting a distributed, rather than simple, relaxation response. To

validate the goodness of fit using the stretched form, a fit to the

data collected at Q ¼ 1.758 �A using the simple exponential

relaxation (i.e. b ¼ 1) is shown in Fig. 2(a).

Finally Fig. 2(d) shows Ao(Q), the reduced elastic incoherent

structure factor (EISF), as determined from the long time

(i.e. t / N) limit of I(Q,t) using both the PG002 and Mi004

analyser types. Analysis of the EISF provides information about

the geometry of the localised motion. Fitting the 3-fold jump

rotation model to the data, as described by eqn (15), provides an

excellent description of the results. The fit suggest a mobile

fraction, pm, of 0.23� 0.04 which is consistent with that expected

for the compositional percentage of non-exchangeable protons

associated with CH3 species in the peptide chain. These I(Q,t)

results at 300 K are fully consistent with our IN16 EWS findings

and again suggest that CH3 motions alone are responsible for the

dynamic response observed at elevated temperatures.

(b) Temperature dependence of the mean line width, < G >.

Fig. 3(a) highlights the temperature dependence of I(Q,t) between

180 K and 300 K (only data for T¼ 200, 250 and 300 K is shown

for clarity). The solid lines are a fit to the stretched exponential

form, eqn (10). Again, the data was deemed reliable up to 100 ps;

beyond which artifacts of the FFT procedure became evident.

Statisticallymeaningful parameterizationwas not possible forT<

180 K. The associated mean quasi-elastic line widths, < G>, and

stretching factors, are presented in Fig. 3(b). Since <s> and the

stretching parameter are seen to beQ-independent at 300K (Fig. 2

(c)) it is not unreasonable to assume this response should hold at

lower temperatures. To improve statistics, therefore, the I(Q,t)

curves shown are the sum of spectra collected between 0.78 and

1.87 �A�1; Qmean ¼ 1.49 �A�1. Furthermore, since the EISF is

a temperature independent function, the EISF value for Qmean ¼1.49�A�1 was fixed at the value determined from the 300Kdata for

the reasons discussed by Arrighi et al. in ref. 24. We find that the

mean relaxation parameter increases with increasing temperature

and follows the Arrhenius form resulting in an activation energy

of 18 � 1.4 kJ/mol. In addition, we find that the stretching

parameter increases, with increasing temperature, from 0.34� 0.1

at 180 K to 0.63 � 0.06 by 300 K.

5. Discussion

Exploring the dynamic landscape in lyophilised apoferritin using

a higher energy resolution neutron spectrometer, IN16, thus


accessing a wider temporal range, gives an elastic window

response which is extremely well described simply using theory

originally developed to describe CH3 dynamics in glassy poly-

mers.24,25 Our results show without ambiguity that over the

length scale range 3.5�A to 9�A, and for time scales straddling 5 ps

to 2 ns, the dynamic response in lyophilised apoferritin is driven by

CH3 species alone where the CH3 groups have a distribution of

relaxation rates. Our analysis shows the width of this distribu-

tion, s, to be 4 kJ mol�1 centered about a mean activation energy

of Ea,ave ¼ 17 kJ mol�1. For comparison, fitting our preliminary

dynamic data collected in the picosecond time regime to the same

theoretical model results in an Ea of 12 kJ mol�1 with a distri-

bution of s � 4.6 kJ mol�1 While similar in magnitude to the

IN16 result, we believe the more pronounced inflexion observed

in Ielinc(Q,T) afforded by the higher resolution of the IN16

instrument allows a more accurate activation value to be

ascertained.

It is not unreasonable to suggest that, as with some polymers,

this measurable distribution is the result of highly heterogeneous

chemical environments ranging from the CH3 species being

exposed to the external surroundings as well as being masked in

the highly hydrophobic environment at the protein core. The

origin of this heterogeneity is still not understood and it could

well be that this diversity plays a role in the diversity of protein

function.43 NMR data analyzed in terms of the Lipari-Szabo

order parameter, S2,44 allows the dynamics of side chain bonds

and back-bone molecules to be quantitatively characterized.

Order parameter studies from a multitude of proteinaceous

materials suggest, on average, side chains are heterogeneously

mobile on a ps–ns time scale but the back-bone atoms are rigid.45

To this end molecular dynamic simulations can provide further

insight into the origin of this heterogeneity and its importance for

protein function.46 Our neutron results lead us to believe that

since CH3 side group motion is the lone mechanism driving the

observed dynamic response in lyophilised apoferritin, both the

main peptide chain and other side groups in this relatively large

spherical globular protein are highly constrained over the length

scales and temperatures probed here. Methyl group dynamics

have been studied in rather smaller and more flexible globular

proteins such as lysozyme26 or myoglobin.16 In dry lysozyme

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methyl groups (pm ¼ 0.26) also exhibit heterogeneous dynamics,

characterised by Ea,ave ¼ 16.6 k J mol�1 and s ¼ 5.8 kJ mol�1.

The results from that study suggest that methyl groups are

responsible for the dynamic response in the ns timescale. In the

ps timescale the authors find a faster ‘rattling in a cage’ process

and simulation data suggests that non-methyl hydrogens also

contribute to some extent above 150 K.47 In myoglobin

an average rotational barrier was reported in the range of

10 kJ mol�1.

The model used to describe the elastic window response,

Ielinc(Q,T), obtained from our QENS measurements provides an

excellent description of the measured data. It does so, however,

under the assumption that the Q-dependence of the EISF asso-

ciate with the observed localized motion follows that expected of

a 3-fold jump rotation model and that the temperature depen-

dence of any associated QENS broadening is Arrhenius like. To

test the efficacy of these assumptions the IRIS instrument was

used to parameterize the intermediate scattering function, I(Q,t).

The time regime accessible using the IRIS instrument was

deemed suitable for such a study since it was clear from the

response of our preliminary, albeit signal limited, Mi004 I(Q,t)

measurement at 300 K that all the dynamic information is con-

tained in the early pico-second, rather than long time nano-

second, regime. Indeed, theMi004 data confirms that the form of

I(Q,t) at 300 K plateaus beyond 150ps. As discussed by Arrighi

et al.24 the level of this plateau allows the EISF to be ascertained

experimentally. Measured EISFs associated with different

geometries, length scales and frequencies are compared to theo-

retical predictions in ref. 18. However, it should be noted that

discrimination between different geometric models is only readily

apparent beyond the first minimum of the Bessel function.

Unfortunately, the Q-range accessible using IRIS was not suffi-

cient to straddle a first minimum. As a result accurate distinction

between the EISF expected from a 3-fold jump rotating process

and other side group motions was not possible from the data

available. Nonetheless, fitting a theoretical 3-fold jump rotation

model to the data provides an accurate description of the

experimental data; the fit giving a pm of 0.23� 0.04. The value of

pm determined in this way is comparable to that deduced from

our lower energy resolution OSIRIS results14 and, based upon its

amino acid residue composition, the theoretical percentage of H

atoms associated with CH3 groups in the apoferritin peptide

chain (pm z 0.24). It is worth commenting that due to the small

coherent contribution to the scattering intensity (z8%) it is

possible that the experimentally determined EISF values are

slightly higher than expected from a wholly incoherent scatterer.

However, at this level we believe the effect is negligible compared

to the accuracy of the extracted parameters. The effect of

coherent scattering on the EISF is considered in ref. 48. Polari-

zation analysis would be required to successfully separate the two

contributions.

In contrast, our assumption that the temperature dependence

of the relaxation rate, thus quasi-elastic line width, follows the

Arrhenius form is fully validated. The resulting activation energy

agrees well with that determined from the IN16 elastic window

measurements and, within error, with our previous EWS

measurements. The accompanying increase in stretching

parameter with increasing temperature is characteristic, and

indicative, of a narrowing distribution of relaxation rates. At

6940 | Soft Matter, 2011, 7, 6934–6941

present, only a small number of protein-based QENS studies

analyze relaxation spectra in the time regime using the empirical

Kohlrausch-Williams-Watt form. As a result, the magnitude and

temperature dependence of the stretching parameter cannot be

compared with other biomaterials. Nonetheless, it is worth

noting that QENS data from polymeric materials (e.g. poly-

(dimethylsiloxane),49 polypropylene50and poly(methyl methac-

rylate)24) which exhibit complex dynamical environment, and

whose data has been modeled in a manner similar to the method

presented here, are found to reveal stretching parameters

between 0.4 to 0.6.

6. Conclusion

By combining elastic and quasi-elastic neutron scattering data,

and by applying theory originally developed to investigate

dynamics in glassy polymers, we have shown for the first

time without ambiguity that in lyophilised apoferritin above

T z 100 K the dynamic response observed in the pico- to nano-

second time regime is driven by CH3 dynamics alone; the methyl

species exhibiting a distribution of activation energies. Our

results suggest that over the temporal and spatial range studied

the main apoferritin peptide chain and other side groups remain

rigid. Our results are supported by findings from NMR. Inter-

estingly, yet seemingly counter-intuitively, similar results are

reported for other smaller, more flexible lyophilised bio-mate-

rials. Having validated, via experiment, the assumptions imposed

by the polymer theory, we believe our work to be an important

and complete result which elucidates fundamental aspects of the

dynamic landscape in apoferritin. A detailed appreciation of the

relationships between dynamics and biological function will

require analysis based on models that realize the full complexity

of macromolecular material. We therefore aim to use these

results to aid development of accurate force fields for the apo-

ferritin molecule as well as further develop, via collaboration,

complex molecular dynamic model simulations of other proteins.

We believe this complete work, and analysis approach, could act

as a benchmark for the investigation of methyl group dynamics

in other proteinacious materials using neutron scattering.

Furthermore, it is clear that there is a need for detailed dynamical

data given the complexity and diversity of bio-macromolecules

and we believe our work will add to this knowledge database.51

Acknowledgements

The authors would like to thank the UK’s Science and Tech-

nology Facilities Council for access to the ISIS facility, Ruth-

erford Appleton Laboratory and the Institut Laue Langevin,

Grenoble, France, for access to the IN16 instrument. The

authors would also like to thank the staff at the Department of

Chemistry, University of Southampton, UK, for assistance with

protein purification and subsequent freeze drying. MTFT would

like to thank Dr V. Arrighi (Heriot Watt, Edinburgh, UK) for

the use of analysis tools developed specifically for the modeling

of elastic window neutron scattering data. MTFT would also like

to thank Prof. S.H. Kilcoyne (University of Salford, UK) and Dr

B Gabrys (Department of Materials, University of Oxford, UK)

for fruitful discussions and support which enabled the comple-

tion of this work.



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Documents

Thermal motion in the multi-subunit protein, apoferritin, as probed by high energy resolution neutron spectroscopy