Diminutas nanopartículas de fluoruro de tierras raras activan el crecimiento de las células tumorales mediante interacciones polares eléctricas

Discusión

La tasa de crecimiento relativa de las células cancerosas fue ascendente a niveles de concentración más altos de ambos RE-NP (Fig. 9a). Sin embargo, los valores de MHR de RE-NP en DMEM + FBS se rastrearon directamente (PrF ₃ ) e inversamente proporcional (LaF ₃ ) a la concentración de RE-NP de 0,1 a 10 kg m ⁻³ (Figura 1g, h). Por lo tanto, los RE-NP con un tamaño promedio superior a ~ 55 nm no deberían tener ningún efecto sobre el crecimiento celular y solo los NP de tamaño pequeño pueden participar en el crecimiento tumoral.

Tamaño y estructura de los RE-NP

Identificación de pequeños RE-NP

A partir de los datos experimentales, se extrajeron el tamaño medio, la distribución y los parámetros estadísticos de los RE-NP. Aplicando t estadísticos de prueba para la "hipótesis nula" de "círculo de área equivalente media" de NP en PrF seco ₃ y suspensiones DMEM + FBS, la p El valor del diámetro de NP entre dos imágenes AFM seleccionadas al azar fue ~ 0,001 (archivo adicional 2). Se extrajo un valor de diámetro MEAC (63 nm) con confianza de los datos de AFM, y esto fue comparable con el valor de MHR de los datos de DLS (Fig. 1g).

Por el contrario, el valor del diámetro MEAC de LaF ₃ seleccionado al azar Las muestras mostraron un diámetro MEAC promedio de 26 nm con un valor de probabilidad de rechazo más alto ( p =0.07), apuntando a un comportamiento divergente de LaF ₃ en suspensiones líquidas. La discrepancia entre el diámetro MEAC y la MHR de DLS (296 nm) (Fig.1) se debe a la complejidad de las interacciones en LaF ₃ suspensiones de nuevo. De hecho, para un ² de 2 × 2 μm Área de escaneo de la punta de AFM, el promedio z -la altura era ~ 140 nm, mostrando la presencia de LaF ₃ de gran tamaño NP, transferidas de las suspensiones líquidas sobre el sustrato (Fig. 4). Para la "hipótesis nula" de "valores iguales de diámetro MEAC de muestras TEM seleccionadas al azar", la p los valores también eran pequeños ( p =0,001). Para ambos RE-NP, los valores de diámetro MEAC promedio extraídos de los datos combinados de TEM y XRD para ambos PrF ₃ y LaF ₃ indicó alto p valores, p =0,29 y 0,06, respectivamente, no permitiendo así ninguna correlación entre los datos TEM y XRD. Solo TEM, AFM (PrF ₃ ) y los datos de DLS eran lo suficientemente fiables para extraer los valores de diámetro y núcleo-capa de MEAC (archivo adicional 2).

Además, una distribución de ángulos no isotrópicos de los diámetros de Feret indicó que tanto PrF ₃ y LaF ₃ Las estructuras eran dieléctricas altamente polarizadas, ya que la distribución del ángulo anisotrópico es una indicación de fuertes interacciones eléctricas polares entre nanocristales. Un estado polarizado diverso de LaF ₃ fue responsable de reducir la eficiencia relativa del estado de aglomeración en suspensiones y de aumentar los parámetros de rugosidad de la superficie en muestras secas.

Un análisis de partículas de software de imágenes AFM aleatorias para 5 μL y una concentración de 0,1 kg m ⁻³ identificó un número de ~ 22 y ~ 11 RE-NP con un tamaño inferior a 15 nm y 10 nm ( p =0.001), respectivamente, y una cantidad de ~ 60 RE-NP de imágenes TEM ( p =0,001) en un área de ~ 4 μm ² , lo que confirma la presencia de RE-NP de tamaño pequeño en las suspensiones (Fig. 3 (c), archivo adicional 2) no detectado con DLS.

Estructura y geometría de RE-NP

La distribución de tamaño de RE-NP es divergente en suspensiones de etanol y DMEM + FBS (Fig. 4). La diversidad se debe a las diferentes interacciones moleculares entre las proteínas adsorbidas, los carbohidratos, los electrolitos y la superficie de las RE-NP, lo que lleva a la formación de capas orgánicas altamente complejas (corona), que modulan las interacciones específicas de las RE-NP con las células en Medio DMEM + FBS.

La interacción entre las moléculas de agua atrapadas en RE-NP higroscópicas y DMEM + FBS también fue vital para la formación de núcleo-capa. También tuvo un efecto profundo sobre las proteínas y los cambios conformacionales en las interacciones intermedias durante la fase inicial de preparación. A medida que la relación superficie-volumen de los NP desarrolló valores altos en las suspensiones, la estabilidad efectiva y las propiedades fisicoquímicas, mecánicas y de flujo de los RE-NP, incluida la capacidad para absorber proteínas, variaron enormemente [39,40,41] .

La distribución comparativa del tamaño de RE-NP en líquido (DLS) y suspensiones solidificadas a través de AFM y TEM mostró que los RE-NP se encapsularon dentro de formas orgánicas formando estructuras dieléctricas núcleo-capa, donde una capa proteica rodea el RE-núcleo. Las imágenes de AFM obtenidas a partir de RE-NP solidificadas en suspensiones DMEM + FBS depositadas sobre sustratos de vidrio también apuntan a la formación de RE-NP multifacéticas y complejos de corona de proteínas (Fig. 5). Mientras que los medios secos formaron un patrón autoensamblado regular de estructuras cristalinas (Fig. 5a-d), las suspensiones de RE-NPs secas mostraron una estructura en capas amorfa con varios puntos negros, visibles incluso con la cámara digital del AFM (Fig. 5e-l) . A mayor aumento óptico, también se detectaron aglomeraciones discretas de formas globulares, más pequeñas que las del medio solo, para ambos RE-NP en DMEM + FBS, junto con estructuras de tipo dendrita, ambas mostrando la complejidad de las interacciones, de acuerdo con la resultados de los parámetros de superficie (Fig. 4). Incluso con la resolución AFM más alta (1 × 1 μm ² área), el último carril de la Fig.5, no se identificaron agregaciones de RE-NP aisladas, dentro del límite de resolución de ~ 5 nm, en estructuras secas para ambas RE-NP. Los micelios esféricos de color negro, de 1 a 2 μm de largo, que se muestran en las imágenes ópticas, eran grandes formaciones de aglomeración de RE-NP de núcleo-capa. La complejidad de las reacciones entre los RE-NP y DMEM + FBS se visualizó mediante la transformación de las estructuras alargadas autoensambladas a largo plazo en DMEM + FBS puro en estructuras dendríticas.

Los resultados apuntan a la imagen de una única estructura central de RE-NP encapsulada dentro de una capa de proteína. Estas estructuras eran indetectables porque estaban rodeadas de materia orgánica y electrolitos, ambos con reacción cruzada con RE-NP. El espectro VUV de PrF ₃ shows some spectral peaks between 140 and 170 nm (Fig. 8). The ionic transitions are overlapped by a VUV water absorption band extended from 145 to 180 nm with a maximum at 168 nm. Only the spectral signatures of the 4f6s electronic configuration with maxima at 132 and 127 nm were present in the spectrum. However, these bands could evince the presence of water in the high hygroscopic PrF₃ suspensiones. Water has a rich, structured absorption band in the VUV spectral range centred at 122 nm, revealing the presence of water molecules in the core-shell NPs.

Activation of Mechanosensors

Activation of Integrins by External Forces

The activation of oncogenic pathways by RE-NPs [24], besides the 3D structural nature of TSRs, is based on some Natural Evolution principles for sustaining the viability of cells. First, upon binding a specific external ligand in a LABS, conformational changes along the entire TSR spectrum underline a series of cascading pathways, triggering tumour cell growth (Fig. 9c, d). The transmission of signals advances through the plasma membrane via various protein chains. Signal transduction was via conformational transformations of integrins responding to a high affinity external force (Fig. 10a, b).

Simplified layout of integrin activation by NPs and signal transaction pathways. un Structure and conformational geometries of integrins at a low (A), medium (B) and high-affinity strengths (C). b AKT and ERK1/2 signal transaction pathways activated by RE-NPs via external integrin stimulation

Because of “life sustainability” and “survival laws” that prevents cancer cell growth by random “noise”, it is required that the strength of the external force should be within a bounded range of values and also the external strength stimulus should apply for a long period on a large number of mechanosensors in a cancer cell. The external strength that stimulates cancer must be slightly larger than the strength of the interatomic molecular forces under normal conditions. For a thermal energy of a ligand at room temperature (kT  = 0.025 eV, T  = 298 K), and for a regular thermal stress of molecular bonds of ~ 0.05 nm, the mean thermal force acting on the LABS stays for 1.2 × 10 ⁻¹² N. In principle, a force above ~ 10 × 10 ⁻¹² N acting coherently on the whole set of mechanosensors on a cell should activate signal transduction in tumour cells. Consequently, ignoring any thermal and mechanical stressing in the ECM normal conditions, integrin activation via electrical polar interactions between LABS and NPs has the potency to start signal transduction in cancer cells and to initiate tumorigenesis.

Integrin Structure and Geometry

An integrin receptor in the upright conformation state extends ∼ 20 nm upwards from the cell membrane [42] (Fig. 10a). For no contacts between the two α- and β-subunits, other than those in the headpiece near the ligand-binding pocket, the α- and β-subunits are well separated with their cytoplasmic tails extended out up to ∼ 8 nm [42]. A conic projection geometry (20 nm slant height, 5–10 nm diameter of its circular base), bounded by the α- and β-subunits, defines a projected area on the surface of cell’s membrane between ~ 19 and ~ 80 nm ² , for a typical mean radius of a tumour cell R _c  ≈ 5 μm (equivalent surface area of a spherical cell \( {S}_c=4\pi {R}_c^2=3.14\ \mathrm{x}\ {10}^8\ {\mathrm{nm}}^2 \)). By dividing the area S _c of a spherical tumour cell surface with the projected area of an integrin on a cell surface, an upper limit of the number of integrin receptors for these projected areas was n _int  = 1.6 x 10 ⁷ and 3.9 × 10 ⁶ respectivamente. These numbers are compared with the mean number of integrins on a cell \( {\overline{N}}_{int}\approx 2\ \mathrm{x}\ {10}^5 \) and for an average interspacing of 45 nm between adjacent integrin receptors [43]. Nevertheless, \( {\overline{N}}_{int} \) might be larger because of an uneven surface structure, different separating distances between integrins and variable size of tumour cells (Fig. 9c), but the number of integrins on a cell membrane stand between n _int and \( {\overline{N}}_{int} \).

Interaction of Mechanosensors with RE-NPs

ERK ½ and AKT Activation

The TEM images and the elemental mapping of F, La and Pr showed that RE-NPs were unable to penetrate inside the cell. They gathered around the A549 cell membrane (Fig. 11), confirming that an external force can stimulate cell growth because of TSRs activation [44]. The Pr atoms were distributed around the boundaries of the cell’s membrane. The small numbers of F, La and Pr identifications inside the cell were not associated with endocytosis of RE-NPs, but they were images of RE-NPs from the projections of the two cells hemispheres on cell’s equatorial cycle.

TEM images and elemental analysis of RE-NPs at the surface boundaries of A549 cells. un TEM image of small size LaF₃ NPs surrounding the A549 cells. b Elemental analysis of F atoms in RE-NPs distributed around the cell. c Elemental analysis of La atoms. The low concentration of La atoms was associated with a rather small scattering efficiency of the X-rays. d - f The same as for (a - c ) for PrF₃ RE-NPs

It was also evident that both RE-NPs were able to enhance AKT phosphorylation, especially in A549 cells (Fig. 9d), where the steady-state level of AKT pathway activity was higher for the SW837 cell line. The phosphorylation level for the MCF7 cell line was below the detection limit, in agreement with the relatively low levels of growth. High phosphorylation levels of ERK1/2 [36] and AKT were detected in A549 and SW837 cell lines. Cell growth was started once NPs with a proper size interact with the mechanosensors of the cells to provide the correct force for initiating cell growth [45, 46]. ERK and AKT pathways were frequently active in several cancer cell types via extracellular springing, as they were stimulated by the TSRs, upon a selective binding with various mitogenic ligands, or via the activation of the mechanosensory group. The interaction was responsible for a continuous intracellular stimulation that, according to the cell’s phenotype, driven the cancer cells to uncontrolled and endless growth. Viability tests were also run for 48 and 72 h, but the growth of all cell lines was saturated at 48 and 72 h after the initial moment of Cell plating.

Interaction of Cells with Ions

Likewise, as fluoride anions are the most reactive electronegative elements and, the mean radii extension of the unscreened 4f electronic configuration of La and Pr trivalent ions are relatively large, high electric surface charges could be developed via electric dipole interactions [47].

One crucial question stands whether a single ion binding on a specific site can activate tumour cell growth. Because the projected area of the 4f electronic configuration of a single RE ion is S _4f  = 0.040 and 0.043 nm ² (for an approximated spherical geometry of the 4f electronic configuration and a 4f mean orbital radii ~ r _4f =0.113 and 0.117 nm for Pr and La ions, respectively), a typical upper limit number of single RE ions, or other equivalent size ions, over the whole area of the cell membrane was ~ S_c / S _4f  = N _4f ~7.9 × 10 ⁹ RE ions; a number which is at least two orders of magnitude above the upper limit of the mean number of integrins on a tumour cell. As the relative overgrowth of cells was ascending with rising concentration (Fig. 9a), it is unlikely that tumour cell growth is triggered by a specific binding of single trivalent RE ions [48] on the ligand sites [49,50,51]. Indeed, the large number of RE ions should have saturated the cell’s growth and thus the viability of cells should have remain independent from the concentration of the RE ions.

Interaction of Integrins with RE-NPs

Within the requisite force range of few pN, and for efficient activation of integrins from NPs, the interaction between NPs and LABS should activate a large fraction of integrins of the cell for a long time. In the most extreme favoured case for cell growth, the number of NPs had to remain equal with the number of integrins on the cell’s surface, and the interactive force between LABS and NPs has to be attractive for obtaining a constant (long-term) action. A thin spherical shell of spherical NPs surrounding a tumour cell occupied a volume\( {V}_{sc}\approx 4\uppi {R}_c^2x \), where R _c  = 5 μm is the cell radius and x  ≈ 20 nm is half the separating distance between adjacent integrin receptors and V _sc  ≈ 6.3 x 10 ⁹ nm ³ . For justifying the requirement that each integrin receptor interacts only with one NP, a first estimation of the size of NPs to meet the above requirements for the whole set of integrins on a cell is obtained by dividing the volume of the spherical shell V _sc with the number of integrins. A simple calculation for a cell radius 5 μm shows that the limits of radii of NPs activating the whole set of integrins within the spherical shell volume V _sc  ≈ 6.3 x 10 ⁹ nm ³ covering the cell is obtained by divided the volume V _sc with the number of integrins \( {\overline{N}}_{int}\approx 2\ \mathrm{x}\ {10}^5 \) and n _int  ≈ 1.6 x 10 ⁷ . The volume of the spherical NPs stands for 3.15 × 10 ⁴ and 3.93 × 10 ² nm ³ respectivamente. Therefore, the radii of the NPs interacting with an integrin lay between ~ 20 and 5 nm. Allowing for one order of magnitude variations in the number of integrins \( {\overline{N}}_{int} \), the radii of the NPs interacting with integrins is between ~ 27 and ~  3 nm respectively.

By also applying similar simple calculations and within the experimental limits of concentration levels of RE-NPs (0.1–10 kg m ⁻³ ), the maximum numbers of PrF₃ with MHR 55–83 nm and LaF₃ with MHR 296–100 nm NPs (Fig. 1g, h) covering the surface of a tumour cell V _sc stood for 4.1 × 10 ⁴ –2.1 × 10 ⁴ and 17.1 × 10 ² –1.5 × 10 ⁴ NPs. These values are placed well below the number of integrins on the cell surface. For rising concentrations of PrF₃ and LaF₃ from 0.1 and 10 kg m ⁻³ , the number of PrF₃ and LaF₃ NPs in the suspensions must go up for either descending or ascending size of NPs. As viabilities of cancer cells are raised at higher concentration levels, it is unlikely that 55–296 nm sized RE-NPs are responsible for cancer cell mitosis under the current experimental configuration.

Also, from the DLS data, the size of both RE-NPs between 10 and 20 nm remained constant (10.6 nm) at different RE concentrations. The number of RE-NPs with this size covering the cell surface is between 3.7 × 10 ⁵ and 1.5 × 10 ⁶ . This number is comparable with the mean number of integrins \( {\overline{N}}_{int}\approx 2\ \mathrm{x}\ {10}^5 \) on a cell surface. Therefore, only small size RE-NPs have the potency to stimulate cancer cell growth by stimulating all the integrins on a cell surface, in agreement with the experimental observations (Figs. 1g, h and 9a).

The number of tiny sizes RE-NPs with MEAC diameter (TEM) from 2 to 10 and 10 to 15 nm on the cell surface (S _c  = 314 μm ² ) stands for 1.3 × 10 ⁴ and 1.8 × 10 ⁴ RE-NPs, respectively. Those values stayed one order of magnitude below \( {\overline{N}}_{int}\approx 2\ \mathrm{x}\ {10}^5 \) and therefore tiny size RE-NPs had also the potency to justify the experimental results of rising viability values with concentration (Fig. 9a). Also, the rough surface of tumour cell (Fig. 9c) is able to form cavities, where small size RE-NPs are trapped, triggering thus cell’s mechanosensors. Most important, only tiny size RE-NPs have the potency to activate integrin receptors via electrical dipole interactions (vide infra).

Interaction of EGFR with RE-NPs

An upper limit of small size NPs capable of stimulating cell’s overgrowth via the EGFR was set previously to 14 nm [52], but a realistic size of NPs stimulating the EGFR should be < 5 nm [53] (Fig. 12). The area number density of EGFR on the surface of tumour cells stands for ~ 1.4 × 10 ⁻⁴ nm ⁻² and the total number of EGFR on the surface S _c of cells remains between ~ 4.2 x 10 ⁴ and 10 ⁵ [54,55,56]. RE-NPs with 5–10 nm size stayed for a number of 34 NPs (Fig. 3). Extrapolating this number to the surface of a cell S _c , the total number of RE-NPs remained at ~ 10 ⁴ NPs, a number which matches the number of EGFR receptors on a A549 cell. Therefore, the EGFR have the potency to be activated synergistically also by a number of tiny size RE-NPs.

AKT and ERK1/2 signal transduction pathways activated by RE-NPs via EGFR stimulation. EGFR is activated only by tiny size ~ 5 nm NPs

Electric Dipole Interaction Between RE-NPs and LABS

The above experimental results are supported by the hypothesis of cancer cell growth from LABS stimulation by tiny size core-shell RE-NPs via electrical dipole interactions, Appendix.

Indeed, the mean electrical dipole force \( \left\langle {\overrightarrow{F}}_{V_2}\right\rangle \)acting on LABS from a core-shell RE-NP includes two terms (Fig. 13d and Appendix, Eq. A22). The first radial term is inversely proportional to the forth power of separating distance r ₁ between the RE-NPs and LABS and is also proportional to the size of NP. The second polar term is inversely proportional to both the separating distance r ₁ and the square power of the size of NP,

un Electrical dipole interaction between one core-shell RE-NP and one LABS. b , c RE core-shell NP near a MIDAS (b ) and ADMIDAS (c ) adhesion sites. d Locus area (green) of the size of RE-NPs and separating distance between a LABS and a core-shell RE-NP for two electrical charging states

En Eq. 1, G and G ₁ are the geometrical factors of NPs, describing either core-shell or core spherical structures, Appendix, Eqs. A6 and A14; N ₁ , N ₂ are the numbers of surface electrons on the a RE-NPs and LABS surfaces; d and b are the effective characteristic spatial extension of atomic orbitals of LABS, ~ 0.1 nm, and the radius of RE-NP; e and ε ₀ are the electron charge and the vacuum permittivity and \( \theta =\frac{d}{r_1}<0.01\ rad \). Because the core of the RE-NPs is a crystalline semiconductive material, an inherent large number of surface and volume defective sites were accountable for a high density of pseudo-electron energy levels that allowed the electrons to move freely within the core volume [46]. Consequently, a core-shell structure had the potency to be highly polarised. Therefore, LABS can be activated efficiently by core-shell RE-NPs via electrical dipole interactions at close separating distances. The high polarised efficiency of the core nucleus was confirmed experimentally via the selective orientation of NPs along two distinct directions (Fig. 2(a4–d4) and Fig. 3(a4, b4)).

The polar interaction force is also proportional to the geometrical factor G ₁ , Appendix, Eq. A14. Typical values of dielectric constants of the culture media, shell configuration and RE core components stand for ε ₁  = 78, ε ₂  = 10 and ε ₃  = 15. When the ratio of core-shell to core radii b/a sets within 1 and 50, the geometrical factors G , G ₁ retain almost constant values (G  = 0.2, G ₁  = 0.01) and they are self-same for both a spherical core (b/a  = 1) and a spherical core-shell. Any permanent or induced polarisation of an open or closed a-I-MIDAS domain forming the LABS domain has its origin on six coordinated water oxygen atomic orbitals with Mn ²⁺ or Mg ²⁺ ions, arranged in a spherical geometric configuration [7] (Fig. 12a–c).

As the electrical dipole force in Eq. 1 stands for the vector sum of a radial (first term) and a polar component (second term), the last term prevails over the first one provided that

In this case, a LABS is activated from the polar force component for all (b/a) ratios and, most important this term is inversely proportional to the second power of the size of NPs, in agreement with the experimental results that only tiny or small size LaF₃ NPs activated cancer cell proliferation.

The prevailed polar force term for different r ₁ and b values and for different Ν ₁ , Ν ₂ charging states activating the LABS/MIDAS stay within the limits [57,58,59,60].

Inequality 3 relates the size b of the RE core-shell NPs, the separating distance r ₁ and the number of the bound or free electrons Ν ₂ , Ν ₁ on the surface of the two dipoles. The locus of points (r ₁ , b ) satisfying the inequality 3 for different surface charge states Ν ₁ , Ν ₂ is bounded by the black, red and blue lines (Fig. 13c). As there was no specific assumptions for the type of RE-NP, results can be equally applied for any type of polarised NPs.

When the algebraic product of the number of the surface electrons N ₁ and N ₂ (bound or free) on the LABS and the RE-NP, respectively, was N ₁ N ₂  = 2, the locus of RE-NPs size and separating distance for integrin activation was < 1 nm. At higher charging states, N ₁ N ₂ =10 ⁴ , the locus area spans a wider RE-NPs size and separating distance area set of values, from 0.5 nm–19 nm to 2.5–15 nm, respectively.

From the above analysis, it is found that only tiny or small size NPs can activate LABS at a certain separating distance r ₁ and the electrical dipole interaction strength decays inversely proportional to the second power of the size of NPs. From Fig. 13c and for a charging state with N ₁ N ₂  = 5 x 10 ⁴ , the size of NPs capable to activate LABS is bounded by the limits