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Neutron Scattering in Biology - Fitter Gutberlet and Katsaras

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16 Quasielastic Neutron Scattering: Applications

377

of the former is appreciably larger than that of the latter. This may be due to one or several of various conceivable reasons. Let us first consider the possibility, that the additional quasielastic scattering may be due to the mobility of small side-groups located on the ligand, which might be higher than that of side-groups in the main part of the complex. Because of the low weight fraction of the ligand, this is not considered as very probable, although it cannot be completely excluded. Further studies employing a deuterated ligand could however clarify this question. Second, multiphonon scattering can in principle lead to a quasielastic contribution due to phonon–phonon annihilation. This e ect should, however, be negligible in the concerned Q-range (below 2.2 ˚A1), and especially at the low temperature of the experiment, where it is estimated to be of the order of only 2% of the one-phonon scattering. Furthermore such a component is not likely to be very di erent for the two kinds of sample. Similar arguments apply for a multiple scattering contribution, which again is negligibly small, because of the large value of the employed sample transmissions (97.7%).

Finally, we come to what is believed to be the main reason for the observed di erence in the spectra. The complexation may lead to an increased importance of relaxational modes and possibly of very-low-frequency optical vibrations in this whole system and thus to an increased flexibility of the macromolecular ensemble, as compared to the uncomplexed case. The intensity increase also extends further into the inelastic region up to 40 cm1. It is likely, but cannot be proved at present, that the latter e ect might be due to complexation-caused damping of the vibrations in the latter intermediate frequency region. Damping could lead to a shift of modes from higher to lower frequencies. The deviation from purely harmonic behavior of both systems, (DHFR+NADPH) and (DHFR+NADPH+MTX), is demonstrated by calculating, in the limit Q → 0, a “generalized” density of states g(ω) using Eq. 16.17 in Sect. 16.3.3. This is shown in Fig. 16.12 presenting the g(ω) curves for the complexed and for the uncomplexed protein. 7 It is seen, that in the frequency region below 20 cm1 the obtained generalized function does not show the well-known ω2-behavior expected for purely harmonic acoustic vibrations at low energies. Furthermore, it seems to be clear that the curves start with finite values at ω = 0, although measured data are of course not available at zero frequency (see Sect.16.3.3). This is of course the phenomenological signature of the quasielastic component. It is also evident from the figure, that the complexed form of DHFR has an appreciably larger g(ω) in

7Note that the low-frequency part (ω below 20 cm1) of this function must be considered as purely phenomenological: because stochastic fluctuations generally do not obey Bose–Einstein statistics, the division of the scattering function by the Bose phonon-population factor does not have quite the same justification as in the case of harmonic vibrations. But this does not change the main result, namely the observation that complexation of DHFR leads to additional relaxational phenomena causing an increase in the quasielastic scattering component.

378 R.E. Lechner et al.

 

8

 

 

 

 

 

 

1.0

 

 

 

 

 

)

4

 

 

 

 

 

 

 

 

 

 

 

1

 

 

 

 

 

 

cm

 

 

 

 

 

 

(mode

0

40

80

120

 

 

0

 

 

0.5

 

 

 

 

 

g(ω)

 

 

 

 

 

 

 

 

 

 

 

 

0.0

 

 

 

 

 

 

0

5

 

10

15

20

 

 

 

 

w (cm1)

 

 

Fig. 16.12. Generalized density of states g(ω) for uncomplexed DHFR (lower curve) and for DHFR complexed with methotrexate (upper curve) at 120 K. Data, derived from measurements with the direct-geometry TOF spectrometer IN6 (see Sect. 16.3.1 in Part I, this volume), have been summed over a large range of scattering angles. Inset: enlarged frequency region of the spectra; after [93]

this low-frequency region, suggesting that complexation of DHFR softens the enzyme and makes this macromolecule more flexible, an e ect which could be relevant for its biochemical activity. However, we have to note, that we do not know, whether this behavior is also relevant to the same extent at physiological conditions, where the level of hydration established initially (see above) is e ective.

Finally, it is interesting to note that, using NMR relaxation experiments, other authors have observed an increased conformational flexibility on binding a hydrophobic ligand to mouse major urinary protein [104]. However, we should note that a flexibility increase does not necessarily occur as a rule upon ligand binding, since this depends on the strength of the involved interaction. In other investigations using NMR and crystallography, a flexibility decrease was observed on binding small organic ligands to proteins [105–107].

16.5 Low-Dimensional Systems

16.5.1 Two-Dimensional Long-Range Di usion

of Rotating Molecules

Low-dimensional di usion plays an important role for certain biological objects, such as ion transport channels and membrane surfaces. Obviously, the concept of low-dimensionality should not be understood for instance in the sense of strictly planar motions, since especially on biological membranes there will be appreciable local deviations from this idealized picture. The essential

16 Quasielastic Neutron Scattering: Applications

379

condition is, that the di using particles stay within or near a fictive di usion plane (e.g., representing the membrane surface) at least during the observation time defined by the energy resolution of the experiment (see Sect. 15.3, Eq. 15.30 in Part I, this volume and the related discussion). This also implies that the mean-square displacement parallel to the di usion layer, the particle has acquired during this time, is much larger than perpendicular to it.

The incoherent neutron scattering function in the low-Q limit for longrange translational di usion (TD) was already considered above (see Eqs. 16.6 and 16.7. Accordingly, in three dimensions, when the di usive motion is isotropic, with a di usion coe cient D3D, we have for this function:

S3D

(Q, ω) =

1

 

D3DQ2

,

(16.30)

π (D3DQ2)2 + ω2

TD

 

 

 

 

 

 

 

Certain analytic results [108] concerning the anisotropic case, where the di u- sion process is restricted to the surface of a plane or to the planes of a layered structure, will be discussed in the following. If single-crystalline samples are available, the dimensionality of the di usional motion can of course be determined directly by studying the orientation dependence in a QINS experiment. For a single crystal we have [109]:

S2D

(Q, ω) =

1

 

D2D(Q sin θ)2

,

(16.31)

π (D2D(Q sin θ)2)2 + ω2

TD

 

 

 

 

 

 

 

where D2D is the coe cient of self-di usion in two dimensions, Q sin θ the component of the scattering vector in the di usion plane, and θ the angle between Q and the normal to this plane. If single-crystals are not available, one has to resort to polycrystalline samples requiring orientational averaging of the above expression. It is known, that the resulting integral over all orientations exhibits a logarithmic singularity at zero energy transfer [109]. This is caused by the fact that di usion planes which are perpendicular (or close to perpendicular) to the scattering vector Q contribute elastic (or almost elastic) scattering to the QINS function. Fortunately, the logarithmic singularity is cancelled by finite resolution. It has been shown that for resolution functions which have the shape of a Lorentzian (with HWHM equal to H) or of a sum of Lorentzians (which can be the case in BSC experiments) the orientationally averaged resolution-broadened QINS function for 2D-di usion,

 

 

 

 

 

1

0

2π

1

0

π

 

< STD2D

(Q, ω) >orientres

.=

dΦ

sin θ dθ L(θ, ω),

(16.32)

 

 

 

 

2π

2

where

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

L(θ, ω) =

 

1

 

 

D2D(Q sin θ)2 + H

 

(16.33)

 

π [D2D

(Q sin θ)2

+ H]2 + ω2

 

 

 

 

can be written in closed form [108]. The explicit expression is lengthy and will not be given here. The determination of such a characteristic line shape is very

380 R.E. Lechner et al.

di cult. It requires an experimental resolution width H D2DQ2, in order to be able to distinguish it from a simple Lorentzian shape. This problem is discussed in detail in [108].

The study of the anisotropy of translational di usion in strongly anisotropic material, such as biological membranes, is straight-forward, if the membranes are well aligned in the samples. Pertinent investigations with quasielastic neutron scattering techniques have been carried out on purple membrane [110,111] and on the superficial layer of porcine skin (stratum corneum) [112]. As an example we discuss the transport of water molecules on the surface of purple membrane which has a two-dimensional crystalline structure. In biological membranes, proton di usion connected with conduction of protons provides an important mechanism of energy transduction in living organisms. The purple membrane (PM) of Halobacterium salinarum, for instance, contains the protein bacteriorhodopsin (BR) which becomes a one-dimensional stochastically pulsed proton conductor, when activated by light (see Sect. 16.5.2). This is a light-driven proton pump generating an electrochemical gradient across the membrane, which is employed by the bacterium as an energy source. After having been pumped from the cell-interior to the membrane surface, the protons are transported by a mechanism of surface di usion towards other proteins located within the same membrane: The light-generated electrochemical potential across the cell membrane is utilised by the halobacteria to furnish the driving force for ATP synthesis by energizing the rotation of the turbinelike machinery in ATP synthase. Water molecules near the surface are known to be relevant for this biological function, since they have been shown to assist the proton conductivity [113]. Hydration water, its interaction with the surface of biological macromolecules and macromolecular complexes, and its di usion generally play an important role in structure, dynamics, and function of biological systems [114, 115]. It is therefore of considerable interest to study the proton di usion mechanism within and close to the hydration layers of membranes. Similar to the case of bulk water, it is expected that during the di usion process protons are exchanged between water molecules acting either as acceptors (forming for instance (H3O)+) or as donors (producing (OH)ions). A “solid-like” Grotthuss feature [116–118] is added to the di usion of protons in the liquid water phase by the presence of fixed protonation sites on the surface of purple membrane. It is worthwhile to note, that these sites are arranged in space in a perfectly regular manner, since the bacteria use the most e cient packing of BR: trimers of BR molecules embedded in a lipid bilayer matrix are aligned in a two-dimensional hexagonal single-crystalline structure [119]. However, the pH-value not being very different from 7, the concentration of charged particles is very low. The protons spend most of the time as part of di using neutral water molecules with only rare events of exchange between di erent “vehicles” [116]. Therefore, for the purpose of analyzing neutron scattering experiments, the whole mechanism of di usion may to a good approximation be classified as that of molecular di usion [116].

16 Quasielastic Neutron Scattering: Applications

381

In the QINS [110] and PFG-NMR [111] measurements concerning the anisotropy of proton di usion on the membrane, the crystalline order of PM has been exploited. For this purpose about 20,000 layers of purple membranes were stacked approximately parallel to each-other (mosaic spread: about 12FWHM) at defined relative humidities (r.h.). The membrane stacks had been produced, starting from an aqueous suspension of membrane pieces, by alignment of the membranes through evaporation of water, using aluminium foils as a substrate. At 100% r.h., with water layer thickness of about 10 ˚A between neighboring membranes, the protons of water molecules were found to participate in a process of two-dimensional long-range translational di usion parallel to the membrane plane, with a self-di usion coe cient Ds = 4.4×106 cm2s1 at room temperature, i.e., about five times smaller than the known bulk value of water. At the same time, they are also participating in a fast localized di u- sive motion which can – at least partially – be assigned to the rotation of water molecules. This was observed to be about six times slower than in bulk water. These motions are su ciently fast to produce quasielastic broadenings clearly seen with an elastic energy resolution of 16 eV FWHM (see Fig. 16.13). Finally, a translational di usion jump distance of 4.1 ˚A was derived from the

alpha=135 phi=90.4 r =1.2 frac=0.05

Counts

100

80

60

40

20

0

0.2

0.0

0.2

0.4

0.4

Energy (meV)

Fig. 16.13. Fit of a model for two-dimensional translational di usion of water to QINS spectra (data points shown as triangles) of hydrated purple membrane stacks oriented with an angle α = 135with respect to the incident neutron beam. These data were taken with the inverted time-of-flight technique (IRIS, see Sect. 15.3.4 in Part I, this volume) at the scattering angle ϕ = 90.4. The spectra were not corrected for multiple scattering, but MSC was taken into account in the fitted theoretical model: The solid lines represent (from top to bottom) the fit result for the total scattering function including all terms, the sum of all rotation-broadened components of the scattering function (including the backgound B), and B. The dotted lines are the two MSC contributions: a rotation-broadened MSC component sitting on the background line, and an MSC component without rotation broadening on top of the rotation-broadened single-scattering contribution; after [111]

382 R.E. Lechner et al.

HWHM (μeV)

12

10

8

6

4

2

0

0.5

1.0

1.5

2.0

2.5

Q2(A2)

Fig. 16.14. Translational di usion linewidths (exhibited by spectra as shown in Fig. 16.13) of water on hydrated purple membrane, plotted as a function of Q2 for two sample orientations: α = 45, open circles; α = 135, full circles. The experimental values are compared with the theoretical width corresponding to an isotropic approximation of the Chudley–Elliott jump-di usion model in two dimensions. Note that for α = 135, the Q vector is exactly parallel to the membrane plane, when the scattering angle is ϕ = 90, whereas Q is perpendicular to the membrane for the same scattering angle, when α = 45. Therefore the linewidth curve for the latter case approaches zero near Q2 = 1.784 ˚A2, in agreement with the values observed experimentally. This means that di usion parallel to the membrane plane has clearly been seen in this experiment, whereas in the direction perpendicular to it the diffusive motion is too slow to be observable with the QINS technique. Dotted lines: behavior of the width according to the DsQ2 law, if this was valid in the whole region of Q2 shown in the figure (after [111])

Q-dependent behavior of the quasielastic linewidth at large scattering angles (see Fig. 16.14). This distance is three times larger than the corresponding quantity of bulk water.

The relative slowness of the di usion process may be partly due to the restricted space available within the hydration layers. It might also be caused, together with the large value of the jump distance, by the presence of fixed protonation sites on the membrane surface. These might have nearest-neighbor distances similar to those of neighboring lipid head groups, which are of this order of magnitude. At these protonation sites, hydrogen bonds are expected to be formed, with life times exceeding those of bonds which exist between neighboring H2O molecules in bulk water.

16 Quasielastic Neutron Scattering: Applications

383

16.5.2 Dynamical Transition and Temperature-Dependent

Hydration: Example Purple Membrane

The study of the relation between the hydration of biological systems and their function has attracted much attention at least over the last 40 years. A large amount of results has been accumulated and summarized in a number of review articles (see for instance [114, 115, 120–124]) and books [125–127]. It is known that the amount of water associated with any specific biological system and the temperature are two of the most important factors controlling the kinetics of the biological function of the involved macromolecules. As an example, we consider studies of the purple membrane (PM) of Halobacterium salinarum. This is a lipid bilayer system containing a two-dimensional hexagonal arrangement of trimers of the integral protein bacteriorhodopsin (BR) [128]. BR is a well-known proton pump and the prototype of a membrane protein (see also Sect. 5.1). The absorption of a light quantum by lightadapted BR leads to the conformational transition from the all-trans to the 13-cis isomer of the retinal chromophore and initiates a sequence of interconversions between a number of spectroscopic intermediates usually designated by the letters K, L, M8, N, and O, finally leading back to the initial state of BR. Under physiological conditions, as a result of the reactions occurring during this photocycle, a proton is released from the retinal’s Schi base and pumped to the exterior surface of BR, while another proton is taken up on the cytoplasmic side to replace the first proton at its original binding site (for a review, see for instance: [130]). Experimental observations have indicated that the gradual removal of water from PM and thus from the protein modifies the photocycle and has specific consequences on the rates of individual transitions between intermediates. While the processes leading to M-formation are only moderately a ected by changes in the amount of water present, the relaxation rate of the M decay strongly depends on the level of hydration. For instance, between 90% and 75% relative humidity (r.h.) the rate decreases by a factor of 10 and slows down by another two orders of magnitude, when the hydration water is removed almost completely by drying at 7% r.h. or less [131]. More recent experimental results [132, 133] in qualitative agreement with [131], suggest that from 100% to 85% r.h. the M-decay rate decreases by a factor of 2, whereas the strong decrease of the M-decay rate essentially starts, when the humidity is decreased below about 85% to 80% r.h. With decreasing humidity less and less light-induced charge translocation occurs across the protein [134]. Upon further lowering of the r.h., the

8From X-ray di raction and FT-IR measurements it is known that the intermediate M splits into the two structurally di erent states M1 and M2, which can not be distinguished spectroscopically [129]

384 R.E. Lechner et al.

photocycle and the actual vectorial proton transport activity of the proton pump are drastically modified [135–137].

It is interesting to compare the hydration dependence of the photocycle to its variation observed as a function of temperature. While the quantum e ciency of BR is practically temperature independent, the decay of all intermediates relying on thermal activation obviously is not. The photocycle slows down with decreasing temperature and is “frozen in” at some intermediate state, when the time constant of the latter has become practically infinite due to the low value of the temperature. It was found, for instance, that bacteriorhodopsin can be “captured” in the M2-intermediate state at 260 K [138]. Furthermore, according to [139, 140], the photocycle stops at the M-intermediate state below T 220 K (at the M1-intermediate state near 230 K, after [141]), at the L-intermediate below T 180 K (near 155 K, after [141]) and at the K-intermediate below T 150 K (near 90 K, after [141]). The N and O intermediates were not observed at all by low-temperature spectrophotometry. Below we discuss the question, whether the T - and h-dependences of the photocycle are significantly correlated with the T - and h-dependent e ects observed in the static and dynamic structure of multilayered stacks of PM.

In a previous study [100] we have investigated the static structure of multilayered stacks of PM as a function of temperature (T ), after having established well-defined levels of hydration (h) by equilibration at fixed relative humidities (r.h.), at room temperature. The lamellar spacing dl of these systems was measured with neutron di raction as a function of T and h. The observed large T -dependent variations of dl indicate that PM is partially dehydrated, when cooled below a “hydration water freezing point.” This e ect is reversible, but a hysteresis is observed, when PM is rehydrated upon reheating. This phenomenon of dehydration and rehydration, induced by cooling and reheating, respectively, appears to be a general property of biological membranes (see also [142]). It is caused by the presence of hydration forces and by the specific (di erent) temperature dependences of the chemical potentials of interbilayer water and ice. These forces result in a local freezing point depression and are the main reason, why nucleation of ice crystals first occurs outside of the space between bilayers. The temperature variation of the chemical potentials leads to a di erence in vapor pressure, causing water to be successively extracted from the interbilayer space in the presence of these ice crystals, when the temperature is lowered. Vice versa upon heating, the water originating from the melting of the same ice crystals, within the closed system, is “sucked” back into the interbilayer space. This e ect is due to the temperature-dependent change in the balance between the hydration forces and the chemical force resulting from ice formation. It is important to note, that this leads to what amounts to an e ective spatial separation of the crystallized water from the biological surface.

For the temperature dependence of the lamellar spacing the following qualitative behavior of dl was observed [100]: During the cooling cycle of samples

16 Quasielastic Neutron Scattering: Applications

385

equilibrated at a given relative humidity (r.h.), starting at room temperature (295 K), dl stays approximately constant down to a few degrees below the freezing point of bulk water (Tf = 273.15 K for pure H2O and 276.97 K for pure D2O). Then, at a temperature which we denote by Tfh, a discontinuity occurs, which is connected with a large decrease in dl by a step of the order of 20–30% . The hydration water remaining bound to the purple membrane below about 240 K is nonfreezing. Its amount was found to be hnf = 0.24(±0.02) [g D2O/g BR] for all PM samples equilibrated at room temperature in the presence of D2O vapor at 84 % r.h..

Figure 16.15 shows an example of such a study of a PM specimen [143]. The lamellar lattice constant of the PM multilayer stack is displayed as a function of temperature in a heating cycle; the sample had been equilibrated at room temperature in an atmosphere of 98% r.h. (D2O vapor). The experimental values (triangles) are shown together with a phenomenological model curve. The vertical arrows labeled with letters, indicate the approximate limiting temperatures, below which – in the course of the photocycle – BR does no longer return to the ground state, but stops at the intermediates K, L, M1 and M2, respectively.

 

100

120

140

160

180

200

220

240

260

280

300

 

90

 

 

 

 

 

 

 

Tmh

 

90

(Å)

85

PM 98 % r.h. at 295K

 

 

 

 

 

85

80

 

 

 

 

 

 

 

 

 

80

l

 

 

 

 

 

 

 

 

 

d

 

 

 

 

 

 

 

 

 

spacing

75

 

 

 

 

 

 

 

 

 

75

70

 

 

 

 

 

 

 

 

 

70

lattice

 

 

 

 

 

 

 

 

 

65

 

 

 

 

 

 

 

 

 

65

Lamellar

60

 

 

 

 

 

 

 

M2

 

60

K

 

 

 

L

 

M1

 

 

55

 

 

 

 

 

 

 

 

 

55

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

*

 

 

50

 

 

 

 

 

 

 

Tmh

50

 

100

120

140

160

180

200

220

240

260

280

300

 

 

 

 

 

 

T (K)

 

 

 

 

 

Fig. 16.15. Lamellar lattice constant of a purple membrane multilayer stack as a function of temperature in a heating cycle; the sample (labeled H1) had been equilibrated at room temperature in an atmosphere of 98% r.h. (D2O vapor). The experimental values (triangles) obtained with the membrane-di ractometer V2 at BENSC in Berlin, are shown together with a phenomenological model curve. The vertical arrows indicate the approximate limiting temperatures, below which – in the course of the photocycle – BR does no longer return to the ground state, but stops at the intermediates K, L, M1, and M2, respectively [141]. Figure taken from [143]

386 R.E. Lechner et al.

Let us now discuss possible correlations between the T -dependent dehydration/rehydration behavior of PM and the variation of its dynamic structure with temperature. It has been shown by studies of purple membrane using quasielastic incoherent neutron scattering (QINS), that the ability of bacteriorhodopsin to functionally relax and complete the photocycle initiated by the absorption of a photon, is strongly correlated with the onset of low-frequency, large-amplitude “anharmonic” molecular motions. This manifests itself as the well-known “dynamical transition” [35, 144–147] starting from a low-temperature harmonic toward a high-temperature “anharmonic” regime [36]. More precisely, the “dynamical transition” announces the onset of overdamped vibrational and/or localized (i.e., spatially restricted) di u- sive (stochastic) molecular motions at temperatures in the neighborhood of 200 K. It is characterized by the appearance of quasielastic neutron scattering due to these motions9. This has also been made visible indirectly by studying the temperature dependence of elastic scattering (“elastic-window scan”, see Sect. 15.3.3 in Part I, this volume), which allows to extract an atomic meansquare displacement <u2>. In this case, for fully hydrated PM, the onset of di usive motions was found near 230 K by an analysis of <u2>. Here, the validity of a Gaussian approximation to the motion of all the hydrogen atoms in PM was assumed, which – for the employed energy resolution (IN13, with FWHM = 10 eV) – includes the frequencies between 1010 s1 and 1013 s1 [36]. In this experiment, a large Q-range (up to Q = 4.5 ˚A1) was used . However at higher energy resolution (FWHM = 1 eV), and in a lower Q-range (up to Q = 1.8 ˚A1), elastic-window scans with IN16 yielded the onset of a dynamical transition already near 150 K [148, 149]10. From

9Note that it is not possible to give one very precise temperature value for this “transition,” for two reasons: (i) there is a multitude of di erent molecular motions that are gradually activated with rising temperature; the transition is therefore occurring in a continuous way over a certain temperature range; (ii) any newly arising motion can only be detected, when it occurs within the energy window of the experiment; therefore, the temperature dependence of this “transition” phenomenon is also correlated with the resolution-dependent variation of experimental observability; see Sect. 15.3.3, Fig. 15.7, in Part I, this volume

10The elastic-window scan method has also been employed in numerous other biological experiments, in order to determine the temperature dependence of motional amplitudes (“mean-square displacements”), concerning for instance the environmentdependence of confined di usive protein motions (see Sect. 16.4.3), the dynamics of hydrated starch saccharides [150], the e ect of myelin basic protein on the dynamics of oriented lipids [151], proton mobilities in crambin and glutathionine S- transferase [152], the dynamic properties of an oriented lipid/DNA complex (proposed as DNA vector in gene therapy) [153], the influence of solvent composition on global dynamics of human butyrylcholinesterase powders [154], the relation between the glass-forming character and the cryoprotective capability of disaccharide–water mixtures [155, 156], and the comparison of the macromolecular dynamics in psychrophile, mesophile, thermophile, and hyperthermophile bacteria [157]