# Water Dynamics in Cancer Cells: Lessons from Quasielastic Neutron Scattering

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. The QENS Technique: A Brief Overview

#### 2.1. Basic Concepts of QENS

^{1}H) that have a comparable mass to protons, a magnetic moment of −1.913 μ

_{b}, and a nuclear spin of ½. Since neutrons exhibit a wave-mechanical duality, their momentum can be described either as $\overrightarrow{p}=m\overrightarrow{v}$, where m is the neutron mass (1.675 × 10

^{−27}kg) and $\overrightarrow{v}$ its velocity, or $\overrightarrow{p}=\hslash \overrightarrow{k}$, where |$\overrightarrow{k}$| = (2π)/λ is the wave vector of the neutron and λ its wavelength. Hence, the neutron energy can be described as:

^{−9}s to 10

^{−12}s, such as the translational and rotational motions of molecules, and obtain a spatial insight of such motions. In a comparison with other neutron scattering techniques that are commonly employed in biology-related research, the vibrational modes observed with Inelastic Neutron Scattering (INS) are on the time scale of 10

^{−14}s to 10

^{−15}s and mostly contribute to the background in a QENS experiment. In addition, crystallography experiments widely used to resolve the structure of drugs, proteins, and others rely on coherent scattering interactions between neutrons and matter where the Bragg reflections are important (the differences between coherent and incoherent scattering are explained further in the paper). The signals collected by detectors largely affected by Bragg reflections are commonly discarded for the QENS data analysis [25,26].

^{1}H). With this, the dynamics of

^{1}H-rich species not only can be probed but also masked out during an experiment via selective isotopic substitution of

^{1}H by deuterium (

^{2}H).

^{1}H-rich samples is usually negligible except when strong structural peaks are encountered. In such cases, the detectors placed at scattering angles under strong influence from Bragg reflections are typically discarded, allowing for the single-particle dynamics from

^{1}H-rich species to dominate the analysis. Therefore, from now on, we only focus on the incoherent part of the double differential scattering cross-section. As depicted in Equation (3), ${\left(\frac{{\partial}^{2}\sigma}{\partial \mathsf{\Omega}\delta \omega}\right)}_{incoh}$ is related to the individual particle’s incoherent scattering cross-section, ${\sigma}_{incoh}$, and the incoherent dynamic structure factor, S

_{incoh}(Q, $\omega $), as:

_{incoh}(Q, ω) contains the information on the single-particle dynamics within the sample and is a time-Fourier transformation of the so-called intermediate scattering function, I

_{incoh}(Q, t). Upon additional space-Fourier transformation, I

_{incoh}(Q, t) gives the single-particle self-correlation function, G

_{self}(r, t), which can be interpreted as the probability of finding a particle at position “r” at a time “t” if it has been at the position r = 0 at the time t = 0.

_{incoh}(Q, t) and S

_{incoh}(Q, ω) are presented in Figure 3. In Figure 3a, curve a-I shows the expected behavior of I

_{incoh}(Q, t) for a static particle. The probability of finding the particle over time is constant and equals one. In this case, no energy transfer between the incoming neutrons and the particle under analysis ought to occur, and only elastic events are perceived in the experiment. Following a time-Fourier transformation of I

_{incoh}(Q, t), one obtains S

_{incoh}(Q, ω) as a simple δ-function, as depicted in II in Figure 3a. However, in a real experiment, S

_{incoh}(Q, $\omega $) is shaped by the inherent resolution of the spectrometers, which, as shown in III in Figure 3a, is convoluted to the collected data. The resolutions of QENS spectrometers depend on their design and are usually improved at the expense of other experimentally relevant factors, most notably, the measurement statistics. For example, the so-called high-resolution backscattering spectrometers have a narrower resolution function (thus allowing for assessing slower motions) than the time-of-flight spectrometers. However, this feature is achieved at the expense of the signal-to-noise ratio and the more limited range of accessible values of energy transfer. Followed with Figure 3b, as the particle under analysis starts to perform motions (by warming up the sample, for example), I

_{incoh}(Q, t) gradually decays, and, as long as such motions are faster than the constraints imposed by the instrumental resolution, they are perceived as additional broadenings in S

_{incoh}(Q, ω), II in Figure 3b.

_{incoh}(Q, t) rapidly decays as Q increases and reaches the limit of I

_{incoh}(Q, $\infty $) = 0, as shown in I in Figure 3c, and S

_{incoh}(Q, $\omega $) broadens accordingly as depicted in II in Figure 3c. In such a scenario, in real-space and time domains, the probability of finding a freely diffusing particle vanishes at very long times, and such an effect is even more pronounced at short distances from the origin of the motion. For particles moving within a constrained geometry, such as a confined translation or rotation of a molecular group, I

_{incoh}(Q,t) plateaus at a finite value at $t\to \infty $ (that is I

_{incoh}(Q, $\infty $) $\ne $ 0) (I in Figure 3d). In these cases, the broadening of S

_{incoh}(Q, $\omega $) assumes a Q-independent constant value (aside from experimental fluctuations) and, since I

_{incoh}(Q, $\infty $) $\ne $ 0, an elastic component, that is a time-independent component of I

_{incoh}(Q, $t$), is introduced in the QENS signal and has been defined as the Elastic Incoherent Structure Factor (EISF). The determination of the time-independent component in I

_{incoh}(Q, $t$) is limited by the instrumental resolution at long times. For less constrained geometries, it is sometimes possible to observe the broadening of S

_{incoh}(Q, ω) assuming a Q-independent behavior at low Q-values and then evolving to a Q-dependent behavior at higher Q [35,36].

#### 2.2. QENS Data Analysis

_{incoh}(Q, $\omega $) can be described as a single Lorentzian function. For example, for a long-range translational motion in liquids, the single-particle self-correlation function, G

_{self}(r,t) must be a solution of Fick’s second law and is, therefore, a Gaussian function:

_{incoh}(Q, t) is an exponential decay, $I\left(Q,t\right)={e}^{-tD{Q}^{2}}$, and S

_{incoh}(Q, $\omega $) assumes the Lorentzian form as:

_{0}is the residence time between two diffusion jumps and D is the diffusion coefficient. In Equation (7), if τ

_{0}= 0, one obtains the equation for a Fickian continuous diffusion. If τ

_{0}$\ne $ 0, then one can also obtain, for systems with fairly low concentrations, a jump length, $L=\sqrt{6D{\tau}_{0}}$. In liquids, L often reflects the distance between two neighboring molecules. While Equation (7) satisfies all the scientific cases to be discussed in this review, other models (usually more complex) may eventually become necessary to accurately describe the evolution of $\Gamma \left(Q\right)$.

_{incoh}(Q, $\omega $) is also defined by a Lorentzian function (with a Q-independent $\Gamma \left(Q\right)$) but $x\left(Q\right)\ne 0$ in Equation (4) due to the presence of the EISF. In addition, one can explore another powerful feature of the QENS technique, since the Q-dependent behavior of the EISF provides valuable information about the geometry, and consequently the origin, of the motions under analysis. For example, the radii of the confined dynamics characteristic of some functional groups, such as methyl rotation, are well known and can be compared with parameters extracted by fitting the EISF using the appropriate models [38]. In addition, the EISF has been recently explored as a minimalist approach for interpreting the intermediate scattering function, I(Q, t). With this method, the QENS data are parameterized in terms of the EISF, a relaxation time scale, and the relaxation form, τ(Q) and α(Q), and subtle changes hidden in the spectra can be captured [39].

## 3. QENS and Cancer Cells

#### 3.1. Experimental Considerations

^{1}H-rich cellular components. On the one hand, with this methodology, one probes the natural dynamics of the system, while on the other, the QENS signal is often dominated by the bulk-like contributions, which hinders observation of the confined-like dynamics. It is common to resort to lyophilization procedures to remove the bulk-like populations of water from the cells as well as most of the confined molecules. With this, the dynamics from the remaining

^{1}H-rich cellular components is highlighted, but the original structure of membranes and proteins can be disrupted (at least partially) [49,50] and the probed dynamics may not fully reflect the conditions within the cells in their natural state. Ultimately, one can also resort to exposing the cells to deuterated media. Culturing cells in a deuterated environment could be, in principle, a sound approach to drastically reduce the signal from cellular water (both confined and bulk-like) and highlight the relaxations from the remaining cellular components. Moreover, the data collected with such cells could be further subtracted from data collected with cells cultured in non-deuterated media, and one would be left with QENS signals mostly from the water itself. However, culturing cells in a deuterated environment has been shown to lead to considerable metabolic changes that could manifest as alterations in water dynamics [51]. Therefore, a less severe approach for deuteration has been used and consists of culturing the cells in non-deuterated media and sequentially washing these with deuterated saline solution [52,53,54]. By doing so, only the signal from extracellular water is drastically reduced in the QENS experiment.

#### 3.2. What Have We Learned So Far with QENS and Cancer Cells?

_{3})

_{2}Cl

_{2}), whose cytotoxic effect is mediated by DNA conformational rearrangements. The cells were cultivated in non-deuterated media, concentrated as pellets, and washed with deuterated phosphate-buffered saline (PBS) solution to remove the contributions from the extracellular water. Additionally, lyophilized samples were prepared to probe the dynamics of the cellular components with minimal interference from water. The QENS experiments were performed at the OSIRIS spectrometer (ISIS Pulsed Neutron Source of the Rutherford Appleton Laboratory, UK) with an energy resolution of 25.4 μeV (FWHM), which allows for the detection of motions on the order of 10

^{−10}s and were combined with inelastic neutron scattering and optical vibrational spectroscopy. The spectra were collected at 298 K and fitted considering an elastic component, assigned to very slow motions from large cellular components and global motions of the macromolecules, and three Lorentzian-shaped contributions assigned to (i) the slow diffusion of water molecules in the hydration shells of biomolecules, (ii) the faster diffusion of non-hydrating water molecules, and (iii) the localized motions within the macromolecules and/or fast rotation of water molecules. Here, it should be noted that the choice of the model to fit any QENS data is hardly ever unique (e.g., in choosing between the model Q-dependence characteristic of Fickian vs. jump-diffusion vs. localized/rotational motion), and any chosen model could be, at least in theory, refined and improved. However, model-free comparison of the QENS data collected from different samples can always provide an unambiguous, even if more qualitative, indication of the effect of parameters of interest (e.g., drug concentration) on the microscopic dynamics under investigation. Interestingly, the authors reported that exposure to cisplatin induces distinct responses in the non-hydrating and hydrating water molecules. In the first case, the non-hydrating (bulk-like) water populations in cancer cells not exposed to the drug presented a diffusion coefficient, D, and residence time, τ

_{0}(as defined in Equation (7)), of $D$ = (1.04 ± 0.05) × 10

^{−9}m

^{2}/s and τ

_{0}= (1.0 ± 0.1) ps, which are on the same order of magnitude as expected for bulk water (${D}_{H2O}$ = ~3 × 10

^{−9}m

^{2}/s and τ

_{0-H2O}= 1 ps). After exposure to cisplatin, the mobility of this water population is drastically damped and D drops to (0.19 ± 0.01) × 10

^{−9}m

^{2}/s, whereas τ

_{0}increases to (7.39 $\pm $ 1.16) ps (considering the highest dose of the drug used in the work, 20 mM). Meanwhile, the water populations confined in the hydration shells of biomolecules experience an increase in their mobility upon the action of cisplatin, with $D$ changing from (0.0300 ± 0.0004) × 10

^{−9}m

^{2}/s to (1.39 ± 0.13) × 10

^{−9}m

^{2}/s. These trends are depicted in Figure 6, in which the bulk-like populations are defined by the authors as cytoplasmic water and the confined populations as hydration water. In the panels of Figure 6a, the full lines indicate the fitting of the QENS broadening with Equation (7). Here, another relevant feature depicted in the figure is that the treatment with the drug leads to distinct patterns in both the cytoplasmic and hydration water, in which the models used to fit the data at low Q-values, with τ

_{0}= 0, do not describe the data at higher Q. As shown in Figure 6b, the component assigned to the localized motions within the macromolecules and/or fast rotation of water molecules only presents detectable differences between the cancer cells treated and not treated if the highest dose of the drug is used, although the lower dose already leads to changes in the components solely attributed to water dynamics.

_{2}Spm (Spm = spermine = H

_{2}N(CH

_{2})

_{3}NH(CH

_{2})

_{4}NH-(CH

_{2})

_{3}NH

_{2}), whose cytotoxic effect is also based on targeting cellular DNA, in human osteosarcoma cells (MG-63) [55]. For this work, the cell pellets were also washed with deuterated PBS to remove the contributions from the extracellular water in the QENS experiments, which were performed at 310 K at the OSIRIS spectrometer and combined with Synchrotron-MicroFTIR. Like the previous work with breast cancer cells, the authors modeled the QENS spectra with an elastic component and three Lorentzian-shaped contributions. Following the same trend observed in the breast cancer cells, the mobility of the bulk-like water populations is reduced by the anticancer agents, and the opposite effect was observed in the confined dynamics. For the bulk-like water, D changes from (1.28 ± 0.01) × 10

^{−9}m

^{2}/s in the untreated cells to (1.00 ± 0.01) × 10

^{−9}m

^{2}/s after treatment with Pd

_{2}Spm and (0.89 ± 0.01) × 10

^{−9}m

^{2}/s with cisplatin (considering the highest doses of the drugs used in the work). For the confined water, D changes from (0.17 ± 0.00) × 10

^{−9}m

^{2}/s in the untreated cells (the null uncertainty is reported here as reported by the authors) to (0.72 ± 0.01) × 10

^{−9}m

^{2}/s after treatment with Pd

_{2}Spm and (0.82 ± 0.01) × 10

^{−9}m

^{2}/s with cisplatin (also considering the highest doses of the drugs used in the work). In this work, the authors rationalize that the increased mobility of the confined water molecules is associated with the biomolecules’ conformational rearrangement upon drug binding that leads to disruption of their highly structured hydration shell. In addition, the authors point out that the differences between the energies associated with the motions from confined and bulk-like populations were found to be less marked in the poorly metastatic osteosarcoma cells than in the highly metastatic breast cancer, and the impact of cisplatin on osteosarcoma’s bulk-like water is less pronounced than in the triple-negative breast cancer cells.

_{Bose}(E) = (exp(E/k

_{B}T) −1)

^{−1}is the Bose population factor, and k

_{B}is Boltzmann’s constant. In the dynamic susceptibility presentation, the characteristic diffusion/relaxation frequencies/times manifest themselves in the positions of susceptibility maxima. For the cells not exposed to the drug, the QENS signal was dominated by a very localized dynamics with a relaxation time of around 67 ps. After the action of the drug, a bulk-like non-localized dynamics was detected with D = (2.21 ± 0.11) × 10

^{−9}m

^{2}/s. Finally, the authors raise another point of interest. The viability of the cells was tested after the QENS experiments and they found that around 70% of the cells (treated and not treated with paclitaxel) were still viable despite being exposed to non-optimal conditions for more than 12 h.

## 4. Perspectives for the Future

## 5. Final Remarks

## Author Contributions

## Funding

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

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**Figure 1.**(

**a**) Typical scattering triangle showing incoming neutrons with incident energy E

_{i}, wavelength λ

_{i}, and wave vector $\overrightarrow{{k}_{i}}$ interacting with the sample and assuming final energy E

_{f}, wavelength λ

_{f}, and wave vector $\overrightarrow{{k}_{f}}$. The momentum transfer $\overrightarrow{Q}$ is defined as the change in wave vector ($\overrightarrow{Q}$= $\overrightarrow{{k}_{i}}$− $\overrightarrow{{k}_{f}}$); (

**b**) summary of the main features of the QENS technique. These are explained in detail in the text.

**Figure 2.**Graphical representation of a single particle scattering. The incoming neutron waves are scattered by a particle i at different times, 0 and t, and positions, $\overrightarrow{{r}_{i}\left(0\right)}$ and $\overrightarrow{{r}_{i}\left(t\right)}.$ The scattered waves interfere with each other before detection. The scattering triangle is also represented in the figure.

**Figure 3.**Schematics of the relationship between I

_{incoh}(Q, t) and S

_{incoh}(Q, $\omega $). In (

**a**), curve a-I shows the expected behavior of I

_{incoh}(Q, t) for a static particle where no exchange of energy occurs between the incoming neutrons and the sample. As shown in a-II, after a time-Fourier transformation of I

_{incoh}(Q, t), one obtains a δ-function-shaped S

_{incoh}(Q, $\omega $), which broadens when convoluted with the experimental resolution (see a-III). In (

**b**), the particles under analysis perform motions upon, for example, heating and I

_{incoh}(Q, t) gradually decays (b-II) and S

_{incoh}(Q, $\omega $) becomes broader (b-II). In (

**c**), an unconstrained diffusive motion is depicted, which leads to a gradual decay of I

_{incoh}(Q,t) over Q (c-I) reaching the limit of I

_{incoh}(Q, $\infty $) = 0, and S

_{incoh}(Q, ω) broadens as a function of Q (c-II). In (

**d**), the motions of particles within a constrained geometry are depicted and I

_{incoh}(Q, t) plateaus at a finite value at $t\to \infty $.

**Figure 4.**Illustration of the complex chemical environment within living cells and the different water populations. The green/pink molecules depict the bulk-like populations, which are subjected to weak interactions with the biological interfaces and are more abundant in cellular media (they are semi-transparent in the figure for presentation purposes). The red/blue molecules depict the confined-like populations, which are subjected to closer interactions with the biological interfaces and present features of confined dynamics that are not comparable with bulk water.

**Figure 6.**Variation of the full widths at half-maximum (FWHM) with Q

^{2}for untreated and cisplatin-treated (8 and 20 mM) MDA-MB-231 cells in deuterated saline medium (washed), at 298 k: (

**a**) Lorentzian functions representing the translational motions of intracellular water—cytoplasmic and hydration water; (

**b**) Lorentzian function representing the internal localized motions within the cell. Reprinted with permission from ref. [53]. Copyright 2017 The Royal Society of Chemistry.

**Figure 7.**Dynamic susceptibilities obtained from QENS data for not-treated breast cancer cells (MCF-7), NTC (

**a**), and breast cancer cells treated with 15nM of paclitaxel for 24 h, TC (

**b**), reprinted from [16] available via the Creative Commons Attribution 4.0 International License (CCBY4.0, https://creativecommons.org/licenses/by/4.0/, 29 March 2022).

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**MDPI and ACS Style**

Martins, M.L.; Bordallo, H.N.; Mamontov, E.
Water Dynamics in Cancer Cells: Lessons from Quasielastic Neutron Scattering. *Medicina* **2022**, *58*, 654.
https://doi.org/10.3390/medicina58050654

**AMA Style**

Martins ML, Bordallo HN, Mamontov E.
Water Dynamics in Cancer Cells: Lessons from Quasielastic Neutron Scattering. *Medicina*. 2022; 58(5):654.
https://doi.org/10.3390/medicina58050654

**Chicago/Turabian Style**

Martins, Murillo L., Heloisa N. Bordallo, and Eugene Mamontov.
2022. "Water Dynamics in Cancer Cells: Lessons from Quasielastic Neutron Scattering" *Medicina* 58, no. 5: 654.
https://doi.org/10.3390/medicina58050654