3.1. Force spectroscopy of the cell wall
To understand the peculiarities of probe measurements of cells at the submicron and nanoscale level and the choice of modes of force action when scanning the shell, let us consider description of the spectra FZ=FZ(Z) of the main significant areas of the reference approach and withdrawal curves describing the features of the mechanical interaction of the probe with the surface depending on the distance of the probe-surface Z.
In the general case, before carrying out the force measurements of the AFM in the ‘setpoint’ parameter, the initial value of the force action of the probe, Fconst=FZ(z0=0), on the membrane at the point of its contact with the surface was set, i.e. the level of the initial force action corresponding to the zero coordinate along the Z-axis (z = 0). At the start of the measurement the initial force action was removed, the probe was retracted from the surface at a predetermined distance Zup≈500 nm, and the approach curve, FZ=FZ(Z↓), was measured by forcibly lowering the probe to the lower point, Zdoun≈-300 nm (Fig. 3, a). After that the FZ=FZ(Z↑) withdrawal curve was measured up to the upper point, Zup≈500 nm. As a reference we used the spectra of the approach and withdrawal curves recorded on the free silicon surface with known mechanical characteristics (Fig. 1a, point I).
Let us consider the spectral characteristic of the approach process (Fig. 3, a, curve 1). The horizontal section AB describes the process of approaching the cantilever with the surface at a sufficiently large distance between them, i.e. in the absence of interaction FZ=0. As it approaches the surface the probe begins to be influenced by Van-der-Waals forces (FVW). First, repulsive forces (FZ> 0) FZ=+FVW1(BС)≈0.1 µN begin to act due to a small potential barrier [ϕb(BC)]=eV in the segment BC, and then act the forces of attraction (FZ<0) FZ=- FVW1(СD)≈-0.31 µN of the potential well U01 (section CD), which reach their maximum value at the immediate vicinity of the surface (point rz0) (Fig. 3, b, curve 1). Barrier, ϕb(BC), most likely, describes the process of overcoming the surface tension forces of the adsorption layer by the cantilever. The depth, [U01]=eV, of the potential well determines the maximum force of attraction of the probe to the surface and the work of adhesive forces. With further movement of the cantilever towards the surface beyond the point D, repulsive forces, FH>0 (H - Hooke's law), begin to act on the probe, preventing its penetration into the near-surface region (Fig. 3, a, section DE). The linearity FZ=FZ(DE) of the section DE of the approach curve indicates the presence of elastic forces leading to the appearance of reversible elastic deformations at the point of action of the probe on the surface, described by the Hooke's law viz. the reaction force is directly proportional to the change in the linear size Δz:
$${F}_{z}=K\times \varDelta z$$
12,
where [K]=N/m is the coefficient of elasticity. For this process, K=8.3±0.2 N/m. Here it is convenient to introduce the concept of an effective surface, i.e. the z-coordinate (point D) at which repulsive forces arise.
The movement of cantilever towards the surface beyond the point E leads to a critical increase in the force FZ>FH, violation of the linearity FZ=FZ(DE) and the appearance of plastic deformations Δhstif, which will not be considered in this work. These areas are shown schematically on the A-A profile of the cross-section of the surface relief of the shell surface of the cell under study (Fig. 2).
The withdrawal curve (Fig. 3, a, curve 2), in general case, has similar characteristic regions, which, depending on the state of the surface can differ markedly from similar regions of the approach curve. Obviously, for homogeneous solid clean surfaces the approach and withdrawal curves must coincide. The discrepancy between the approach and withdrawal curves (for example, a large by modulus force of attraction |-FVW3|>|-FVW2|, the absence of a barrier ϕb, an increase in the coordinates of the bottom of the potential well U02), i.e. the hysteresis, usually indicates the presence of certain features in the state of the surface and near-surface area. The higher coordinate of the potential well, rz02>rz01, indicates the presence of an adsorption layer (adsorbate) with an effective thickness, Δza<100 nm, on the surface at the point where the probe touches. The presence of a thin nanometer layer of adsorbate in this case is most likely caused by the remains of the buffer solution. According to the theory of capillary phenomena by T. Young, P. Laplace and J. Gibbs, the adsorption effect is largely determined by the Van-der-Waals forces [31]. The coincidence in the DE region of the linear sections of the approach and withdrawal curves, as well as their identical slope (angle ∠α), confirm the uniformity of the mechanical properties of the near-surface region of the epitaxial silicon layer, and also indicate the correct tuning of the AFM system and the operation of the cantilever. Thus, for the Si surface the shape of the approach and withdrawal curves fully corresponds to the well-known physical model of the interaction of two atoms by means of Van-der-Waals forces and located at a distance, r, from each other in accordance with the Lennard-Jones potential ULD eq.(3).
Thus, it becomes clear that depending on the state of the surface and the value of the pressing force it is possible to exert various force effects on the surface of the shell (approach curve) with the registration of the values of the parameters of the membrane response reactions (withdrawal curve) to an external stimulus. The correct choice of the initial value of the force, FZ=Fconst, during AFM measurements of the surface of a biological object is a very important preparatory stage. For example, an excessively large Fconst value can lead to large plastic deformations, or even rupture of the cell membrane, and an excessively small value can lead to excessive sensitivity of the method and the occurrence of various kinds of interference associated in most cases with various inhomogeneities.
According to preliminary results the cell membrane possesses good elastic properties and withstands elastic deformations along the Z-axis significantly exceeding 300 nm with a force F>28 nN. In addition, elastic deformations commensurate with the thickness of the cell point out on non-destructive action of the probe (integrity, tightness of the membrane), which excludes the leakage of the contents of the cell under study to the outside.
To select the optimal value of the constant pressing force, Fconst, we selected relatively flat areas of its surface (Fig. 1, a, point II), under which there were no organelles (Fig. 1, a, arrows). As a result, for the AFM measurements by the contact method the pressing force, Fconst≈18–22 nN, was chosen, which provides not only a sufficient force effect, but also a good signal-to-noise ratio at a level of elastic deformations of at least 150 nm. Note that repeated scanning in more gentle modes (at Fconst<5 nN) did not reveal any destructive effects from the cantilever.
Preliminary studies by the AFM Kelvin probe method have shown the halo around the cell in Fig. 1 is due to the difference in electrostatic potentials, Δϕ, of the cell and the silicon surface and is not associated with a violation of the integrity of the membrane. The electrostatic field surrounding the cell, caused by the potential difference, Δϕ, stimulates the predominant precipitation from the buffer solution in the area of the halo during sample preparation when the aliquot is dried. The study of the electrical characteristics of the cell membrane requires more detailed independent studies and will not be considered in this work.
As expected the features of the micromechanical properties of the cell wall are manifested in significant differences in the approach and withdrawal curves (Fig. 4). It was found that the reaction of the membrane of a living cell to the action of the probe is not a simple mechanical process, but, depending on the method of action, is a selective and non-trivial process, and will be described in detail in subsequent publications. In this paper we are only interested in the elastic reaction of the shell.
The greater slope (angle α) of the linear sections of the approach curves indicates a greater elasticity of the cell membranes, i.e. a greater value of the elasticity coefficient, K. According to Fig. 4a at Fconst=6.2 µN the deformation was Δhdfrm=115 nm, and K=67.4±0.15 N/m. In this case the region of deformations, Δhdfrm≤115 nm, falls in the elastic region. The regions of plastic deformation will not be considered in this paper. In accord with the authors of [32] the coefficient of elasticity of the cell membrane turned out to be higher than the coefficient of elasticity of the cantilever beam.
Differences are also visible in the near-surface region of action of adhesive forces. First of all attention is drawn to the absence of repulsive forces (barrier ϕb(BC)) on the approach curves when approaching the surface and the significantly shallower depth of the ‘potential well - U0’, FVW2 (Fig. 4, a, curve 1). This fact indicates a relatively low hydrophilicity of the cell membrane. In other words micro- and nano-objects approaching this point in the absence of a noticeable effect (pressing force Fconst) on the membrane will be very weakly held by its surface. This circumstance, on the one hand, can allow the cell to move more freely in the external environment (due to low wettability), and, on the other hand, it is easy to overcome surface tension forces due to the lack of hydrophobicity.
In the general case withdrawal curves have a more complex dependence on the coordinate and, most likely, cannot be characterized by elasticity coefficient. At the same time even a relatively small effect from an external nano-object on a cell leads to an increase in the adhesive forces of attraction, which allows the cell to fix itself on external objects, or to retain on its surface the external micro- and nano-objects leaving it.
Retract curves have more in common with test retract curves (Fig. 4). They also have a region of elastic deformations DE, a potential well region BD, and a neutral region AB of the absence of interaction. According to the behavior of the withdrawal curves a rather thick Δza<100 nm adsorption layer of the buffer solution was present on the cell membrane surface (Fig. 4b, Δza). This layer protected the cells from complete drying out for a sufficient (3-4 hours) period of time needed for measurements. Such conditions for AFM scanning of the surface of a living cell are intermediate between measurements of a completely dried (dry) non-living cell and measurements of living cells in a liquid medium. Obviously, such a (mixed) scanning method for AFM measurements of biological objects is easier to use, and to some extent combines the advantages of the classic ‘dry’ and ‘wet’ scanning methods.
The authors of [7, 9] observed a similar behavior of the approach and withdrawal curves, but providing no explanation when studying the elasticity of local 20×20 µm sections of the membranes of human intestinal cells Caco-2 by AFM force spectroscopy.
3.2. Tribological properties of the cell membrane surface
Due to the fact that the weight of the observed micro- and nano-particles is insufficient for the occurrence of any noticeable plastic deformations of the shell Δhstif (for example, the weight of a lead ball with a diameter of 1 µm is only ~ 4×10−13 N), the first term in eq.(2) can be excluded, then the condition eq.(4) 1<<µ is satisfied and the friction force will be completely determined by the adhesion forces Fadh≡FVDV on the membrane surface, i.e. by the Van-der-Waals forces:
$${F}_{fr}={F}_{adh}$$
13.
It is clear that for satisfying the conditions eq.(4) and eq.(13) in AFM it is necessary that Fconst=0.
In repose, between the nanoparticle and the point (or region) of interaction with the surface (z=0) located under it, adhesive Van-der-Waals forces of attraction arise, described by the potential eq.(3). The experimental dependence of these forces on the distance to the surface Fadh=Fadh(z) is shown in Fig. 5, a. It is important that the interaction of a particle (object) is carried out not with the entire surface, but with a limited area under the particle (object) approximately equal to the area of its projection, i.e. the cross section of the tip of the cantilever tip with a radius of <6 nm. In such case it can be assumed that the connection with the point of interaction (the place of landing), when the particle moves along the surface, is also retained within lLF1≈100 nm. It follows from the electronic nature of chemical bonds that as long as one bond exists, a particle cannot organize a second analogous bond with another place on the surface. When a particle moves (moves away) along the surface from the place of initial interaction, the force Fadh=Fadh(x) will decrease according to the known law, and only at a distance, x=lLF1≈100 nm, it will become equal to zero. In order to break this connection, it is necessary to do some work A≈〈Fadh〉lLF, which, in fact, will be equal to the work of friction forces. Only in this case the particle will be able to organize a similar connection with a new local area on the membrane surface (Fig. 5a, inset). With further movement of the nano-object over the surface everything will be repeated in the same way. As a result, we can assume that the movement of the nanoparticle over the membrane surface should be discrete. It is clear that such discreteness should manifest itself for objects whose sizes do not exceed, or are commensurate with lLF. Objects that are much larger than lLF will not experience noticeable discreteness in the friction force Ffr=FL=FL(x) due to the fact that the resulting FL value will always be averaged over the projection area (the contact area of the object). It should be noted that such discreteness is not associated with discreteness of the atomic structure of the surface.
Direct measurements of FL showed that on relatively smooth areas of the surface (Fig. 6, a) the FL value really changes abruptly due to discrete fluctuations ΔFL1 with an interval equal to lLF1≈100 nm (Fig. 6, b). In this case the multifractal geometry of the membrane surface relief leads to the fact that the functional dependence FL=FL(x) along the entire trajectory of the object's motion is also a multifractal curve. The average value of the fractal dimension, determined by the triangulation method, shown in Fig. 6, b of the FL=FL(x) curve, was 〈Df〉=1.24, and the surface relief h=h(x) – 〈Df〉=1.29.
To study the behavior of the friction force depending on the size of micro- and nano-objects by the contact method in the LF method, a cyclic scanning of a 10⋅10 µm section with zero pressing force Fconst=0 was carried out with an increasing number of ki scanning points in frame and line scans (i = 1, 2, ..., 9; k1=100, k2=150, k3=200, k4=250, k5=300, k6=350, k7=500, k8=1000 and k9=2000). The absence of the pressing force makes it possible to exclude the deformation µF⊥ in eq.(2), and leave only the adhesive component, Fadh, of the friction force, Ffr eq.(13). This procedure makes it possible to study the effect of the adhesive component of the friction force, Ffr, depending on the size of the measurement scale - the scanning step li=10/ki: l1=100 nm, l2=66.7 nm, l3=50 nm, l4=40 nm, l5=33.3 nm, l6=28.6 nm, l7=20 nm, l8=10 nm and l9=5 nm. The measurement results were three-dimensional arrays of the values of the relief, h=h(x, y), and the lateral force, FL=FL(x,y)=Ffr(x,y). Then, using the methods of mathematical statistics, from the distribution histograms Ni=N(FL,i) for each ki-th case the mean values 〈FL,i〉 and the variance σi were calculated. Recall that according to Section 2.3 due to the impossibility of direct measurements of Ffr values it was necessary to operate with their relative values [Ffr]=[FL]=pA. The result is shown in Fig. 5, b. It was found that an increase in the measuring scale, the scanning step li, leads to a decrease in the modulus |Ffr| keeping the values σi = 0.018-0.020. At l2=66.7 nm, the value of |Ffr| goes to saturation.
In this case the fractality of the functional dependence FL=FL(x) leads to the fact that with an increase in the size of the object l to ≤lLF1, the adhesion force, and, consequently, the friction force, in accordance with eq.(11), decreases according to the power law (14):
$${F}_{fr,i}={F}_{adh,i}={F}_{adh,0}{\left[\frac{{l}_{i}}{{l}_{0}}\right]}^{{D}_{T}-{D}_{f}}$$
14.
This contradicts the nature of the manifestation of the friction force of macro-objects in the global approximation with l>>lLF1. For such macro-objects the friction force behaves in a classical way, i.e it increases with an increase in their size and mass. Thus, it was obtained that nanoparticles of large sizes in the local approximation under the condition l≤lLF1 can move along the surface of the cell membrane with a lower friction force.
Despite the absence of direct AFM methods for measuring the friction force Ffr, the results obtained in this work still make it possible to find the absolute values of Ffr. Let's use the graphical method. To do this it is necessary to align (compare) the scales along the ‘z’ and ‘x’ axes of the functional dependencies Fadh=Fadh(z) (Fig. 5, a) and FL=FL(x) (Fig. 5, b). When done one can easily determine which values of [FL] = pA in pico-Amperes on the FL=FL(x) curve correspond to the values of [Fadh]=nN in nano-Newtons on the Fadh=Fadh(z) curve (Fig. 5, graphic method).
Thus, knowing the value of Df of the cell membrane surface using eqs.(13) and (14), one can easily determine the work of a particle that must be expended to move it across the membrane surface.
According to the carried studies, an increase in the pressing force, Fconst, in the area of elastic deformations can lead to an increase in the effect of discretization of the friction force Ffr, which manifests itself in an increase in discrete fluctuations, ΔFL, and the sampling interval, lLF. For example, an increase in Fconst>1 µN leads to an increase in ΔFL by a factor of ~ 2.5, and lLF2 almost to 1.5-2 µm, as evidenced by the profile of the C-C section of the raster image of a periodically striped LF-signal on the membrane surface area 5⋅5 µm (Fig. 6, b) and 10⋅10 µm (Fig. 1, b, inset). In general case the value of the lLF interval does not depend on either the resolution (the number of scan points), nor on the speed, nor on the scanning direction, but is determined only by the pressing force Fconst, which excludes the instrumental influence on the process of removing the LF-signal. Network structures with the manifestation of various types of scale bands are very characteristic of the structures of cell membranes (for example, the scale bands of 30 nm described in [33]).
Presumably, this tribological effect is determined by the fractality of the functional dependence FL=FL(x). In the case when the level of external influence Fconst begins to exceed small fluctuations of one of the levels of statistical similarity, FL1, and reaches or exceeds fluctuations of the next level of statistical similarity, FL2, they begin to appear in the raster LF image FL=FL(x,y) in the form of more wide dark and light stripes with an increased period lLF2 (Fig. 6b, inset). This fact may indicate that micron-sized particles can also be influenced by the discrete nature of the friction force. It should be noted that the LF-contrast in the obtained raster images does not always coincide with the contrast of the relief, as, for example, was shown in [34]. This suggests that the forces of adhesion are not the main reason for the formation of the relief of the cell membrane and can manifest themselves regardless its shape.
At the same time the axisymmetric structure of the LF-contrast relative to the cell nucleus does not allow for a complete lack of communication between the adhesive forces and the mechanical structure of the cell membrane formed by a network of glycan chains linked by peptide side branches, which in many cases has a local axisymmetric structure at the submicron and nanoscale levels (Fig. 1, b), as, for example, local regions of the membranes of gram-positive cells of the hay bacillus Bacillus subtilis, Staphylococcus aureus [28], or Lactococcus lactis WT [34].
The halo around the cell in the LF raster image, as indicated in Section 2.2, is not associated with a violation of the membrane integrity, but is formed by a precipitate from a buffer solution, the precipitation of which in the halo area was stimulated by the cell's own electrostatic field, formed by the difference in electrostatic potentials, Δϕ, between the cell and silicon surface (Fig. 2, b). The electrostatic nature of the cell membrane requires a special study and will not be considered in this work.
3.3. Mapping the tribological properties of the buccal epithelium cell membrane
The study of the architecture of the outer shells of cells requires complex mapping of their functional characteristics with the necessary resolution both in absolute value and in spatial coordinates. As such functional characteristics (hereinafter referred to as characteristics), in particular, one can consider lateral forces FL=FL(x,y) and adhesion forces Fadh=Fadh(x, y). Due to the complex and time-consuming technical implementation of AFM measurement of the parameters of these characteristics, a point (by several points) or grid method of local research with a very limited resolution of only 16×16 points (pixels) is often used, as, for example, in [34], aimed mainly at increasing the statistical sample. In this case the sizes of local areas usually do not exceed a few micrometers, which makes it difficult to study the architecture of the external exoskeleton of the cell membrane, as well as the relationship of the morphology of the membrane surface with its micromechanical and tribological characteristics. Currently there are no general recommendations for choosing the necessary scanning conditions. Everything is determined by the capabilities of the AFM, the requirements of the researcher, the size and condition of the cell, and external conditions.
The cells of the human buccal epithelium belong to rather large biological micro-objects - the size of adult eukaryotes can reach hundreds of micrometers, with a sufficiently developed landscape of the surface of their membranes. The mapping of the complex functional characteristics of such objects, in particular, the adhesion forces and lateral forces, was carried out in 10×10 µm regions with a minimum resolution of 100×100 scanning points in frame and line scans.
To solve the problem of mapping by AFM methods a hybrid mode was used, which makes it possible to simultaneously obtain data on the relief and the above tribological surface properties at each scanning point. With the aim of reproducibly obtaining and registering at each point of the measurement results, i.e. the approach and withdrawal curves, an extended range of external force effects from 0 to 40 µN was used with a sufficiently high level of the initial force action Fconst≈21 µN significantly exceeding the level required for the appearance of elastic deformations Δhdfrm. The case of destructive deformations was not considered in this work.
As reported in Section 3.2, the outer shell of adult living cells of human buccal epithelium is not a smooth surface, but has a self-affine multifractal Brownian relief with an average vertical size of irregularities (tubercles) up to 500 nm. In the horizontal plane the surface has a rather coarse cellular structure ranging in size from 200 nm to 2000 nm (Fig. 7a, highlighted by a dotted line). The size of the irregularities depends on the age of the cell and its condition. More detailed studies of the cells (in the semicontact scanning AFM mode at a higher resolution of 500–500 points), in turn, revealed their grid structure with sizes from 50 nm to 350 nm (Fig. 7). It should be noted that the mesh structure of the exoskeleton at the nanoscale is very widespread among cell membranes (for example, [28]). In this case it clearly manifests its fractal geometry not only at the submicron level, but also at the micron level. Of interest are the size and shape of such cells, which, according to the available data, can be ‘bags’ of a disordered porous peptidoglycan gel - a three-dimensional network in a liquid medium [35].
In the previous (section 3.2) section it was shown that the tribological properties of cell membranes at the nanoscale level are almost completely determined by the action of adhesive forces. In this regard it is of interest to map the adhesion forces, Fadh=Fadh(x,y), and friction forces, Ffr=FL, which are essentially equal to the lateral forces, FL=FL(x,y)≡LF(x,y) (LF-contrast). From the contrast of the raster image Fadh=Fadh(x,y) it is also possible to determine the shape, size of cells and their boundaries, the position of which fully corresponds to the raster images of the shell relief section (Fig. 7, a). The range of Fadh variation at an increased level of external influence can vary in a fairly wide range from 0 to ~ 45 µN. It is clearly seen that local sections of cells with different elastic and plastic properties can have different adhesive forces. The highest values of Fadh are reached at the boundaries of the cells, and the lowest - at the areas with the lowest plastic deformations and the highest elastic properties. The average value of the fractal dimension Fadh=Fadh(x,y) determined by the triangulation method was 〈Df(Fadh)〉= 2.78. The histogram N=N(Fadh) is well described by three Gaussian functions.
Comparing Fig. 8, a and Fig. 8, b one can see that the maximum modulus values of adhesive forces |Fadh| correspond to the maximum modulus values of lateral forces |FL| and, accordingly, friction forces |Ffr|. The histogram, N=N(FL), is also well described by three Gaussian functions, which correlates with the number of Gaussians in N=N(Fadh). This confirms the important role played by the adhesion forces in the formation of friction forces at the nanoscale level. The average value of the fractal dimension, FL=FL(x,y), determined by the triangulation method was 〈Df(FL)〉=2.80, which practically coincides with the average value 〈Df(Fadh)〉=2.78.