Elastic neutron scattering in Biophysics Carmen Abia Sanz Physics - - PDF document

Elastic neutron scattering in Biophysics

Carmen Abia Sanz Physics Oviedo University November 6, 2017

By investigating water dynamics of biological samples at different temperatures, a better understanding of biological mechanisms determining our state of health can be gained. With this purpose, an elastic incoherent neutron scattering experiment was performed at the IN13, a backscattering spectrometer of the Institut Laue-Langevin (ILL), in Grenoble, France. The aim of this document is to show the learning, work and results accomplished during a four week internship at the ILL, as a student of the 2017 Summer School Programme.

1 Motivation

Water is a key component of most physical sys- tems of our planet; it plays an important role in biological systems. Therefore, the study of the properties of water is necessary for the under- standing of the structural stability, the dynamics and the functions of biological molecules. This type of studies has an impact in areas such as medicine, where understanding biological mecha- nisms determining our state of health can improve life expectancy, as well as the quality of life. In this experiment in particular, neutron scattering technology is used to study water properties of several tumoral systems and, by comparing them with regular biological systems, relevant informa- tion will be obtained.

2 Theoretical background

Neutron scattering techniques use neutron beams as a probe to investigate macromolecules and wa- ter molecules dynamics. Due to their electri- cal neutrality, neutrons are non-destructive and can penetrate deeply into matter which makes them an ideal probe for studying biological sam- ples. Since neutrons appear to behave either as parti- cles, as waves or as microscopic magnetic dipoles, all these specific properties enable them to yield information which is often impossible to obtain us- ing other techniques. Focusing on thermal neutron wavelengths and energies (∼ 1.8 ˚ A and 0.025 eV), it is remarkable that they are comparable to the interatomic distances and to thermal energy of ex-

• citations. Consequently, these particles are sensi-

tive to the amplitudes and frequencies of molecu- 1

lar motions simultaneously, making neutron scat- tering an outstanding technique to provide infor- mation about both dynamics and structure of bi-

• logycal systems.

In an scattering event, see (Figure 1), there is an incoming neutron beam, with an initial energy Ei and an initial wave vector ki, it interacts with the atomic nuclei of a sample and neutrons with final energies Ef and final wave vectors, kf, are

• btained. There are two kinds of scattering pro-

cess: elastic and inelastic. In the elastic case, which is the one studied, there is not energy trans- fer, Ei = Ef, only momentum transfer. As it is shown in (Figure 1), the kf is pointing to the cir- cunference so that the modules of both ki and kf are the same, but their direction can experiment a change. The momentum transfer is defined by the scattering vector Q = kf − ki; it is linked to the inicial wavelength and the scattering angle by Q =

4π sin θ

2

λi

. ki kf kf kf Q θ

θ 2

Incoming neutrons bean Inelastic scattering Ef < Ei Inelastic scattering Ef > Ei Elastic scattering Ef = Ei

Figure 1: Scattering event

During the scattering event, a neutron interacts with a nucleus. The probability of this event is proportional to the expose surface of the nucleus. Such surface is so-called cross section, σ, and is specific for each element in nature; the bigger the cross section is, the scattering event is more likely to happen. What the instruments are able to measure is the scattering function, S(Q, ω), which is proportional to the cross section. In a scattering function, two contributions can be distiguished: coherent and incoherent. S(Q, ω) ∝ σcoh + σinc The coherent contribution provides information about the correlation between two particles, in two different positions at two different times (crystals). While the incoherent contribution provides infor- mation about the autocorrelation (correlation over the same particle) at two differen times, which gives directly access to molecular motions. The table (Table 1) compares the coherent and incoherent cross section of some elements. Since hydrogen has one of the largest incoherent cross section of all nuclei, neutron scattering from a non- crystalline biological sample is dominated by inco- herent scattering of this element. It is important to consider that when a neutron measurement is done both contributions are acquired, they are not

• ditinguishable. However, neutron scattering sig-

nals from hydrogenous compounds are essencially incoherent. Element σcoh (barns) σinc (barns) H 1.76 79.91 O 4.23 0.01 C 5.55 0.00 N 11.01 0.49

Table 1: Incoherent and coherent cross sections

The elastic incoherent scattering function, Sinc(Q), can be written within the Gaussian ap- proximation, in which it is supposed that the hidrogen atoms (in this case) have small fluctu- ations around their equilibrium positions. Math- ematically, when u2Q2 ≪ 1:

Sinc(Q) ∝ e− 1

6 u2Q2

(1) where u2 are the atomic mean square displace- ments (MSD), which is a measure of the devia- tion time between the position of a particle and the equilibrium position. In this particular ex- periment, thermal elastic neutron scattering gives directly access to the vibrations of hidrogen atoms and how they change as the temperature is modi- fied. 2

3 Material and methods

Backscattering spectrometer: IN13

The IN13 instrument at the ILL is a thermal neu- tron backscattering spectrometer mainly devoted to life sciences. Due to its high energy resolution and high momentum transfer, this spectrometer is useful for the microscopic study of single particle motions which are observed by incoherent neutron scattering. The expression of the energy resolution can be deduced by differentiating Bragg’s law λ = 2d sin θ (2) the following expression is obtained ∆ E E = 2 ∆λ λ = 2 cot θ ∆θ + 2 ∆d d (3) The distintive high energy resolution of IN13,

• nly 8 µ eV, is achieved by working with the

largest possible Bragg angle at the monochroma- tor and the analyser crystals (ideally θ = 90◦ so that cot(θ) = 0); which is approached with the backscattering geometry . The second term in (3) is only dependent on the crystal quality. Regarding the high momentum transfer (be- tween 0.5 and 4.9 ˚ A−1) it is relevant to mention that a small wavelenght has to be used in order to achieve it. For that reason, the spectrometer is installed at the termal guide H24. Thermal guide H24 Ei 16.45 meV FWHM 8 µeV λi 2.23 ˚ A Angular range 8◦ < θM < 89◦ Q-range 0.5 − 4.9 ˚ A−1 Q-resolution ∆Q < 0.1˚ A−1 Dynamics time observed ∼ 80 ps Monochromator CaF2(422) Analyser CaF2(422)

Table 2: IN13 Characteristics

In an IN13 experiment, the neutron beam comes from the thermal moderator passing through the thermal guide H24 and arrives to the monochro- mator crystals, which are CaF2 crystals mounted in a cryofurnace and orientated in (422) direction to obtain the wavelength 2.23 ˚ A and an energy of 16.4 meV. The neutrons are diffused with a small angle of 1.8 ◦. It is not possible to fulfill the backscattering condition, which would improved the energy res-

• lution, since it is not possible to backscatter the

particles into the guide. The graphite deflector, composed by pyrolytic graphite crystals, serves to focus the beam on the sample position, following the lambda variations induced by the change of lattice parameters of the heated monochromator crystal. Before hit- ting the sample, the energy-selected neutrons pass through a chopper and a monitor. The chopper (with a speed of 6756 rpm) is used to suppress the neutrons scattered directly from the sample into the detectors and to suppress higher orders of the reflection of the monochromator CaF2 crystals, since the incident neutron beams are imperfectly monochromatic due to instrument characteristics. The monitor is a detector which measures the in- coming neutron flux intensity. Once the neutron beam is scattered by the sam- ple, they are analysed in momentum and energy transfers by a set of nine CaF2 crystal analysers. These are also glued in a 422 orientation on the surface of spherically curved concave aluminium plates (Figure 2); in this way, the elastic scatter- ing geometry can be reached selecting the neu- trons with the right energy (Ei = Ef). This selected neutrons will go to the detectors

• f the instrument. Specifically, they are counted

by individual 3He detectors and a cylindrical mul- tidetector consisting of several 3He detector tubes. The neutrons can ionize the

3He gas produc-

ing electrons, so an electric current is measured through an electric potential difference. 3

Figure 2: IN13

In the process described, the cases where the neutrons have been absorved or have travelled through the sample without being scattered have not been considered. The signal porduced by these neutrons is easily eliminated considering the time range of the process and with the help of a beam stop; therefore, only those neutrons who have travelled from the sample to the analysers and back to the detectors are counted. It should be mentioned that, with this instru- ment, it is possible to do elastic and quasi-elastic scattering experiments by changing the tempera- ture of the monochromator, which would lead to a change in the interatomic distance d in the CaF2

• crystals. In the first case, the temperature of the

cryofurnace of the monochromator does not vary, however, in the second case the variation of the temperature, and therefore of d changes the wave- length of the scattered neutrons, that is equivalent to a change of the initial energy, Ei. However, in this is experiment we are focusing on an elastic scattering event.

Samples and utensils

The samples used during the experiment are bio- logical cells in a state between liquid and powder (paste state) and in various shapes and sizes. Due to their richness in water populations (30 − 50%), elastic neutron scattering gives access mostly to the dynamical characteristics of the hydrogen con- tained in them. The samples on which the exper- iment is focused are two types of well studied and basic microorganisms and two types of tumoral

• cells. These samples ordered by complexity are :
• E. Coli bacteria, Yeast, Glioma and PC12.
• E. Coli. (Escherichia coli) a bacterium that is

commonly found in the gastrointestinal tract

• f humans and warm-blooded animals. E.

coli have the ability to exchange genetic ma- terial via mobile genetic elements such as plasmids and bacteriophages, as an adap- tation response to new and stressful envi- ronments. These genetic elements are be- lieved to contribute to environmental sur- vival and persistence in food systems; more-

• ver, the bacterium can be grown easily in

a laboratory setting. Consequently, E.Coli has been intensively investigated for several decades, becoming one of the most widely studied model organism and an important species for genetic experiments in the fields

• f biotechnology and microbiology.

Figure 3: E. Coli

Yeast: single-celled microorganisms, members of the fungus kingdom. One of the more well known characteristics is the ability to fer- ment sugars for the production of ethanol. These fungus are characterized by a wide dispersion of natural habitats: common on plant leaves and flowers, soil and salt water, but they are also found on the skin surfaces and in the intestinal tracts of warm-blooded animals, where they may live symbiotically

• r as parasites.

For the past decades has been the model system for much of molecular genetic re- search because of its basic cellular mechanics 4

• f replication, recombination, cell division

and metabolism. It is a centrally important model organism in modern cell biology re- search and biotechnology.

Figure 4: Yeast

Glioma: A glioma is a type of tumor that starts in the brain brain or spine. It is called a glioma because it arises from glial cells. Glial cells are brain cells which provide sup- port and protection for neurons in the cen- tral and peripheral nervous systems; they surround neurons and hold them in place, supply nutrients and oxygen to neurons, de- stroy pathogens and remove dead neurons. Gliomas constitute about 80% of all ma- lignant brain tumors; therefore, the impor- tance of its study.

Figure 5: Giloma

PC12: PC12 is a cell line derived from a pheochromocytoma (a neuroendocrine tu- mor) of the rat adrenal medulla; essentially, a cancer nerve cells. The study of these inva- sive cells has given a large a mount of infor- mation about brain diseases and it is useful in many research fields in medicine

Figure 6: PC12

Note: All the samples were provided by the

Neuro Science Department in Grenoble; and the pictures were taken with an optic micro- scope at EMBL.

The samples mentioned are kept inside an alu- minium sample holder (Figure 7), mounted on a long can called stick. Because of the nature of the samples studied, a papel aluminium folder is also needed in order to keep them in place inside the sample holder. This utensils mentioned might vary depending on the type of the temperatures and preassures used during the experiment.

Figure 7: Sample holder

4 Method

Data analysis

The project consists to analyze raw data from elas- tic neutron scattering experiment using IN13 in-

• strument. The software to treat and manipulate

data is LAMP. LAMP stands for Large Array Ma- nipulation Program; it is a software which was ini- tially developed for the treatment of data obtained from neutron scattering experiments at the Insti- tute Laue-Langevin. Currently, it has acquired more general purposes by adding common fea-

• tures. The programme provides a predictable and

5

intuitive graphical user interface which integrates scientific visualisation with an enhanced data lan-

• guage. Many high level modules are predefined to

enable interactive data analysis and visualisation

• f 2D, 3D data and atomistic representations.

The input in the software consists of the col- lected raw data and a proxi file, which is a file written in IDL language. IDL, short for Inter- active Data Language, is a popular programming language used for data analysis in areas of science, such as astronomy, atmospheric physics and med- ical imaging. The programme also requires some instrumental parameters. For this specific project, several proxi files were written with the purpose of correcting the raw data recorded on the instrument and working with it in order to get the results needed. As it shows in Listing 1, LAMP reads the run-numbers of the experiment selected and using numerous functions (Table 3), the desired information is stored in sev- eral workspaces, from which it can be exported for a deeper treatment.

w1=rdrun(1234) reads run number 1234 into w1 rdsum(1234,1237) sums together runs 1234 to 1237 rdand(1234,1237) join together runs 1234 to 1237 rdopr(’1234+1237’) would sum runs 1234 and 1237 elascan_format transforms into common for- mat elascan_groupt groups temperature if neces- sary bsnorm normalizes to total monitor counts elascan_slab corrects sample data from an elastic scan. elascan_vnorm averages values and normal- izes elascan_remove removes bad detectors elascan_logplot changes x-axis and intensi- ties in order to plot ln I(Q) vs Q2 elascan_phi2q transforms x-axis from angle to Q and sort and join detec- tors w1_output exports files containing the

• utput selected

Table 3: LAMP functions

As it was mentioned, it is necessary to correct the raw data recorded on the instrument. In the neutron scattering intensity we have contributions coming from the sample holder and the aluminium paper folder that must be subtracted with the soft- ware programme. In order to do that, some mea- surements of the empy sample holder and only the aluminium folder are done. Furthermore, the scattered intensity of the sam- ple is lower in reality, because there are absorption and multiply scattering effects. For that reason, the measurements are normalized with respect to vanadium, since it is an element whose incoher- ent scattering cross section is close to zero. This permits to correct the detector eficiency.

Listing 1: Extract of a Proxi file ;*************************************** ;********** ECOLI ********************** ;*************************************** ;++++++++++ Empty cell ++++++++++++++++++ w1=rdsum(80707,80711) w1=elascan_format(w1) w1=bsnorm(w1) ;++++++++++++++ Aluminium ++++++++++++++ w2=rdsum(80713,80717) w2=elascan_format(w2) w2=bsnorm(w2) ;++++++++++++++++ Vanadium +++++++++++++ w3=rdsum(80434,80437) w3=elascan_format(w3) w3=bsnorm(w3) ;+++++++++++++++ Ecoli ++++++++++++++++++ w4=rdopr(’80720:80764’) w4=elascan_format(w4) w4=elascan_groupt(w4,dt=1,sort=1,average=1) w4=bsnorm(w4) ;+++++++++++ Correction sample+++++++++++ w5=elascan_slab(w4,background_w=2,angle=135, t_s=0.924,t_c=0.99,twice=1,f=1,corr=20) ;++++++++ Correction Vanadium+++++++++++++ w6=elascan_slab(w3,background_w=1,angle=135, t_s=0.83,t_c=0.99,twice=1,f=1,corr=20) w7=elascan_vnorm(w5,w6) w8=elascan_remove(w7,[1,24,25,26,27,28,29, 30,31,32,33,34,35,36,37,38]) w9=elascan_phi2q(w8,dQ=0.01) w10=w9[*,0:6] w11=total(w10,2) w12=elascan_logplot(w10) elascan_output,w11,file=’Ecoliw11’ elascan_output,w12,file=’Ecolilog’

6

Results

After the programming process is completed, the data can be treated and some results are going to be shown. In figure (Figure 8), the scatter- ing intensity as a function of the scattering vec- tor Q is displayed at different temperatures (280, 285,..., 315 K) for the E. Coli sample. See Ap- pendix (page 10) for the results of the rest of the samples used. It is clear that the tendency in all

• f them is essencially similar: the higher Q is, the

less scatttering intensity is detected. Furthermore, it is noticeably that the intensity decreases as we increase the temperature of the samples.

1 2 3 4 0.1 0.2 0.3 0.4 0.5 Q (˚ A−1) Scattering intensity 280 K 285 K 290 K 295 K 300 K 305 K 310 K 315 K Figure 8: Scattering vs Q for E. Coli

In the following plots (9) and Appendix (page 10), the natural logarithmic of the scattered in- tensity as function of Q2. According to the equa- tion (1) explained in the theoretical introduction, in the Gaussian approximation, the natural loga- rithm of the intensity obtained is proportional to

• Q2. Since the slope is − u2

6 , values of the mean

square displacement for each temperature can be estimated, as it is shown in the data table.

1 2 −2 −1 Q2 (˚ A−2) ln (Scattering Intensity) 280 K 285 K 290 K 295 K 300 K 305 K 310 K 315 K Figure 9: Scattering intensity vs Q2 for E. Coli

T (K) m u2 (˚ A2) 280 −0.6 ± 0.05 3.6 ± 0.3 285 −0.58 ± 0.06 3.5 ± 0.4 290 −0.65 ± 0.07 3.9 ± 0.4 295 −0.69 ± 0.08 4.1 ± 0.5 300 −0.69 ± 0.07 4.1 ± 0.4 305 −0.71 ± 0.09 4.3 ± 0.5 310 −0.74 ± 0.09 4.4 ± 0.5 315 −0.79 ± 0.09 4.7 ± 0.5

Table 4: Scattering intesity vs Q2 for E. Coli

For each measurement, a linear fit with a straight line is made from which the MSD is calcu- lated; it is taking into account that for the results to stay within the validity of the Gausssian ap- proximation, we used a limited range of Q-range, so that the condition u2Q2 ≪ 1 is accomplished. It is not surprising that, as the graphs and the data present, the values for the MSD coefi- cient increase with temperature. It is a quite in- tuitive thought that the higher the temperature, the molecules would experience an amplification in their motions; therefore, the coeficient mentioned will increase with the temperature. This can also be represented in another graphic (10). As it was expected, the dependence between the MSD and the temperature is linear for all the samples. How- 7

ever, although the tendency is consistent with the previous statement, it is shown by the error bars that the stadistical error is significant. As a conse- cuence, no determining conclussions can be made.

280 290 300 310 320 3 4 5 6 7 8 T (K) u2 (˚ A2) Ecoli Glioma Yeast PC12 Figure 10: MSD vs T

To overcome this problem, the stragedy is to represent the summed scattering intensity as a function of the temperature for Q ∈ [0, 2.2]˚ A−1, (Figure 11). The advantage of this different way to present the data is that the stadistical error is considerably lower, since it is a direct result. Moreover, some unexpected phenomenons are

• bserved in the representation (Figure 11). While

the regular biological samples present straight line behaviours, there is an interesting tendency in the summed scattering intensity of the tumoral cells, there is a change in the slope at around 300−305 K which happens to be ambient air temperature. The changed observed could be connected to some dynamic transicions that could be studied in the future in order to understand tumor mechanisms, having a great impact in life sciences and medical research.

280 290 300 310 0.6 0.7 0.8 0.9 1 T (K) Summed Scattering Intensity Ecoli Glioma Yeast PC12 Figure 11: Summed Scattering intesity vs T

5 Conclusions

Thermal neutron scattering is an outstanding technique to provide information about both dy- namics and structure of the systems under study. Regarding the results collected in this IN13 ex- periment, the mean square displacement values are consistent and their tendency, as the tempera- ture is modified, is logical. However, not much in- formation can be extracted from these values due to the significance of the statistical error. The low flux of IN13 was one of the main factors which have contributed to this problem; at the moment, an upgrade of the instrument is being made so the flux in future studies would be adequate. Fur- thermore, in biophysics experiments the requiered sample mass is rather large, which was signifi- cantly difficult to obtain, especially the tumoral cells. The stragedy followed to decrease that stadisti- cal error, led to the perception of a different be- haviour of the tumoral cells in comparison with the healthy microorganisms. This interesting re- sult could be the base in future research projects focused on the study of a disease as relevant as

• cancer. Therefore, it is undeniable that the use
• f neutron scattering technology in health-related

fields has a great impact, playing a unique role in the life sciences and medical research. 8

Acknowledgements

I am very grateful to the organizers of the 2017 ILL-ESRF Summer School Programme for making the wonderful experience of working in a scientific research institute become true. I want to give a special thank to my tutor during the internship

• Ms. Irina Piazza for the help given.

References

[1] M B´ ee, Quasielastic neutron scattering. Adam Hilger (1988). [2] Frank Gabel, Dominique Bicout, Ur- sula Lehnert, Moeava Tehei, Martin Weik and Giuseppe Zaccai, Protein dy- namics studied by neutron scattering. Cam- bridge University Press (2002). [3] Kittel, C., Introduction to Solid State

• Physics. John Wiley & Sons, Inc. (1953).

[4] D. Richard, M. Ferrand, G. J. Kear- ley, LAMP Languaje. [5] A. D. Bradle, The LAMP Book. [6] Magazu, Salvatore, Strumentazione per spettroscopia di neutroni: spettrometro IN13 ad ILL. 9

Appendix

1 2 3 4 0.1 0.2 0.3

Q (˚ A−1) I

280 K 285 K 290 K 295 K 300 K 305 K 310 K 315 K (a) Glioma

1 2 3 4 0.2 0.4

Q (˚ A−1) I

280 K 285 K 290 K 295 K 300 K 305 K 310 K 315 K (b) Yeast

1 2 3 4 5 · 10−2 0.1

Q (˚ A−1) I

280 K 285 K 290 K 295 K 300 K 305 K 310 K 315 K (c) PC12

Figure 12: I vs Q

10

0.5 1 1.5 2 2.5 −3 −2 −1

Q2 (˚ A−2) log I

280 K 285 K 290 K 295 K 300 K 305 K 310 K 315 K (a) Glioma

0.5 1 1.5 2 2.5 −3 −2.5 −2 −1.5 −1 −0.5

Q2 (˚ A−2) log I

280 K 285 K 290 K 295 K 300 K 305 K 310 K 315 K (b) Yeast

0.5 1 1.5 2 2.5 −4.5 −4 −3.5 −3 −2.5 −2

Q2 (˚ A−2) log I

280 K 285 K 290 K 295 K 300 K 305 K 310 K 315 K (c) PC12

Figure 13: log I vs Q2

11