Extension of the concept of an anomalous water component to images of T-cell organelles

Abstract. Microscopic images of a living cell are the main source of information on its functional state. Modern interference microscopy techniques allow the numerical parameters of cell images to be obtained with an accuracy not available with other methods. Quantitative analysis of phase images of T lymphocytes (TCs) in different functional states demonstrated that variations of the properties of intracellular water should be taken into account. This conclusion agrees with the current view that the physical parameters of water, including the refractive index (RI) of a water layer, depend on the hydrophilicity and other characteristics of the adjacent surface. Application of this concept to phase images of TCs showed that the contribution of the fourth phase of water (4-water) or the structured water component, which has an increased RI, should be considered. The proportion of 4-water depends on the functional state of the cell determined by the culture medium composition. Normally, the proportion of 4-water in organelles is as high as 30%; it is considerably lower in organelles of cells with inhibited metabolism.


Introduction
Water is one of the best studied environmental objects.Its properties are dealt with in a number of studies (reviewed in Ref. 1).Therefore, new data on structured water or the fourth phase of water (4-water) summarized and systematized in a recent book by Pollack 2 are of particular interest.The 4-water has a number of anomalous properties expressed in the so-called exclusion zones of water layers adjacent to hydrophilic surfaces and in gels.Two simple examples clearly illustrate these properties of 4-water.The refractive index (RI) of a gel containing 99% of water has been found to drastically decrease from n ¼ 1.43 to n 0 ¼ 1.333 (a value characteristic for ordinary water) upon heating by only 1°C. 3 The second example is an RI of a water n ≈ 1.43 at the hydrophilic surface of Nafion, a synthetic polymer with ionic properties. 4,5,6ells of most organisms contain as much as 80% of water; in jellyfish, the percentage exceeds 95%.][9][10][11] However, we have not found any mention of such a phenomenon in the literature.][14][15] Quantitative analysis of phase images of various cell types [7][8][9][10][11][12] has shown that the changes in their optical parameters caused by external factors cannot be solely explained by alterations of their proteins.In solving this problem, we suggested [7][8][9][10][11][12] that not only the change in protein RI averaged by the cell volume should be taken into account, but the possibility that the RI of intracellular water is changed should also be assumed.To test this hypothesis, we took advantage of the unique properties of cell phase images 16 and original algorithms. 10,11ere, we used RI measurements of T lymphocyte (TC) to calculate the proportion of the anomalous water component (4-water) in the organelles.To our knowledge, these are the first quantitative estimations of the mass fraction of 4-water in TC organelles.We present data on the 4-water effect on the organelle contrast in the phase image of a cell.For this purpose, we proposed a multicomponent optical model of a TC.
The basic assumption of our hypothesis is the existence of 4-water as a factor that contributes to RI.We also hypothesized that the proportions of 4-water and ordinary water in a living cell depended on its functional state. 6,7Below, we provide a biophysical interpretation of the variation of the 4-water contribution to the RIs of organelles and an explanation of its dependence on the hydrophilic/hydrophobic properties of organelles' membranes.We believe that our results can be used for explaining other phenomena in cell biophysics.Common for all interference methods is the representation of the images in the form of a two-dimensional distribution hðx; yÞ of optical path difference (OPD) in the image plane.The most important and the unique advantage of the interference microscopy is the measurement of OPD in absolute units of wavelength [7][8][9][10][11][12][13][14][15][16][17][18][19] with a very high precision, which is hardly achievable or is even impossible with other methods.Normally, the phase image is described as the function hðx; yÞ ¼ Z ðnðx; y; zÞ − n 0 Þdz in the image plane ðx; yÞ, where nðx; y; zÞ and n 0 are the refractive indices of the object and the environment, respectively.The function hðx; yÞ can be interpreted as a "projection" of the refractive index onto the image plane.Under certain conditions, the inverse problem can be solved when the function hðx; yÞ is restored from its projection.We also used an optical model of TC. 11 Its structure was represented by a limited number of spherical layers with different RIs (n i ) or refractivities Δn i ¼ n i − n 0 .In the phase image hðx; yÞ, these layers were projected onto the plain ðx; yÞ as zones outlined with the contours h ij ðx; yÞ ¼ const (Fig. 1).We have previously shown the possibility of determining the physical parameters of structural elements at the boundaries of these zones 10,11 as a system of concentric spherical layers with the diameters d ij and volumes V ij ¼ πðd 3 i − d 3 j Þ∕6.In general, the value of OPD at the boundary of j, j þ 1'th zones can be represented as the sum: h j;jþ1 ¼ P H ji Δn, where Δn i ¼ n i − n 0 is its refractivity; in the geometric path H ji , the first index j corresponds to the position of the point, and the second index i corresponds to the number of the layer (1 ≤ i ≤ j).The OPD "jumps" in the image plane ðx; yÞ in the proximity of the points that are the projections of the adjacent layer due to the difference (Δn jþ1 − Δn j ).
7][18][19] The phase thickness (h ij ) at the boundaries of organelles 11 was determined from the coordinates of the characteristic points (CPs) of the integral functions of area: and phase volume WðhÞ ¼ Z Δnðx; y; zÞdx dy dz: (2) These plots are shown in Figs.1(c) and 1(d), respectively.The positions of the S ij ðh ij Þ and W ij ðh ij Þ, the CPs and their abscissas on the plots were determined from the maxima of the derivatives dS∕dh and dW∕dh.This allowed us to exclude the minor nonuniqueness of the abscissas (h ij ) related to the asymmetry of cell shape and phase thickness profiles in Fig. 1(a).The following equation was used to determine the "equivalent" symmetric half-profile hðrÞ shown in Fig. 1(e): This made it possible to use the diameters of circles interpreted as the boundaries of zones [Fig.1(a)]: Double indices (i and j ¼ i þ 1) were used to designate the phase thickness (h ij ) and other parameters of the CPs.For example, the index ij ¼ 01 corresponded to the outer boundary of the cell and cytoplasm.The following main zones were distinguished: 0, environment (incubation medium); 1, peripheral cytoplasm; 2, its dense part (endoplasmic reticulum); 3, nucleus; and 4, nucleoli.
One can hypothesize that each organelle can be represented as a multicomponent spherical layer in the TC optical model.

Multicomponent Optical Model
The ultimate goal of the study was to determine the proportion of 4-water in each layer at different functional states.For this purpose, we used the condition of additive contributions of components, which is well known from the physics of dielectrics.It consists in the presentation of the electrical (or optical) properties of a multicomponent medium as a sum of the electrical susceptibilities of its components: This is important since only susceptibility, but not RI, meets the condition of additive contributions of the components.
Here, we considered only two water and two protein components designated by double left subscripts (11 and 12 for water and 22 and 21 for protein).The subscripts for ordinary water and protein components are 11 and 22, respectively; those for anomalous components are 12 and 21, respectively.Component 12 is the aforementioned susceptibility of water molecules (4-water), e.g., in layers adjacent to the hydrophilic areas of membranes.Correspondingly, component 21 is the expected change in the susceptibility of protein molecules (4-protein).The notations used here for the proportions of components ( 0 11 η and 0 22 η), where the obvious condition 0 11 η þ 0 22 η ¼ 1 should be met in an ideal medium (in the absence of anomalous components).The zero left superscript in 0 ii η indicates the ideal medium.The summary susceptibility of this ideal binary medium ( 0 Σ χ) with the proportions 0 11 η and 0 22 η and susceptibilities 0 11 χ and 0 22 χ can be calculated as For the known susceptibilities of the main components, ordinary water and protein ( 0 11 χ and 0 22 χ, respectively), it depends only on their weight proportions.Correspondingly, the total susceptibility of the four-component medium (including the anomalous water and protein components) is represented in the form of the equation or as the Σ χ i ¼ P klkl η ikl χ i , where summation is performed over the indices of organelles (i) and their components (kl ¼ 1, 2) determining the susceptibility of each i'th layer.The normalization condition for the weight proportions of all components ( kl η i ) has the standard form P klkl η i ¼ 1.Our third hypothesis is that the susceptibility of the medium of the i'th organelle and the parameters of the organelles of a T cell in the functional state p can be represented by the refractive and susceptibility indices of each i'th layer: In these notations, the change in the susceptibility of the i'th organelle medium upon transition of the T cell from states p to q is Within the correctness of the aforementioned three hypotheses, the refractivity and susceptibility profiles based on measurements of a TC can be used to quantitatively estimate the changes in the proportions of the components of their medium.In particular, this method allows the proportion of the anomalous water component (4-water) in organelles to be determined and used for biophysical interpretation.
We represented the functional state of a TC as its phase portrait, with "primary" parameters in the zones and their values of at the boundaries.These parameters are universal because their estimates in the phase image of the cell are independent of its type and the optical model used.It has been demonstrated that, in the context of the aforementioned three hypotheses, the RIs of organelles found from the measurements can be used to quantitatively estimate the parameters of their medium.In particular, the proportions of the anomalous water component (4-water) in organelles have been determined and used for biophysical interpretation.The change in the proportion of 4-water ( p 12 η i − q 12 η i ) can be estimated from the values of ( p 11 χ i − p 12 χ i ) known a priori and the results of the measurement of organelle refractivities (Δ p n i and Δ q n i ) as 3 Materials and Methods TCs isolated from the blood of a healthy donor were in the G0 phase.][10][11] The functional state of TCs was changed by the addition of compounds with a known mechanism of pharmacological action.We used the concentrations of compounds generally reported in the literature for treatment of whole cells and organelles.Media are designated as follows: N, phosphate buffer saline (PBS); P, R, and F, PBS supplemented with 2 μg∕ml prednisolone, 1 μM rotenone, and 4% formalin, respectively.We also exposed TCs to controlled He-Ne laser radiation (λ ¼ 633 nm, 1 mW) with a light dose of 10 5 J∕m 2 .This laser was used as a source in the Airyscan coherent phase microscope for phase imaging of cells.The cells were placed into a cuvette under a cover slip, then the cuvette was fixed on a microscope stage.][10][11] All experiments were performed with the Olympus MD Plan 20* objective, NA 0.4.3][14][15] New physical parameters of TC organelles (the phase volume, exclusion zone areas, phase thickness, and RIs profiles) were obtained using our originally developed algorithms. 10,11

Results
The proposed approach is illustrated by TC images obtained with the Airyscan coherent phase microscope. 11Irradiation for as long as 40 min caused changes in the cells, expressed most distinctly in a decreased contrast of CPs in the plots of integral functions 10 and a decreased phase thickness.Earlier we have demonstrated that the decrease of phase height of the isolated mitochondria and chloroplasts is proportional to the drop of the transmembrane potential. 8,9This state designated D was considered to correspond to a complete de-energization of cells (stopped metabolism).The refractivity profile ΔnðrÞ (Fig. 2) corresponds to this energetically lowest state.Hereafter, we refer to the coordinates of CPs and the parameters at the boundaries of organelles, with the organelles indicated by the following subscripts: 1, cytoplasm; 2, endoplasmic reticulum; 3, nucleus; 4, nucleolus.As seen in Fig. 2, the N, P, R, and F components of the medium had differential effects on the refractivity profile of organelles.Prednisolone caused a local decrease in refractivity in zones 4 (the nucleolus) and 2 (the endoplasmic reticulum).The effects of rotenone and formalin were characterized by a more monotonous and a significant decrease in refractivity toward the cell periphery (zones 2 and 1).Noteworthy is a decreased contrast of the intermediate CPs (ij ¼ 12, 23 and 34) in the R and F refractivity profiles. 11e effects of the incubation medium and other environmental factors on the functional state of TCs have been previously analyzed.It is known that rotenone blocks the complex 1 of the respiratory chain, and formalin inhibits metabolic processes.Manteifel and Karu 20 have studied the effect of laser radiation on TCs in detail and obtained electron microscopic images of irreversible changes in the cell structural elements. 20he main goal of our study was quantitative estimation of the effect of 4-water and changes in its proportions in cell organelles Δ pq 12 η i on the parameters of TC phase images.][10] For the anomalous protein component, we assumed 21 n ≈ 1.4 (at a susceptibility of 21 χ ¼ 1), the mean protein susceptibility being assumed to be 22 χ ¼ 1.2 ( 22 n ¼ 1.44).These values corresponded to a difference of susceptibilities of 12 χ − 11 χ ¼ 0.273.
Figure 3 shows the calculated profiles of changes in the proportions of 4-water Δ pq 12 η i ðrÞ in different media.Note that the change Δ ND 12 η i ðrÞ upon transition from the normal state into the de-energized one (ND) was the largest.The maximum changes were observed in the endoplasmic reticulum zone (i ¼ 2, Δ ND 12 η 2 ≈ 40%) at a distance of r ≈ 3.2 μm from the nucleolar zone (i ¼ 4, Δ ND 12 η 4 ≈ 20%).In the nuclear zone (r ¼ 1.5 to 2.0 μm), the decrease in the 4-water share was smaller (Δ ND 12 η 3 ≈ 10%); in the peripheral cytoplasm, it was almost indistinguishable (Δ ND 12 η 1 ≈ 3%).As expected, the changes upon transitions  from the R and P states into the D state (Δ RD 12 ηðrÞ and Δ PD 12 ηðrÞ, respectively) were smaller.Noticeable changes in the proportions of 4-water occurred only at the periphery of the nucleus and in the endoplasmic reticulum zone, and only in the cells incubated in the prednisolone containing medium.The changes were detected only in the region of the maximum refractivity [point Δ ND 12 η 2 ðr ¼ 3.2Þ].Interpreting the results shown in Fig. 3, we used the refractivity profile of the whole cell (Δn i ).Equation ( 6) was used for quantitative estimation of the changes in the proportions of the components for protein and water.The ratio between the complete protein and water amounts was taken as 2 η i ∕ 1 η i ¼ 1∕4 according to the assumed constant 80% water content of the cell.
We also performed estimations for an alternative model of a cell, where the constant contribution of the protein component (20%) to the cell image was ignored.As expected, the changes in the refractivity (Δ p n i − Δ q n i ) and susceptibility of water ( pq 1 χ i ) were increased by For an alternative and unrealistic case of an "equivalent" cell with the constant parameters of ordinary water (Δ p n i ¼ Δ q n i ¼ 1.333 ¼ const), the changes should be attributed to the protein component alone.This leads to the conclusion that the changes in the protein refractivity and susceptibility should be four times higher ( 1 η i ∕ 2 η i ¼ 4) than those indicated above for the variable water component.In such an "equivalent" cell, the ratio of refractivities Δ p n i and Δ q n i in organelles upon pq transition would be two times higher: Obviously, these changes cannot be explained by any reasonable assumption.
As seen in Fig. 2, the changes in refractivity are the largest upon ND transition in the endoplasmic reticulum zone (i ¼ 2), where the difference reached Δ N n 2 − Δ D n 2 ≈ 0.025.
Therefore, even if we take the 25% underestimation of the 4water RI that results from neglecting the contribution of the protein into account, we obtain reasonable values of the change in refractivity (n 21 ¼ n 0 − Δ N n 21 ¼ 1.37) or the values Δ N n 3 − Δ D n 3 ≈ 0.037 upon ND transition at a protein proportion of 2 η ¼ 0.2.This corresponds to changes in susceptibility of Δ ND χ 3 ð3Þ ≈ 0.051 and Δ ND χ 3 ð2.5Þ≈ 0.034.
In an alternative model, it should be assumed that the minimum RI of the nucleus in the completely de-energized state always remains within the interval D n 3 ≈ 1.38 − 1.39 ( D χ 3 ≈ 0.9 − 0.93).Hence, in the energized states, the nucleus RI should vary only within the interval N n 3 ≈ 1.5 − 1.59.Obviously, this result cannot be explained on the basis of known data.
Our analysis leads to the following preliminary conclusions: 1.The measured RI values in different metabolic states of a TC cannot be explained assuming an 80% water component with invariable standard physical parameters.
2. The only feasible explanation is the assumption of variable parameters for water.

Discussion
This study considers a number of debated issues.The main one is the hypothesis of the existence of 4-water in a living cell.Monographs by Ling 21 and Pollack 2 were apparently the first to discuss the problem of a structured water component in cells.However, only the experimental finding of exclusion zones in water layers adjacent to hydrophilic surfaces made it possible to discuss the issue in terms of modern physics. 6The first and very important finding was the existence of 4-water with a higher RI compared to ordinary water.5][6][7] Unfortunately, judging from the available literature, this fact has not been addressed at the level it deserves.Measurements of RIs (or refractivity) of organelles of living cells, in particular, TCs, 11 constituted the next step of research.We believe that this step was of no less importance for cell biophysics, because the use of cell volume averaged RI was insufficient for calculating the contribution of the anomalous 4-water component.
The available literature does not contain any discussion of the problem considered here, including that of 4-water in living cells.We were the first to use the numerical analysis of the dependence of refractivity values on electric susceptibility for determination of the cell organelle response to external factors, including the incubation media. 7There are grounds to believe that the concept of 4-water can be extended to other cell types, and new algorithms can be developed to quantitatively estimate this parameter.Evidently, similar results can be obtained for various cells using other types of interference microscopes.

Concluding Remarks
In this study, we considered only two water components (indices 11 and 12) and two protein components (indices 22 and 21).Component 12 reflects the expected change in the contribution to the susceptibility of water (4-water) molecules in layers adjacent to hydrophilic areas of membranes.Correspondingly, component 21 should reflect a similar change in the susceptibility of protein (4-protein) molecules.We do not know a more primitive and a simple optical model of a cell that would allow the proportion of the anomalous water component to be estimated.Apparently, our third hypothesis that a cell (a TC, in the given case) can be considered as a multicomponent layered medium with ð p n i Þ 2 ¼ 1 þ p χ i does not contradict current views (see Sec. 2.2).
An important general conclusion is that the changes of the i'th organelle in the initial functional state p of a TC can be represented in terms of the contributions of different components of its susceptibility:

1
Optical Model: Concept of Zones and Characteristic Parameters in the Phase Image of the Cell

Fig. 1
Fig. 1 Physical basis of the concept of significant parameters of phase images.Algorithms and other tools used for phase image analysis.(a) A phase image hðx; yÞ of a T lymphocyte (TC) obtained using an interference microscope as a two-dimensional distribution of the optical path difference in the plane ðx; yÞ.Structural elements differ from one another in the refractive index; their boundaries are shown as the contours h ij ðx; yÞ ¼ const.Dotted circles d ij have the same areas (S ij ) as those outlined with the contours h ij .Zones (1 to 4) represent TC organelles.(b) Phase thickness profiles hðx Þ and hðyÞ (dotted line) in diametric sections of a TC image.The values h ij (j ¼ i þ 1) correspond to the boundaries between structural elements: 01, the external medium and the peripheral cytoplasm; 12, the cytoplasm and the endoplasmic reticulum; 23, the endoplasmic reticulum and the nucleus; 34, the nucleus and the nucleolus.(c) The plot of the integral function of the area SðhÞ.Characteristic points with coordinates [S ij ; h ij ] where the derivative dS∕dh has maxima are shown.The h ij values correspond to the positions of boundaries in Figs.1(a) and 1(b).(d) The hðr Þ plot interpreted as a centrally symmetric equivalent of the real profiles hðx Þ and hðyÞ of the TC phase thickness in the normal state.The radius of the circle at the boundary of organelles in Fig. 1(a) (r ij ) is determined from the area S ij ¼ πr 2 ij S ij ¼ πðr ij Þ 2 in the ij'th characteristic point in Fig. 1(c).(e) The integral function W ðhÞ of the phase volume reflects the optical heterogeneity of the TC.The peripheral cytoplasm makes a contribution to the phase volume of zone 1 (W 1 ¼ W 01 − W 12 ) limited by the radii r 01 and r 12 .The largest contribution to the phase volume of zone 3 is made by the nucleus.The W ij values are related to the organelle refractivities and are important parameters of the phase portrait of the cell.These images have been obtained using the raster scanning method. 16-19(f) The refractivity profile Δnðr Þ of the TC in the normal state.The low Δn 1 ðr Þ ≤ 0.01 between r 01 and r 12 in the region of zone 1 corresponds to the peripheral cytoplasm.A considerable increase in refractivity has been observed in the optically dense endoplasmic reticulum region (zone 2) in the normal state.The nucleus (zone 3) accounts for the largest part of the cell volume with a somewhat lower optical density [Δn 3 ðr Þ ≈ 0.032 − 0.035].The local increase in refractivity δn 45 ¼ Δn 45 − Δn 34 ≈ 0.01 in the center of the cell corresponds to a higher density of the nucleolus.Twenty cells were measured in each media.

Fig. 2
Fig. 2 Refractivity profiles of a TC in different media.The indices N, P, R, and F indicate the states of the cell in these media: N, physiological phosphate buffer saline (PBS; normal state); P, medium containing prednisolone; R, the medium containing rotenone; F, medium containing formalin; D, PBS, 40 min of laser irradiation.The differences between the responses of organelles are represented in the refractivity profiles.Points with double indices indicate the radii (r ij ) of the organelle boundaries.The smallest changes have been observed in the prednisolonecontaining medium.The general decrease in refractivity attributable to de-energization is the most distinct in the endoplasmic reticulum region.Twenty cells were measured in each media.

Fig. 3
Fig.3Changes in the proportion of fourth phase of water (4-water) Δ 4 ηðr Þ upon the transitions from N, R, P, and F states of TC (see Fig.2) to fully de-energized D state (ND, RD, PD, and FD transitions).The largest changes have been observed in the endoplasmic reticulum (zone 2) and the nucleolus (zone 4).